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Advanced Portfolio Management May 2009

Alberto Dominguez, ASA CFA

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Table of Contents Risk Management Chapter 7.............................................................................................................................. 2 Risk Management Chapter 8.............................................................................................................................. 7 Risk Management Chapter 9............................................................................................................................ 11 Risk Management Chapter 10.......................................................................................................................... 15 Key features of credit risk models.................................................................................................................... 17 Risk Management Chapter 11.......................................................................................................................... 18 Risk Management Chapter 12.......................................................................................................................... 20 Risk Management Chapter 14.......................................................................................................................... 24 Investment Management for Insurers Chapter 3 ............................................................................................ 29 Investment Management for Insurers Chapter 19 .......................................................................................... 33 Investment Management for Insurers Chapter 20 .......................................................................................... 36 Investment Management for Insurers Chapter 21 .......................................................................................... 38 Investment Management for Insurers Chapter 25 .......................................................................................... 40 Investment Management for Insurers Chapter 26 .......................................................................................... 42 ALM of Financial Institutions Chapter 6........................................................................................................... 44 ALM of Financial Institutions Chapter 13......................................................................................................... 46 ALM of Financial Institutions Chapter 14......................................................................................................... 53 ALM of Financial Institutions Chapter 16......................................................................................................... 56 Modern Investment Management Chapter 10................................................................................................ 58 Modern Investment Management Chapter 26................................................................................................ 60 Modern Investment Management Chapter 27................................................................................................ 62 Modern Investment Management Chapter 28................................................................................................ 65 Managing Investment Portfolios Chapter 11................................................................................................... 68 Managing Investment Portfolios Chapter 12................................................................................................... 72

APMV Syllabus Study Notes 1 Textbooks© 2009 Alberto Dominguez

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Risk Management Chapter 7

Introduction Most rating systems are based on both quantitative and qualitative evaluations, final decision not usually calculated using a strictly formulaic basis that would show how to weight all attributes in a normative way; clearly rely on experience and judgment of rating evaluators; rating process is governed not by rigid rules, formulas and ratios, but by concepts and guidelines that function in a dynamic process wherein each rating is evaluated case‐by‐case

Challenge for banks to get information about companies that have not issued public securities; must use pro forma accounting data

Analysts must take into consideration ⎯ Structure of debt issued by company as well as collateral or guarantor ⎯ Business and financial fundamentals, operating and financial health, whether earnings and cash

flows are sufficient to cover debt obligations, quality of balance sheet and assets, liquidity position, financial measurement and ratio analysis

⎯ Overall economic conditions, effects of macroeconomic events on firm and its industry

Rating agencies External agency rating process ⎯ Moody’s (1909) and S&P (1916) started to rate public debt issues; considered unbiased and relied

upon by investors ⎯ S&P started rating MBSs (1975), mutual funds (1983) and ABSs (1985) ⎯ Issue specific ratings focus on specific liability and distinguish between long and short term ⎯ Moody’s ratings of investment grade bonds have primarily reflected default probability with

expected severity in event of default has played secondary role; in speculative grade bonds ratings place more emphasis on expected loss than on relative default risk

⎯ There are issuer credit ratings of obligor’s overall capacity to meet its obligations which are not specific to any particular liability and issue specific credit ratings which consider quality of collateral and creditworthiness of guarantors if any; includes counterparty, corporate, sovereign; not investment recommendations

⎯ Debt rating process − Company requests a rating − Assign analytical team, conduct basic research, meet issuer − Rating committee meeting, issuer can appeal by supplying additional information − Rating issued, usually 4‐6 weeks after request − Ratings reviewed once a year, credit watch issued if there is reason to believe rating will change

Credit ratings ⎯ S&P Long Term Ratings

− AAA – highest rating, extremely strong − AA+/AA/AA‐ – differs from highest rating only in small degree, very strong − A+/A/A‐ – strong, somewhat more susceptible to adverse effects than higher ratings − BBB+/BBB/BBB‐ – adequate protection − BB+/BB/BB‐ – less vulnerable to nonpayment than other speculative issues − B+/B/B‐ – more vulnerable to nonpayment than higher ratings − CCC+/CCC/CCC‐ – currently vulnerable to nonpayment


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− CC – currently highly vulnerable to nonpayment − C – bankruptcy petition or similar action taken but payments being continued − D – default

⎯ Moody’s Long Term Ratings − Aaa – best quality, smallest degree of investment risk, gilt edge − Aa1/Aa2/Aa3 – high quality by all standards, high grade − A1/A2/A3 – many favorable investment attributes, upper medium grade − Baa1/Baa2/Baa3 – lack outstanding investment attributes, medium grade − Ba1/Ba2/Ba3 – speculative − B1/B2/B3 – generally lack characteristics of desirable investments − Caa1/Caa2/Caa3 – poor standing − Ca – speculative in a high degree − C – lowest rating, extremely poor prospects of ever attaining investment standing

⎯ S&P Short Term Ratings − A1+ – extremely strong − A1 – strong − A2 – satisfactory, somewhat more susceptible to adverse effects than higher ratings − A3 – adequate, adverse conditions more likely to lead to weakened capacity − B – significant speculative characteristics − C – currently vulnerable to nonpayment − D – default

⎯ Moody’s Short Term Ratings − Prime1 – superior ability for repayment − Prime2 – strong ability for repayment − Prime3 – acceptable ability for repayment

Differences in ratings ⎯ Of 1168 firms rated by both Moody’s and S&P on 12/31/1993 53% of AAA or AA were rated same

by both agencies; for A or BBB 36% were rated same; for those below investment grade 41% were rated same

⎯ Comparing 298 firms rated by Moody’s, S&P and Duff & Phelps and 161 firms rated by Moody’s, S&P and Fitch‐IBCA, Duff & Phelps and Fitch‐IBCA tend to rate issues higher or same as S&P and Moody’s

⎯ Two questions are raised: (1) how much is quantitative and how much is judgment? (2) does rated companies paying for rating affect process?

Internal risk rating Objectivity and methodology ⎯ Goal is to generate accurate and consistent risk ratings yet also allow professional judgment to

significantly influence a rating where appropriate ⎯ A Risk Rating System (RRS) initially assigns an obligor rating that identifies expected probability of

default, then assigns a Risk Rating to each individual credit facility to identify risk of loss; also helps understand risk, determine capital charges and establish loss reserves

⎯ Expected Loss = Exposure x Default Probability x Loss Rate Given Default ⎯ Use of internal risk rating systems not all consistent so they are tough to compare; raises lots of

questions


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− What is meaning of being in each risk rating category? Does it mean expected default probability is within a specified range? Or is it associated with a specified loss rate given default? Or expected loss?

− What is horizon over which estimations are derived? One year would be consistent. − Is number of gradations appropriate to distinguish among range of risks? − How can bank link rating to measurable credit loss? − Are all appropriate risk factors incorporated?

⎯ Notwithstanding issues internal ratings would pave way to adoption of full credit risk modeling for banking in future, a la 1999 Basel consultative paper for new capital adequacy framework

Measuring default probabilities and recovery rates – Altman & Sanders (1998) compare four models for credit scoring ⎯ Logit – assumes default probability is logistically distributed and applies a few accounting variables

to predict default, research finds it useful in predicting bankruptcy ⎯ Linear probability – based on linear regression and makes use of a number of accounting variables

that seem best at predicting bankruptcy ⎯ Discriminant analysis – based on finding linear function of both accounting and market variables

that best discriminate between firms that default and firms that do not default ⎯ Probit

Debt rating and migration Bankruptcy is a discrete event yet it is also final point of a continuous process; analysts that focus solely on bankruptcy disregard a lot of useful information about firm value

For Moody’s 1950‐1979 2.26% of ratings were upgraded within a year and 2.18% of ratings were downgraded within a year; for Moody’s 1980‐1993 3.2% of ratings were upgraded within a year and 6.8% of ratings were downgraded within a year; 60% of rating changes were one notch, 30% two notches, 10% three or more notches

Drift = (Σ Upgrade Notches – Σ Downgrade Notches) / Number of rated companies 1,2,5,10 year rating transition matrices ⎯ Baa have equal likelihood of upgrade or downgrade, higher rated have larger probability of

downgrade and lower rated have larger probability of upgrade ⎯ Can also determine average life of given rating, Aaa lasts about 10 years and Caa 4 years ⎯ Older bonds tend to change ratings more than newly issued bonds

Moody’s suggests a Wiebull distribution most closely models bond ratings

Financial assessment (Step 1) Introduction – analyst should study financial reports to determine if earnings and cash flows are sufficient to cover debt, degree to which trends associated with financials are stable and positive, cash reserves / working capital, leverage, degree to which firm has access to capital markets, and capacity to borrow money; ratio standards are more relaxed for companies that have better overall business outlook

Procedure – There are three main assessment areas; emphasize current year but include past years when relevant; adjust seasonal or cyclical results; view structure in light of other obligations ⎯ Asset values, liquidity and quality ⎯ Financial size, flexibility and debt capacity

Industry benchmarks – ratio analysis can be extremely useful for comparing to peer companies ⎯ Interest Coverage = EBIT / Interest Expense (or EBITDA / Interest Expense)


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⎯ Funds From Operations / Total Debt ⎯ Free Operating Cash Flow / Total Debt ⎯ Pre‐tax return on capital ⎯ Operating Income / Sales ⎯ Long Term Debt / Capital ⎯ Leverage Ratio = Total Debt / Net Worth ⎯ Total Debt / Capitalization ⎯ Current Ratio = Current Assets / Current Liabilities

Balance sheet, Income statement, Ratio Analyses ⎯ Working Capital = Current Assets – Current Liabilities = Long Term Debt + Net Worth – Fixed Assets ⎯ Working Capital Leverage Ratio = Current Liabilities / Working Capital

First group of adjustment factors for obligor credit rating Management and other qualitative factors (step 2) ⎯ Has no effect if obligor reaches acceptable standard, else may bring about a downgrade ⎯ Account Operations – Is financial and security reporting timely? Is it of good quality? Does it

satisfactorily explain significant variations from projections? Are credit limits and terms respected? Does company honor its obligations to creditors?

⎯ Management Assessment – Are skills sufficient for size and scope of business? Does management have a satisfactory record of success and appropriate industry experience? Does management have adequate depth and are succession plans in place?

⎯ Is there an informed approach to identifying, accepting and managing risks? Does management stay current on how to conduct operations? Does management address problems promptly? Is a reasonable business and financial plan in place? Is management remuneration prudent and appropriate?

⎯ Environmental Assessment – Does firm comply with all relevant regulations and practices? Industry Rating (step 3a) – analyst assigns a score of say 1 (minimal risk) to say 5 (very high risk) for each established criterion; sum of scores is converted to an industry rating ⎯ Competitiveness – potential of industry to sell its products/services given its cost structure,

reputation and effectiveness ⎯ Trade environment – all factors that affect commerce, trade agreements ⎯ Regulatory framework – laws, regulations, taxation; policies and trends, industry’s ability to absorb

and influence these policies and trends; impact of supply and demand ⎯ Restructuring – process of adjusting to changes in market conditions ⎯ Technological change – vulnerability to technological change that could result in changing costs,

alteration in range or price of products/services; R&D must be taken into account ⎯ Financial performance – standard ratios ⎯ Long term trends – demographics, vintage of durables and infrastructure, lifestyle changes and

consumer attitudes ⎯ Vulnerability to macroeconomic environment – sensitivity to downturns, fiscal policy, interest rates,

exchange rates Tier Assessment (step 3b) – establish relative position of firm within its industry, local or global ⎯ Tier 1 – Major players with dominant market share, diversified and growing customer base, low

production costs based on sustainable factors ⎯ Tier 2 – Important or above‐average players with meaningful market share ⎯ Tier 3 – Average or modestly below‐average players with moderate market share


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⎯ Tier 4 – Weak players with declining customer base, high production costs Industry/Tier position (step 3c) – combine industry rating and tier assessment; if assessment is weak obligor rating can be lowered; weak companies in vulnerable industries have high defaults

Financial statement quality (step 4) – bank must always be fully satisfied as to quality, adequacy and reliability of financial statement information irrespective of risk rating; exceptions may be made for subsidiaries or new entities

Country risk (step 5) ⎯ Risk that obligor will not be able to pay because of restrictions on convertibility or availability of

currency; also an assessment of political and economic risk of country ⎯ Exists when more than a prescribed percent (say 25%) of cash flow or assets is located outside of

local market

Second group of adjustment factors for facility rating Third party support (step 6) – only 100% clean guarantees should qualify for consideration Term (step 7) – there is increased risk associated with longer term facilities Structure (step 8) – priority of security, covenants or lack thereof attached to facility; if structure contains very strong covenants it may be appropriate to make an adjustment to fully or partially offset effect of term

Collateral (step 9) ⎯ Security should be valued as it would be in a liquidation scenario ⎯ If security includes collateral from various categories, one should generally use worst category on

which any significant reliance is placed ⎯ Documentation and completion of security is always a concern and should be considered when

assessing level of protection


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Introduction To qualify as an internal model for specific risk, regulator should be convinced that concentration risk, spread risk, downgrade risk and default risk are “appropriately” captured; capital charge for specific risk is multiplier (minimum value of which is currently set to 4) times sum of VaR at 99% for spread risk, downgrade risk, default risk over 10 day horizon

There are several problems with this piecemeal approach ⎯ Spread risk is related to both market risk (which carries a multiplier of 3 instead of 4) and credit risk;

downgrade risk is pure credit risk and adding spread risk to it may lead to double counting ⎯ Problem of disentangling market risk and credit risk components in spread changes is further

obscured by fact that often market participants anticipate credit events before they happen ⎯ Default is simply a special case of downgrade; adequate credit VaR model should therefore address

migration risk and default risk in consistent integrated framework ⎯ Changes in market and economic conditions, as reflected by interest rates, stock indices, exchange

rates, may affect firms; hence credit risk is linked to market risk, and risk framework should integrate them

All models assume deterministic interest rates and are inappropriate for measuring credit risk of swaps, credit derivatives and other derivative‐like products like loan commitments; this simplification is not crucial to valuation of short maturity options but is unrealistic for longer maturity options; next generation of models should be integrated ∋ default and migration probabilities are affected by stochastic interest rates

CreditMetrics framework CreditMetrics (J P Morgan) is based on estimation of forward distribution of changes in value of portfolio related to migration of credit quality of obligor

Involves estimating a probability distribution of credit losses by MC simulation ⎯ Liable to be computationally quite time intensive ⎯ Has advantage that credit losses are defined as arising from credit downgrades as well as defaults;

can use transition matrix from rating agency study ⎯ Impact of credit mitigation clauses and other unique situations can be incorporated into analysis

Credit rating changes should not be assumed to be independent; a Gaussian copula model can be used for credit rating changes same as for defaults

In comparison to market VaR credit VaR poses three challenges ⎯ Credit returns are not normal, they are highly skewed and fat tailed; upgrades bring limited upside

but downgrades or defaults bring substantial downside; percentile levels of distribution cannot be estimated from mean and variance only

⎯ To measure effect of diversification we need correlations for all pairs of obligors which entails making some strong simplifying assumptions basing evaluations on joint probability of equity returns

⎯ Information on loans is not as complete as it is for traded instruments such as bonds


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Credit VaR for a bond (building block 1) Step 1 – Specify transition matrix (S&P, Moody’s or internal) adjusted for current economic environment; also produce cumulative default rates consistent with transition matrix

Step 2 – Specify credit risk horizon consistent with transition matrix, usually one year to match accounting data and rating agency reports

Step 3 – Specify forward pricing model ⎯ Seven spread curves are needed, one for each credit quality AAA to CCC, to discount future cash

flows; obtained from current spot curve ⎯ In event of default apply recovery rate; if losses determined through MC then beta distribution is

assumed for recovery rate Step 4 – Derive forward distribution of changes in portfolio value from transition matrix ⎯ Forward bond price is computed for each rating category ⎯ VaR is determined by observing transition distribution ⎯ Distribution generally exhibits a long downside tail

Credit VaR for a loan/bond portfolio (building block 2) Correlations between changes in credit quality are not zero but are not directly observable; overall credit VaR is quite sensitive to these correlations; their accurate estimation is therefore a key determinant of portfolio optimization

CreditMetrics makes use of stock price as proxy for asset value and estimates correlations between equity returns of obligors and infers correlations between changes in credit quality ⎯ Joint normal distribution f(r1,r2,ρ) = (1/(2π√(1‐ρ2)))exp{[‐1/(2(1‐ρ2))][r12+r22‐2ρr1r2]} ⎯ Prob(Def1,Def2) = N(‐d2,1,‐d2,2,ρ) ⎯ This is equivalent to assuming all firm activities are financed by equity which is a major drawback

especially when applied to highly leveraged companies CreditMetrics expands Merton model to include changes in credit quality ⎯ Threshold z levels for each rating are calculated based on transition matrix values ⎯ Plugging into BSM one can solve for asset value that would trigger a default

Default correlations are higher for firms in same industry As credit quality of portfolio deteriorates, default correlations increase; correlations are higher in bad economic environments

Analysis of credit diversification using MC (building block 2) For a large portfolio of obligors establishing an analytic distribution of joint migration probabilities is not practical; instead MC is used to generate full distribution of portfolio values at credit horizon ⎯ Derive asset return thresholds for each rating ⎯ Estimate correlation between each pair of obligors asset returns ⎯ Generate asset return scenarios from multivariate normal distribution with estimate correlation

matrix; standard technique is Cholesky decomposition ⎯ For each scenario and obligor, map standardized asset return into corresponding rating according to

thresholds in step 1 ⎯ Given spread curves that apply for each rating, revalue portfolio ⎯ Repeat procedure large number (100,000) of times; plot distribution of portfolio values and derive

percentiles of distribution


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CreditMetrics as a loan/bond portfolio management tool (building block 2) Capital charge is a function of unexpected losses, C = EV – P(c); bank should hold reserves against these unexpected losses at a specified confidence level (1–c)

For each asset CreditMetrics calculates marginal standard deviation, impact of asset on overall portfolio standard deviation, isolating individual marginal risk contributions

By comparing marginal standard deviation to standalone standard deviation, one can assess extent of benefit derived from portfolio diversification when adding asset to portfolio allowing effective risk reduction

Same framework can be used to set up credit risk limits and monitor credit risk exposures

Estimation of asset correlations (building block 3) Even with simplification of using equity return correlations, this still requires correlations for all pairs of obligors; to reduce dimensionality of this estimation problem CreditMetrics uses multifactor analysis and maps obligors into countries and industries

Exposures (building block 4) “Exposures” is term CreditMetrics gives to use of forward pricing model applied to each credit rating ⎯ For bonds, loans, receivables, commitments to lend, letters of credit, exposure relates to future

cash flows at risk beyond one year horizon using forward yield curve ⎯ For swaps and forwards, there is no way to derive future cash flows at risk without making

assumptions about dynamics of interest rates − Value of swap in 1 year = Forward riskless value in 1 year – expected loss in years 1 to maturity − Expected loss in years 1 to maturity = average exposure from year 1 to maturity x probability of

default in years 1 to maturity x (1 – recovery rate) − This ad hoc calculation is not satisfactory; only a model with stochastic interest rates will allow a

proper treatment

Conditional transition probabilities / CreditPortfolioView CreditPortfolioView is based on observation that default probabilities and credit migration probabilities are linked to economy; when economy weakens (strengthens) both downgrades and defaults increase (decrease)

Multi‐factor model that models unemployment rate, GDP growth rate, long‐term interest rates, foreign exchange rates, government expenditures, aggregate savings rate, with a transition matrix

Industries will react differently to these factors Applies better to speculative grade obligors whose default probabilities vary substantially with credit cycle than to investment grade obligors whose default probabilities are more stable ⎯ Default probabilities are modeled as logit functions Pj,t; to calibrate one has to solve system

− Pj,t = 1/(1+exp(‐Yj,t)) − Macroeconomic Yj,t are derived from a multifactor model Yj,t = βj,0 + Σβj,i,tXj,i,t + εj,t − Factors Xj,i,t follow a univariate AR(2) model Xj,i,t = γj,i,0 + γj,i,1Xj,i,t‐1 + γj,i,2Xj,i,t‐2 + εj,i,t

⎯ Once system has been calibrated, one can use Cholesky decomposition of error covariance matrix Σ=AA’ to simulate distribution of default probabilities; using specific realizations of error terms one can derive corresponding values for X, then Y and finally P

⎯ Probabilities can be defined separately for each country or industry


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Conditional transition matrix is derived from unconditional Markov transition matrix M based on Moody’s or S&P historical data; adjustment consists of shifting probability mass into downgrades where ratio of Pj,t/Mj,default is less than 1 and into upgrades where ratio is more than 1

This approach can generate multiperiod transition matrices MT = ∏Mt Limitations ⎯ Requires reliable default data for each country and possibly each industry within countries ⎯ Assumes that historical average default rates and transition probabilities equal actual values ⎯ It is not clear that ad hoc methodology for adjusting migration matrix works better than Bayesian

model; interesting future research would be to compare transition matrices produced by both models

⎯ Assumes that all firms within rating class have same default rate and spread curve – cannot be true since we know default rates evolve continuously while ratings are adjusted discretely

⎯ Makes no provision for market risk


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Introduction Overlap in default probability ranges of adjacent rating classes may be quite large Ran a simulation of 50,000 runs assuming true probability of default was equal to reported Moody’s 25‐year average using several different levels of correlation from 15% to 45%; distribution of default rates varies greatly with correlation, with distribution skewed right

Structural default approach – economic value of default is presented as a put on value of firm’s assets; merit is that each case can be analyzed individually and precisely; this is also principal drawback since information for such an analysis is rarely available to bank or investor

Probability of default, Conditional expected recovery value, Default spread, Estimating credit risk as function of equity value

In Merton model bank can buy a put P0 as an insurance policy against expected loss with premium P0 = [Fe‐rT – (N(‐d1)/N(‐d2))V0]N(‐d2) ⎯ First term inside bracket is value of riskless bond maturing at time T ⎯ Second term inside bracket is PV of recovery value given a default occurs ⎯ N(‐d2) is probability that a default occurs

Formulas above are for a risk neutral world; in real world μ is substituted for r A put can be created synthetically by selling short N(‐d1) of firm’s assets and buying Fe‐rTN(‐d2) units of riskless bonds; such a put on equity can be used to hedge against loan default

KMV approach Derives default probability for each obligor based on Merton model; capital structure consists of equity, short term debt, long term debt

Step 1 – Estimate asset value and volatility ⎯ S = f(V,σ) ⇒ V = h(S,σ) ⎯ σS = g(V,σ) is unstable and there is no simple way to measure it precisely from market data ⎯ To calibrate model for σ KMV uses an iterative technique

Step 2 – Calculate distance to default ⎯ Problems that need to be addressed

− KMV observed that firms default when asset value reaches a level somewhere between value of total liabilities and value of short term debt; assuming firms default when assets are below total debt may not be accurate measure of probability of default

− Loss of accuracy may also result from non‐normality of asset return distribution and simplifying assumptions about firm capital structure

− This may be further aggravated if company is able to draw on otherwise unobservable lines of credit; if company is in distress using these lines may unexpectedly increase liabilities while actually providing necessary cash to honor payments

⎯ Default Point DP = Par value of current liabilities = Short Term Debt to be serviced over horizon + ½ of Long Term Debt

⎯ Distance to Default DD = [ln(V0/DP) + (μ + ½σ2)T] / (σ√T) or DD = (EV – DP)/σ ⎯ Probability of default is N(‐DD)


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Step 3 – Expected Default Frequency (EDF) and resulting implied rating can be derived from DD using a default database

EDF as predictor of default – EDFs have proved to be a useful leading indicator of default or at least of degradation of creditworthiness of issuers; when financial situation of a company starts to deteriorate EDFs tend to shoot up quickly until default occurs; changes in EDFs tend to anticipate by at least one year downgrading of issuer by Moody’s/S&P

EDFs and Ratings – EDFs vary quite a bit for firms that have same rating ⎯ Average default rate for each class is higher than default rate for typical firm; this is because each

class contains some risky firms that should have been downgraded but no downgrade has yet occurred and such firms outnumber firms that should have been upgraded but no upgrade has yet occurred

⎯ Because rating agencies are slow to change ratings, Moody’s/S&P historical frequencies of remaining in a rating class overstate probability of maintaining a particular credit quality; therefore transition probabilities are too small

⎯ Average Moody’s/S&P historical probability of default overstates true probability of default because of difference between mean and median, particularly for low grade credits; certain firms should have already been downgraded

KMV valuation model for cash flows subject to default risk If we know how to derive risk‐neutral probabilities from EDFs then valuation of risky cash flows proceeds in two steps similar to option pricing ⎯ Valuation of default free component ⎯ Valuation of component exposed to credit risk

Derivation of risk‐neutral EDFs ⎯ QT = N[N

‐1(EDFT) + ρV,M(π/σM)Tθ] where π/σM is market Sharpe ratio and ρV,M is estimated in terms of linear regression of asset returns against market (difficult to estimate and varies over time)

⎯ θ is calibrated using bond data, should in theory be equal to ½ Risk neutral valuation using risk neutral EDFs ⎯ Single cash flow – use standard risk‐neutral martingale discounting ⎯ Pricing model can be generalized for a bond/loan subject to default risk by taking a sum of single

cash flows ⎯ Spread = [LGD x Q x (1+rF)] / [1 – LGDxQ] where Q is risk‐neutral default probability

Difficulty in practice is that EDF does not correspond precisely to probability of assets being below default point

Asset return correlation model CreditMetrics and KMV derive asset return correlations from a structural model that links correlations to fundamental factors; by imposing a structure on return correlations sampling errors inherent in simple historical correlations are avoided and better accuracy is achieved; portfolio also becomes computationally feasible

To avoid defining a different correlation between each pair of companies a multi‐factor model is used; KMV constructs a three‐layer factor structure model ⎯ Composite company‐specific factor ⎯ Country and industry factors ⎯ Global, regional and industrial sector factors


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Integrating yield spread with options approach We can use data for corporate bonds vs Treasury bonds to evaluate implied default parameter Cost of credit is derived from value of put that eliminates credit risk P0 = D(e

‐rT – e‐yT) Then we solve for firm value V0 and hence equity value S0 numerically

Limitations of Merton model and some extensions Practical difficulties in implementing Merton model ⎯ Asset value and volatility are not directly observable and hard to estimate; KMV’s methodology

derives these from equity prices ⎯ Riskless interest rates are constant and relationship between interest rate risk and equity risk

cannot be modeled; several authors have relaxed this assumption ⎯ Reliance on priority rule to describe payoff to debt holders makes valuation of coupon debt

difficult; coupon debt can be viewed as a compound option where value depends on whether previous coupon payment passed without incident

⎯ Seniority is not considered but for complex capital structures seniority rules are not fully enforceable; several recent papers abandon this concept in favor of cross‐default

Empirical evidence – Jones, Mason & Rosenfeld (1984) compared Merton model to naïve method of discounting cash flows at riskless rate ⎯ Merton model outperforms naïve approach only for non‐investment‐grade securities ⎯ Merton model consistently prices investment grade bonds higher than market prices, implied credit

spreads are too low due to several factors − Violation of seniority rules − Choice of capital structure that is too simplistic − Deterministic interest rates – introduction of stochastic interest rates significantly improves

performance of model − Poor quality of bond data and calculated yields that do not correctly adjust for call features

Extensions of Merton model ⎯ Geske (1977) shows that multiple default options for coupons, sinking funds, junior debt, safety

covenants, can be treated as compound options; default may occur at a coupon payment date even though asset value is greater than coupon if value of remaining equity will be close to 0 ∋ shareholders are better off not paying coupon

⎯ Black & Cox (1976) reinterpreted default as occurring whenever assets fall below some specified boundary even before maturity; default occurs simultaneously for all securities so there is no need to model bankruptcy process

⎯ Kim, Ramaswamy & Sundaresan (1993) propose a model with stochastic interest rates where financial distress arises out of cash flow restraints and bankruptcy is costly

⎯ Anderson & Sundaresan (1996) extend previous model by allowing firm to make a “take it or leave it” offer to debt holders; this model generates spreads consistent with observed market spreads even at very low level of debt and liquidation costs

⎯ Longstaff & Schwartz (1995) build on Black & Cox and allow deviations from absolute priority rule by adding a constant recovery rate, but allocation of value of bankrupt firm is specified exogenously rather than being outcome of endogenous negotiation process − Riskless interest rate follows one‐factor Vasicek process with mean reversion that is correlated

with asset value process, dr = β(m‐r)dt + ηdzr, dV/V = μdt + σdzv, corr(dzr,dzv) = ρdt − Credit spreads increase with any correlation between assets and interest rates


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− Bankruptcy occurs when assets drop below a specified level; does not account for priority of debt

− Model produces negative correlation between level of Treasury yields and credit spreads, consistent with Merton model

⎯ Saa‐Requejo & Santa‐Clara (1997) suggest boundary value should represent PV of liabilities rather than being a fixed number

⎯ Leland & Toft (1996) – shareholders choose leverage to maximize value of equity; bankruptcy is endogenized and occurs when it ceases to be in interest of shareholders to give up $1 to pay next $1 of interest; model provides useful insight but in its current form is too restrictive to be of practical use


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Introduction CreditRisk+ (Credit Suisse, 1997) is a purely actuarial model; probabilities are based on historical statistical data; distribution for number of defaults over any period of time follows a Poisson distribution

Reduced‐form approach also uses Poisson process; default is treated as a random stopping time with a hazard rate process; less intuitive than structural model but calibrated using credit spreads that are observable

Actuarial Approach / CreditRisk+ Probability of default ⎯ Only default risk is modeled, downgrade risk is ignored ⎯ There is no attempt to relate default to capital structure of firm, based just on rating ⎯ P(n) = λne‐λ / n! where λ is average number of defaults ⎯ Poisson distribution underestimates probability of default

Frequency of default events (building block 1) ⎯ Standard deviation of default rate is equal to √λ, although historical analysis shows variance should

be greater than mean ⎯ CreditRisk+ suggests we make additional assumption that mean default rate λ is stochastic with

standard deviation σλ which makes sense because rate changes with business cycle; when we incorporate this assumption, distribution becomes more skewed and exhibits a fat right tail

Severity of losses (building block 2) – Loss Given Default (LGD) is exogenous to model and independent of market risk and downgrade risk ⎯ Expected number of defaults by band – individual loans are grouped into LGD bands assumed to be

independent − Expected loss for each band is ELi = ΣLGDiPi − Expected number of defaults for each band is ni = ELi/Li

Distribution of default losses for a portfolio (building block 3) ⎯ Step 1: Probability generating function for each band is Gj(z) = Σ (λjne‐λj / n!) znLj = e‐λj+λjz^Lj ⎯ Step 2: Probability generating function for entire portfolio – since we assume each band is a

portfolio of exposures independent from other bands, G(z) = e‐Σλj+Σλjz^Lj ⎯ Step 3: Loss distribution for entire portfolio P(nL) = (1/n!) dnG(z)/dzn|z=0

Basic model can easily be extended to multiple periods and/or variability of default rates can be linked to multiple factors

Advantages of CreditRisk+ ⎯ Relatively easy to implement; closed form can be derived for probability of losses ⎯ Marginal risk contributions by obligor can be easily computed ⎯ Focuses on default and therefore requires relatively few estimates and inputs

Limitations of CreditRisk+ ⎯ Assumes credit risk has no relationship with market risk ⎯ Ignores migration risk, exposure for each obligor is fixed and not sensitive to possible future

changes in credit quality


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⎯ Credit exposures are taken to be constant and not related to changes in underlying stochastic factors; does not work well with nonlinear products such as options

Reduced‐Form Approach or Intensity‐Based Models Basic model ⎯ Securities are priced using cash flows discounted using risk‐neutral probabilities ⎯ Y = (R + λLGD) / (1 ‐ λLGD) is discount rate including probability of default ⎯ On continuous basis yield equals riskless rate R plus risk neutral expected loss rate λLGD ⎯ Yield could also be adjusted to include other factors like liquidity Y = R + λLGD + L ⎯ To value a risky bond binomial tree would be constructed using Y rather than R ⎯ From credit spreads to default probabilities1

− Forward conditional default rate λ(t) = Forward Credit Spread / LGD − Cumulative default probability Pt = Pt‐1 + (1‐Pt‐1)λt − Unconditional default probability pt = Pt – Pt‐1 represents probability of defaulting in year t as

seen from time 0 Hazard rate depends on state of economy (Duffie & Singleton, Jarrow & Turnbull) ⎯ λ(t) = λ(Xt) is a Cox process which keeps properties of a Poisson process conditional on Xt ⎯ Intensity level λ(t) = λ0 + λ1r(t) + λ2Wmkt(t) where r(t) is a one‐factor extended Vasicek model ⎯ Market follows lognormal process dM(t)/M(t) = r(t)dt + σdWmkt(t)

Hazard rate depends on credit rating of issuer – Markov process (Jarrow, Lando & Turnbull) ⎯ Inputs

− Term structure of default‐free rates − Term structure of credit spreads for each credit category − Loss rate for each rating category − Credit rating transition matrix

⎯ Assumptions − There is no correlation between rating migrations and dynamics of riskless interest rates − Credit spreads are deterministic as long as there are no rating changes − Recovery rates are constant − When there is a default recovery takes place at maturity of instrument

⎯ Output: term structure of default probabilities Spread‐based models – make direct assumption about stochastic process that governs credit spread ⎯ Parsimonious model which may prove useful for valuing certain credit derivatives ⎯ dr = (α ‐ βr)dt + σrdzr ⎯ du = (a – bX)dt + σudzu ⎯ corr (dzr,dzu)

1 Text p419 provides examples of this


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Key features of credit risk models Credit

Migration Approach

Credit Migration Approach

Contingent Claim Approach

Actuarial Approach

Reduced Form Approach

Software Credit Metrics Credit Portfolio View

KMV Credit Risk+ Kamakura

Definition of risk

Change in market value

Change in market value

Default losses Default losses Default losses

Credit events Downgrade or default

Downgrade or default

Continuous default probability

Default Default

Risk drivers Asset values Macro factors Asset values Expected default rates

Hazard rate

Transition probabilities

Constant Driven by macro factors

Driven by term structure of EDF and asset value process

N/A N/A

Correlation of credit events

Standard multi variate normal distribution (equity factor model)

Conditional default probability function of macro factors

Standard multi variate normal asset returns (asset factor model)

Conditional default probability function of common risk factors

Conditional default probability function of macro factors

Recovery rates Random (beta distribution)

Random (empirical distribution)

Random (beta distribution)

Deterministic loss given default

Deterministic loss given default

Numerical approach

Simulation and analytic

Simulation Simulation and analytic

Analytic Tree‐based and simulation

Crouhy Chapter 8 8 9 10 10


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Introduction If we compare various models by applying them to same large diversified benchmark portfolio, results show that models produce similar estimates of VaR

Asset return correlation model appears to be critical factor in CreditMetrics, CIBC’s internal credit risk model CreditVaR, and KMV

For models based on credit migration, results are quite sensitive to initial rating of obligors; results for CreditRisk+ are also very sensitive to default correlations and standard deviation of default rate

Comparison of industry‐sponsored credit risk models Authors ran an early version of KMV that derives loss distribution analytically; approximation is only accurate for confidence levels beyond 10 bp

CreditMetrics and CreditVaR are very close, e.g. for a $900 million portfolio, 1 year 1% and 0.1% VaR are very close; KMV 0.1% VaR is almost 40% lower

All models produce fairly consistent results; 0.1% VaR for CreditRisk+ is close to CreditMetrics and CreditVaR

Theory indicates that if parameters are correctly harmonized we can expect little difference in results; differences become more important at higher percentage loss levels

Stress testing and scenario analysis For credit migration approach, key parameters are asset return correlations, credit quality of obligors, transition matrix, recovery factors and spread curves; VaR most sensitive to credit quality of portfolio and correlation model

For contingent claim approach, key parameters are asset return volatilities and correlations For actuarial approach, key parameters are standard deviation of default rate and rate of recovery; when standard deviation of default rate is lowered from 100% to 0% 0.1% VaR drops 60%

Authors were only able to carry out extensive sensitivity analysis on their own model CreditVaR ⎯ Each issuer is downgraded two full grades, with a floor at CCC; produces results similar to those of

speculative sub‐portfolio ⎯ If equity return correlations are 0 VaR is reduced by a factor of 2; if correlations are 1 VaR goes up

by a factor of 6 When default probabilities are doubled VaR increases by only 50%, a relatively low sensitivity; increasing default risk reduces migration risk, which partially compensates

When recovery rates fall (increase) by 10% VaR increases (falls) by approximately 15% There was not much sensitivity to transition matrix

Implementation and validation issues Use of credit models for allocating bank economic capital should be first step in improving capital allocation for credit risk; banks have to convince regulators that they trust their internal rating models enough to use them to manage their loan portfolios before there is a real chance their internal models will be approved for regulatory capital calculations


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Credit models are difficult to validate because default is a rare event so direct testing imposes an impossible demand on available data (default frequency and recovery rate data is scarce); this does not mean models cannot be tested at all ⎯ Reduced form models can be validated in same way as market VaR models, they should explain

term structure of credit spreads observable in market ⎯ Models can be tested against cumulative credit P&L; requires banks to record P&L separately for

market and credit risks, which is a daunting task; a more realistic alternative is to use static P&L to disentangle market and credit risks2

⎯ It is worth exploring indirect testing; model input can be validated; models are evaluated in terms of their forecasts at a given point in time for simulated portfolios; problem with this approach is that statistical test to assess quality of forecasts is not powerful

⎯ A more appropriate test of a credit risk model is a stress test or sensitivity analysis that identifies areas where model may be more apt to generate inappropriate results

2 Method for actually performing this split is in Chapter 6 of text, which is not on syllabus


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Introduction Over years banks have developed various traditional techniques to mitigate credit risk – bond insurance, netting, marking to market, collateralization, termination, reassignment, selling

These mechanisms lack flexibility and do not unbundle credit risk from underlying positions ∋ it can be redistributed among a broader class of investors

Credit derivatives are specifically designed to strip credit risk out from market risk and price it independently; allow users to manage or transfer credit risk independently of funding and relationship management much as interest rate and foreign exchange derivatives allowed banks to manage market risk independently of liquidity risk

In a related development wholesale securitization allows credit securities to be sold to a wide pool of investors who would not have been interested in purchasing bundled credit risk

Credit derivatives also contribute to price discovery of credit and improve market efficiency for pricing credit

Credit risk enhancement Bond insurance ⎯ New insured municipal bond issues in 1991 amounted to $52B, one third of total market ⎯ Fierce competition has led bond insurers to guarantee ever riskier issues while being paid less and

less for this service3 ⎯ Guarantees or letters of credit from a third party of higher credit quality than original borrower

reduces credit risk exposure of transaction Embedded puts – puts provide investors with credit protection by allowing them to liquidate position without loss if issuer declines in quality

Netting – True credit risk is limited to net replacement value of all transactions between two parties provided parties have legally enforceable netting agreements in place

Marking to market – marking to market by exchanging cash equal to daily change in market value of position is one of most efficient credit enhancement techniques; can practically eliminate credit risk (by reducing it to at most one day’s loss) but requires sophisticated monitoring and back‐office systems only large institutions can afford

Collateralization – Collateral in form of liquid assets may be pledged (1) up front and once and for all, (2) once an agreed marked‐to‐market threshold for all transactions has been crossed, (3) when counterparty is downgraded, or (4) in real time as percentage of marked‐to‐market value of transaction

Termination or reassignment ⎯ Another credit enhancement technique is early termination by means of a mid‐market quote after

an agreed event such as a downgrade has occurred ⎯ Reassignment conveys right to assign one’s position to a third party in event of downgrade

Derivative Product Companies (DPCs) A Derivative Product Company or AAA Derivatives Subsidiary is an over‐collateralized subsidiary of a parent company with a lower credit rating

3 In 2007Q4 this got several major bond insurers into trouble


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DPCs allow firms that have relatively low ratings (usually A) to deal with users that can accept only highly rated counterparties

When first DPC was set up by Merrill Lynch in 1991 it was thought they might revolutionize credit structure; in fact only 13 DPCs have been launched; apparent lack of success is attributed by some bankers to large amount of capital required for limited amount of business

By means of mirror trades DPC passes through derivative cash flows and offsets market risk of transaction with original client; DPC is left with credit risk exposure of parent which should also be offset through over‐collateralization to obtain AAA rating

DPC is bankruptcy remote from its parent, assets not consolidated if parent defaults ⎯ Continuation structure – well‐capitalized institution is substituted for parent in case of default to

honor existing obligations ⎯ Termination structure – failure of parent leads to immediate termination of DPC and unwinding of

its portfolio Two AAA DPCs were shut down in August 1996; in both cases counterparties experienced losses although they were on a relatively small scale

Credit derivatives History – initiated in early 1990s, growing, total market $234B in 3Q19994 Why a market for credit derivatives? ⎯ Investors

− Way to enhance yield by accepting more credit exposure with or without leverage; a cheaper way to invest in high‐yield markets

− Unbundling of credit and market risks; reduction of credit risk − Provide quality‐conscious investors with ready if indirect access to previously unavailable high‐

yield markets (loans, junk bonds, foreign credits, emerging market debt, ABSs) − May also be used to exploit inconsistent pricing between loan and bond markets for same issuer

or to take advantage of any particular view that an investor has about pricing of credit spreads or build a portfolio with customized credit exposure

− Structured products can be customized to investor’s individual specifications regarding maturity and leverage

⎯ Banks − Way to shift part of credit risk of their asset portfolio, focus on origination and servicing − Provides additional mechanism for reducing credit concentration, diversifying credit risk and

managing risk profile of loan portfolio − BIS regulation on capital requirements, Risk‐Adjusted Return On Capital (RAROC) attribution

systems and internal objectives for ROC ⎯ Corporations – Hedging trade receivables, reducing exposure to customer/supplier credit risk,

hedging credit‐related project risk Three credit risk exposures influence marked‐to‐market value of any type of credit derivative ⎯ Credit risk of underlying ⎯ Risk of default of counterparty to credit derivative; can be substantial risk in case of a leveraged

transaction ⎯ Risk of default by seller of credit derivative; often neglected by bank when pricing deal

4 Contradicts Hull Chapter 21


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Types of credit derivatives CDSs, TRSs Credit Linked Notes (CLNs)5 ⎯ An asset‐backed CLN is a debt instrument with embedded credit options, forwards and/or swaps;

coupon and redemption are tied to performance of underlying bonds or loans; allow investors to customize credit exposure; often issued as 144A securities

⎯ Maturity ranges from 3 months to several years, with 1‐3 years being most common ⎯ Some CLNs can obtain Moody’s or S&P credit rating ⎯ May be leveraged up to a factor of 10; offers investors limited downside (loss of initial principal)

and unlimited upside ⎯ CLNs may constitute a natural hedge to a TRS; CLNs can also implement investor’s credit view ⎯ CLNs with embedded options maintain principal protection; if investor is right he gets a higher

coupon and if he is wrong he gets a lower coupon, e.g. buy note and sell put on credit rating ⎯ CLNs with embedded forwards do not necessarily protect principal; depending on ending value of

forward noteholder may receive more or less than face value; tradeoff for higher risk is usually a higher coupon payment

⎯ Cost of CLN to investor in terms of lower coupon payment can be quite high; without a deep liquid market for credit options issuer may not be able to effectively hedge exposure embedded in note; only way to hedge is to buy underlying at its financing cost which is passed on to investor in lower coupon payment

Spread options ⎯ Underlying is yield spread between a specified corporate bond and a Treasury of same maturity;

strike is forward spread at maturity, and payoff is greater of zero and difference between spot spread at maturity and strike

⎯ Payoff is (Spread – Strike)+ x D x Notional, where D is Macaulay duration dP/P = ‐[D/(1+y)]dy, approximating price change due to spread change

Credit intermediation swaps ⎯ A third party, usually a AAA DPC or other SPE, stands between two counterparties that might be

otherwise unwilling to trade directly with one another ⎯ Third party enters into offsetting transactions and therefore incurs no market risk but bears

counterparty risk of both parties, for which service it is paid a spread on floating rate in both transactions

Credit risk securitization for loans and high‐yield bonds US markets for Collateralized Loan Obligations (CLOs) and Collateralized Bond Obligations (CBOs) have grown dramatically over past few years

Used mainly as a way for banks to free regulatory capital, reduce economic capital and leverage business

Allows loans or bonds rated below investment grade to be pooled together and cash flows prioritized to achieve investment grade ratings attracting more institutional investors

It is easier to produce securities with investment grade ratings from CLOs than from CBOs ⎯ Well‐secured loans have higher recovery rates than unsecured corporate bonds (70% vs 30‐40%) ⎯ Loans amortize, resulting in shorter duration and thus lower risk

5 Text p459 provides an example


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Rating agencies have their own methodology to rate senior CDO tranches, running cash flow models that employ cumulative default rates and stress default rates based on weighted average credit quality of underlying pool

Main motivation for issuing CLOs is to arbitrage regulatory capital from which point it is less costly to hold equity tranche than to hold underlying loans themselves; in fact economic risk borne by bank may not be reduced at all

Paradoxically credit derivatives which offer a more effective form of economic hedge have so far secured little regulatory capital relief

J P Morgan (1998) partially bridged gap between economic hedging and efficient regulatory capital management by combining securitization and credit derivatives in a structure called a “bistro” ⎯ SPE owned by J P Morgan entered into CDS with J P Morgan itself; CDS referenced portfolio of

commercial loans and corporate and municipal bonds as well as counterparty credit exposure arising out of derivatives

⎯ SPE then sold bonds to investors with performance referenced to performance of CDS ⎯ Economically efficient as it successfully transferred credit risk to bondholders, but far less

regulatory capital efficient than more straightforward CLO deals

Regulatory issues Regulators have yet to make a major move wrt credit derivatives market; some regulators now allow banks to price derivatives with internal models and treat counterparty risk separately

Under EU Capital Adequacy Directive (CAD) there is an 8% capital charge for credit derivatives if they are held in banking book, yet there is a charge of only 1.6% if they are held in trading book

Bank of England reversed its position and removed distinction between CDSs and TRSs; accepted principle of marking to market credit derivatives provided appropriate pricing models are available

Fed’s new guidelines state that capital treatment for credit derivatives will be same as for other derivatives in trading book

CAD does not recognize offsets for credit derivatives unless position is perfectly hedged; in fact a regulatory capital penalty could result from use of credit derivatives as a bank could find itself taking a risk charge on a loan and an additional risk charge on credit derivative that it has entered into to hedge that loan even though credit risk has been lessened

Regulatory capital treatment differs quite substantially depending on whether position takes form of a corporate credit in banking book or position has been created synthetically by means of a credit derivative; capital required for synthetic approaches is much less

Credit derivatives can be used to arbitrage capital regulatory rules; opportunity arises because rules are not consistent with real levels of risk exposure


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Introduction RAROC analysis benefits ⎯ Reveals how much EC is required by each business line, product, customer, and how these create

total ROC by firm ⎯ Provides an economic basis from which to measure all risk types and positions consistently ⎯ Promotes consistent, fair, reasonable risk‐adjusted performance measures and provides managers

with information to make trade‐off between risk and reward efficiently During late 1990s began to be accepted as best practice; made possible by development of sophisticated risk measurement tools; however implementation still requires a well judged blend of art and science

Definition of capital – EC is designed to absorb unexpected losses (as opposed to reserves which absorb expected losses) through a certain horizon up to a certain level of confidence while regulatory capital is designed to ensure enough capital in banking system; most institutions hold more capital than regulators require

RAROC =6 (Revenue – Expenses + Return on EC – Expected Losses) / EC Integrated goal congruent RAROC process ⎯ To be successful and consistent RAROC process must be integrated into overall risk management

process; must synthesize methodologies without making them too simplistic ⎯ Policies (consistent with business strategies) are implemented as methodologies (relying on

analytical models) which are supported by infrastructure (data, processing ability, skilled staff) ⎯ Affects how bank allocates limits, performs risk analysis, manages capital, adjusts pricing strategies,

performs portfolio management; feeds back into strategic and tactical financial planning, balance sheet management, compensation practices

Risk Management Information System – information s/b credible, regular, useful; critical to RAROC ⎯ When banks first attempt to build a risk MIS they often start with a prototype RAROC approach that

tries to collect limited amounts of high level data; as a result of business pressure limited manually intensive prototype is often pressed into production prematurely

⎯ Typically banks then embark on a more comprehensive and integrated MIS with sophisticated detailed data collection, powerful computation engine, massive storage capability, information distribution capability

Guiding principles of RAROC implementation Capital management – capital s/b employed to earn shareholders at least minimum risk adjusted required return above riskless rate on a sustainable basis

GAAP (yesterday) → banking industry has made significant advances in terms of generally accepted risk principles (today)7 → next evolution is toward a set of generally accepted capital principles

Ten commandments of RAROC ⎯ Include all business activities and global operations of bank ⎯ Strive to implement a RAROC system impervious to arbitrage ⎯ Be explicit, consistent, goal congruent with other policies

6 Text pp532-3 provide an example of calculating RAROC 7 Given this quarter’s headlines perhaps not as significant as author believes


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⎯ Recognize different types of capital but primary emphasis s/b on EC ⎯ Use a single risk adjusted hurdle rate charged as cost of capital ⎯ Develop and implement an economic risk framework comprising credit, market, operational risks ⎯ Recognize funding and time‐to‐close liquidity ⎯ Attribute capital as a function of risk and authority to take risk ⎯ EC s/b based on confidence level deemed appropriate to achieve target rating ⎯ Promote matching of revenues and risk charges where risks are incurred

Full cooperation of senior management is an essential success factor; risk adjusted numbers s/b used for performance management and compensation

Implementation stages ⎯ Initial product, educational phase where one prototypes top of house indicative numbers ⎯ Producing reports that are used on regular basis, results used to add value to analysis and provide

input to planning process ⎯ RAROC begins to have an impact on business decision making, business goal, risk strategy; used as a

critical input for pricing and structuring deals, applied to performance measurement and compensation

Relationship of RAROC capital to market, credit, operational risks Capital for market risk ⎯ Market risk is risk of losses from changing market factors such as interest rates, foreign exchange

rates, equity prices, commodity prices ⎯ Has evolved to attributing RAROC capital as a linear function of amount of risk expressed in VaR

calculation; coefficient accounts for exception shocks, day‐to‐day event risk not captured in VaR ⎯ Practitioners often charge RAROC capital as a function of both unused market risk VaR limits and

penalties for exceeding VaR limits, e.g. RAROC capital charge = 2 ⋅ VaR + 0.15 ⋅ Unused VaR + 3 ⋅ VaR Over Limit

⎯ Mismatch between interest rate sensitivities of liabilities and assets is major source of market risk in banks; banks are also exposed to foreign exchange risk and risk originating from embedding options in mortgages

⎯ Horizon depends on whether positions are structural and are core positions for bank franchise, size and liquidity of positions

⎯ Attaining a AA 99.96% confidence level for bank as a whole translates into a lower confidence level for individual businesses to account for diversification benefit, say 99.865%

Capital for credit risk ⎯ Credit risk is risk of losses related to credit quality including credit grade migration ⎯ Capital factor is percent of market value of position as a function of risk rating and term, obtained

from public sources, proprietary external models, publicly available models or proprietary internal models

⎯ Derivation of credit risk factors typically follows a four step process − Select a representative time period to study portfolio, ideally over a full business cycle − Map risk ratings to portfolio − Estimate expected and unexpected losses − Exercise appropriate management judgment wrt assigning capital factors to adjust for

imperfections in data Capital for operational risk


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⎯ Banks measure credit and market risk because they can, not because they are biggest risks; operational risk is larger and more dangerous but nobody knows how to quantify it or exactly what to do about it

⎯ Operational risk is risk of losses from various breakdowns, e.g. inadequate computer systems, mistakes; also covers regulatory, legal, fiduciary risks

⎯ One approach is to define operational VaR as loss likely to arise from an operational failure over a certain time period; difficulty is that very few internal data points available; some information can be gathered externally (court records, credit card fraud)

⎯ One must be careful not to double‐count, e.g. some operational risk may already be reflected in loan losses

⎯ Measurement of operational risks is least reliable at catastrophic end of spectrum, those risks that occur very rarely even at an industry level but might destroy bank

⎯ One simple approach is to assign a risk rating to each business based on operational risk factors defined in terms of people, process, technology; expected loss and RBC charge are assigned to a position on a nonlinear sliding scale; bank needs to develop capital factors based on internal loss history, losses at other banks; management judgment

Loan equivalent approach Loan equivalence for guarantees, commitments, banker acceptances ⎯ Guarantees and standby letters of credit vary from a high of 100% for financial related products

through 50% for non‐financial related products to a low of 20% for documentary products; also depends on risk rating

⎯ Banker acceptances and financial letters of credit are best treated as loans since bank can do little to reduce risk within timeframe of instrument

⎯ For credit commitments a number of factors may reduce likelihood of drawdown; in particular they are often at discretion of bank; term commitments are more likely to suffer a drawdown in event of customer default so they are affected by remaining term and customer credit quality

⎯ In all cases percentages are multiplied by undrawn amounts; amounts already drawn are multiplied by 100%

Loan equivalence for derivatives is calculated at both deal and counterparty levels, is an estimate of average positive exposure over life of deal; counterparty loan equivalent, counterparty risk rating and term are used to calculate capital similar to risk rated lending

Measuring exposures and losses for derivatives Measuring exposures ⎯ Properly quantifying future credit risk exposure is a complex problem; affected by instrument

structure and changes in underlying variables ⎯ Expected credit risk exposure is an exposure at a particular point in time; cumulative average

expected credit risk exposure is average of expected credit risk exposure over a given period of time ⎯ Worst case credit risk exposure and cumulative average worst case credit risk exposure are also

measured, specified as a given number of standard deviations; applicable for setting counterparty limits

⎯ Amount and cost of capital set aside for a transaction are vital factors in determining profitability of that transaction and in calculating a fair price for that transaction

⎯ Cumulative average worst case credit risk exposure = 2/3 ⋅ worst case credit risk exposure


27

⎯ Expected terminal credit risk exposure = cumulative average worst case credit risk exposure / 3.33 = worst case credit risk exposure / 5

From exposure to loss ⎯ Probable loss on any transaction depends on amount exposed to credit risk, probability of

counterparty defaulting, amount likely to be recovered if counterparty does indeed default; combined by integrating across combined function

⎯ Default rates – An institution needs to develop techniques to calculate default rate path and distribution around it, can be modeled through analysis of S&P or Moody’s default data; most institutions combine rating agency data with proprietary default rate data and also analyze credit spreads

⎯ Recovery – Need to calculate recovery rate path and distribution around it, can be modeled through analysis of S&P or Moody’s recovery data and proprietary recovery rate data

⎯ Difference between worst case loss and loss is unexpected loss or EC, distribution is highly asymmetric

⎯ If a MC approach is adopted then one first simulates an exposure value from a credit risk exposure distribution given default at a particular point in time, then one simulates a default distribution typically a binomial with a single probability of default, finally assuming negligible recovery one summarizes credit losses across all points in time

⎯ This approach is a proxy for more sophisticated approaches, has virtue of facilitating comparison to a more conventional loan product

⎯ Alternate approaches − Generate full distribution of losses and then select appropriate confidence interval percentile − Multiply binary probability of default by difference between average worst case credit risk

exposure and average expected credit risk exposure; this may not provide same answer as other two approaches

Measuring Risk Adjusted Performance First generation RAROC – only activities for which RAROC exceeds a fixed hurdle rate are pursued – can result in decisions that adversely affect shareholder value

Second generation Adjusted RAROC corrects inherent limitations of RAROC ⎯ Compare risk of business to that of firm equity; only activities for which RAROC exceeds firm cost of

equity capital are pursued ⎯ Maintaining probability of default constant as RAROC does is inconsistent with a constant expected

rate of ROE and vice versa8 − To keep probability of default constant debt‐to‐equity ratio must decrease as standard

deviation of assets increases − However RAROC can change as risk of business changes even if probability of default is kept

constant; higher beta will increase expected return ⎯ ARAROC = (RAROC – rF) / βE ⎯ A project will increase shareholder value when ARAROC is greater than expected excess rate of

return on market ⎯ Four points are worth noting

− RAROC is sensitive to level of standard deviation of risky asset – if volatility is high enough project will be chosen even if NPV is negative

8 Text pp560-1 discuss this in more detail


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− RAROC is sensitive to correlation of return on underlying asset and market portfolio − If a fixed hurdle rate is used in conjunction with RAROC high volatility and high correlation

projects will tend to be selected − ARAROC is insensitive to changes in volatility and correlation

Assumptions in calculating exposures, expected default, expected losses Methodology ⎯ Typically it is assumed that default rates are stochastic but LGD is constant ⎯ For first generation RAROC models it is typical to assume that default rate can be expressed as a

simple distribution ⎯ Assume further that default probability p ∋ z = p/(1‐p) is lognormal ⇒ y = ln z ~ N(μy,σy) ⇒ p = ey /

(1+ey) Worst case default rates and expected loss ⎯ If mean and standard deviation of default probability are α and β, then mean and standard

deviation of z can be approximated by μz = α/(1‐α) and σz = β/(1‐α)2 and variance of y can be approximated by σy

2 = ln (1 + σz/μz2)

⎯ Worst case value of y at 99.865% confidence which is three standard deviations away from mean is given by x = E(z)exp(3σy–½σy

2) and worst case probability of default corresponding to x is k = x/(1+x) ⎯ Capital factor =9 LGD ⋅ (k – α)

Conclusion Several trends seem likely to secure a growing role for RAROC analysis ⎯ Trend toward integrated risk, capital, balance sheet management ⎯ Integration of credit risk and market risk ⎯ Regulatory community move toward use of internal models for calculation of capital charges

RAROC provides a link between management and stakeholders; debtholders, regulators, rating agencies are interested in solvency in terms of safety; shareholders are interested in profitability; RAROC provides a common language

Regulatory trend – integrated RAROC framework that links regulatory capital and EC might well evolve; however regulators have trouble keeping up with new developments

9 Text pp573-7 provide a numerical illustration


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Investment Management for Insurers Chapter 3

Introduction Any benchmark a firm uses to facilitate performance measurement should be designed in a manner that is consistent with a firm value focus ⎯ Senior investment management should be judged on how well their strategies meet overall needs

of firm ⎯ Portfolio managers should be judged against performance of comparable securities; goal should be

to outperform unmanaged portfolio Changes in market value are not recognized on mortgages or most bonds, so insurers have traditionally relied on yield as primary performance measure

There has been growing disenchantment with use of yield measures; higher yields may merely reflect fact that company’s investments have more credit risk, less liquidity, more call risk, greater foreign currency exposure or worse duration mismatch ⎯ Recent years have witnessed increase in interest rate volatility ⎯ High yield market where yield can be traded off for credit quality ⎯ Mortgage securities where yield can be traded off for prepayment risk

Yield focus can spawn accounting games and foster book value based portfolio reshuffling; where yield is important it should be a constraint on investment process rather than primary objective

Enhancing Firm Value Investing in projects or securities with positive NPV; finding undervalued assets ⎯ For typical industrial firm this is area with most potential for enhancing firm value; however for

financial intermediaries investing in securities EMH dictates that publicly traded securities have NPVs of 0

⎯ Investments in private placements or real estate have positive NPV, but these generally have less liquidity and firm value may not increase as much as might be expected or at all

Altering firm’s financial structure ⎯ Higher leverage to a point is associated with higher stock prices ⎯ Insolvency guarantee programs create obvious incentives for excess leverage especially among

lower‐tier companies Altering firm’s duration and convexity mismatches ⎯ Companies with better asset/liability matching command higher stock prices relative to liquidation

value of their surplus ⎯ This finding was particularly significant during years of high interest rate volatility and among

companies that were not precariously leveraged; market recognizes insurer has going concern value and a company with a better match is more likely to be around to capture that value

⎯ A better match resulted in higher relative stock prices for all but marginal companies which exhibited higher stock prices by being less well matched; value to this group arises from option to default (put liabilities to state) which increases as business becomes more volatile

Outperforming firm’s liabilities – unlike other actions this can only be evaluated over long term ⎯ Whenever firm earns more on its assets than it pays on its liabilities, excess accrues to economic

surplus; to extent additions to surplus are greater than required ROE economic value of company will rise


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⎯ Operations side of insurer may be issuing liabilities on favorable terms and through cost efficient distribution networks

⎯ Investment department may be experiencing favorable returns relative to product pricing assumptions; this can include strategic asset allocation, asset selection within classes, market timing

⎯ Sometimes these two sources of value creation work together; for example prolonged pattern of superior investment performance will aid sales force in attracting good clients on favorable terms

Structuring a performance measurement system Establishing a liability benchmark ⎯ A liability benchmark that will mirror changes in value of company’s liabilities (which are untraded)

must be devised based on traded securities − Benchmark must be based on traded securities for which there is an active market; this will

allow firm to get reliable quotes on a timely basis − More importantly benchmark must behave in a manner that closely parallels market value of

company liabilities over time and under disparate economic circumstances; must be adjusted over time as liabilities change

⎯ Asay et al provide a methodology to measure costs of various policyholder options and interest rate risk inherent in SPDAs and interest sensitive life policies

⎯ Replicate cash flows of liabilities with capital market instruments so it is possible to track market value of liabilities over time; this mimicking procedure has desirable properties − Returns reflect shape of yield curve and cost of embedded options − Effects of important sources of interest rate risk other than just duration are directly

incorporated ⎯ Outperforming this liability benchmark index ensures asset managers are acting in a manner

consistent with increasing firm value; measuring against an arbitrary index even of correct duration does not ensure this result

Levels of performance measurement ⎯ Managers should measure performance on total return basis and compare to total return on

liability benchmark index ⎯ Ideally insurers should calculate total return daily; in practice a monthly basis may be sufficient for

insurers ⎯ Time Weighted Rate (TWR) of return eliminates impact of insurance cash flows over which

investment manager has no control, allowing for unbiased comparisons ⎯ Using a liability benchmark is appropriate for asset portfolios funding reserves; however proper

benchmark for assets funding capital and surplus should be based on management’s return objectives and risk tolerance

Structuring a performance measurement system ⎯ Level 1 – Characterize each liability in terms of market characteristics such as duration, convexity,

volatility, etc ⎯ Level 2 – Set up Sub Liability Benchmarks (SLBs) to mirror each liability; in designing a portfolio to

serve as a SLB use Treasuries, their derivatives and other securities of minimal default risk − They are liquid and widely traded so price quotes are easily obtained − They are typically benchmark used for valuing other asset classes and starting to be used as

benchmarks for valuing liabilities as well − Their diversity of characteristics allows them to be combined into portfolios that can emulate

market value behavior of almost any default‐free cash flow stream, since insurance policies are


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very close to being considered default‐free from consumer standpoint so consumers should no expect insurance premiums to reflect interest rates any higher than other similar near default‐free securities

− To extent insurer must offer a premium for competitive reasons it can add an appropriate spread to return of SLB

− It is preferable to model separately portion of economic surplus derived through default put and franchise value

⎯ Level 3 – SLBs can be aggregated into overall Liability Benchmark (LB); weights used in aggregating should reflect shares of total liabilities

⎯ Level 4 – Create an asset allocation optimization where LB becomes a constraint − Investment managers could set up an Asset Proxy Portfolio (APP) that reflects their desires

regarding asset allocation and timing − To achieve target profit margins managers probably include risky assets (credit risk, call risk,

market risk) in APP rather than limit it to just very high quality liquid assets of LB ⎯ Levels 5 and 6 – APP can be divided into Sub APPs (SAPPs) that could serve as benchmarks to

individual managers − While each SAPP could correspond to a particular SLB it may be more convenient to have

investment professionals organized according to investment class independent of SLBs − SAPPs must aggregate to overall APP both in terms of investment characteristics and total rate

of return − Some SAPPs may be sufficiently large that it will be convenient to subdivide them even further

⎯ Level 7 – actual performance of investment managers should be measured against passive portfolio with similar constraints on permitted investments

Investment income allocation ⎯ It may be desirable to develop an alternate benchmark for purposes of investment income

allocation and tracking accounting results ⎯ This can be accomplished by creating a benchmark portfolio to mirror future liability flows under all

likely future interest rate paths; to be done correctly this requires a sophisticated modeling system that can generate an appropriate set of interest rate paths and then forecast asset and liability cash flows for each path taking care to handle embedded options

Taxation and liability benchmark ⎯ Taxation of investment and underwriting income is a complex consideration to incorporate in a

performance management system, particularly for a P&C insurer in light of AMT ⎯ Taxes on investment income are supposed to be passed along to consumers on theory that equity

owners of insurer could invest directly in securities held by insurer without undergoing an extra layer of taxation; how well this works in practice is open to question

⎯ It is difficult for investment manager to optimize tax position of firm by choosing appropriate mix of taxable and tax‐exempt bonds

⎯ Recognition of capital gains and losses can be managed to optimize tax impact ⎯ Recommend measuring total return on pre‐tax basis

Performance Attribution A useful starting point is to compare spread between actual total return on combined investment portfolios (level 7) and total return on overall LB (level 3)


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It is important to periodically perform economic valuations of liabilities and see whether their realized behavior has been well reflected by asset portfolios that are used as proxies for them; if not there are three areas where discrepancy could have occurred ⎯ Level 1 if actuaries improperly characterized nature of liabilities in terms of their investment

characteristics (duration, convexity, lapse, drifts) or other attributes (mortality, frequency, severity) ⎯ Level 2 if financial technician has incorrectly created LBs ⎯ Level 3 if market value weightings in overall LB are incorrect or evolved over time in a manner

inconsistent with that assumed when devising benchmark If examinations prove satisfactory then total spread between levels 3 and 7 can be attributed to performance achieved at levels 4, 5, 6 and 7

Individuals responsible for corporate investment strategy can be evaluated on basis of how their overall APP performed relative to overall LB; however it is possible that strategic plan is satisfactory but implementation is not, or that strategic plan is poor but persons responsible for implementation exceed targets ∋ assets outperform liabilities

Next we measure performance of portfolio managers against their targets at levels 5 and 6 ⎯ At times need to achieve minimum yield will conflict with manager’s perception of relative value in

market ⎯ To account for this while recognizing annual planning cycle at most companies, performance can be

measured over both 1 year and rolling 3 years ⎯ If traders outperform their target indices we can undertake further investigation to determine how

this was achieved. Did they demonstrate superior asset selection? Superior timing? Or did they simply deviate from their risk norms and win their bets?

Conclusion In long run, time, effort and expense required to measure total return should increase firm value


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Mechanics of hedging Identifying sources of price risk ⎯ For corporates changes in interest rates and credit spreads are primary factors; effects of interest

rates on embedded optionality need to be explicitly accounted for ⎯ For option embedded bonds shape of yield curve and movements in volatility also affect value

− As volatility increases callable spreads widen and put spreads tighten − If curve flattens (steepens) callable spreads widen (narrow)

⎯ Once sources of price risk have been identified next step is to determine amount of price volatility that is acceptable and hence amount of price protection that is required from hedge strategy

⎯ A perfect hedge will theoretically (although never practically) eliminate all price risk but at cost of eliminating any price appreciation potential; goal of hedge may be to eliminate some but not all price uncertainty in order to achieve some incremental return

Determining appropriate hedge position ⎯ Next steps are to find appropriate hedge instruments and determine optimal investment ⎯ Appropriate position in hedge instrument is a function of dollar value of a bp (DVBP) ⎯ DVBP = price change for 1 bp change in interest ≈ (Price + Accrued) x Par Amount x Modified

duration / 1,000,000 ⎯ Implicit assumption is that interest rate and yield movements are simultaneous and identical; this

typically is not true for option embedded bonds and bonds priced off two benchmark securities ⎯ DVBP = Dollar par amount x Change in constant OAS price / (Yield curve shift in bp x 100) ⎯ Price changes must be determined either from a theoretical model or empirically ⎯ Hedge ratio = DVBP of security to be hedged / DVBP of hedge instrument

Choosing a hedge instrument Treasury securities are most common hedge instruments especially for hedging individual positions, but futures and swaps may be more appropriate instruments for many hedging applications

Cash market securities ⎯ Since most corporates are priced off Treasuries using similar Treasuries provides ideal protection;

Treasuries also have no credit risk and are extremely liquid ⎯ Disadvantages

− Many corporates are priced off on‐run Treasuries that may be “on special”; when a security is on special it is in short supply and can be expensive to borrow in repo markets which increases cost of hedging

− Treasuries are on balance sheet which for some market participants may have capital structure implications

− They only provide protection against interest rate risk and not spread risk Futures instruments ⎯ Treasury futures are based on hypothetical 8% coupon instruments maturing in 2,5,10,20 years ⎯ They require physical delivery at maturity; generally low duration issues tend to be cheapest to

deliver when rates are low and high duration issues then to be cheapest when rates are high ⎯ They tend to lose duration in a rallying market and gain duration in a bear market making them

negative convexity ⎯ Advantages relative to hedging with cash instruments


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− Because contracts typically track off‐run issues cost of shorting is reduced − Enables hedge to participate in off‐run market using a more liquid instrument; this is especially

useful when hedging corporates priced to off‐run Treasuries ⎯ Disadvantage is basis risk – movements in futures prices need not correspond to movements in spot

prices ⎯ Generally futures are used in hedging portfolios rather than individual positions

Interest rate swaps ⎯ Advantages over Treasuries

− Off balance sheet − When off‐run maturity needs to be hedged or when hedging Treasury security is on special,

swap can be a less expensive hedging instrument − Provide spread protection

⎯ Advantages over interest rate futures − Available for any maturity − Does not expose portfolio to basis risk

⎯ Disadvantage – Lack of liquidity; bid/offer spreads amount to a few bp; not readily tradable ⎯ In general they are more useful in managing overall interest and credit risk of a portfolio than an

individual position ⎯ DVBP Swap = DVBP Fixed Rate Bond – DVBP Floating Rate Bond ⎯ In general DVBP of a swap is approximately equal to DVBP of fixed rate bond with term spanning

from next reset date to swap maturity date ⎯ DVBP will decline at each reset date by DVBP of floater immediately after reset and then won’t

change much as fixed bond and floating bond decline in similar fashions

Hedging applications Bulled bond hedge ⎯ A Citicorp bond position that would lose up to $352,500 if rates increase 50 bp can be very well

hedged against interest rate risk with Treasuries (max loss $907), swaps (max loss $1,079) or futures (no loss)

⎯ Hedges are not perfect because of effect convexity has on DVBP; for modest movements this effect is not large

⎯ Futures based hedge is best because of negative convexity ⎯ However futures do not account for basis risk; if yield curve steepened or flattened futures hedge

would be far less successful than other instruments Spread risk ⎯ General sector risks may be hedged to an extent if properly anticipated ⎯ Effect of widening spreads may be mitigated by buying puts on sector or shorting a basket of stocks

in addition to any positions used to hedge interest rate risk ⎯ If there is a known correlation between direction and magnitude of interest rate changes and

spread changes; if spreads widen when market rallies and tighten when market sells off then price volatility can be reduced by shorting fewer Treasuries than given by hedge ratio

⎯ Swaps provide best protection against spread risk; generally swap spreads and corporate spreads move in same direction although degree and timing are not always symmetric; to extent swaps are correlated with corporate spreads, swaps are more effective hedges than Treasuries or futures

Hedging option embedded bonds


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⎯ Constant OAS approach to determining DVBP explicitly accounts for changing value of embedded options

⎯ Assumption of constant OAS may not hold in market, which can be accounted for in DVBP approach by using different OASs

⎯ A FNMA callable bond position that would lose up to $352,200 if rates increase 50 bp can be relatively well hedged against interest rate risk with Treasuries (max loss $15,325), swaps (max loss $15,924) or futures (max loss $13,820)

⎯ Futures contract performs best because of small negative convexity but is not perfect because FNMA callable is more negatively convex

Hedging considerations for option embedded notes ⎯ Hedge ratios are not static because callable notes are negatively convex; if rates rally position in

hedge instruments needs to be reduced ⎯ One way to hedge option embedded notes is to use bullets like Treasuries or swaps to hedge bullet

component of notes and options to hedge option component of notes; this will not need to be monitored as frequently and hedge ratio will be less volatile

⎯ Alternative is to use callable swaps; for short time horizons this can be expensive given reduced liquidity

⎯ Typically individual option embedded notes are hedged using just Treasuries or futures with hedge ratio adjusted periodically

⎯ Use of empirical hedge ratio where historical data are used would implicitly account for changing OASs

⎯ If volatility risk is of concern use of options is necessary; if changes in volatility can be anticipated as interest rates move this can be accounted for by under/over utilizing hedge

⎯ To hedge yield curve risk it is best to use multiple hedge instruments from all parts of curve that affect pricing of security being hedged

⎯ Typically for individual positions yield curve risk is generally not directly accounted for in hedging; hedge ratio is just adjusted to account for particular view of future yield curve

Must always analyze cost and effectiveness of hedge strategy


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Valuation techniques (background only) Valuation of a MBS should take into account principal and interest payments as well as possibility of prepayments; analysis is carried out using simulation in three phases ⎯ Generate arbitrage free interest rate scenarios consistent with prevailing term structure ⎯ Project prepayment activity and generate cash flows for each interest rate scenario ⎯ Use cash flows and short term interest rates along each path to compute PV of cash flows, usual

derivatives (duration, convexity), and option adjusted premium over Treasuries Pricing ⎯ Use a binomial lattice interest rate model such as Black‐Derman‐Toy ⎯ Pj0 = (1/S0) Σ Σ CFjts / Π(1+ri

s) ⎯ Since we need to examine paths not just vertices this results in extremely large computational

complexity even for moderate time horizons ⎯ It is usual to work only with a small sample of paths using statistical sampling

Option Adjusted Premium (OAP) ⎯ Most fixed income securities cannot be priced using riskless discount rates; price has to reflect

credit/default, liquidity and prepayment risks; in order to value we compute OAP ⎯ We can observe market prices and solve Pj0 = (1/S0) Σ Σ CFjts / Π(1+ρjris) for OAP ρj which can then

be used to price new securities with similar risk characteristics ⎯ Differences in OAP of similar securities are indicators for identifying mispriced securities

Duration and Convexity are calculated using MC simulation ⎯ Initialize stochastic process of interest rates with current rates and use it to compute OAP ⎯ Shift term structure by ‐50 bp and recalibrate stochastic process of interest rates; sample interest

paths; use security cash flow projection to compute option adjusted price P+ ⎯ Shift term structure by +50 bp and recalibrate stochastic process of interest rates; sample interest

paths; use security cash flow projection to compute option adjusted price P‐ ⎯ Duration Δ = (P+ ‐ P‐) / 100 ⎯ Convexity Γ = (P+ ‐ 2P0 + P‐) / 502

Holding period return is Rt = (Fjts + Vjt

s) / Pj0 where Vjts = Bjt

sPjts and

⎯ Fjts is accrued value of cash flows generated by security reinvested at short term rates under scenario s

⎯ Vjts is value of unpaid balance at end of hold period, Bjt

s is unpaid balance and Pjts is price per unit

face value, all conditioned on scenario s

Portfolio risk management techniques Manager’s problem is to construct a portfolio of mortgage securities whose performance measures will remain invariant under a wide range of uncertain scenarios

Static models ⎯ Static models hedge against small changes from current world state ⎯ One such model is a least cost dedicated portfolio using duration matching ⎯ To account for stochasticity of cash flow and term structure, model can be extended to match

sensitivities of assets and liabilities to such stochasticity


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⎯ Model could be extended to match convexity and even higher derivatives; in limit derivative matched portfolio will be identical to cash flow matched portfolio

⎯ Duration and convexity matching became overly simplistic with increased volatility of term structure following monetary deregulation in late 1970s

Single‐period stochastic model: capturing correlations ⎯ Single‐period model does not permit stochastic processes that describe changes from current world

state ⎯ SDEs or MC can be used to model distribution of returns; movements on both sides of balance

sheet are highly correlated; Markowitz 1952 pioneered this for equities but approach for fixed income has only recently received attention

⎯ Model is myopic; does not account for fact that manager is likely to rebalance portfolio once some surplus is realized; single period model may recommend a conservative strategy while a more aggressive approach would be justified once we recognize rebalancing or vice versa

⎯ Optimization based on a Mean Absolute Deviation (MAD) model is suitable for securities with embedded options since they exhibit highly asymmetric return distributions

⎯ Instruments with fixed term are vanishing; furthermore payout functions have become path dependent; hence we cannot resort to statistical analysis of historical data; we need MC simulation to generate holding period returns for each security

⎯ Optimal portfolio is one that minimizes deviations in holding period return subject to having a mean asset return greater than liability return

Multi‐period dynamic stochastic optimization model – First stage decisions deal with purchase of portfolio; second stage decisions deal with borrowing (lending) decisions when cash flows lag (lead) liabilities as well as decisions to rebalance as more information about uncertain scenarios becomes available

Portfolio risk management applications Example applications: (1) Indexation (2) Liability payback (3) Debt issuance Immunization of an insurance liability stream – immunized portfolio lies below efficient frontier; MAD model is superior

Creating a tradable portfolio that tracks Solomon Index of MBSs


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Introduction When properly managed mortgages are not market directional investments Proper management begins with separating mortgage valuation decisions from decisions about appropriate interest rate sensitivity of portfolio

Mortgage security risks Spread risk ⎯ We invest in mortgage securities when their spreads vs Treasuries are large enough to compensate

for risk ⎯ If we hedge against spread widening we give up benefit from spread narrowing ⎯ Instead we seek to capture OAS over time, increasing allocation when spreads are wide and

reducing allocation when spreads are narrow ⎯ Over past few years prepayment models have changed significantly making comparisons to

historical OASs tenuous Interest rate risk – corresponds to interest rate risk of comparable Treasuries Prepayment risk – when interest rates change we must offset change in mortgage durations to keep overall risk of portfolio at desired target; we adjust by buying options, buying POs because of their positive convexity, or hedging dynamically

Volatility risk ⎯ Spreads tend to widen when expected volatility increases and narrow when it decreases ⎯ We manage volatility by buying options or hedging dynamically

− When volatility implied in option prices is high and we believe future realized volatility will be lower than implied we hedge dynamically; this has tended to be case historically

− When volatility implied in option prices is low and we believe future realized volatility will be higher than implied we buy options

Model risk ⎯ Models calibrated to past behavior will understate impact of innovation ⎯ We do not know magnitude of model error going forward, but we can measure sensitivity to model

error

How interest rates change over time When interest rates change 2 year yields move about twice as much as 30 year yields Therefore yield curve typically steepens in rally and flattens in selloff

Hedging method To hedge a security we begin by expressing it in terms of an equivalent position in Treasuries, then we calculate quantities of these Treasuries that will simultaneously hedge security in both level and twist scenarios

In many cases average price change is a good approximation of how security price will change for a small movement in interest rates10

10 Text p440 provides two hedging examples


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Cuspy coupon mortgages Some (“cuspy”) securities are right on cusp of being optimal for prepayments and hence are very sensitive to rates in which case averaging price changes will not work

Have more negative convexity than other mortgage securities which must be hedged out


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Integrated approach to segmented market Barriers to free flow of capital in US: (1) self‐imposed by investors or client guidelines, and (2) imposed by regulations and tax laws

In past few decades a market segmented into style groupings has been formalized by actions of investment consultants; as manager performance is measured against given style index managers who stray too far from index territory are taking on extra risk

Approach that specializes in one market segment recognizes that markets are not entirely homogeneous and can optimize application of talent and maximize potential for outperformance; this is most likely true for traditional fundamental analysis since in‐depth labor‐intensive research can become ungainly without some focusing

Such an approach may be disadvantaged when it ignores many forces (e.g. arbitrage) that keep segments in check and work to integrate rather than segment market; all stocks are defined by same fundamental parameters in a continuum ⎯ Many managers switch styles when economic conditions change ⎯ Individual stocks can move between segments

Market calls for a complex unified approach that takes into account behavior of stocks across broadest possible selection universe without losing sight of significant differences in price behavior that distinguish particular market segments; this offers three advantages ⎯ Provides coherent evaluation framework ⎯ Can benefit from insights to be garnered from diverse range of securities ⎯ Poised to take advantage of more profit opportunities

Coherent framework Investment approach that models each industry or segment as if it were a universe unto itself is not best approach ⎯ Different models could yield different results for same stock ⎯ To extent market is integrated pricing in one segment may contain information relevant to pricing

in other segments

Disentangling General considerations ⎯ Variables are often closely correlated; for example small cap stocks tend to have low P/Es; low P/E

is correlated with high yield; both low P/E and high yield are correlated with DDM estimates of value; variables may be correlated with industry for example low P/E screen will select a large number of banks and utilities

⎯ Such correlations can distort attempts to relate returns to potentially relevant variables; a true picture of relationship emerges only after disentangling variables via multivariate regression to isolate variables of interest by controlling for other variables

⎯ Disentangling distinguishes real effects from proxies and avoids redundancies Noise reduction – Univariate regression on a single variable shows a great deal of volatility due to extraneous variable noise that is not present in pure return attributed to same variable in a multivariate regression

Return revelation – pure returns are not nearly as closely correlated as appears from univariate analysis


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Predictability ⎯ DDM value is a poor indicator of stock’s ability to withstand receding prices ⎯ High book‐to‐price ratio has a regression coefficient of ‐0.10 in univariate form and is virtually

uncorrelated in pure form; appears to be picking up effects of high yield ⎯ Regression coefficients for high yield indicate significant negative market sensitivity; high yield

stocks may be expected to lag in up markets and hold up relatively well in down markets ⎯ Pure returns to small size may be expected to be negative in four months following an unexpected

increase in corporate borrowing rates and positive in first month following an unexpected increase in industrial production; investors can move into or out of small cap market appropriately

Additional complexities ⎯ Psychology including investor tendency to overreact, desire to seek safety in numbers, selective

memory, also play a role in security pricing ⎯ Effects of positive earnings surprises tend to be arbitraged away quickly; effects of negative

earnings surprises appear to be longer lasting ⎯ Consider signals such as corporate decisions to issue or buy shares or legal insider trading

Constructing, Trading, Evaluating Portfolios Portfolio construction process and optimizer software should consider exactly same dimensions found relevant by stock selection model

Insofar as stock selection and portfolio construction is model driven it is more adaptable to automated electronic trading systems ⎯ Less costly, lower commissions and market impact, smaller opportunity cost ⎯ Allows real time monitoring which can also further reduce trading costs ⎯ Can take account of more factors including trade urgency and market conditions

Performance attribution should be congruent with dimensions of selection model Feedback loop between evaluation and research/modeling can help ensure that model retains robustness over time

Profiting from complexity IR = IC x √BR ⎯ IR is information ratio (active return / active risk) ⎯ IC is information coefficient or correlation between predicted and actual results ⎯ BR is number of independent observations upon which investment decisions are made


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Linear Payoffs: Swaps Example: parties swap return on equity index for interest return such as LIBOR; seller of swap has effectively created synthetic cash while actual portfolio is invested in equities; purchaser has created synthetic equity while actual portfolio is invested in cash11

It has become popular in recent years to use swaps to create enhanced index funds; investor with expertise in managing cash portfolio can earn more on it than has to be paid to seller of swap so investor ends up with index return with an extra spread generated by difference in return; this is called transporting alpha

Swaps on international indices are popular because they are more cost effective than buying international securities

Linear Payoffs: Futures Applications of buying futures ⎯ Cash equitization – prevent cash drag in equity portfolios ⎯ Synthetic index fund – futures contracts and cash reserves are often easier to liquidate at lower cost

than underlying stocks ⎯ Enhanced index fund – same as swap but with shorter maturity ⎯ Help manage net market exposure as stocks are purchased or sold

Applications of selling futures ⎯ Temporarily hedge market exposure – shift risk to others willing to bear it ⎯ Synthetic cash position

Hedge ratios using futures ⎯ H = ‐ΔS/ΔF = ‐βS/βF where S is a diversified equity portfolio and F is a futures contract on

appropriate index ⎯ N = H x Value of Portfolio to Hedge / Futures Contract Size

Non‐Linear Payoffs: Options Selling covered calls: exchanging appreciation for income Asymmetric hedges: protecting downside ⎯ Protective put ⎯ Protective put spread constructed by purchasing a put and selling a put further out of money ⎯ Collar, range forward or fence is constructed by selling a call and purchasing a put at a lower

exercise price Buying calls or call spreads: creating market exposure while limiting downside risk Short call and long put with same exercise price creates a synthetic futures contract Covered call can be achieved through a collateralized put by selling a put and investing funds in cash reserve; protective put can be substituted by purchasing a call and investing remaining funds in cash reserve

Automatic changes in market exposure

11 Text confuses interest rate on a fixed income instrument with a fixed interest rate


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⎯ Selling some index calls against a long futures position or exposure in underlying stocks effectively pre‐sells a portion of exposure at exercise price; premium effectively pays investor for making decision to sell in advance; sale of a put allows investor to pre‐purchase at exercise price

⎯ Sale of options is frequently used to automatically reposition portfolio if certain market levels are reached; premium effectively increases sale price of appreciated stocks or reduces purchase price of depreciated stocks

Valuation framework for selecting derivative strategies Problem with BSM ⎯ BSM and CRR are geared to valuing options as opposed to computing expected return from a

combined stock and option position; these models do not help an investor in selecting an optimal choice of option or structure

⎯ In order to estimate value from option conditional on investor’s expected return distribution on stock it is necessary to calculate actuarial value of option12

Observed prices may differ from BSM since underlying assumptions are violated in practice Generalized actuarial model: Expected return = ∫ PT(Sf/S0) ln [Wf(Sf)/W0] dSf

12 Text includes a completely incorrect example that indicates a plan should not short an overpriced option if manager’s expectation of stock return is different from market; such an option would indicate a pure arbitrage that should be taken advantage of regardless of manager’s expectations


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ALM of Financial Institutions Chapter 6

Types of hedge funds Market directional strategies ⎯ Equity long/short – specializations are typically along geographical, industry, style lines ⎯ Dedicated short selling – it is not clear if this strategy is superior to purchasing puts to protect

overall long market exposure ⎯ Tactical trading

− Macro Managers – implement views based on broad geopolitical and economic themes − Managed Futures or Commodity Trading Advisers – implement market views using futures and

forwards − Opportunity or directional value – implement views based on market micro elements such as

capital flows or institutional investment/hedging needs ⎯ Commodities and natural resources – trade in futures or physical underlying ⎯ Emerging markets – stock, bond, currency ⎯ Real estate – physical properties and securitized assets

Market neutral strategies ⎯ Equity long/short arbitrage – zero or minimal dollar exposure or beta exposure ⎯ Relative value – identify relationships between securities; when prices deviate from expectations

structure trades that will profit when price reverts to “normal” − Convertible bond arbitrage − Statistical arbitrage – find relative mispricings or inefficiencies between similar stocks − Fixed income relative value and arbitrage – exploit mispricings or anomalies in fixed income

market; sovereign debt or MBSs/ABSs ⎯ Credit and capital structure arbitrage ⎯ Options arbitrage – exploit variations in volatility

Idiosyncratic strategies ⎯ Event driven – identify corporate events expected to affect valuation and construct trades to

extract value when event occurs − Merger or risk arbitrage – typically buy shares in target and short sells in acquiring company − High yield debt – generally involves resolution of short term liquidity crisis − Distressed or defaulted debt

⎯ Special situations

History In 1980s led by DBL and KKR corporate takeover investing and LBOs were popular Traditional hedge funds popularized when Quantum Fund broke Bank of England in 199213 1998 was peak of public outcry that hedge funds were risky (LTCM) and against public good (Soros and Malay currency)

Bursting of internet bubble focused attention on funds that had been earning steady rather than spectacular returns

Since then many private equity and venture capital funds have closed down

13 Text says 1991 which is not correct


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Hedge funds from an ALM perspective Factors driving demand ⎯ Search for yield which has intensified in today’s low interest rate environment ⎯ Search for investment skill and requisite infrastructure ⎯ Broadening of investment universe wrt style, ability and content ⎯ Diversification and correlation characteristics of hedge funds ⎯ Reduced dependence on indexation in earning returns which can wreak havoc on efforts to match

liabilities ⎯ Income generation needs ⎯ Need for pension plans to meet pre‐defined targets under all market conditions ⎯ Mature hedge fund industry which has begun to shed its gunslinger image

Private and pension funds are increasing allocations to hedge funds in an attempt to boost returns Endowments – University and private endowments were among pioneers in alternative investment vehicles; Yale has one fourth of its investment in hedge funds averaging 17% annual return; UNC has 55% in hedge funds; University of Virginia has 60% in hedge funds

Insurers face a significant level of regulation wrt investments but there is room for alternative investments in small amounts; insurers have developed special account structures to gain access to hedge fund universe

Rewards and risks of investing in hedge funds Introducing hedge funds into a portfolio improves mean‐variance characteristics resulting in higher returns with lower volatility because of low correlation with bonds or long only equity

Hedge funds have higher Sharpe ratios and lower betas than traditional mutual funds Gains come at a price since hedge funds affect skewness and kurtosis of overall portfolio For hedge funds to have meaningful impact on portfolio allocation has to be greater than conventional wisdom in some quarters of 1‐5%

Basic issues of investing in hedge funds Matching alternative investments to liabilities ⎯ In current interest rate environment it is difficult to find or structure securities that offer returns

assumed by many institutions in hedging liabilities14; stocks are not a hedge against fixed income liabilities even in long run

⎯ Allocation to alternative assessments can be counted as a floating asset that can be matched to floating liabilities

Investment principles ⎯ Invest in opportunities where odds of success are favorable ⎯ Target maximum returns ⎯ Deploy capital taking into account likelihood of loss; manage downside risk ⎯ Recognize that arbitrage has limits

Sometimes best opportunities are available when market is under stress which is time when investors often decide to pull money out of hedge funds

It is possible as hedge funds become more mainstream that there will be an increase in M&A of independent hedge funds into asset management firms

14 Perhaps all that is needed is to change expected return assumption


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Rating Methodology Introduction ⎯ Both authors work for Moody’s so focus of discussion is Moody’s approach to evaluating credit risk

of life insurers paying particular attention ALM, which is one of key components of comprehensive credit analysis in life insurance sector

⎯ Insurance Financial Strength Rating (IFSR) is for senior policyholder claims and obligations of operating insurers regulated by applicable state insurance department so it is typically highest rating within control group

⎯ Unsecured debt at life insurer is typically rated 2 or more rating notches lower than IFSR because debt obligations are subordinate to policyholder claims under insurance regulation

Rating increasingly reflects expected loss including both expected default probability and loss severity and is moving closer to a modified expected loss framework ⎯ However Moody’s still assigns extra weight to default risk and rating transition risk for highly rated

credits because of their importance to market ⎯ Usage of expected loss improves comparability in ratings across different sectors and provides a

consistent framework for assessing relative value across market segments ⎯ As segments of bond market continue to converge and investors demand greater consistency

Moody’s will continue to increase weight given to expected loss Downside orientation – ratings encompass a time horizon of 3‐5 years; investors buying insurance are typically in for long haul, lack equity investor’s ability to move in and out, and do not share upside potential that can reward equity investors

Rating outlooks are an indication of rating direction looking forward 12‐18 months Concepts and guidelines govern analytic approach, both qualitative and quantitative

Qualitative factors Industry factors – trends, concentration, demographics and competitive issues, impact of financial consolidation, accounting and regulatory environment

Organization structure, ownership, corporate governance ⎯ Examine stand‐alone legal entity, examine structural factors and determine if there is any explicit or

implicit guarantee or support coming from stronger parent or affiliate; conversely could cause its capital to be tapped to service a debt‐laden parent or affiliate

⎯ Company’s strategic importance within total organization, degree to which markets and operations are integrated, branding within enterprise

⎯ Non‐insurance affiliates are evaluated on their own merits and within group concept to determine if their presence adds to or reduces risk of enterprise as a whole

⎯ Holding company is analyzed focusing particularly on capital structure and approach to managing subsidiaries; demands on operating company cash flows can have a substantial impact on level and quality of capital retained by operating company to grow operations

Strategic issues that affect long‐term financial strength ⎯ How a company responds to economic changes, market conditions, regulatory issues, competitive

pressures, may have a direct bearing on its long‐term financial strength ⎯ Growth strategies – acquisitions, joint ventures, strategic alliances – can alter risk profile ⎯ Ability to maintain or develop sustainable competitive advantages is critical


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Management quality is very important ⎯ Competence, credibility, experience, reliability ⎯ Ability to develop a strategic vision and execute that vision ⎯ Overall risk culture, discipline in financial planning

Franchise strength – Sustainable competitive advantages, strength of market position, cost position, prospects for internal growth, status within industry

Distribution – types of markets, cost structure of distribution network, retention and productivity of distributors, ability to control distribution and gain control over ultimate customers, exclusive or non‐exclusive nature of distribution relationships

Variable product risk characteristics, ranked in descending order of creditworthiness as assessed from a rating perspective of general product class ⎯ Retail participating whole life – Aaa or Aa

− Tend to produce steady earnings and cash flows, have stable long‐term liabilities and largely spare writer from ALM risks associated with interest‐sensitive products

− Low interest rate guarantees, typically 3‐4%, and conservative mortality guarantees give these products a high degree of financial flexibility

− Also contributing to flexibility is issuer ability to factor investment and actuarial performance into participating dividend mechanism

− Major risks are mortality (which is well understood by industry) and lapse ⎯ Retail variable life – Aa or A

− Structure moves much asset risk from issuer to policyholder − Because less capital is required to support asset risk, ROE tends to be higher − Profit margins (ROA and policy charges) tend to be lower than for par whole life

⎯ Retail Variable Annuities (VAs) – Aa or A − Because asset risk is moved to policyholder these products are efficient capital users and

typically earn higher ROE than spread‐based products − Because profit margins are thin scale becomes important to effectively manage expenses;

amount of assets under management is also important to profitability − Equity markets play a vital role in generation of fees and profits − Significant secondary guarantees can significantly increase risk profile and exposure to low

interest rates and/or equity market declines and reduce product rating ⎯ Asset management fee business – Aa or A ⎯ Retail universal life and term life – Aa3 or A, embody mortality and persistency risk although

universal life also exposes issuer to interest rate risk and ALM risk ⎯ Structured settlements – A

− Has very long‐tailed liabilities that carry ALM risk, interest rate risk and mortality underwriting risk

− However payouts typically occur over period of many years and involve no persistency or disintermediation risk

⎯ Retail fixed annuities – A or Baa, carry a large amount of ALM risk and surrender risk ⎯ Institutional spread business – A or Baa, carries more ALM risk than fixed annuities as well as

sizeable refinance and rollover risks ⎯ Disability insurance – A or Baa, potentially volatile line that is often subject to vagaries of economic

cycles and social factors ⎯ Long Term Care insurance – A3 or Baa, has high risk characteristics because of underwriting and

pricing issues and relative sparseness of available claims experience data


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⎯ Medical expense and other health insurance – A to Ba, higher risk product line subject to changing market forces, increased regulatory oversight and relatively high volatility

Quantitative analysis Financial strength measured quantitatively may be robust but not sufficient to offset certain key qualitative weaknesses; importantly qualitative strengths will ultimately tend to show up in key financial indicators

Ratios can be very useful for indicating where to delve deeper and for tracking trends over time and for comparative purposes

Moody’s has guidelines but no predetermined ratio requirements to fit companies into rating categories; nevertheless correlations as well as many individual ratios have a good degree of statistical explanatory power

In general debt ratings correlate with GAAP ratios and IFSRs correlate with statutory ratios Moody’s use of financial ratios is grounded in a belief that these tools have real limitations ⎯ They are static historical measures that apply only to a given point in time and are often lagging

indicators; offer no guidance for assessing corrective actions or changes in strategic plans; to be more effective as predictive tools ratios would need to be adjusted to include a number of assumptions for what might happen

⎯ Ratios can be subject to manipulation; there is temptation to “manage” ratios important to rating agencies; individual ratios when used in vacuum can send inaccurate messages

⎯ It is important to be measuring right things, something that is often seen most clearly in hindsight; exclusive focus on numeric values may mask other issues

Ratios Capital adequacy measures – accurately assessing capital adequacy involves evaluating company and parent capital relative to size of operations, risks assumed, efficiency with which capital is deployed to generate profits, and growth of capital base ⎯ Ratio 1: Consolidated capitalization = amount of capital / general account assets

− In some cases it may be necessary to add guaranteed separate account liabilities to denominator in order to capture GICs, funding agreements and other liabilities that for accounting purposes are not reported in general account but have same characteristics as general account liabilities

− Ignores different risk levels associated with assets and liabilities ⎯ Ratio 2: NAIC RBC ratio

− Incorporates asset risk, underwriting risk, interest risk; helps to gauge if company’s capital base adequately supports amount of risk it is carrying

− Changes in ratio over time may provide information on how approach to risk is changing − Can be managed through reinsurance that masks true economic position of company; it may

sometimes be necessary to adjust reported surplus for impact of reinsurance transactions that may have a temporary effect or do not effect true risk transfer but are structured to produce an accounting benefit

− In evaluating trend it is important to adjust for periodic changes in formulas ⎯ Ratio 3: Growth of statutory surplus, driven primarily by net income less dividends to parent

− Companies that retain adequate amounts of capital to support growing operations tend to have relatively stable earnings profile and moderate‐to‐low financial leverage


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− Companies with slow or negligible growth in capital and surplus often have less efficient and profitable operations, greater earnings volatility or higher leverage; as these companies grow their capital base can become more strained negatively impacting Moody’s view of their capital adequacy

− These measures can include as surplus funds raised as debt by parent company and injected as capital; this is called double leverage and highlights pressure placed on operating company to upstream capital as dividends to service debt which can cause financial strain in future

⎯ Ratio 4: Intangible assets as a percentage of shareholder equity − Intangible assets most commonly are goodwill and Deferred Policy Acquisition Costs − May increase because of acquisitions adding to goodwill, strong sales growth adding to DPAC

and/or aggressive accounting policies − Some intangibles can reasonably be included in economic capital but not leverageable as true

equity, so this measure can provide different view of strength of capital base and absolute financial leverage

Financial leverage measures – holding company debt capacity is largely a function of ability to distribute cash flows from operating subsidiaries, which in turn depends heavily on level, stability and quality of subsidiaries operating earnings and adequacy of their capital positions; as a result a company can have relatively low leverage and still lack sufficient cash flow to meet its debt service and other cash needs; but in general higher leverage generally means higher probability of default ⎯ Ratio 5: Financial leverage = short and long term debt and hybrid capital securities / total capital

base (proportion of capital financed through borrowing) − A company with higher leverage will place more strain on its supporting operations − In short term issuing debt is an effective way to lower company’s cost of capital and improve

return to shareholders; in long term increasing leverage can reduce financial flexibility particularly during times of stress

− Amount of leverage that may be acceptable varies by company and is influenced by other business fundamentals and qualitative issues

− Ratio may be adjusted for hybrid securities, or adding back off‐balance‐sheet obligations, or adding back a portion of unrealized gains for certain assets, or to exclude debt and equity from stand‐alone subsidiaries that have self‐liquidating debt

⎯ Ratio 6: Pre‐tax interest coverage = interest and preferred dividends as a percentage of GAAP pre‐tax income − Because statutory limitations affect dividend capacity, GAAP pre‐tax income may not be a good

proxy for available cash flow ⎯ Ratio 7: Cash interest coverage = maximum allowable dividends from consolidated group of

operating subsidiaries is compared to cash needed at holding company to pay interest and preferred dividends − Maximum dividends have been estimated as greater of 10% of consolidated statutory surplus or

100% of consolidated statutory operating income, adjusted for regulatory limitations and to include any recurring sources of cash including dividends from unregulated subsidiaries

Ratio 8: Profitability: Statutory operating return on average total capital ⎯ ROC is a good measure of how efficiently a company is using its capital base; earnings diversification

can increase stability ⎯ Because policy acquisition expenses are not capitalized for statutory accounting, capital strain from

growing even profitable business can place downward pressure on this ratio


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⎯ ROC excludes capital gains, which have contributed strongly to industry earnings, particularly for mutual companies; capital gains are often timed to offset poor operating earnings or credit‐related investment losses

⎯ Mutual companies often exhibit low ROC in part because nature of par whole life encourages insurers to return earnings to policyholders as dividends

⎯ Moody’s also looks at GAAP ROE; management often finds itself responding to shareholder expectations by increasing ROE, but this often entails lowering E rather than increasing R

Ratio 9: Liquidity: Liquid assets as percentage of surrenderable annuity liabilities ⎯ Helps determine if a company is prepared for surrenders ⎯ In June 2003 Moody’s introduced a model that calculates ratios of liquid assets to surrenderable

liabilities at one month, six months, twelve months; a ratio of less than 1 implies that a company’s liquid assets fall short of potential liquidity demands

⎯ In such a case a stage 2 test is performed, measuring haircut that a company could take on its illiquid assets in process of satisfying its remaining liquid liabilities while still maintaining a reasonable level of risk‐adjusted capital

Ratio 10: Asset Quality: Risk assets as percentage of capital ⎯ Many companies allocate a portion of their investment portfolios to higher risk assets – high yield

debt instruments, commercial mortgages and real estate, common stock and other assets – riskier asset classes should be monitored, unrealized losses should be scrutinized

⎯ Lower level of risk assets are associated with lower rating categories; disparity can be explained in part by unique characteristics of relatively small group of companies in Aaa universe, which have a stable long‐duration liability structure with few embedded options and strong track records and proven expertise in managing risky asset classes, which offsets increased liquidity risk

⎯ Particularly useful in monitoring changes in tolerance for investment risk over time and indicating how company might fare in stressful situations

Ratio 11: Business Fundamentals: Market presence ratio = ln surplus / ln industry surplus ⎯ Accounts for logarithmic relationship between market share and relative business position ⎯ Is a relative measure so is only meaningful when evaluation company within peer group as

companies with strong competitive position are better able to survive in difficult market conditions

ALM and liquidity General considerations ⎯ Many companies have adopted general account asset segmentation to group liabilities with similar

investment requirements together; companies may even use techniques like internal coupon stripping ∋ each segment can acquire investments tailored to its needs − Accountability is bestowed upon each segment’s manager − Close cooperation is fostered between product line management and investment management

⎯ In addition to common methodologies like duration matching and key rate duration exposure, Moody’s also evaluates ALM procedures like dynamic cash flow testing and considers secondary guarantees in certain product types

⎯ Incorporated into process is a detailed examination of potential liquidity needs as well as contingency planning in event of period of strained market liquidity which can quickly result in company’s inability to meet liabilities

Retail fixed annuities, in particular SPDAs ⎯ Some contracts provide multi‐year interest rate guarantees while others provide short‐term

interest guarantees after which rate is periodically reset subject to a minimum; most contracts


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provide book value surrender guarantee subject to sliding scale surrender charge to offset unamortized acquisition costs

⎯ Primary risk in a period of rising rates is disintermediation; to protect their in‐force business most companies will raise rate and accept lower margin; issuer accepts reduced profitability over time rather than locking in an immediate loss due to realizing capital loss on underlying fixed income investments or diverting cash flows that could be invested at higher rates

⎯ In January 2000 to May 2003, rates fell and insurers increasingly experienced spread compression with rates pushing up against minimum 3‐4% guarantees; many companies have restricted new business writing rather than continue to write unprofitable business; regulatory relief is being provided with 1.5% guarantees for new business in many states

⎯ Many VA writers have seen large transfers out of equities into fixed interest investment option15; many companies have responded by eliminating fixed option on new contracts and substituting a money market fund option

⎯ Companies have thus far shied away from using derivatives to protect against interest rate declines because of cost of purchasing option and/or mark‐to‐market accounting volatility

⎯ If low interest rate environment persists Moody’s anticipates more significant spread compression and consequent downward rating pressure

VAs ⎯ In addition to fixed interest option many VA writers offer a variety of guarantees that present ALM

risk management issues ⎯ GMDBs range from conservative return of premium feature to aggressive roll‐up of premiums at

guaranteed interest with annual ratchet ⎯ GMAB, GMIB or guaranteed withdrawal benefit can be added to base contract for a fee ⎯ These benefits are equivalent to exotic options incorporating interest rates and equity whose values

depend on customer behavior ⎯ Some companies hedge by entering coinsurance agreements essentially passing 100% of risk to

assuming reinsurer − Moody’s believes this to be effective provided reinsurer’s senior debt rating is close to IFSR of

ceding insurer, since assumed reinsurance is generally subordinate to reinsurer’s own policyholders, and uncollateralized statutory reinsurance reserve credit is not significant relative to statutory capital of VA writer

− Availability of reinsurance at affordable cost has been fairly limited ⎯ Majority of VA writers neither hedge their risk with reinsurance nor attempt an internal hedge

citing cost; lack of effective risk management has created problems and resulted in downward rating pressure for a number of issuers

⎯ Many companies adopted a pay as you go approach − As equity markets tumbled these companies saw current losses mount as revenues from assets

under management were declining creating a double whammy on earnings − Failure to hedge at outset caused what might have been a manageable cost to grow into a

prohibitively expensive cost once option became significantly in money − Cigna, largest reinsurance of GMDBs, ultimately bit bullet, implemented a hedging program and

took an after‐tax charge of $700M in 2002Q3 to lock in unhedged losses and prevent them from worsening16

− Allmerica Financial and Annuity & Life Re experienced extreme financial stress in 2002 15 Duh, these policyholders are selling equities at lowest point 16 Ironically by doing this they locked in equity prices at absolute bottom


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⎯ There is evidence of currently greater interest in hedging; consultants are offering models to calculate and implement hedges using futures and options; this still leaves basis risk

⎯ NAIC RBC C‐3 Phase 2 will use simulation to calculate required capital and reserves Institutional Investment Products (IIP) ⎯ Refers to GICs, Funding Agreement‐backed Note Issuance Programs (FANIPs) and Collateralized

FHLB funding agreements issued to institutional investors, usually very large and often putable ⎯ Investor is promised a specified fixed or floating coupon at maturity or at an earlier put exercise

date ⎯ ALM issues similar to retail fixed annuities but more “lumpy” since a single transaction is generally

significant in size compared to dispersion of retail annuity account values ⎯ There is much greater liquidity and rollover risk; institutional investors are much more likely to

abandon issuer at first hint of credit trouble straining issuer at worst possible time ⎯ Hence Moody’s believes there is only limited capacity for an issuer to write this type of business,

generally no more than 20‐30% of company’s total general account insurance reserves plus guaranteed separate accounts; in 2002 Moody’s introduced risk weighting

⎯ Insurance quick ratio = NAIC Class 1 and 2 bonds maturing within one year / total IIP maturities over next 12 months, assesses ability to fund near term maturing liabilities without having to roll them over or sell assets

⎯ Collateral required to support FHLB funding agreements is typically held in separate account for benefit of FHLB rather than in issuer’s general account; rapid growth of this type of business can use a significant share of available liquidity reducing financial flexibility

⎯ Some companies report 0 C‐3 risk wrt separate account IIP business by using a liberal interpretation of rules; from an economic perspective however interest rate risk is usually identical to that of a general account funding agreement, so company should hold same C‐3 capital against this business; Moody’s makes an adjustment to reported RBC to account for this

Ratio analysis cannot capture all forms of financial risk Off‐balance‐sheet items such as securitizations and contingent liabilities represent areas that can add to company’s financial stress

Availability of bank lines, presence of material adverse change clauses in bank revolvers and contingency planning for potential stress period cannot be captured by ratios

Key factors in assignment of credit ratings ⎯ Liquidity and cash flow, proactive liquidity management program, committed bank lending

agreements, ownership of highly liquid securities, alternative funding arrangements ⎯ Financial flexibility, excess cash flow, access to debt and equity markets

Blending qualitative and quantitative factors Because qualitative factors carry strong weight, companies with very similar financial pictures may receive different ratings

Companies often ask for blueprint to help them raise rating, but because of qualitative factors it is difficult for them to mold themselves into a particular rating purely by adjusting financials


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Introduction ALM task at life insurers is one of most challenging among all financial institutions; must confront multiple risk factors, proliferating product variation, multiple measurement frameworks

Life insurance product types Life insurance ⎯ Insurance types are term, whole, universal, variable universal ⎯ Main elements of profit and loss are

− Mortality margin – explicit or implicit charge for mortality protection less actual cost − Investment margin – difference between investment income and explicit or implicit interest

credited to policy − Commissions and expenses which must be covered by mortality and investment margins

Annuities ⎯ Annuity types are immediate or deferred, fixed term or life contingent, fixed or variable or equity

indexed ⎯ Profit is investment spread margin, typically highly dependent on first few years experience much

more so than for most other products due to high commissions, so insurers impose surrender charges

⎯ Additional features are GMDB, GMAB and GMIB

Life insurance investment practices Challenges arise from early withdrawal provisions and right to vary premium payments Two principal asset classes in which life insurers invest are bonds and mortgage‐related assets Separate accounts including equity expose policyholder not insurer to investment risk

Financial reporting (FAS) considerations FAS 60 – applies to traditional life insurance, defines reserves and DAC to make reported profits emerge in relation to premium

FAS 97 – applies to universal life, variable life and annuities; policyholder account value is carried as a liability; DAC is amortized in relation to expected future profits; deviations from assumptions may necessitate adjustment to income

FAS 115 – assets designated as hold to maturity are reported at book; trading assets are marked to market

FAS 133 – derivatives and product embedded options are reported at fair value

Statutory reporting considerations Focus is on solvency; reserves are calculated using conservative assumptions For interest sensitive products asset adequacy must be demonstrated by cash flow testing Assets are generally valued at amortized cost under assumption of hold to maturity


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Historic metrics and methods Interest rate risk ⎯ Historically life insurers did not devote substantial attention to connection between assets and

liabilities; investment risk was broadly controlled by regulatory prescriptions regarding types of investment (fixed income) and quality (investment grade)

⎯ Although simplistic this framework was adequate until late 1970s due to comparative stability of capital markets and most insurers were mutual companies

⎯ First ALM technique used by life insurers was dedication, focused on interest rate risk ⎯ Further impetus came from interest rate spike in early 1980s when combination of book value

withdrawals and adverse market value effects on asset side resulted in severe losses ⎯ Guarantees on credit rates are written calls, book value withdrawal provisions are written puts; end

result is that when market rates decrease withdrawals diminish lengthening duration and when market rates increase withdrawals increase shortening duration

⎯ Life insurers turned to immunization as solution, sometimes with segmentation for lines of business with varying exposures to interest rate risk − If only duration is matched insurer still exposed to large interest rate movements because

callable assets have negative convexity and putable liabilities have positive convexity − Imbalances can most easily be repaired by using an overlay of interest rate swaps or other

derivatives; convexity and key rate duration are also used; cash flow testing is very useful for assessing risk

Equity market risk ⎯ Dimensions of exposure

− Equity market risk has become a major source of risk rivaling interest rate risk − Because M&E fees are account value based, variable annuity writers can be exposed to

significant revenue risk − Overall beta of underlying variable annuity accounts falls within range of 0.5 to 0.9

⎯ Use of reinsurance − Prior to 2000 VA ALM was in its infancy; actuaries exempted VAs from cash flow testing − In late 1990s reinsurers stepped forward to supply reasonably priced coverage for GMDBs but

their sales success caused them to reach capacity and very concentrated market risk quickly and stop writing

Events of 2002 and their aftermath Prolonged drop in market interest rates brought new money investment rates that were not sufficient to meet investment margin targets for newly issued policies given minimum credited rates specified by regulation; in 2003 a number of states adopted regulations specifying dynamic minimum credited rates

With bond defaults at 12 year high asset base was ravaged, capital losses surpassed $27B, junk exposure surged as investment bond ratings slid

Refinancing caused accelerated prepayment on mortgage backed assets that had been earning attractive rates of interest

S&P500 dropped 50% drastically cutting revenue for variable annuity writers

Future directions Derivatives solutions


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⎯ By 2002 due to a combination of uneconomically designed guaranteed benefits, continued instability in capital markets and mounting industry losses, reinsurance was mostly off table

⎯ Derivatives now provide powerful weapons for attacking virtually all investment risk; in VA world some insurers buy puts on S&P500

⎯ Other insurers with strong ALM capabilities have gravitated toward dynamic hedging to offset equity risk; challenges are − Requires an almost continuous effort and considerable analytical machinery − Significant transaction costs that must be weighed against desired hedge effectiveness − Under extreme market conditions may become temporarily ineffective when most needed

⎯ Impending accounting and regulatory RBC developments may affect use of derivatives; under GAAP companies for first time will be required to establish explicit reserves for GMDBs; but new rules will permit derivatives to partly offset capital charges if part of a well‐defined hedging strategy

Product design ⎯ Thoughtful insurers took a hard look at role played by design escalation and recognized need to

restrain risky product development behavior ⎯ Key design modifications that should help rein in equity market risk but not do major damage to

product appeal − Limit maximum possible guaranteed benefits and reduce roll‐up rates − Offer complementary benefits such as combined GMDB/GMIB since only one can actually be

exercised or equity index annuities as natural hedges for VA risk − Adjust commission schedules from traditional up‐front to shift some equity market risk to

distributor − Enforce/encourage intra‐policy diversification to mitigate risk

⎯ Example of innovative but risk‐conscious product design is GE Life & Annuity Retirement Answer product

Accounting based metrics ⎯ To motivate a stronger link of ALM with shareholder objectives, metrics such as Earnings at Risk

(EaR) are employed to quantify economic impact of investment risk on reported earnings and manage volatility

⎯ One study showed GAAP net income explains 98% of share price variation of life insurers ⎯ Some life insurers have advocated a function on embedded value, PV of future distributable

earnings ⎯ Still in gestation is concept of fair value accounting; FAS 115 and FAS 133 are steps in that direction

Case study of equity market risk mitigation: Life insurer hedges revenue risk exposure by buying puts on S&P index to keep M&E fees at current level less cost of options


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Introduction Modern life insurance products are neither pure capital market instruments as capital market practitioners deem them to be nor probabilistically determined averages of features and benefits as actuaries deem them to be

Many challenges of insurance industry over past decades have arisen because actual economic outcomes turned out significantly different from what was measured, quantified and priced for via actuarial or simulation methods

Historical experience and losses In late 1970s and early 1980s insurers faced challenges as interest rates rose to unexpectedly high levels; cash surrenders and policy loans were greater than anticipated from historical experience; a major insurer was nearly insolvent and eventually taken over because of guaranteeing crediting rates on GIC premiums received in future

In late 1980s several insurers faced problems in their high yield portfolios as well as in their real estate investments leading to insolvency and takeover of two formerly AAA rated carriers

In early 2000s equity puts embedded in GMDBs and guaranteed living benefits have caused significant losses and strain on capital

Risks going forward include pressure to credit rates on short term liabilities based on long term assets and minimum interest rate guarantees under non‐forfeiture laws that force companies to invest in assets that are longer than their liabilities

Recent losses, difficulties in making yield bogies and increasingly risky balance sheets may all be signs of things to come; recent experience has persuasively shown that actuarial approach is insufficient

Even if range of scenarios could be developed and risk properly priced, economic risk cannot be diversified away; a robust ALM process must combine actuarial approach with use of capital markets to manage embedded options to protect company from whatever economic conditions

Role of expected return assumptions in pricing insurance products If company is comfortable with level of risk demonstrated by historical data and MC simulations and feels it has adequate capital to absorb this level of risk, it may well come to erroneous conclusion that hedging economic risk is an expense that reduces economic returns

In reality hedging is a risk management technique for reducing volatility of economic returns by transferring impact to third party that can better absorb it

Example: LTC policies that assumed 7% reinvestment rate; as late as late 2002 companies could have successfully managed their reinvestment risk so as to lock in a 7% rate but decided not to hedge in this way; they reached erroneous conclusion that interest rates were at a low point, but rates continued to fall and opportunity to hedge disappeared forcing companies either to purchase assets with yield below rate assumed in pricing or take a greater level of asset risk to achieve pricing yield

Options written by insurers Increased competition in recent years has forced insurers to reduce their pricing margins, pay increasing amounts for distribution, and provide an increasing number of options

At same time increasing volatility and efficiency of capital markets has increased cost of options


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Companies that fail to manage these options actively are betting on financial markets and policyholder reactions remaining within bounds of predetermined assumption; this bet has resulted in financial difficulties and insolvencies in past

Options embedded in insurance products ⎯ Multi‐year level premium contracts provide holder with option to renew at guaranteed renewal

rates; company is guaranteeing at issue that they will be able to invest future proceeds at pricing interest rate; company is essentially short a call

⎯ If policy has a cash surrender benefit, insurer is also short a put on this amount ⎯ Fixed annuities typically guarantee a certain minimum rate of return; insurers are short a put on

value of fixed annuity; other types of options are calls on value of policy ⎯ For some guaranteed benefits company is essentially short an equity put; insurers used MC

simulation back‐testing 1973‐4 as their worst case scenario17, but in 2000‐2 equities significantly underperformed 1973‐4 resulting in losses that in late 1990s were viewed as extremely remote and cost of equity hedges was viewed as being too expensive

Current approaches do not provide adequate protection; creative firm‐wide ALM solutions are needed

Options granted to insurers In addition to more rigorous ALM insurers must make use of a tremendously underutilized asset, options and rights granted to insurer by policyholders

For a multi‐year premium contract, if policyholder fails to pay premium accumulated assets of policy are forfeited to company ⎯ Historically this has been used to reduce reserves ⎯ Company can implement a number of strategies to actively manage this asset to protect itself from

a fall in interest rates: Sell right to this cash flow and use proceeds to purchase assets today whose yield equals or exceeds rate on which liabilities are priced or interest rate swaps up to 30 years in future at current forward rates

In a falling interest rate environment company can but does not have to lower its crediting rate; company essentially has option to enter into a fixed‐for‐floating interest rate swap; rather than wait for rates to fall to enter into an interest rate swap company can sell option to a counterparty that wants this risk profile as a swaption; with proceeds from sale company can purchase protection against a rising interest rate environment such as a cap

For VAs company can use equity derivatives to reverse its exposure to decreasing equity values that reduce its M&E charges

17 Why not 1929-1933?


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Modern Investment Management Chapter 10

Modeling liabilities Three drivers of long‐term performance: bond/equity split, level of diversification, duration of bond portfolio

If payments were known with certainty liability stream could be priced using term structure of interest rates just like a bond; in presence of uncertainty one can still use this approach keeping in mind that value of liabilities calculated in this way is noisy

Intuitive way to model liabilities is to assume value consists of two parts – a bond that reflects best guess about future obligations and a noise term that reflects uncertainty ⎯ RL,t – RF,t = β(RB,t – RF,t) + εt

Evaluating investment decisions in presence of liabilities In context of asset‐liability framework there are two shortcomings in measuring trade‐off between risk and return using Sharpe ratio ⎯ Considers only assets in isolation and ignores any liability stream; some assets are better suited to

hedge against changes in value of liabilities ⎯ Only theoretically well founded in single period model; assuming a pension fund cares only about

distribution of assets at one future point is inappropriate − It is unclear how to choose future date since pension funds expect to remain indefinitely − Pension funds care about funding in intermediate periods to ensure all payments

Static single‐period analysis Pension plans care about return on surplus rather than return on assets Risk Adjusted Change in Surplus ⎯ Natural extension of Sharpe ratio to accommodate presence of liability stream ⎯ RACSt = Et[St+1 – St(1+RF)] / σt[St+1]

For a fund that does not know exactly its future liabilities (i.e., most funds) there is no riskless strategy to lock in a certain rate of return on surplus; least risky strategy (i.e., lowest surplus volatility) is to purchase bonds that represent best guess about future liabilities and invest remainder into riskless asset

Example: pension plan fund with a duration of 12; duration of Lehman Long Government and Credit Index is 10.5, so even for a fund with a surplus an all‐bond allocation is a losing strategy in long since assets will grow more slowly than liabilities on average

Liability index is more correlated with Lehman Long Government and Credit Index, so bonds appear to be a better hedge against changes in value of liabilities than equities

Fund with a deficit might18 invest in bonds because they offer a better hedge leading to a lower surplus volatility; fund with a surplus may want to invest in bonds up to a point that they duration match liabilities and investing in equities beyond that point

Surplus risk is minimized when equity allocation is (1 ‐ βLt/At)(σB2 ‐ ρσBσE) / (σE

2 + σB2 ‐ 2ρσBσE)

Minimum equity allocation to prevent surplus from shrinking on an expected return basis is [μB(βLt/At – 1) + (Lt/At)RF(1‐β)] / (μE‐μB)

Numerical results

18 Text p110 uses word “must” which contradicts p118 which suggests an equity allocation


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⎯ For an underfunded plan (funding ratio = 0.8) minimum equity allocation is a little over 40%; overfunded plans will see their surplus grow even for a 0% equity allocation

⎯ For both underfunded and exactly funded plans RACS is strictly increasing as a function of equity allocation and for underfunded plan slope is steeper implying that this plan is rewarded more on a risk adjusted basis for taking additional equity risk

⎯ For overfunded plans (funding ratio = 1.2) RACS increases very steeply early on but reaches maximum at equity allocation around 30%

⎯ When we introduce noise ability of bonds to hedge changes in liabilities is negatively impacted and equity with its higher Sharpe ratio looks relatively more attractive

Global diversification ⎯ Global equity has a higher Sharpe ratio but lower correlation with liability index ⎯ Overfunded plan can eliminate liabilities and invest some surplus in global equity; at high equity

allocations liabilities are no longer exactly eliminated and benefit from global diversification is diminished

⎯ Also at higher noise levels overfunded plan actually experiences a decrease in RACS when switching from domestic to global equity

⎯ Global fixed income will cause a decrease, sometimes very large, in RACS Choosing right duration of bond portfolio – All funds lose from investing in a bond index with different duration than liability index

Dynamic multi‐period analysis Given a fixed fraction p of liabilities paid out at end of each period what expected return R in excess of return on liabilities will keep funding ratio F = A/L constant on average? ⎯ Et(Rt+1) = {[(1‐p)Et(Ft+1) + p] / Ft} – 1 is general result ⎯ E(R) = {[(1‐p)F + p] / F} – 1

What return R in excess of return on liabilities is required to reach full funding ratio F = 1? ⎯ E0(Ft) = [(1 + E(R)) / (1‐p)]tF0 + p {1 ‐ [(1 + E(R)) / (1‐p)]t} / (E(R) + p) ⎯ Set LHS to 1 and fix time horizon t, then find value for E(R) that satisfies equality

Conclusion There is a dichotomy between over and under funded plans ⎯ Underfunded plans might be19 better off taking a large amount of equity risk to try to improve their

funding status; overfunded plans may be better off with lower equity allocation ⎯ Overfunded plans benefit from global equity diversification while underfunded plans are better off

investing domestically to benefit from higher correlation ⎯ Benefit from duration matching bond portfolio with liabilities is much greater for underfunded

plans

19 Text p118 uses absolute word “is” which contradicts p110 which suggests a bond allocation


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Introduction Investors are interested in hedge funds because they believe hedge funds (1) offer opportunity to increase expected portfolio returns and (2) diversify total portfolio risk

However allocations to hedge funds are difficult to analyze largely because of general lack of consistent quality data

Instead ask what return or hurdle rate can justify a specific allocation; implied hurdle rates can be quite low especially for modest allocations

Potential advantages of hedge funds to investors A traditional active manager’s return can be reconstituted as a long position in benchmark index plus a long position in a long/short portfolio representing differences in security weights between actual portfolio and benchmark plus a short position in cash

Active manager difference between long/short portfolio and cash can now be compared to excess return on hedge funds relative to cash

Three fundamental characteristics that give hedge fund managers potential to add value ⎯ Hedge funds do not face same constraint on short positions as traditional active managers ⎯ Not limited to investments in particular benchmarks so have broader investment universe ⎯ Not restricted to one particular investment style hence they have potential to generate

outperformance through market timing

Hedge fund data There are several major hedge fund indices, although they do not typically pass tests to be considered traditional benchmarks; for many constituents or weights are not known in advance, and some contain funds in which investors cannot place capital

No existing database or index of hedge funds is comprehensive Self‐reporting biases – in most hedge fund indices managers choose to report which can introduce a number of potential biases ⎯ Survivorship – managers are dropped if they stop reporting; periods of non‐reporting can coincide

with periods of significant loss; index performance is biased upward and downside volatility is possibly understated

⎯ Backfill – funds are added after they have a few successful years; biases toward firms that manage to survive first few difficult years

⎯ Investability – indices potentially include funds that are no longer accepting new assets ⎯ Transparency – some indices do not reveal actual names of managers, so not useful for

benchmarking ⎯ Incorrect fund categorization – some funds report themselves in categories in which they do not

manage capital ⎯ Frequency of reporting – many hedge fund managers report results only monthly which tends to

understate true peak‐to‐trough losses; short‐term periods of significant loss would be revealed if daily data were available

⎯ Leverage measurement – differences in return are caused to some degree by different levels of leverage


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⎯ Constituent weightings – some indices equal weight funds which overweighs small funds ⎯ Completeness – many of most successful managers choose not to report

Framework for developing, implementing and evaluating hedge fund allocations Very features that make hedge funds attractive also complicate their evaluation Most effective way to evaluate is relative to assets already held; assess impact of hedge fund allocation on portfolio risk, then calculate implied hurdle rate and determine whether specific hedge fund can achieve it

Why? Reason is historical time series are better suited to estimation of volatility and correlation than expected return especially for hedge funds where data is limited

Two examples: (1) equal investments in several hedge funds, and (2) beginning with a target of equal risk contributions and working backwards to find hedge fund weights

There are two ways to implement allocation to hedge funds: (1) make an outright allocation same as other asset classes, or (2) treat hedge fund portfolio as a substitute for other active strategies through a portable alpha strategy

An investor who chooses to make an outright allocation must also choose how to fund it; there are two alternatives: (1) scale down all other assets proportionately, (2) substitute away from one or some but not all other assets; choice of how to fund matters only at more significant hedge fund allocations

Analysis of impact on total and marginal portfolio volatility is important because (1) it reinforces that investors should analyze hedge funds prior to investing and (2) it provides an easy decision rule that how you fund depends in part on how much risk you want to take in overall portfolio

What about returns? Preferred approach is to find implied excess returns associated with alternative allocations; implied returns are best interpreted as hurdle rates

Evaluating implied hurdle rates Begin with an evaluation of risk characteristics and then analyze historical performance; our purpose is to determine whether it is feasible to construct a portfolio of hedge funds for each strategy whose volatility matches that of hedge index for that strategy

An investor does not need to hold an exceptionally large number of managers in each hedge fund sector to approximate index, partly explained by low levels of manager correlation for some sectors; results suggest investors need to rely on thoughtful portfolio construction tools to develop initial hedge fund portfolio and robust risk management systems to ensure portfolio remains within prescribed risk tolerances

Each strategy’s alpha is positive but only two strategies (convertible arbitrage and equity market neutral) have statistically significant (t test) alphas; of course even though composite performance of a particular strategy does not have statistically significant alpha there may be specific managers in that strategy who have generated significant outperformance

This analysis helps us evaluate implied hurdle rates as investors can draw three inferences ⎯ Historical adjusted performance exceeds implied hurdle rates, so they are achievable ⎯ Investors are advised to carefully consider funds since there is variation across strategies ⎯ Investors need to be quite careful about selecting managers since there is variation across

managers


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Introduction Managing a portfolio of hedge funds involves same steps as managing any portfolio ⎯ Universe of investable assets needs to be defined and if possible classified intro groups ⎯ Manager must develop views on characteristics of each asset ⎯ Risk budget is set, and assets are assembled into a portfolio ⎯ Assets and portfolio are monitored to ensure they continue to meet investor’s goals

Hedge funds are designed to represent pure form of active management, providing expert investment skills in one or more markets and focused on maximizing absolute returns

Approximately 3000‐5000 hedge funds have $400‐600B under management

What is a hedge fund? Constraints – no consideration of a benchmark, unconstrained wrt use of short selling, leverage or strategy

Regulation – not regulated by SEC, typically structured as partnerships restricted to 99 or 499 “qualified investors”, not allowed to solicit investors

Fee structure – fixed management fee of 0‐2% of assets, performance fee of 20‐50% of returns subject to a high‐water mark

Lack of transparency ⎯ Most hedge funds will not reveal assets held or especially short positions, leverage, types of

strategies being managed, let alone models or trading strategies ⎯ Secrecy reflects trade‐off between transparency so investors can understand process and manager

vs fact that hedge funds typically invest in strategies with limited capacity and are concerned about increased flow of capital into these strategies reducing returns as well as market contagion or predatory trading by its competitors

Short lives – half life of hedge funds is about 2.5 years; funds with poor performance even if modestly positive and funds below high‐water mark are often not viable

Illiquidity – hedge funds have redemption windows at least as infrequent as monthly; redeeming investors must notify manager well in advance

Capacity constraints – many managers reach point where it is in their best interest to turn away new investment; extremely successful funds may even return capital to investors

Developing views on hedge funds Compensated risks are strategy and people executing that strategy; uncompensated risks are created by hedge fund organization

Investment strategy ⎯ Begin with evaluation of general investment proposition’s potential to generate returns ⎯ Give consideration to how manager develops investment views including information sources and

analytical tools; does fund have informational, analytical or size advantage ⎯ Implementation, trade structuring and execution, portfolio construction and rebalancing, risk

monitoring, use of leverage are all important ⎯ Decision making is important particularly if there is a team with more than one key person


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⎯ Understanding each manager’s style will help in creating portfolio that is not overly exposed to any single return‐driving factor as well as framing return expectations

People ⎯ Experience, education, track record ⎯ In addition to investing expertise, ability to manage a company is key

Organization ⎯ Organizational distractions can disrupt investment decision makers ability to focus on managing

portfolio ⎯ Appropriate trading and compliance infrastructures have to be in place; manager needs to have

legal counsel ⎯ Manager plan for growth is important; hiring plans, forecast of capacity, plans to monitor capacity

constraints; fund size has to be evaluated in context of strategy ⎯ Alignment of interests between employees and investors; extent to which principals and employees

are themselves significant investors Track record ⎯ If sufficient data are available evaluation of return/risk trade‐off can be performed ⎯ Chasing past performance has a number of pitfalls

− 45% of top performing equity long/short funds in top quartile in 1999 were in bottom quartile in 2000; top performer (+334%) was worst performer (‐69%)

− Looking at past performance does not incorporate changes in investment approaches or new financial products

⎯ Relevant data measures: monthly returns, standard deviation, largest drawdown, Sharpe ratio, return‐to‐drawdown ratio, beta to S&P 500, alpha

⎯ Quantitative measures need to be considered in context of fund strategy and market environment Final evaluation ⎯ Reasonable expectations for worst case loss need to be laid out prior to investing ⎯ Expectations for potential positive returns should also be specified since unexpectedly large positive

returns may indicate manager is taking unanticipated risks

Portfolio construction Begin with clear understanding of objectives and fit of hedge fund portfolio into overall portfolio; set a risk budge consistent with objectives and allocate to managers most likely to deliver returns that fulfill objectives

Investors should understand expectations for return and volatility as well as how large a loss they are comfortable sustaining and their liquidity requirements

Correlations between sectors range from 0.08 (event‐driven vs tactical trading) to 0.66 (equity long/short vs event‐driven); correlations between strategies within a sector are potentially modest

Tactical overweights and underweights are a potential source of value added but are impeded by fund illiquidity

Hedge funds should have exposure only to manager’s views with little permanent exposure to any asset class; consequently over long enough time correlations across funds are expected to be low and benefits of diversification to be large


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Ongoing monitoring and management Much monitoring is intended to detect style drift; for investors who receive only fund NAV style drift may be detected by noticing outsized positive or negative returns or that strategy does not exhibit expected correlations

Investor will want to be aware of material changes in organization, personnel, assets or service provides In addition to monitoring individual funds, portfolio must be reviewed for appropriateness and allocations

There may be an incentive at margin not to actively trade funds, particularly if they are below high‐water mark

Funds of hedge funds Funds of funds may be able to obtain better access to information and managers than individual investors; they also offer opportunity to invest with a lower minimum amount

Need to weigh trade‐off of additional fees vs benefits provided


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Why private equity? Private equity managers have an informational advantage in accessing deals, assessing transactions and making investment decisions

Private equity investors have a chance to add value to both start‐up companies and larger businesses in need of restructuring or repositioning; best private equity investors often control companies and boards, choose management, drive strategy and affect operational and financial decisions

Private equity investors are often able to acquire companies at prices lower than comparable public companies, sometimes due to less efficient sales process

Types of private equity investment Private equity ranges from start‐up seed financing (angel investor) through growth and development (incubator) and general venture capital and mezzanine financing to private buyouts and possible turnaround and distressed investments

Companies that involve innovations in technology or business might be expected to have returns that are based substantially on effectiveness of innovation and have relatively little to do with trends in public market

Other kinds of private investments might have returns substantially based on public market; buyouts that involve nothing more than financial leverage, startups or ventures that are really just copies of other recent companies

Risk is related to strategy, industry, company size, geography

Mechanics of private equity investment Most private equity transactions involve a change in control Most common way to make private equity investments accessible to financial investors is partnership interest ⎯ General partner has some form of expertise in particular kind of private equity investment ⎯ Financial investors are limited partners who make firm commitment to provide up to a specified

amount of cash during a specified period of time (typically five years) once an attractive investment is found

⎯ General partner manages investment, working with management or installing new management, helping with operational management, or adding value in other ways

⎯ Finally investment is liquidated often by an IPO and proceeds distributed to limited partners ⎯ Limited partners pay fees to general partner, and general partner usually receives 20% of profit

often called carried interest

Valuation and return statistics in private equity Since private equity investments do not trade regularly there are difficulties in establishing valuations and hence return statistics for them; typically investments are held at cost or at value based on most recent significant transaction by an outside investor

Thus valuations can be seriously out of date; businesses able to finance investments out of cash flow will not change reported valuation while economic value of business increases markedly; failing business might be held at cost until it ceases operations


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Since not all investments will have transactions at any one time, valuation of partnership as a whole is almost always out of date to some extent; hence periodic return and volatility series are highly unreliable

Most common quoted measure of performance is IRR which will be reliable but of limited utility compared with period returns

Historical returns in private equity Median value is around 10% after fund fees and carried interest have been accounted for, very close to long‐term return of S&P500 suggesting that private equity as a class does not have significant returns in excess of public equity

In US upper quartile returns on unliquidated private equity ranged from 19.8% to 726% while bottom quartile ranged from –5.2% to –100%

In any given year venture and buyout funds may have different returns, but in aggregate over time this appears not to be case

Sources of return in private equity Conclusions about building a model of private equity for purposes of asset allocation ⎯ Standard risk and return statistics cannot be measured with any degree of accuracy ⎯ Because of stale valuations, illiquidity and long commitment periods, market weights cannot be

used to infer equilibrium expectations ⎯ Any two portfolios may have different risk and return profiles ⎯ Returns are partly related to returns in public equity markets and partly on excess information or

skill on part of private equity manager; μprivate = βμpublic + α ⎯ Risks are partly but not solely related to risks in public equity markets; σprivate

2 = β2σpublic2 +

σidiosyncratic2

What values should be assumed for parameters? ⎯ Since private equity is equity a value of β near 1 seems a priori reasonable; for companies with

strong innovative component a lower value might be expected; for companies that use a higher degree of financial leverage or are copies of recent companies a value closer to 2 might be expected; carried interest paid on investments reduces effective β − Simulations on Venture Economics database suggest β ≈ 0.7

⎯ A very small or poorly diversified portfolio could have a very large value of σidiosyncratic perhaps in vicinity of 100% consistent with single stocks of companies recently gone public; a larger more diversified portfolio might have a significantly smaller value; at lower extreme a portfolio of 20 partnerships each with 20 investments could have σidiosyncratic = 5% − Simulations on Venture Economics database suggest σidiosyncratic ≈ 15‐25%

⎯ Fees reduce expected return 2‐3%; a value of α very close to zero is consistent with data; managers with skill may be able to deliver high α by doing unusual deals which may also have effect of lowering β

Optimal allocation Optimal private equity weight is (1/λ)[α + (λσpublic

2 – μpublic)(1‐β)] / [σidiosyncratic2 + (1‐β)2σpublic

2] ⎯ λ is risk aversion parameter ⎯ Numerator shows two reasons to allocate to private equity: (1) if there is some source of positive

return α, and (2) if β < 1 there is a diversification rationale


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⎯ If β = 1, w = (1/λ)α / σidiosyncratic2

⎯ When expected excess return for private equity is exactly equal to expected excess return for public equity α = μpublic(1‐β) this is exactly equivalent to selecting private equity allocation to minimize total volatility in total equity portfolio − In this case w = [1‐β] / [(σidiosyncratic/σpublic)

2 + (1‐β)2] for any value of λ

Effect of sub‐optimal allocation We can derive optimal allocation as a consequence of estimated statistics but these are not very reliable; also resulting range of results (10‐50%) is rather broad to be useful

One way to address this is to calculate impact if statistics turn out to be inaccurate, then investors can decide if potential gains are worth additional risk

(σtotal/σpublic)2 = (1‐w)2 ‐ 2βw(1‐w) + w2[β2 + (σidiosyncratic/σpublic)

2] ⎯ For private equity weights up to 10% volatility increases by a factor of no more than 1.06 for any β

up to 1.5 ⎯ For w = 25% and β = 1.5, volatility increases by factor of 1.19

Key ideas Private equity differs from public equity in several ways: (1) Information does not flow freely, (2) Illiquidity, (3) Transaction costs are high

These factors create opportunity for higher returns but cause valuations and return statistics to be unreliable

Available data on IRR suggests that median rates of return are roughly comparable to public equity but dispersion is much higher

Risk and return depend very strongly on how portfolio is constructed Private equity can be modeled as having a mixture of characteristics that depend on equilibrium returns in public equity and non‐equilibrium non‐public factors

Simple diversification is usually an inadequate rationale for investing in private equity; investments make sense only when there is a reasonable likelihood of additional return due to superior information or skill

Great care must be taken to understand underlying sources of risk and return For investors who can realistically expect an alpha of at least 3% with beta no greater than 1.5 it may be optimal to allocate at least 10% of total equity portfolio to private equity

Allocations toward low end of range have only modest penalties for sub‐optimal allocations, but penalties increase markedly toward high end of range


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Managing Investment Portfolios Chapter 11

General comments Fiduciaries need to pay particular attention to adequate monitoring

Monitoring Investor ⎯ Circumstances including wealth and constraints

− For private wealth clients, changes in employment, marital status, birth of children − For institutional clients, operating performance, constituent pressures, change in governance

practices − Net worth is central; return and risk requirements may change as a result

⎯ Liquidity requirements − Need for cash in excess of new contributions or savings as a consequence of some anticipated

or unanticipated event; managers need to hold in liquid and low price risk assets such as money market instruments

− Individual clients – unemployment, illness, court judgments, retirement, divorce, family death, new home

− Institutional clients – payment of claims or benefits, funding of capital project − Managers who do not face major withdrawals are better positioned to earn return premium

that illiquid investments provide ⎯ Time horizons

− Reducing investment risk is generally advisable as an individual moves through life cycle and his time horizon shortens; bonds become increasingly suitable

− Some entities hope for perpetual life and passage of time in and of itself does not change their time horizon

− Many private wealth clients have multi‐stage time horizons − Some changes can happen abruptly, for example death of last income beneficiary of a trust

⎯ Tax − Make all decisions on an after‐tax basis − For taxable investors holding periods and turnover rate are important due to tax effects − Take into account each strategy’s tax efficiency: defer realization of income from higher tax year

to anticipated lower tax year, accelerating expenses to high tax year, realizing short term losses at year end to offset realized short term gains in same year, deploying assets with high unrealized gains to use step‐up in tax basis, reducing or increasing allocation to tax exempt securities

− Tax law changes could make certain asset categories more or less favorable ⎯ Laws and regulations

− Uniform Prudent Investor Rule (vs older prudent man rule) − Uniform Principal and Income Act

⎯ Unique circumstances − Need to retain concentrated stock position − Socially responsible investing, particularly endowments and public employee pension plans;

client should be aware of potential costs in adopting


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Market and economy ⎯ Asset risk attributes

− Returns, volatilities, correlations sometimes meaningfully change − Successful active managers assess differences between actual risk and perceived risk

⎯ Market cycles – may make tactical adjustments to asset allocations based on market cycle ⎯ Central bank – expansionary vs restrictive monetary policy ⎯ Yield curve and inflation

− Premium on long term bonds over short term bonds tends to be counter‐cyclical because investors demand greater rewards for bearing risk during bad times

− Short term yields tend to be pro‐cyclical because central banks tend to lower short rates to stimulate economic activity during recessions

− Yield curves thus tend to become steeply upward sloping during recessions, flatten in course of expansions, and become inverted before an impending recession

Portfolio – Evaluate (1) events and trends affecting prospects of holdings and asset classes and their suitability and (2) changes in asset values that create unintended divergences from strategic asset allocation

Rebalancing portfolio Benefits and costs of rebalancing ⎯ Benefits

− Track optimal strategic asset allocation that takes into account investor risk and reward appetite − If we let asset mix drift higher risk assets will tend to represent an ever larger proportion of

portfolio over time − Maintain client’s desired systematic risk exposures − Sell assets that have become overpriced − Despite six year losing streak in late 1990s annual rebalancing outperformed a drifting mix for

January 1988 to July 2003 period by 27 bp a year while reducing risk by more than 1% per year; 1973‐2003 period shows even better results for annual rebalancing

⎯ Costs − Transaction costs: relatively illiquid investments such as private equity and real estate have

become increasingly important to endowments and pension funds but pose special challenges to rebalancing because costs represent a high hurdle; sometimes it is more efficient to rebalance by reinvesting cash flows

− Tax costs – for taxable investors realizing gains, sometimes short term, can be very costly Rebalancing disciplines ⎯ Calendar rebalancing – quarterly is popular

− Simplest, does not require continuous monitoring − Drawback is it is unrelated to market behavior

⎯ Percentage of portfolio rebalancing – Triggers set as a percentage of portfolio value − Can exercise tighter control on divergences from target, related to market − Monitoring needs to occur frequently, ideally daily − Five factors should play a role in setting corridors: (1) higher transaction costs should lead to

wider corridors, (2) greater tracking risk tolerance should lead to wider corridors, (3) higher correlation with other classes should lead to wider corridors, (4) higher volatility should lead to narrower corridors, (5) higher volatility of other classes should lead to narrower corridors

⎯ Other rebalancing strategies


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− Combined calendar and percentage of portfolio rebalancing − Equal probability rebalancing – corridor for each class is common multiple of its standard

deviation − Tactical rebalancing – a variation of calendar rebalancing that specifies less frequent

rebalancing when markets appear to be trending and more frequent rebalancing when markets appear to be characterized by reversals

⎯ Rebalancing to allowed ranges rather than to exact target weights; no conclusion whether this is better

⎯ Setting optimal thresholds – maximizing net benefit of rebalancing remains a complex challenge − Benefits of rebalancing are hard to quantify − Rebalancing strategy may need to reflect changing relationships among asset classes − Decisions at different points are linked and affect subsequent decisions − Accurately reflecting transaction costs may be difficult, costs can be non‐linear in size − Optimal strategy is likely to change through time

Perold‐Sharpe analysis of strategies ⎯ Buy and hold strategies

− No adjustments are made resulting in drifting asset mix − Upside is unlimited, but portfolio value can be no lower than allocation to cash − Strong bull market favors buy and hold20

⎯ Constant mix strategies − Superior if equity returns are characterized more by reversals than by trends − Supplies liquidity, represents sale of portfolio insurance

⎯ Constant proportion strategy − Dynamic strategy in which target equity allocation is a function of value of portfolio less a

specified floor − Buy and hold is a special case of constant proportion strategy − Constant Proportion Portfolio Insurance (CPPI), which requires manager to sell stocks as they

decline and buy them as they rise, is also a special case of constant proportion strategy − Performs well in strong bull or bear markets; inferior if equity returns are characterized more by

reversals than by trends − Uses liquidity and is momentum oriented

⎯ Linear, concave and convex investment strategies – functions in terms of stock returns − Buy and hold strategies are linear − Constant mix strategies are concave − CPPI is convex

Execution choices in rebalancing ⎯ Cash market trades

− Most direct means of portfolio rebalancing, but more costly and slower to execute − For taxable investors, tax considerations may favor cash market trades as there may be no exact

derivative market equivalent on an after‐tax basis and derivative trades may have unfavorable tax treatment

⎯ Derivative trades – futures contracts or total return swaps − Lower transaction costs and more rapid implementation, but may face liquidity limits − Leaves strategies undisturbed

20 Study note claims strong bear markets also favor this strategy but that is incorrect


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Managing Investment Portfolios Chapter 12

Importance of Performance Evaluation Fund Sponsor Perspective ⎯ Performance evaluation provides exhaustive quality control, emphasizing not only performance and

its constituent parts relative to objectives but sources of relative performance as well ⎯ Should be an integral part of fund’s investment policy and documented in its investment policy

statement; enhances effectiveness of investment policy by acting as a feedback and control mechanism identifying strengths and weaknesses

⎯ Increased complexity has brought greater need for sophisticated performance evaluation Investment Manager Perspective – some managers may wish to seriously investigate effectiveness of various elements of their investment processes and examine relative contributions of those elements

Three Components of Performance Evaluation Performance Measurement – What was account’s performance? Performance Attribution – Why did account produce observed performance? Performance Appraisal – Is account’s performance due to luck or skill?

Performance Measurement Performance measurement without intra‐period external cash flows ⎯ R = [MV1 – (MV0+CFbegin)]/MV0 or R = [(MV1 – CFend) – MV0]/MV0

Total rate of return ⎯ Widely accepted solutions to problem of measuring returns in presence of intra‐period external

cash flows are relatively recent developments (1960s) ⎯ Issue received little attention because prevailing measures were income‐only excluding capital

appreciation, due to several factors − Portfolio management emphasis on fixed‐income assets; in low‐volatility interest rate

environment that existed prior to late 1970s bond prices tended to be stable − Limited computing power − Less competitive investment environment

⎯ Acceptance of total rate of return as primary measure was assured by BAI 1968 TWR ⎯ Requires account be valued every time an external cash flow occurs; sub‐period returns are then

chain‐linked together to compute TWR for entire evaluation period ⎯ Note that unless all sub‐periods constitute a year, TWR will need to be annualized

Money Weighted Rate (MWR) of return, or IRR ⎯ Rate that solves MV1 = MV0 + ΣCFi(1+R)N‐Ti is MWR per unit of time; there exists no closed form

solution for R, must be solved numerically ⎯ MWR for entire evaluation period is r = (1 + R)m – 1

TWR vs MWR ⎯ MWR represents average growth rate of all money invested in account; TWR represents growth

rate of a single unit of money invested in account for entire period ⎯ Consequently MWR is sensitive to size and timing of external cash flows, while TWR is unaffected


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⎯ When external cash flows occur that are large relative to account value and account performance is fluctuating significantly during measurement period, MWR and TWR can differ materially

⎯ Practitioners generally prefer a measure that is not sensitive to cash flows; BAI recommended TWR as appropriate measure; recommendation has received almost universal acceptance since publication; GIPS generally requires a TWR methodology

⎯ Managers of some types of private equity investments typically operate under arrangements that permit them to call capital from investors at manager’s discretion and determine when original capital and any earnings on it are returned to investors; in these opportunistic scenarios MWR is more appropriate measure

⎯ Disadvantage of TWR is it requires account valuation on every date that an external cash flow takes place

Linked IRR (LIRR) ⎯ Although daily pricing is becoming more common, use of pure TWR is not yet standard practice

except for mutual fund industry ⎯ BAI suggested LIRR, which approximates TWR by calculating MWR over reasonably frequent time

intervals and then chain‐linking results over entire period; BAI estimated that for an account experiencing “normal” cash flow activity LIRR would fall within 4 bp of TWR, immaterial given inaccuracies in pricing even most liquid portfolio

⎯ LIRR fails to provide an acceptable representation of TWR if large external cash flows (generally over 10% of account value) and volatile swings in performance occur during evaluation period

Annualized Return represents compound average annual return earned over evaluation period; with measurement periods shorter than a full year it is inadvisable to calculate annualized return

Data quality issues ⎯ For accounts invested in illiquid and infrequently priced assets underlying valuations may be

suspect, invalidating reported rates of return; for example valuations of venture capital funds typically have limited economic content as an investor may not be able to enter or leave account at a value anywhere near reported valuations

⎯ Matrix pricing, based on dealer quoted prices for securities with similar attributes, may be used for many thinly traded fixed income securities

⎯ For highly illiquid securities managers may carry them at cost or price of last trade ⎯ Stated value of account should reflect impact of any unsettled trades and any income owed by or to

account but not yet paid; settlement date accounting and/or exclusion of accrued income would incorrectly reflect account market value

Benchmark Concept of a benchmark ⎯ A benchmark B is a collection of securities or risk factors and associated weights that represents

persistent and prominent investment characteristics of an asset category or manager’s investment process

⎯ Portfolio P has 3 components: market M, style S = B – M, active management A = P – B Properties of a valid benchmark: (1) Unambiguous, (2) Investable, (3) Measurable, (4) Appropriate, (5) Reflective of current investment opinions, (6) Specified in advance, (7) Owned

Types of benchmarks ⎯ Absolute return objective – not investable, and often not appropriate


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⎯ Manager universe – Median account in a typical universe does not have properties of a valid benchmark except for being measurable; most significant deficiency is that median account cannot be specified in advance; also universes are subject to manager survivor bias

⎯ Broad market indices – often acceptable benchmarks, particularly for asset category performance measures or for core type investment approaches; not appropriate if manager style deviates considerably from style reflected in market index

⎯ Style indices – ability to pass validity tests can be problematic − Some contain weightings in certain securities and/or sectors that are much larger than what

many managers consider prudent; definition of style implied by benchmark may be ambiguous or inappropriate

− Differing definitions of style can at times produce rather extreme return differentials; in 1999 S&P Large Value Index returned 12.72% but Russell Large Value Index returned 7.35%; users should closely examine how indices are constructed and assess applicability to specific managers

⎯ Factor model based − Can set market model benchmark, based on manager’s usual portfolio beta − Incorporating multiple factors can enhance richness of approach, can set benchmark based on

normal portfolio with exposures to systematic risk factors typical for manager − Not always intuitive or easy to obtain, potentially expensive to use, ambiguous since we can

build multiple benchmarks with same exposures but materially different returns, benchmark may not be investable

⎯ Returns based − Constructed using series of manager’s account returns and series of returns on several

investment style indices over same period; use regression to solve for allocation of indices that most closely tracks account returns

− May contain weightings that managers consider imprudent; require many months to establish statistically reliable pattern; for managers who rotate among style exposures a pattern may be impossible to discern

⎯ Custom securities based − Manager’s research universe weighted in a particular fashion − Overwhelming advantage is it meets all required benchmark properties and satisfies all validity

criteria; also valuable tool to monitor and control investment process and allocate risk across teams

− Disadvantage is that they are expensive to construct and maintain; also perception of lack of transparency can be of concern

Building custom securities based benchmarks ⎯ Identify prominent aspects of manager’s investment process; must make fine distinction between

manager’s normal or policy investment decisions and manager’s active investment judgments ⎯ Select broad universe of securities consistent with investment process ⎯ Devise weighting scheme for benchmark securities including cash position, include aspects of equal

weighting and cap weighting depending on investment process and client restrictions ⎯ Review preliminary benchmark and make modifications ⎯ Rebalance benchmark portfolio on predetermined schedule

Tests of benchmark quality ⎯ Comparison of good and poor benchmarks


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− Good benchmarks increase proficiency of performance evaluation and highlight contributions of skillful managers; poor benchmarks obscure manager skills

− Good benchmarks enhance capability to manage risk; poor benchmarks promote inefficient manager allocations and ineffective risk management

− Poor benchmarks increase likelihood of unpleasant surprises, counterproductive actions and unnecessary expense

⎯ Quality criteria to distinguish good benchmarks from poor ones (Bailey) − Lack of systematic biases – historical average beta of account relative to benchmark should be

close to 1; correlation between A and S is not statistically different from 0; statistically significant positive correlation between E=P‐M and S

− Tracking error – volatility of account returns relative to a good benchmark should be less than volatility of account returns against market index, indicating benchmark is capturing important aspects of manager’s investment style

− Risk characteristics – benchmark’s exposure to systematic sources of risk should be similar to account’s

− Coverage ratio is defined as market value of securities held in both portfolio and benchmark divided by market value of portfolio; high coverage indicates a strong correspondence between manager’s universe of potential securities and benchmark; low coverage indicates benchmark has little relationship on a security level with opportunity set generated by manager’s investment process

− Benchmark turnover should not be so excessive as to preclude successful implementation of benchmark as a passively managed portfolio

− Active positions – when a good benchmark has been built manager should be expected to hold largely positive active positions for long‐only accounts; a high proportion of negative active positions is indicative of a benchmark that is poorly representative of manager’s investment approach; violations often occur when benchmark is market cap

Hedge funds and hedge fund benchmarks ⎯ There are performance measurement issues as well as numerous administrative and compliance

issues that are created when there are short positions in an account ⎯ Revised performance measurement methodology needed

− Net assets of a long‐short position could theoretically be zero, making rate of return calculations impossible

− Even though in real world account will have positive NAV due to margin and administrative requirements, as NAV gets smaller account’s return will become nonsensically extreme

− One approach to address this problem is to think in terms of active management performance impact A, which can be determined by summing performance impacts of individual long and short security positions

− Another approach is to specify denominator as sum of all absolute values of positions ⎯ Advent of hedge funds added a new dynamic to discussion of use and design of benchmarks; some

practitioners eschew use of benchmarks entirely for hedge funds contending that absolute return mandate associated with hedge funds implies that relative performance comparisons are meaningless

⎯ Discussion of benchmarks is confounded by vagueness of definition of “hedge fund”; this vagueness has led to widespread use of Sharpe ratio to evaluate hedge fund managers − Difficult to identify universe of other hedge funds that have similar mandates − Exposed to benchmark validity criticisms against manager universe comparisons


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− Use of standard deviation as risk measure is questionable when strategy incorporates a high degree of optionality and skewness as is case for many hedge funds

Performance Attribution Impact equals Weight times Return Macro attribution overview – Fund controls broad allocation to different classes of securities as well as allocations to individual managers within a class

Macro attribution inputs ⎯ Policy allocations based on fund sponsor’s risk tolerance, long term expectations and liabilities to

fund ⎯ Benchmark portfolio returns ⎯ Fund returns, valuations and external cash flows

Conducting a macro attribution analysis ⎯ Net contributions ⎯ Riskless asset, which is usually 90‐day Treasury bills but for a pension fund might be a portfolio of

bonds that best hedges its liabilities ⎯ Asset Categories, rAC = Σwi(ri – rf)

− Most fund sponsors view riskless asset investment strategy as too risk averse and therefore overly expensive

− It would be entirely appropriate for a fund sponsor to stop at asset category investment strategy; an EMH proponent might view this all passive approach as most appropriate

− Difference in performance between investment styles can easily be in 15‐30% range; active managers cannot realistically hope to consistently add more than 2‐3%

⎯ Benchmarks − Assume fund is passively invested in aggregate of managers’ respective benchmarks − r = ΣΣwiwij(rBij – ri) where rBij is return for j

th manager’s benchmark in category i and ri is portfolio return on ith category;

− rBij – rCi is misfit return or style bias; expected value is 0 but it can be highly variable; some fund sponsors employ special risk control strategies to keep misfit risk within acceptable tolerances

− This effect should be relatively small unless manager style deviates significantly from asset category benchmark

⎯ Active investment manager – r = ΣΣwiwij(rAij – rBij) ⎯ Allocation effects

− If fund sponsor had invested in all asset categories and managers precisely at established policy allocations, this contribution would be zero

− However most fund sponsors deviate at least slightly, so this contribution becomes a reconciling factor between value calculated at end of last step and actual fund value

Micro attribution overview ⎯ Manager’s value added return is r = Σ (wPi – wBi) x (ri – rB) ⎯ Security by security analysis is unwieldy and typically provides little useful insight; large number of

securities in a well diversified portfolio makes impact of any individual security largely uninteresting ⎯ A more productive form of micro attribution involves allocating value added return to various

sources of systematic returns using a multi‐factor model ⎯ Sector weighting / Stock selection micro attribution

− Sector weighting value added return is r = ΣwPirPi ‐ ΣwBirBi


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− This attribution is buy‐and‐hold or holdings based; advantage is that only holdings and their returns need be input; disadvantage is that buy‐and‐hold return will not equal TWR

− Include a Trading & Other category for reconciling item; in actively managed accounts with high turnover this factor can be significant; when this is an issue transaction based attribution analysis can be used instead of holding based attribution analysis

− r = Σ(wPi‐wBi)(rBi‐rB) + ΣwBi(rPi‐rBi) + Σ(wPi‐wBi)(rPi‐rBi) • First term represents pure sector allocation • Second term represents pure selection within sectors • Third term represents allocation/selection interaction; this term is more difficult to

understand and often source of some confusion; in particular note that a decision to increase allocation to a particular security also adds to weight of sector to which security belongs

⎯ Factor model micro attribution – attributes manager value added return to four primary sources − Market timing − Exposure to firm fundamental factors; contrasted to “normal” benchmark exposure − Exposure to sectors; contrasted to “normal” benchmark exposure − Specific or unexplained return, attributed to manager

Fixed income attribution ⎯ Bonds are unlike stocks, so an approach that merely isolates allocation and selection effects among

bond market sectors will be of limited value in analyzing sources of return ⎯ Major determinants are general level of interest rates represented by Treasury curve and spreads

due to sector or credit quality ⎯ Effect of external interest environment effect

− Expected return implied from forward rates − Unexpected difference between actual realized return and return from forward rates

⎯ Effect of management process − Interest rate management – manager can modify interest rate risk profile to benefit from

expected advantageous movements or attenuate impact of expected adverse movements; price each security as if were default‐free and subtract return of Treasury universe; result indicates how well manager predicts interest rate changes; can be further broken down into duration, convexity and yield curve shape change

− Sector/Quality – price each security using average yield premium in its respective category and subtract external interest environment effect and interest rate management effect; measures manager’s ability to select “right” sector and quality

− Security selection – total return on securities minus all other components of return on securities; can compare return to average performance of its sector

− Trading activity – total return on portfolio minus all other components of return; captures effect of sales and purchases of bonds over period

Performance Appraisal Risk adjusted performance appraisal measures ⎯ Systematic risk is measured by beta; total risk is measured by return standard deviation ⎯ When evaluating managers many fund sponsors focus solely on level of value added returns

produced while ignoring value added return volatility; as a consequence superior managers may be terminated or not hired and inferior managers may be retained or hired on basis of statistically questionable performance data


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⎯ Four risk adjusted performance appraisal measures have become widely used − Ex post alpha or Jensen’s alpha – uses ex post CAPM SML as benchmark; ex post alpha can be

interpreted as differential return compared to expected return based on CAPM; (rP – rf) = α + β(rM – rf) + e; it is intercept of regression when portfolio excess return is plotted against market excess return

− Treynor ratio or reward‐to‐volatility T = (rport – rf) / β; equals slope of ex post SML when excess return is plotted against beta; represents excess return on non‐diversifiable risk; logically equivalent to ex post alpha since an account has positive ex post alpha iff it plots above ex post SML

− Sharpe ratio S = (E[rP] – rf) / σ; uses ex post CML as benchmark; can be viewed as a self‐financing strategy of borrowing at riskless rate and investing in account

− M2 has also received some acceptance, mean incremental return over market index of a hypothetical portfolio formed by combining actual portfolio with borrowing or lending at riskless rate to match standard deviation of market index; M2 = rf + (rP – rf)(σM/σP) = rP + Sharpe Ratio x (σM – σP); its use leads to decisions logically equivalent to those using Sharpe ratio; can be thought of as risk‐adjusted excess return

⎯ It is possible for Sharpe ratio and M2 to identify a manager as not skillful while Jensen’s alpha and Treynor ratio come to opposite conclusion; this outcome is most likely when manager takes on non‐systematic risk that is large relative to systematic risk

⎯ Information Ratio IR = (rP – RB) / σP‐B = active return / active risk ⎯ Criticisms of risk adjusted performance appraisal methods

− Reliance of ex post alpha and Treynor ratio on questionable validity of CAPM − Problems with use of surrogates such as S&P500 for true market portfolio − It is difficult in most cases for manager to replicate precisely benchmark return over time; in

particular transaction costs related to creating and rebalancing benchmark as well as costs and problems related to reinvesting income flows

− Lack of stability of parameters and estimation error Quality control charts plot annualized cumulative value added returns ⎯ Assumptions underlying quality control charts

− Null hypothesis is that manager has no skill ∋ expected value added return is zero and ex post returns differences have no directional biases and are entirely due to chance

− Manager value added returns are independent from period to period and normally distributed around expected value

− Manager’s investment process does not change from period to period ∋ variability of value added returns remains constant over time

⎯ Addressing multiple periods give funnel shaped confidence intervals on quality control charts since standard deviation decreases at rate of √T

Interpreting quality control chart – Quality control chart analysis provides a likely range of value added returns results for a manager who possesses no skill; for a manager whose investment results are within that range we have no strong statistical evidence to reject null hypothesis of no manager skill

Practice of Performance Evaluation Connection between past performance and future performance is tenuous at best; indiscriminate use of quantitative data can lead to counterproductive results; most fund sponsors incorporate both quantitative and qualitative elements with latter receiving more weight

Sponsors review six criteria for manager selection


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⎯ Physical – organizational structure, size, experience, other resources ⎯ People – investment professionals, compensation ⎯ Process – investment philosophy, style, decision making ⎯ Procedures – benchmarks, trading, quality control ⎯ Performance – results relative to appropriate benchmark ⎯ Price – investment management fees

Noisiness of performance data – past performance is not that related to future results; over typical evaluation periods (3‐5 years) odds that superior managers will underperform their benchmarks or inferior managers will outperform their benchmarks are disturbingly high; using historical performance as only criteria will generate high manager turnover

Manager Continuation Policy (MCP) ⎯ Purposes of a MCP

− Retain superior mangers; remove inferior managers preferably before they can produce adverse results

− Ensure relevant non‐performance information is given significant weight in evaluation process − Minimize manager turnover − Develop procedures that will be consistently applied regardless of investment committee and

staff changes ⎯ Manager monitoring – ongoing phase of MCP

− Goal is to identify warning signs of adverse changes in existing managers’ organizations − Information is divided into two parts: (1) operational matters such as personnel changes,

account growth, litigation, etc, and (2) manager investment strategies on both retrospective and prospective basis

⎯ Manager review – occasionally manager monitoring identifies an item of sufficient concern to trigger a manager review − Should view this as a zero‐based process, would we hire this manager again today? − What has fundamentally changed in manager’s operation? Is change significant? What are

likely ramifications of change? Are costs of firing manager outweighed by potential benefits? MCP as a filter ⎯ Grossman & Stiglitz (1980) and Sharpe (1994) suggest that zero and negative value added managers

must predominate, with former outnumbering latter ⎯ MCP can be viewed as a statistical filter to remove negative value added managers and retain

positive value added managers ⎯ Zero value added managers present a problem because they are so numerous and are statistically

difficult to distinguish from positive and negative value added managers ⎯ Errors

− Type I – rejecting null hypothesis when it is correct – keeping or hiring managers who are at best zero value added; a coarse filter will be conducive to these errors; this error also happens if manager has no skill but we reject null hypothesis because manager’s returns fall outside of confidence band on quality control chart

− Type II – not rejecting null hypothesis when it is incorrect – firing or not hiring managers with positive value added; a fine filter will be conducive to these errors; if manager is skillful but we fail to reject null hypothesis because manager’s returns fall inside confidence band on quality control chart


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⎯ Both types of errors are expensive; art of a MCP is to strike a cost‐effective balance between them that avoids excessive manager turnover yet eliminates managers likely to produce inferior performance in future

⎯ Due to high costs and uncertain benefits of replacing managers it would seem advisable to develop procedures that are tolerant of type I errors (keeping unskillful managers) in order to reduce probability of type II errors (firing a skillful manager); this can be managed by widening confidence band on quality control chart

Table of Contents Chapter 1: Overview........................................................................................................................................... 2 Chapter 10: U.S. Treasury and Agency Securities .............................................................................................. 4 Chapter 11: Municipal Bonds............................................................................................................................. 6 Chapter 12: Private Money Market Instruments............................................................................................... 8 Chapter 13: Corporate Bonds .......................................................................................................................... 10 Chapter 14: Medium Term Notes .................................................................................................................... 14 Chapter 15: Inflation Linked Bonds.................................................................................................................. 16 Chapter 16: Floating‐Rate Securities................................................................................................................ 19 Chapter 20: Emerging Market Debt ................................................................................................................. 21 Chapter 22: Overview of Mortgages and Mortgage Market ........................................................................... 24 Chapter 23: Agency MBSs ................................................................................................................................ 26 Chapter 24: CMOs ............................................................................................................................................ 29 Chapter 25: Non‐agency CMOs........................................................................................................................ 35 Chapter 26: Residential ABSs ........................................................................................................................... 38 Chapter 27: CMBSs........................................................................................................................................... 39 Chapter 30: Cash CDOs .................................................................................................................................... 41 Chapter 31: Synthetic CDOs ............................................................................................................................. 44 Chapter 44: Quantitative Management of Benchmarked Portfolios............................................................... 45 Chapter 47: Bond Immunization: An Asset/Liability Optimization Strategy.................................................... 51 Chapter 48: Dedicated Bond Portfolios ........................................................................................................... 53

APMV Syllabus Study Notes 2 Fixed Income Securities© 2008 Alberto Dominguez

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Chapter 1: Overview

Bonds Domestic bond market is $29.7T as of 12/31/2007; there are six types of domestic issuers ⎯ #1 – Federal government and its agencies (chapter 10) – 25% of market ⎯ #2 – Mortgage sector (chapters 22‐25) – 24% of market ⎯ #3 – Domestic corporations (chapter 13) – 20% of market ⎯ #4 – Money market (chapter 12) – 14% of market ⎯ #5 – Municipal governments (chapter 11) – 9% of market ⎯ #6 – ABSs – 8% of market ⎯ Foreign governments and firms also issue bonds in US, but not as large as domestic issuers

Maturity – money market (up to 1 year), short term (up to 5 years), intermediate term (5‐12 years), long term (12+ years); maturity is critical because it indicates expected life and affects yield and volatility

Coupon – higher coupon bonds have lower volatility Put provisions ⎯ Poison puts – included in corporate bonds to deter unfriendly takeovers ⎯ Hard puts must be redeemed for cash; soft puts which can be redeemed for cash, common stock or

another debt instrument are often found in convertible debt Convertible or Exchangeable debt ⎯ Allow investor to convert bond for a specified number (conversion ratio) of shares of stock ⎯ Typically callable which effectively permits issuer to force conversion ⎯ Some issues have protection: (1) issuer is not allowed to call before a specified date, or (2) issuer is

not allowed to call until stock price has increased a specified percent above conversion price at issuance

⎯ Exchangeable bonds can be exchanged from common stock of a firm other than issuer ⎯ Liquid Yield Option Note (Merrill Lynch 1985) is a convertible, callable, putable zero

MTNs (chapter 14) Structured notes are debt instruments linked to a derivative position Warrants permit owner to buy a certain number of shares of common stock at specified price which may change over time, sometimes issued with new bonds, with rather a long life (2 years+) compared to options; detachable warrants are often traded on AMEX

Preferred Stock Cumulative (missing dividend payments accrue until paid) vs non‐cumulative; failure to pay preferred dividends does not cause bankruptcy but may impose certain restrictions such as granting voting rights; priority over common stock in bankruptcy

Fixed rate vs adjustable rate (reset quarterly based on spread from highest of three points on Treasury curve, usually perpetual) vs auction (dividend reset periodically through auction process) vs remarketed (dividend rate determined periodically so stock can be tendered at par and resold at original offering price, resets either every 7 days or every 49 days)

70% of dividends are tax exempt if recipient is a corporation Perpetual preferred stock is issued without a maturity date Almost all preferred stock has a sinking fund provision Some preferred stock is convertible to common stock, sometimes conversion is mandatory at maturity


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Historically utilities have been major issuers making up more than half of each year’s issuance; since 1985 financials have been major issuers

Residential MBSs Mortgage pass‐through securities (chapter 23) CMOs (chapters 24 and 25) Stripped MBSs ⎯ Introduced by Fannie Mae in 1986 ⎯ Alter distribution of principal and interest from pro rata to unequal distribution ⎯ Risk/return characteristics make them attractive for hedging pass‐throughs and mortgages ⎯ Synthetic coupon pass‐throughs result in coupon rate different from underlying collateral ⎯ IOs, POs introduced in 1987

Commercial MBSs (CMBSs, chapter 27)

ABSs Generally backed by home equity loans (chapter 26), credit card receivables or automobile loans/leases Can be CDOs (chapters 30 and 31) or straight pass‐throughs There are also pools of manufactured home loans, SBA loans, student loans, boat loans, equipment leases, RV loans, senior bank loans, healthcare receivables


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Chapter 10: U.S. Treasury and Agency Securities

Treasury Securities $3.7T in marketable Treasuries as of 3/31/2004 Treasury bills have maturities less than 1 year and are issued as discount securities, 27% of market Treasury notes are issued with maturities of 2, 3, 5, 10 years; 54% of market Treasury bonds are issued with maturities of 30 years1; 20 and 30 year bonds constitute 15% of market TIPS, 5% of market Treasury has not issued callable securities since 1984, but some outstanding issues are callable

Zero Coupon Treasury Securities Treasury does not issue them; they are created through coupon stripping Enable close matching of liabilities to Treasury cash flows, popular with pensions and insurers STRIPS introduced in 1985 allows components to be held separately in Fed’s entry system As of 3/31/2004 $177B was held in stripped form

Agency Securities Securities ⎯ Typically not backed by full faith and credit of US government, but considered very low risk ⎯ Government National Mortgage Association (Ginnie Mae) is part of HUD Department and is fully

guaranteed; $457B outstanding as of 6/30/2004 ⎯ Short term discount notes, medium term coupon notes ⎯ Fixed or floating, can be callable, indexed, and even foreign denominated ⎯ Late 1990s Fannie Mae’s Benchmark Notes and Freddie Mac’s Reference Notes are intended to

produce a yield curve for liquid agency securities Primary Market ⎯ Allocation to dealers, competitive dealer bidding, direct sales, sales through dealers ⎯ In 2003, agencies issued $9.2T in short term debt and $1.3T in long term debt ⎯ As of 9/30/2003 outstanding debt was $2.7T, 92% from FNMA, FHLMC and FHLB

Secondary Market – OTC, volume is significantly lower than Treasuries but still reasonably high, averaging $78B a day

Issuing Agencies Housing ⎯ Federal National Mortgage Association (Fannie Mae) – provides liquid secondary market for home

mortgages – $1.6T outstanding as of 12/31/20052 ⎯ Federal Home Loan Mortgage Corporation (Freddie Mac) – $1.21T outstanding as of 12/31/20043 ⎯ Federal Home Loan Bank System – GSE established in 1932 – $719B outstanding as of 6/30/2004

Agriculture ⎯ Farm Credit System – GSE established in 1916 – $90B outstanding

1 Text says 30 year bonds are not issued, but they were reintroduced in 2006 after text was published 2 Chapter 23 contradicts this claiming $1.88T as of 6/30/2004, but this figure is from Fannie Mae’s annual report 3 Chapter 10 contradicts this claiming $774B as of 9/30/2003, but this figure is from Freddie Mac’s annual report


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⎯ Farm Credit System Financial Assistance Corporation – GSE established in 1988 but fully guaranteed – $1.3B outstanding

⎯ Federal Agricultural Mortgage Corporation (Farmer Mac) – corporation chartered in 1988, provides liquid secondary market for farm and rural home mortgages – $3.8B outstanding

S&L ⎯ Financing Corporation – GSE established in 1987 – $8.2B outstanding ⎯ Resolution Funding Corporation – GSE established in 1989 – $30B outstanding

Student Loan Marketing Association (Sallie Mae) – corporation chartered in 1972 – $54B outstanding Tennessee Valley Authority – Government owned corporation in 1933 – $27B outstanding


6

Chapter 11: Municipal Bonds

Introduction $1.8T as of 1/1/2004, 60K distinct issuers and 1.4M individual issues Primary owners are individual investors and mutual funds (72%); banks have dropped their percentage holdings since TRA86

In past considered second in safety only to Treasuries; however there have now developed ongoing concerns about credit risk ⎯ NYC financial crisis of 1975, bankruptcy of Orange County in 1994 ⎯ Federal bankruptcy law 1979 makes it easier for municipal issuers to seek protection ⎯ Proliferation of “innovative” financing techniques and legally untested securities, highlighted by

default of Washington Public Power Supply System in early 1980s ⎯ Cutbacks in federal grant and aid programs ⎯ Fundamental changes in US economy

Features of municipal securities Coupon features ⎯ For floaters reference rates that have been used include JJK Municipal Index, LIBOR, BMA Rate,

Treasury bills ⎯ Some municipals are inverse floaters; some are Original Issue Discounts; some state a coupon rate

but interest is accrued and paid only at maturity Maturity date – municipal issuers frequently schedule their bonds as serial bonds to mature over many years; after last of serial maturities some issues lump together remaining debt as term bonds maturing at one or two date; term bonds have become increasingly popular because active secondary markets can develop if issue is of sufficient size

Legal opinion ⎯ Bond counsel should check

− Issuer is legally able to issue bonds − Issuer has properly prepared bond sale by enacting ordinances, resolutions and indentures and

without violating any other laws or regulations − Security safeguards and remedies are supported by laws and regulations

⎯ Popular notion is that legal work is boilerplate in nature, but if all else fails bondholder may have to go to court so integrity and competence of counsel are very important

Types of municipal obligations General obligation bonds ⎯ Issued by states and counties, secured by issuer’s unlimited taxing power although some smaller

jurisdictions can use only property tax ⎯ Double barreled bonds are secured by general taxing power as well as certain identified revenues ⎯ Limited tax general obligation bonds are limited as to revenue sources and/or tax rates

Revenue bonds – backed by revenue generated from specific project ⎯ Airport and seaport – traffic‐generated sources and lease revenues ⎯ College and university – tuition and fees ⎯ Hospital – government reimbursement, insurance, patient payments


7

⎯ Single‐family mortgage – FHA, VA ⎯ Multi‐family for seniors and low income – federal subsidies ⎯ Industrial development and pollution control ⎯ Public power ⎯ Resource recovery – disposal fees, revenues from fuel sold, scrap revenues ⎯ Sewer and water ⎯ Sports complex and convention center – event revenue, hotel room taxes ⎯ Toll road and gas tax

Valuation methods In traditional valuation method investor determines relative attractiveness of bonds based on yield to worst

Equivalent taxable yield = Tax exempt yield / (1 – marginal tax rate) ⎯ Drawback with this formula relates to assumption that coupon is reinvested at same rate ⎯ Formula will not work for bond selling at premium or discount because only coupon payments are

tax exempt Traditional valuation method leaves much to be desired; basic problem is that with yield to maturity or yield to worst call risk is not analyzed properly; interest rates can change and actual timing may not be same as what was projected; most callable bonds are priced too richly and most non‐callable bonds too cheaply, especially for longer dated bonds


8

Chapter 12: Private Money Market Instruments

Commercial Paper (CP) General considerations ⎯ $1.3T as of April 2001 ⎯ CP is short‐term unsecured notes issued as alternative to bank borrowing ⎯ Used for seasonal and working capital needs and as bridge financing ⎯ Maturity is less than 270 days to avoid SEC security registration rules, most common maturity is 45

days; to be eligible collateral to borrow from Fed maturity may not exceed 90 days ⎯ Most issuers maintain 100% backing of paper because rating agencies require backup bank line of

credit to reduce rollover risk as a precondition for a rating ⎯ Most investors are institutional, 1/3 are money market mutual funds

Issuers ⎯ Financial firms issued 78% of all CP

− Captive finance companies – GMAC is largest issuer of CP in US − Bank‐related finance companies − Independent finance companies

⎯ In recent years lower credit rated corporations have issued CP by obtaining credit support or enhancement (credit‐supported CP, line‐of‐credit CP) or collateralizing (asset‐backed CP)

Directly placed vs Dealer placed Secondary market is small since typical investor plans to hold until maturity; dealer or issuer will often repurchase security

Yields track other money market instruments, about 14 bp higher than three‐month Treasuries ⎯ Credit risk ⎯ Treasuries are tax exempt ⎯ Less liquid

Bankers acceptances Created to facilitate commercial trade: (1) importing of goods into US, (2) exporting of goods to foreign countries, (3) storing and shipping of goods between two foreign countries, and (4) storing and shipping of good between two entities in US; have declined in importance in recent years in favor of other forms of financing

Bankers acceptances that do not exceed six months may be eligible as collateral at Fed Bank charges customers for issuing a bankers acceptance by (1) calculating discount spread at which it will have to sell acceptance, (2) commission, (3) for acceptances ineligible to be collateral to borrow from Fed an offset reserve amount is added

Bankers acceptances are sold in open market on discounted basis like Treasuries and CP; there is some credit risk so yield is higher than on Treasuries

Negotiable CDs General considerations – Large denomination (> $100K) negotiable CDs were introduced in early 1960s; at that time bank interest rates were capped so this innovation helped banks increase amount of funds raised (Small denomination negotiable CDs were introduced by Merrill Lynch in 1982)

Investment companies are largest buyers Issuers


9

⎯ Domestic banks ⎯ Thrifts ⎯ CDs denominated in US$ but issued outside US (Eurodollar CDs or Euro CDs) ⎯ CDs denominated in US$ but issued by foreign bank with branch in US (Yankee CDs)

Yields ⎯ Yields depend on several factors

− Credit rating of issuing bank – at one time CDs issued by money center banks traded on a non‐name basis; recent financial crises have caused investor to take a closer look; prime CDs trade at a lower yield than non‐prime CDs

− Because of unfamiliarity of foreign banks generally Yankee CDs trade at a higher yield than domestic CDs

− Maturity, depending on yield curve − Supply, driven by demand for bank loans, and demand

⎯ Euro CDs offer higher yield than domestic CDs; since 1990s liquidity of Euro CDs has increased dramatically and perception of higher risk has decreased considerably; as of October 2003 spread was 2 bp − Fed reserve requirements do not apply to issuers of Euro CDs − Domestic bank must pay FDIC insurance premium − Euro CDs expose holders to sovereign risk

⎯ As of October 2003 spread over Treasuries of same maturities was around 8 bp, due to credit risk and less liquidity

⎯ At one time there were more than 30 dealers; today fewer dealers are interested and market can be characterized as illiquid

Repurchase agreements A repurchase agreement is sale of a security with commitment by seller to buy it back from purchaser at a specified price at a specified future date; basically it is a collateralized loan

Open maturity repos give both counterparties option to terminate repo each day; this reduces settlement costs if counterparties choose to continuously roll over overnight repos

Dollar Interest = Dollar Principal x Repo Rate x Repo Term / 360

Federal funds Banks with less than required Fed reserves borrow from banks with excess reserves, typically overnight; spread from repo rate is approximately 25 bp since loan is unsecured


10

Chapter 13: Corporate Bonds

Corporate Trustee Indenture is made out to corporate trustee who acts as fiduciary for bondholders; Trust Indenture Act requires that all bond offerings of more than $5M use a corporate trustee ⎯ Protects bondholders but can only enforce what is in debenture ⎯ Trustee must authenticate bonds and make sure issuer meets all requirements of indenture over

life of bond ⎯ Trustee is paid by bond issuer, but must avoid conflicts of interest

Registered bond certificate is on its way out as more bonds are sold in book‐entry form

Bond Fundamentals Issuer type ⎯ Public utilities – telecom, electricity, gas, water ⎯ Transportations – airlines, railroads, trucking ⎯ Industrials – manufacturing, mining, retailers, service ⎯ Bank and finance companies ⎯ International issuers – supra‐nationals, sovereign issuers, foreign municipalities & agencies

Maturity – Usually less than 30 years; 100‐year bonds making comeback since 1993 when Walt Disney offered first 100‐year bond issued since 1937

Interest payment characteristics ⎯ Semiannual coupons are norm in US; annual coupons are norm in Europe ⎯ A few bonds pay principal and interest in a foreign currency ⎯ Participating bonds share in profits of issuer or rise in certain assets above minimum levels ⎯ Income bonds omit or delay coupons if firm’s earnings are too low; interest may be cumulative or

non‐cumulative; mostly issued by railroads, rare today ⎯ Zero coupon bonds eliminate reinvestment risk but increase credit risk, first issued in 1981; now tax

benefits are not as great so not as popular ⎯ Deferrable bonds, popular in 1990s, subordinated bonds that give issuer option to defer coupon in

event of financial distress; there are three types − Deferred Interest Bonds, generally subordinated issues of speculative grade issuers structured ∋

they don’t pay interest for first 3‐7 years − Step up bonds with coupon rates that increases over time − Payment In Kind bonds – issuer pays out interest in additional pieces of security for first 5‐10

years ⎯ Extendible reset bonds reset coupon rate so bond will trade at a predetermined price, either

annually or once over their term, introduced in 1987 − Coupon will be average of rates suggested by two investment banks − New rate will reflect level of interest rates and credit spread market wants on issue − Experience has not been favorable during periods of difficulties in high yield market

⎯ Ratchets bonds have coupon rates that reset (up or down) periodically over their term ⎯ Range notes are floaters as long as reference rate is within a certain range, and if reference rate is

outside range coupon rate is 0


11

Security Mortgage bonds ⎯ Grants bondholders a first mortgage lien to specified property, hence lower interest rate; if

property sold other property must be substituted ⎯ A blanket mortgage allows company to issue a series of bonds under one mortgage and indenture ⎯ It is common for a first mortgage bond indenture to have an after acquired clause specifying that

property acquired subsequent to granting lien shall be subject to lien as well; indenture usually permits issue of additional bonds up to some specified percent of value of property acquired

⎯ Another customary requirement is that earnings in immediately preceding period must equal some multiple of annual interest on all bonds including proposed additional bonds

⎯ Second mortgages are euphemistically called first and consolidated, first and refunding, general and refunding

Collateral trust bonds ⎯ Companies without fixed assets such as holding companies pledge stocks or bonds as collateral;

collateral market value must be at least a minimum percentage of bond value; collateral can usually be substituted

⎯ Indentures usually provide that in event of default voting rights are transferred to trustee ⎯ Sale of collateral to pay bonds is a drastic measure that is seldom used

Equipment trust certificates – developed by railroads to get low interest ⎯ Legal claim is generally better than a mortgage lien; legal title to railway equipment is vested in

trustee who leases it to railroad; manufacturer is paid off by proceeds from equipment trust certificates plus railroad’s initial rent payment

⎯ Lease payments are used by trustee to pay interest and principal; once certificates are paid off, trustee sells equipment to railroad for nominal price

⎯ Usually structured in serial form ∋ certificates amortize to match equipment depreciation ⎯ Railroads have always paid since they need equipment

Debenture bonds – unsecured bonds, most bonds sold this way except utilities ⎯ Debenture holders have same right as general creditors; it is customary to have a negative pledge

clause which provides that debentures will be secured equally with any bonds that may be issued in future

⎯ Common restrictions are minimum working capital of not less than amount of debentures outstanding or limiting proportion of current earnings that may be used to pay dividends

⎯ Trend in recent years at least with investment grade companies is away from debenture restrictions Subordinated debentures rank after secured debt and debenture bonds; often inducement is convertible or exchangeable feature

Guaranteed bonds – Sometimes a corporation may guarantee bonds of another corporation

Alternative mechanisms to retire debt before maturity Call and Refunding provisions ⎯ Call features permit borrower to retire some or all of bond (generally at a premium) and replace it

with lower‐interest bond if rates fall; it may also help escape restriction about disposition of collateral; some firms will retire debt to alter their capital structure or improve financial/managerial flexibility

⎯ Bad for investors because (1) they must reinvest money in lower interest rate securities and (2) it limits appreciation on bond value; hence typically have higher yields


12

⎯ A period of call protection for a specified number of years in early life of bond may be offered: (1) bond are non‐callable for any reason, called a bullet bond, (2) bond is non‐refundable but can be called with internal cash flow or non‐debt financing

⎯ Municipal bonds can be pre‐funded by placing riskless securities in a trust to fund all cash flows on bond issue

⎯ Fixed Price Call Provision – Indenture contains call price schedule that specifies when bonds can be called and at what prices, often call prices start at a substantial premium and decline toward par over time

⎯ Make Whole Call Provision, introduced in 1995, growing in popularity − Investor will not demand as much of a yield increase due to call provision, so currently most

popular type of call feature − Make whole call price is PV of bond’s remaining cash flows with floor price of par, so call price

moves inversely with interest rates − Discount rate is yield on CMT or comparable maturity Treasury plus a make‐whole call premium − Issuer will call if PV of interest savings is greater than call premium and cost to issue new

securities Sinking Fund provisions ⎯ May be designed to liquidate entire issue or only a part by end of term; common in private

placements ⎯ Firm will purchase in open market if price is below call/par or make payment to trustee who will call

bonds at call/par price by lottery; a few indentures prohibit open market purchase ⎯ Issuer is granted a special call price; usually this is par if bonds were originally sold at par, or if

originally sold above par then a sliding scale down to par ⎯ Advantages from investor’s perspective: (1) orderly retirement of debt and less risk of default, (2)

enhances liquidity, (3) prices are presumably more stable even if interest rates rise since issuer may become active participant

⎯ Disadvantage to investor is that bond may be called at a time when rates are lower ⎯ Sometimes there is an optional acceleration feature where firm is free to retire more than sinking

fund requirement ⎯ Many utility bond issues can satisfy requirement by utility certifying that it has made additions to its

property and plant in required amount, normally $1,667 of plant per $1,000 of sinking fund requirement

⎯ Usually periodic payments are same; gas companies often have increasing requirements; some indentures permit variable payments, most common condition is level of earnings

⎯ Industrial issues almost always include sinking fund requirement, finance companies almost never do

⎯ May be a non‐specific sinking fund that applies to all debt outstanding Maintenance & Replacement funds, most common with old utility issues ⎯ Original motivation is that replacement fund ostensibly helps maintain integrity of property

securing bonds ⎯ M&R fund requires firm to fund difference between a specified percentage of gross revenues and

what is actually expended on maintenance; in some cases this excess fund could be used for retirement of debt

⎯ Many investors thought calls of this type were unlikely but were wrong (trust funds escalated when revenues shot up due to increasing fuel prices); read contract carefully to see when issuer may retire debt early


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Redemption through sale of assets and other means ⎯ Release of property (can retire debt if collateral is sold) and substitution of property clauses are

found in most debentures; some clauses stipulate if government takes over asset (common in utilities) bonds must be redeemed

⎯ Bondholders don’t want collateral sold and proceeds distributed to stockholders ⎯ Texas New Mexico Power Company was successfully sued in 1997 for using a release of property

clause to redeem bonds before first call date Clawback – in 1992 some speculative bonds started to appear with provisions granting issuer limited grant to redeem all or a portion of bonds during non‐call period (usually just first three years) if proceeds are from an IPO, with redemption price usually 110% of par

Tender offers – Recently tender offers have been executed using a fixed spread as opposed to fixed price; tender offer price is PV of remaining cash flows using Treasury plus fixed spread; do not need to be included in bond’s debenture

High yield bonds Types of issuers ⎯ Original issuers

− Young growing concerns without strong balance sheet or income statement − Established firms neither measuring up to strength of investment grade corporations nor

possessing weakness of companies on verge of bankruptcy − Debt is often sold with story projecting future financial strength, hence term story bond − Bonds from bottom of investment category (BBB) or top end of speculative category (BB) are

referred to as a businessman’s risk ⎯ Fallen angels – companies with investment grade rated debt that have come on hard times;

investors may be interested in workout value of debt in reorganization or liquidation ⎯ Restructurings and Leveraged Buy Outs

Return experience ⎯ Volatility of high yield bonds is 8.58% vs 7.23% for investment grade bonds ⎯ Average annual return is actually lower, 6.36% vs 8.13% for investment grade bonds, largely

attributable to massive underperformance during 2000‐2002 Some issues have special features (as discussed elsewhere)

Default rates Default rates can be measured per issuer or per total value of all bonds outstanding 2.15‐2.40% of speculative grade issuers default annually A majority of studies place annual dollar default rate at 3‐4%

Recovery rates Moody’s found that recovery rate for all bonds is 38%, with higher seniority bonds having a greater recovery rate


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Chapter 14: Medium Term Notes

Introduction Medium Term Notes (MTNs) are non‐callable unsecured senior debt securities with an investment grade rating and term from 9 months to 30 years, most commonly 1‐5 years

History ⎯ Established in early 1970s as an alternative to short term CP market and long term bond market ⎯ In 1980s grew from obscure niche market ($800M) to major market for large companies ⎯ In 1990s continued to attract new borrowers and has grown at phenomenal rate

Differ from other bonds in their primary distribution process, sold on best‐efforts basis by investment banks and other broker‐dealers

Although originally fixed, many MTNs are now issued with floating interest rates or rates that are computed according to formulas tied to equity or commodity prices

Often include calls or puts; many issues involve simultaneous derivative transactions

Economics of MTNs Offering size, liquidity, price discrimination ⎯ For large standard financings (e.g., $300M 10‐year) cost of underwritten corporate bonds may be

lower than MTNs − Economies of scale in bond market − Liquidity premium in MTN market, but it has narrowed in recent years to 5‐10 bp

⎯ Because debt does not have to be priced for marginal buyer (firm can increase its MTN offering rate or issue at a different maturity for some buyers) financing costs can be lower with MTNs

Flexibility of MTNs ⎯ Because of fixed costs in bond market, offerings below $100M are impractical; also offerings of

straight bonds are clustered at certain maturities; these features prevent matching of assets and liabilities

⎯ By contrast draw‐downs from MTN programs typically amount to $30M and have different maturities and special features tailored to needs of borrower; flexibility allows firm to match assets and liabilities

⎯ Firm can average out its cost of funds by issuing continually rather than coming to market on a single day and risk financing at high point

⎯ Also allows borrowers to raise a sizable amount of debt in extremely short time − Bond shelf registrations take longer due to arrangement of syndicate, negotiation of agreement,

pre‐selling to investors − Some corporations require that underwriting receive prior approval of CEO or board, but

treasurer may finance with MTNs at discretion without delay Discreet funding ⎯ Bond underwriting results in a lot of information to investment community; in MTN market only

issuer, investor and agent have to know about transaction ⎯ Firms often avoid bond market in periods of heightened uncertainty about interest rates and course

of economy; underwritings at such time could send a distress signal ⎯ Firms in distressed industries can use MTN market to avoid risk of negative publicity in high profile

bond market Reverse inquiry


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⎯ Investors often play an active role in issuance process through reverse inquiry; investor who desires to purchase specific debt can relay an inquiry to an issuer through its agent

⎯ Often include embedded options and pay interest using unusual formulas ⎯ If issuer finds terms sufficiently attractive it may agree to transaction even if it was not originally

posting rates

Structured MTNs In a structured MTN a firm issues an MTN and simultaneously enters one or several swap agreements to transform cash flows that it is obligated to make; simplest involves a plain vanilla interest rate swap

Issuers may be able to borrow at a lower rate than it would pay on a fixed rate note; issuers participate when they can reduce borrowing costs by 10‐15 bp; for complicated structured transactions most issuers require greater compensation

Many structured transactions originate with investors through a reverse inquiry; investor may want specific risk characteristics that are not available but is prohibited from creating synthetic security; through reverse inquiry investor can obtain a custom‐tailored security; issuer creates customized MTN and then uses swaps to unwind undesired features

Example is 1991 inverse floaters that paid 12% minus LIBOR; at time of transaction issuer usually entered into a swap to eliminate exposure

Investment banks also identify market opportunities, informs investors to propose they purchase specialized securities, and contacts MTN issuer with proposed structured transaction

Most investors require that issuers of structured MTNs have AAA or AA credit ratings; consequently federal agencies and supra‐naturals issue a large share of structured MTNs; in recent years some investors have become more willing to purchase from A credit ratings in exchange for a higher yield

Structured MTNs account for 20‐30% of market; issuers build flexibility into documentation which makes them able to reduce borrowing costs by responding quickly to temporary opportunities

Wide variety of structured MTNs that pay interest or principal according to unusual formulas ⎯ Floating rates; many MTNs include caps and/or floors ⎯ Step ups ⎯ LIBOR differential notes which pay interest tied to spread between LIBOR in two currencies ⎯ Dual currency MTNs that pay interest in one currency and principal in another ⎯ Equity linked MTNs ⎯ Commodity linked MTNs

Euro MTNs Major underwriters and dealers are located in London Issuers with Euro‐MTN programs have great flexibility in size, currency and structure of offerings Characteristics of Euro‐MTNs are similar but not identical to MTNs ⎯ Ratings of Euro‐MTNs tend to be higher ⎯ Offerings with maturities longer than 10 years are less common in Euro market ⎯ Euro market is less liquid ⎯ Euro market is more diverse both in terms of issuers and investors, but is not as deep ⎯ Structured MTNs account for 50‐60% of Euro market, often involving currency swaps


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Chapter 15: Inflation Linked Bonds

Introduction Inflation Linked Bonds (ILBs) repay principal in amount of original investment adjusted by NSA CPI‐U, coupons are calculated based on adjusted principal amount

US TIPS launched in 1997, as of 4/30/2004 $212B outstanding Since 1940s at least 15 governments and numerous corporations have issued ILBs In UK account for 20% government bonds outstanding, as of 4/30/2004 $152B TIPS are highly correlated with each other and not very correlated with other asset classes

Mechanics and Measurement How TIPS work ⎯ Example: May’s CPI increase is reported around June 15 and incorporated intro TIPS accruals

beginning July 1 and ending July 31 ⎯ For settlement dates other than first of month, use linear interpolation

Real vs nominal frame of reference ideally would be dictated by one’s goals but in practice choice is dictated by characteristics of instrument; TIPS are more easily described in real terms

Real yield ⎯ Real yield of a TIPS is calculated in standard way using quoted market price, coupon and maturity ⎯ Real yield of a nominal bond can only be precisely determined in hindsight; in practice when

analysts speak of a nominal bond’s real yield they are really referring to one of following − Current real yield approximated based on most recent year‐over‐year inflation − Guesstimating expected real yield based on expectations of future inflation − Historical realized real yields on bonds that have matured

Nominal yield ⎯ Nominal yield of a conventional bond is determined directly ⎯ Nominal yield of TIPS depends on trajectory of inflation over bond’s lifetime ⎯ TIPS realized nominal yield ≈ (1 + real yield) x (1 + average inflation) – 1

Nominal yields vs Real yields ⎯ Correlation of real yields with nominal yields historically has tended to be quite low ⎯ Real yields tend to be significantly less volatile than nominal yields ⎯ Recently this has not been case perhaps due to high confidence in Fed’s ability to successfully

perpetually target a stable inflation rate of 2‐3%; correlations have been high and TIPS yield has been almost as or more volatile than nominal yield; history will judge how rational this turns out to be

Break Even Inflation Rate (BEIR) – holder of TIPS breaks even with holder of nominal bond ⎯ BEIR = [(1 + nominal yield) / (1 + TIPS real yield)] – 1 ⎯ For most purposes approximating BEIR as difference between two yields is good enough and is

industry practice ⎯ Fall 1998 was marked by a significant deflationary scare; an astute investor might have construed

dramatic decline of BEIR to below 1% as an opportunity ⎯ BEIR may be useful to assess market inflation expectations or to gauge requirements for narrowly

constrained investors, it generally overstates risk‐adjusted break‐even inflation for long‐term strategies; in particular conventional bonds already embody an inflation risk premium of 0.5‐1.0%; at least part of such premium should not be embedded in TIPS


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⎯ Citing tremendous supply and illiquidity of TIPS and substantial exposure to changes in real interest rates Lucas & Quek suggest that part or all of inflation risk premium may be offset

Real duration ⎯ Real duration is percentage change in market value per 1% change in real yield ⎯ D = 100 x [MVyield‐50bp – MVyield+50bp] / MVyield ⎯ This does not quantify exposure to changes in nominal yields

Effective duration ⎯ Since calculation must infer a real yield change from given nominal yield change, measure is

statistical rather than deterministic ⎯ Initially managers concluded that risk exposure of TIPS could not be managed within conventional

fixed income portfolio, but it was soon realized that in 1980s MBSs overcame similar problems ⎯ Crude metric for converting TIPS real duration into effective duration is to apply a 75%

multiplicative factor; should be used only as a loose metric because substantial basis risk remains ⎯ Occasionally nominal yields fall and real yields rise, negative effective durations ⎯ Conversely occasionally nominal yields rise and real yield rise even more, meaning TIPS experience

capital losses greater than ex ante effective durations predicted Relative volatility is ratio of TIPS volatility to volatility of similar nominal bond

Valuation and performance dynamics Over long term real yields in US should remain at levels below 2%, historically even this is high Taylor rule argues that over long term real fed funds rate should average same as long term growth rate of economy which is about 2%

Investors Tactical uses ⎯ Speculate on changes in inflation and interest rates ⎯ May make relative valuation assessment compared to other debt instruments with similar credit,

effective duration and liquidity; must diligently manage tracking risk ⎯ International ILB market is larger than US, so tactical opportunities exist to exploit currencies,

monetary policies, and other local phenomena; credit profile of issuing country is important; also a country that issues a lot of ILBs will likely drive yield up

Strategic uses ⎯ High real yield and muted volatility, low correlation to traditional financial assets ⎯ Those looking for higher returns without increased risk may investigate moving out of cash ⎯ Those looking to preserve past gains might consider moving out of equities or real estate ⎯ ALM – TIPS give managers opportunity to manage both assets and liabilities that are predominantly

real; can focus on surplus management ⎯ Risk/Return – historical ILB return, variance, correlations can be inputted in standard Markowitz

mean‐variance optimization ⎯ Managing dedicated ILB portfolios

− First choose a target real duration − Then devise a variety of candidate portfolio structures (bullet, barbell, etc) − Select appropriate structure based on its exposure to changes in yield curve slope

Investor types


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⎯ DB plans – ILBs match active lives liabilities extremely well but plan sponsors typically do not rely on them exclusively for backing these liabilities; plans may also use ILBs to protect a surplus, offset equity risk exposure or reduce variability of annual funding

⎯ Endowments and foundations typically require 5% real return to meet IRS requirements; ILBs will not typically achieve this in isolation but they go a long way toward engineering out much downside risk; however right now they use ILBs only at margin

⎯ Individuals in late 40s or older seeking to protect financial assets from inflation


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Chapter 16: Floating‐Rate Securities

General Features and Major Product Types Introduced in early 1970s Adjustable or variable (as opposed to floating) refers to securities that reset not more than annually or based on a long term interest rate, but distinction is without substance

Reference rates ⎯ Usually depend on money market rate (LIBOR, Treasury, prime, fed funds, CDs, CP) but can depend

on a wide variety of economic variable indices (equity, currency, commodity, inflation) ⎯ For ARMs or CMOs floater reference rates include one‐year Constant Maturity Treasury or six‐

month LIBOR, as well as less popular 11th District Cost Of Funds Index and National monthly median cost of funds index

⎯ For municipals reference could be JJ Kenney index, Bond Buyer 40 index, Merrill Lynch Muni index May have a maximum and/or minimum coupon rate Inverse floaters have formulas Coupon Rate = K – L x Reference Rate where L is coupon leverage; inverse floaters can be created by acquiring a fixed rate security and using it as collateral to create a floater and an inverse floater

Stepped spread floaters provide for a change in quoted margin at certain intervals A range note is a floater where coupon payment depends on number of days specified reference rate stays within pre‐established collar

Dual index floaters depend on more than one reference rate, e.g. Federal Home Loan Bank issued a floater with Coupon Rate = 10 Year CMT – 6 Month LIBOR + 4%

Floaters may be callable and/or putable just like fixed‐rate issues – exercised when either market interest rates or required margin moves in favorable direction

Spread Measures Spread for life (aka simple margin) accounts for accretion (amortization) of discount (premium) as well as constant index spread over security’s remaining life

Adjusted simple margin or effective margin adjusts spread for life for one‐time cost‐of‐carry effect when floater is purchased with borrowed funds from settlement date to next coupon reset date

Adjusted total margin adds interest on difference between floater’s par price and carry‐adjusted price Discount margin indicates average spread investor can expect over security’s life given a particular assumed path that reference rate will take to maturity; assumption that future levels of reference rate are equal to today’s level is current market convention ⎯ Determine cash flows assuming reference rate does not change over security’s life ⎯ Select margin ⎯ Discount cash flows by current value of reference rate plus margin ⎯ Compare PV with price; if not equal adjust selected margin and discount again

Really should use MC and account for embedded options

Price Volatility Characteristics Since a floater’s coupon resets periodically its sensitivity to interest rate changes is reduced; floaters are more defensive than fixed bonds

Factors that affect a floater’s price


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⎯ Time remaining to next coupon reset date – floater behaves more like a fixed rate security with larger fluctuation as time to next coupon reset date is longer

⎯ Changes in market’s required margin – if market requires a higher/lower margin than at issue floater’s price will decrease/increase; required margin depends on several factors − Margin available in competitive funding markets − Credit quality of issue; credit spreads required of issuer, sector or whole market − Presence of embedded call or put − Liquidity

⎯ Whether or not cap or floor is reached – if cap (floor) is reached floater behaves more like a fixed rate security as capped (floored) rate is further below (above) prevailing market rate and value will decrease (increase)

Duration ⎯ Index duration measures sensitivity to changes in reference rates holding margin constant ⎯ Spread duration measures sensitivity to changes in margin holding reference rates constant

Price volatility of inverse floaters ⎯ Combined change in value of floater and inverse floater must equal change in equivalent collateral ⎯ Since duration of floater is small duration of inverse floater must be a multiple of collateral ⎯ Effectively inverse floater is a leveraged position in collateral

Portfolio Strategies Basic ALM – institutions can try to lock in a spread over their short term funding by investing in floating rate products; this strategy is not without risks ⎯ Cap risk – floater’s coupon rate likely will be capped whereas short term funding may not ⎯ Basis risk – floater’s reference rate may not be same as funding reference rate

Risk arbitrage such as borrowing through repos to invest in agency securities that earn a higher spread over their borrowing rate; of course this is not risk free arbitrage ⎯ Cap risk, basis risk ⎯ Price risk if floater’s risk changes for worse and floater sells at a discount ⎯ No serious investor believes a risk arbitrage strategy is a reliable source of spread income

Betting on changes in required margin – buy a floater if you expect margin to decrease Arbitrage between fixed and floating rate markets using asset swaps


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Chapter 20: Emerging Market Debt

Debt Universe Includes sovereign debt as well as securities issued by public and private companies in emerging market countries; over $3T of tradable markets

Domestic debt is issued locally under local laws of country where issued and comprises 77% of total debt; this debt has lower liquidity, varied practices, higher convertibility risk and frequently has investment and trading restrictions; difficult for foreign investors

External debt – mostly sovereign bonds ($440B) with vast majority of those in global bonds (registered in jurisdiction of major financial centers) or Eurobonds (issued and sold to international investors and not subject to registration) issued under laws of foreign country

Debt stock by region ⎯ Latin America – 48%, of which domestic debt comprises 57% ⎯ Asia – 25%, of which domestic debt comprises 89% ⎯ Emerging Europe – 20% ⎯ Middle East and Africa – 7%

Diversification of issuers ⎯ Since 1991 emerging market countries in market index have increased from 4 to 36 ⎯ Since 1993 five largest issuers in Merrill Lynch Emerging Markets Sovereign Plus Index have

dropped from 98% to 66% ⎯ Since 1996 external debt issuance has been running at average rate of $70B annually, over half in

sovereign debt Quality of emerging market countries ⎯ Emerging markets as an asset class have improved in credit quality; many countries have pursued

economic policies that allow them to better weather external shocks ⎯ Since 1998 there have been more positive than negative rating actions ⎯ Since 1993 percentage of investment grade bonds has risen from 8% to 25%+ and average credit

quality rose a notch from BB‐ to BB Investor base ⎯ Ownership was once concentrated in hands of a few commercial banks and inter‐market dealers

but now is distributed more widely through actively traded global bonds; aggressive fund managers were first then domestic high yield investors followed

⎯ Investor base grew further after upgrades of key countries to investment grade (Poland 1996, Mexico 2000) and very high returns (41% in 1996)

⎯ After Asian currency crisis of 1997 and Russian default of 1998 capital flows diminished drastically; in recent years market has matured, liquidity has improved, volatility has declined

⎯ In 2000‐2 as US interest rates reached 45 year lows and stock market crashed demand appeared from more conservative investors, insurance companies and pension funds; many bond indices now include emerging market debt which brings over more investors

Debt Performance History Historical returns ⎯ From 1992 through 2003, emerging market debt returned 368% (compared to 178% for US high‐

yield debt or 106% for US equities) or 13.7% a year


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⎯ This was due to Treasury yields reaching historic lows as emerging market spreads touched historically tight levels, so this cannot be replicated over next 12 years

⎯ Exhibit 20‐1 indicates how (a) since peak of tech bubble in 2000 emerging market yield and US high yield have been very highly correlated and (b) since late 2001 emerging market yields have actually been below US high yields

Annual volatility is 16%; Sharpe ratio is about same as that for US Treasuries, better than European or emerging markets equity with historically high volatility and low returns

Correlation with other asset classes ⎯ Highest correlations are with US high‐yield market and emerging markets equity ⎯ Until 1997 highly correlated with US Treasuries, but Russian debt crisis ended that

Liquidity ⎯ Average daily trading volume is about $16B ⎯ Emerging markets debt play a role in high‐yield portfolios offering greater liquidity when needed;

fewer but larger issues making pricing more transparent and bid‐ask spreads narrower

Brady Bonds General considerations ⎯ Debt relief introduced in 1989 by SecTreas Brady ⎯ Defaulted commercial bank loans converted to restructured sovereign bonds with lower interest

rates or lower face amount in exchange for macroeconomic reforms; 17 countries took part but Brazil, Mexico, Argentina and Venezuela represented 78%

⎯ $42B still outstanding out of an original amount of $144B ⎯ Russia restructured debt in this same period but did not conform to Brady Plan

Types of Brady Bonds ⎯ Brady market is unique in several ways

− Yields always have been higher than on non‐Brady bonds − Some issues were extremely large and liquid − No bond was a simple fixed rate bullet; every bond had some combination of step up coupons,

floating rates, amortizations, long grace periods, capitalizations and collateral ⎯ Principal reduction bonds were option 1

− Required 35‐50% reduction on face value of defaulted loans − Offered coupon rate of LIBOR + 13/16%, although market would have been higher

⎯ Par bonds were option 2, had face value of loans but paid fixed below market interest, allowing banks to keep loans on their books at face value but resulting in interest reduction

⎯ In addition investors were given a past due interest bond with face value equal to past due interest that had accrued since last payment prior to default

⎯ As each successive Brady exchange took place terms typically progressed more in favor of sovereign; haircuts crept higher, collateral decreased, past due interest calculations were reduced

Brady Bond Valuation – To account for complicated features investors need to be more bond structure savvy; collateralized bonds and amortizing or capitalizing bonds also require more sophisticated approaches

Retirement and Exchanges of Brady Bonds ⎯ Many countries gained access to capital markets and made a concerted effort to retire Brady bonds,

important economically and politically ⎯ Most exchanges while keeping market value fairly constant replaced Brady bonds priced below par

with new Eurobonds priced close to par, resulting in smaller face value


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⎯ Exchanges produced large issues that are liquid and actively traded ⎯ Main approaches

− Exercise call at par on any coupon date, as Mexico did with all its remaining Brady debt and Poland with much of it

− Discreetly buy back Brady bonds in open market, as did Argentina, Brazil, Mexico, Panama, Poland

− Initiate a formal Brady exchange program for a new Eurobond issue, first done by Mexico in 1996; subsequent exchanges included Argentina, Brazil, Mexico, Panama, Venezuela, Philippines, and most notably Uruguay 2003

− Offer a formal exchange into local debt, as Argentina did − Agree to a private exchange whereby large holders of a sizable block of bonds would agree to

an exchange for a reopening of an existing sovereign Eurobond − Accept Brady bonds as payment in certain privatizations, as Brazil did − Pay amortizing principal on schedule; most have been repaying large amounts of principal;

Brazil’s past due interest bond became first Brady bond to actually mature − Default, as did Ecuador, Ivory Coast, and most notably Argentina 2001


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Chapter 22: Overview of Mortgages and Mortgage Market

Introduction As of 12/31/2003 total face value of residential mortgage debt was $7.3T Approximately $4.2T has been securitized

Product definition and terms4 Overwhelming preponderance of mortgages originated have first lien status Vast majority of mortgages have a 30 year term; 15 year mortgages are also common Interest can be fixed, ARM (CMT or LIBOR), or hybrid ARM Credit guarantees, from FHA/VA, securitized by Ginnie Mae Loan balance ⎯ Conforming loans ($417K in 2006‐2008) constitute about 80% of market ⎯ GNMA/FHA/VA has lower conforming limits than Fannie Mae and Freddie Mac and differentiates

between high cost and low cost states ⎯ Jumbo loan sector is significant ($843B) but dwarfed by agency sector

Loan credit documentation characteristics – Fastest growing sector of mortgage market has been sub‐prime and alt‐A

Mortgage industry Direct lender (retail) vs Loan broker (wholesale) Depository vs Non‐depository ⎯ Mortgage banks sell virtually all their loan production in capital markets ⎯ Depositories may hold their loan production in their loan portfolio as a balance sheet asset or sell

securitized loans into capital markets; can be more aggressive in how they price different products Originators vs Servicers ⎯ Top 10 servicers comprise 48% of market ⎯ Base servicing is 25 bp for GSEs; excess servicing is additional interest ∋ loan can be securitized with

an “even” coupon Loan underwriting process ⎯ Credit score – Experian (Fair Isaac), Transunion, Equifax ⎯ LTV ratio

− High LTV indicates a greater likelihood of default − Combined LTV (CLTV) accounts for existence of any second liens

⎯ Income ratio − Front ratio (monthly home payment / monthly gross income) less than 28% − Back ratio (all monthly debt payments / monthly gross income) less than 36%

⎯ Documentation − Over last several years there has been a relaxation in documentation standards − Increased flexibility is part of general trend towards risk‐based pricing5

⎯ In addition to evaluating ability and willingness of borrower to repay loan timely, must also ensure integrity of property and whether it can be sold to pay off loan in event of default

4 No need for notes on mechanics of mortgages and amortization as I know all this stuff well 5 Of course as we now know problem is that risk was not priced correctly


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⎯ Lender is also exposed to interest rate risk once loan rate is locked in


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Chapter 23: Agency MBSs

Introduction Agency MBSs have no credit risk and are preferred investments from standpoint of capital requirements; yet they pose tremendous risk owing to uncertainty of prepayments

History of secondary mortgage market Fannie Mae and Freddie Mac MBSs are viewed by markets as having credit status better than AAA due to close ties with federal government

FNMA was established in 1938 as a government agency to purchase and sell FHA loans and starting in 1948 VA loans

In 1968 FNMA was divided into GNMA government agency and shareholder‐owned GSE FNMA In 1970 GNMA issued its first mortgage pass‐through, Freddie Mac was chartered to provide a secondary market for conventional mortgages as well as FHA/VA loans, and Fannie Mae was allowed to purchase conventional mortgages too

GNMA MBS issuance has remained relatively steady; Fannie Mae and Freddie Mac issuance has skyrocketed from under $400B in 2000 to over $1.5T in 20036

Agency pool programs Pool characteristics ⎯ Weighted Average Coupon, either gross or net of servicing fees (usually 50 bp); pass‐through rate is

lower due to guarantee fee paid to GNMA/FNMA/FHLMC ⎯ Weighted Average Maturity, current and original ⎯ Weighted Average Loan Age ⎯ Original loan size ⎯ Starting in 2003 Fannie Mae and Freddie Mac began disclosing additional characteristics – loan

purpose, original LTV, FICO scores, occupancy status, property type Programs ⎯ Ginnie Mae I – fixed rate loans all issued by a single lender; holders receive separate principal and

interest payments on each certificate ⎯ Ginnie Mae II – allows greater flexibility (fixed or adjustable, multiple issuer pools) and smaller

pools than Ginnie Mae I; holders receive aggregate payment on all certificates; interest on pool is 50‐150 bp below coupon on underlying mortgages

⎯ Ginnie Mae Platinum – securities created by combining pools with uniform coupons and original terms to maturity into a single certificate; provides liquidity

⎯ Fannie Mae ⎯ Freddie Mac – provides timely payment of interest and ultimate payment of principal ⎯ Freddie Mac Gold – similar to Fannie Mae, provides timely payment of interest and principal ⎯ Freddie Mac Giant – similar to Ginnie Mae Platinum

6 Chapter 23 contradicted itself on this figure – showing $1.9T on p521 and $1.5T on p519; $1.5T seems more consistent with other figures in text


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Trading characteristics Settlement ⎯ For pass‐through MBSs during any month active month for which most trades will settle will be next

month; dealers will make markets for current month settlement but not with as much liquidity ⎯ Forward market facilitates origination because originator can sell MBS forward prior to creating

pools to hedge rates they have locked in from borrowers ⎯ Active trading in forward market also stems from CMO market; among most Wall Street dealers

frequently biggest trading counterparty of MBS pass‐through trader is same dealer’s CMO desk ⎯ As current settlement approaches, there are sometimes attractive opportunities for investors who

can sell their MBS today and enter into a repo to repurchase at a later date at a lower price; drop is greater as demand for MBS settling in current month increases

⎯ TBA = pricing of to‐be‐announced pass‐through securities with next month settlement ⎯ An interesting feature of TBA market is that purchaser does not know number of pools or

characteristics of pools or exact price that will be delivered until just prior to settlement; generally TBAs are analyzed using average characteristics of given mortgage program

⎯ Trades also occur on a specified pool basis reflecting special inventory that a dealer holds or a client needs, at prices above current TBA quotes; has grown tremendously since 1995

Delay of cash flows ⎯ GNMA and FHLMC 14 days actual but can be up to 45 days; FNMA 24 days actual but can be up to

55 days ⎯ While delay is meant to cover exigencies, it also provides an important source of income; both

Fannie Mae and Freddie Mac get a significant fraction of their net income from float earned between time they collect cash flows and disburse them to investors

Delivery standards ⎯ Trades between dealers and institutional investors usually take place in even lots of $1M ⎯ At settlement buyer must pay seller accrued interest through settlement date ⎯ In settling seller can modify amount of principal delivered by up to ±0.01% except for specified pool

trades which must be exact; in a declining market MBS sellers will deliver as much as possible taking advantage of upper end of variance limit and in a rising market sellers will deliver as little as possible

⎯ Bond Market Association (formerly PSA) limits number of pools delivered in a trade to prevent sellers from unloading all their small pools

Prepayments Mortgages are prepaid for several reasons: (1) prepay entire mortgage when they sell home, (2) refinance if rates drop substantially or as a result of homeowner credit curing or for cash‐out, (3) foreclosure, (4) if property is destroyed insurance pays off mortgage, (5) if mortgage rate is higher than other available investments pay down (curtail) balance

When current mortgage rates fall below 150 bp of WAC prepayment speed increases Full prepayments of loans reduce outstanding balance but do not reduce average maturity; curtailments have more of an effect on pool

Three methodologies for calculating prepayments ⎯ Single Monthly Mortality – percent of outstanding dollars paid in any month

− SMM = (Scheduled Balance – Actual Balance) / Scheduled Balance ⎯ Conditional Prepayment Rate – percent of non‐amortized balance prepaid on an annual basis,

converted to a monthly rate


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− CPR = 1 – (1 – SMM)12 ⎯ PSA model – increases by 0.2% per month for first 30 months then remains level at 6% CPR; most

prepayment models are expressed as a multiple of PSA − PSA = CPR / (min(age,30) x 0.2%)

Important factors that affect prepayments are interest rates, aging, burnout, seasonality


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Chapter 24: CMOs

CMO Market Developed in mid‐1980s to broaden appeal of mortgage‐backed products to traditional fixed income investors by allowing them to more closely control when they receive principal and interest from MBSs

Numerous innovations in structuring CMOs have created classes of bonds with one or more of following characteristics: ⎯ Greater stability of cash flow over a wide range of prepayment speeds ⎯ Better matching of floating rate liabilities ⎯ Substantial upside potential in a declining interest rate environment with less downside risk in a

rising interest rate environment ⎯ Properties that allow them to be used for hedging mortgage‐related products

Issuance in 2003 topped $1T, dwarfing Treasuries and corporates Liquidity, hampered by lack of homogeneity, is typically less than pass‐throughs and more comparable with corporates; typical spreads are pretty tight

In new issue market CMOs generally settle in book entry via Depository Trust Company month after trade to allow dealer to finish structuring deal; in secondary market CMOs mostly trade on a T+3 settlement basis

CMOs pay interest monthly, often with same delay as underlying collateral but some have reduced delays to make comparable to bonds; tranches eligible to receive principal receive it at same time

Some agency deals and all non‐agency deals contain cleanup calls when only a small portion of deal (1‐10%) remains to avoid burden of high fixed trustee costs

Every CMO deal is made primarily from two basic flavors – sequential or Planned Amortization Class (PAC); these deals can be altered or dressed up slightly, PACs and sequentials can be divided further, tranches with special features can be added, but not matter how complex deal is one must always start with question of which deal type is it

CMO Tranche Types Sequential or “vanilla” ⎯ Takes principal and time tranches it; standard sequential tranches have a specified cash flow

priority and absorb all scheduled and prepaid principal in turn until they are retired − Investors may want a shorter or longer duration than underlying collateral − Initial principal lockout period may be valuable to some investors who do not want to receive

principal for some period of time ⎯ Window of time that principal is returned to investor is narrower than for collateral ⎯ All classes receive interest based on principal outstanding for that class ⎯ Coupon on a sequential can be different from collateral; portion of interest can be stripped from

collateral extending duration of tranche; this interest is diverted elsewhere in deal, e.g. to create an IO tranche or added to a regular tranche to create a premium tranche with interest larger than collateral

⎯ Short duration sequentials that are currently paying can be analyzed by looking at yield and comparing to other short duration bonds like short agencies, ABSs, hybrid ARMs, keeping in mind extension risk; longer duration sequentials are often compared with underlying collateral using OAS or yield analysis plus potentially a total‐rate‐of‐return analysis that compares expected returns under different interest rate scenarios


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PAC ⎯ PACs are given a preset schedule for principal paydown; hence cash flows and average life are

relatively stable; if prepayment speeds remain within specified prepayment PAC bands, PAC would adhere to its original schedule and behave similarly to a corporate bond with a sinking fund structure

⎯ If all companions are gone PACs are broken and behave like sequential bonds, but broken PACs trade more cheaply than similar sequentials possibly creating relative value opportunities

⎯ Decision to buy PACs over sequentials or pass‐throughs involves a few questions − Is cash flow stability cheap via purchasing PAC? − Is hedging pass‐through or sequential cash flows using OTC derivatives expensive or

cumbersome from an accounting perspective? − Does investor think bond market is range‐bound or could break out of a range? − What do implied and actual market volatility look like and where are they going?

PAC 2 ⎯ Effectiveness of PACs is enhanced by creating these structures similar to PACs but with tighter PAC

bands ⎯ In priority of cash flows PAC takes priority, followed by PAC 2 and finally companions; if companions

are all retired and PACs remain then PAC 2s effectively become companion bonds ⎯ PAC 2s will suffer extension or call risk before PACs; in return for higher cash flow variability PAC 2s

will yield more than similar PACs ⎯ PAC 2 analysis needs to be very careful because they exhibit much more variability of structure,

cash flows and value than PACs or sequentials Companion ⎯ Companions take whatever principal is left over each month after PACs have been paid as close to

schedule as possible ⎯ If prepayments are fast excess principal will pay down companions once planned PAC principal

payments are made; if prepayments are slow all principal may go to PAC with companions receiving no principal that month

⎯ Companions have highly variable cash flows and average lives and a wide variety of performance characteristics; because of this yields tend to be quite high

Target Amortization Class (TAC) ⎯ Similar to a one‐sided PAC, has some call protection from high prepayments but can have a lot of

extension risk if prepayments drop too low ⎯ Some behave more like PACs or PAC 2s; others look more like companion bonds

PAC‐quential ⎯ Blends characteristics of a PAC and a sequential ⎯ While a PAC typically has a lower band of 100 PSA, a PAC‐quential more typically has a lower bound

of 150 PSA and hence has more extension risk ⎯ Nevertheless it does have a PAC band and is supported by its own companions, so it is more stable

than a standard sequential Z Bond ⎯ Initially interest accrues and is added to principal instead of being paid and at some point starts to

pay down interest and principal; this creates a long duration security (average life about 20 years) with attractive yields

⎯ Accrued interest taken in from a Z can be used to pay down accelerated principal on another tranche, particularly VADM bonds


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⎯ Increases size of other classes while keeping their weighted average life same; also helps stability ⎯ There are a few main differences when analyzing a Z versus a regular tranche

− Is Z currently a payer? If not audience of investors may be reduced. − Option Adjusted Duration (OAD) can swing extremely widely in different interest rate scenarios;

OAD can be much longer than collateral ⎯ Fundamental question is whether investor would prefer a Z or a zero Treasury; two can best be

compared using total rate of return analysis ⎯ Bond prices are extremely sensitive to small changes in model assumptions

Very Accurately Determined Maturity (VADM) Bond – Structured to have short maturities ⎯ Size of VADM class is determined by amount of accrual at 0% prepayment; faster prepayments will

shorten maturity but no event (other than delinquencies) can lengthen maturity ⎯ Use accrued interest from Z to pay off principal, so no deviation unless prepayments are so fast that

Z begins to pay down; in general average life is more stable than comparable duration sequential; they are especially resistant to extension risk because maturity is guaranteed even if prepayments drop to zero

Floater ⎯ It is possible to construct tranches with floating rate by dividing a fixed rate tranche into a floater

and an inverse floater ⎯ Floaters and inverse floaters will have caps and floors on interest rate paid ⎯ Discount margin refers to effective spread over index once price and prepayment assumption are

factored in ⎯ Most of option adjusted duration of floater would be due to duration from cap

Inverse Floater ⎯ As market rates fall inverse floater’s coupon rises but faster prepayments may eat away value of

this to bondholder; effectively inverse floater is leveraged to prepayments ⎯ To compare inverse floater vs leveraged collateral one cannot simply compare OAS; collateral must

be levered by implicitly borrowing money to same OAD as inverse floater ⎯ Creation value can be used to analyze inverse floaters; floaters are relatively liquid and easy to

price, underlying tranche is typically easy to price, difference is value of inverse floater Interest Only (IO) and Principal Only (PO) ⎯ In a trust IO/PO deal, dealers contribute collateral and IO and PO tranches are returned to dealers

in proportion to their collateral contribution; can also be created by stripping interest off a CMO tranche

⎯ IOs typically have negative duration; if rates rise prepayments slow which benefits IO; if rates drop prepayments rise which benefits PO

⎯ POs are sometimes bought for prepayment protection or to add duration ⎯ Under typical assumptions convexity of a PO is positive but OAS is negative ⎯ IOs and POs are notoriously sensitive to even small changes in prepayment assumptions, making

OAS models very complex ⎯ Creation value can be used to analyze but IO/PO combo may trade at a price significantly above

collateral ⎯ Tranche arbitrage is another way to analyze – e.g. PAC IO plus stripped PAC should equal full PAC; in

practice investors are willing to accept tighter spreads for lower dollar price PACs which is what makes restructuring PAC attractive in first place

⎯ PAC IOs behave like a high yield PAC within band but if prepayments speed up will pay off quickly perhaps leaving investor with a loss


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Exotics ⎯ Inverse IOs created by stripping an inverse floater; in some respects behave as a knockout interest

rate floor; highly leveraged to one’s interest rate scenario and prepayment forecast ⎯ Structured POs – POs can be structured into TAC POs, super and companion POs, etc ⎯ Jump Zs

Agency CMOs Agency CMOs are generally structured by dealers who approach agency to wrap deal for a fee and take all risk; occasionally agency will purchase some tranches itself; Fannie Mae and Freddie Mac exert some control to prevent a squeeze or even shortfall for deals in a month

CMO Analysis Analysis for regular CMO tranches ⎯ Investor goals and constraints

− Insurers and banks sometimes have yield bogies below which they will not purchase bonds − Relative value investors may require a certain OAS or OAS vs collateral − Hedge funds may require a certain liquidity − Funded investors may need to issue debt or raise equity before adding MBSs or CMOs − Banks may require CMOs to pass FFIEC − Individual or institutional investors may have a top dollar price limit above which they will not

purchase bonds ⎯ Cash flow analysis

− For most tranche types cash flow analysis consists of testing various prepayment models to determine sensitivity

− For some investors analysis becomes more details because they are trying to hedge liabilities or perhaps they are hedging CMO with an amortizing swap

− For non‐standard tranches it pays to examine cash flow waterfall and test various interest rate scenarios; anything that could cause a bond to have a longer than expected maturity or a gap when principal was not paid would be suspect

⎯ OAS analysis − For similar tranches off similar collateral OAS can be used to determine relative value − Comparing OAS for CMOs vs underlying collateral is straightforward − More difficult issue is how to compare OAS of tranches with different durations

⎯ Hedging − For normal CMO tranches, OAD is an acceptable way to calculate how to hedge − Wide window sequentials may require hedging on multiple points on yield curve

There are a number of issues in OAS analysis to determine OAS on bond is truly what investor seeks, spread of MBS ex option cost vs benchmark; in 1980s and early 1990s primary variable was prepayment model, but now term structure model has become equally important ⎯ Term structure model

− As mortgage market has linked more tightly over time with OTC derivatives market, modeling relationship between them has become critical

− To extent swaps and swaptions are used to hedge MBSs or vice versa markets need to be evaluated using same term structure model and assumptions

− While a one‐factor interest rate model was used in past and works reasonably well for pass‐throughs, it is not enough for ARMs, floaters or inverse floaters, or derivatives


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− To keep analysis consistent it therefore appears critical to use least common denominator of term structure models that will accommodate all possible tranches; inconsistent models can misprice a security and allow arbitrage

− Advances in term structure modeling have placed following features in hands of mortgage analysts: (1) multiple knots on yield curve, (2) correct pricing of OTC derivatives, (3) pricing in a volatility skew, and (4) simulation of future mortgage rates based on swap curve and volatility

⎯ Forward curve bias in term structure models creates a paradox − In order to remain arbitrage free term structure models must use forward yield curve as its base

case − In practice forward yield curve is usually wrong − If we do not believe what forward yield curve is predicting we can trade against it, which may

be easier in derivatives or futures market than in mortgage market ⎯ Prepayment model – prepayments have become more efficient over time, a trend that appears to

be continuing bolstered by competition ⎯ Why A+B can be greater than C even if A and B are made up of component cash flows of C

− A and B are unique and more cannot be created − A or B is getting squeezed, in particular POs often get restructured in other deals so remaining

POs are in very high demand to hedge IOs − Underlying collateral is valuable, in particular seasoned collateral generally commands a

premium ⎯ Examining deal call risk

− Cleanup call is not discussed often and sometimes not modeled; last cash flow holder is exposed to call; a call that sounds small for entire deal like 1% actually may make up a large portion of last tranche

− Call might not happen if price of collateral is significantly below par; bondholder may want to value bond with and without call to assess impact

Investor types and behavior ⎯ Banks (44%)

− Long durations and possible duration extension of pass‐throughs do not match their liabilities adequately; banks achieve shorter duration or less extension risk by buying appropriately structured CMOs

− In general banks will accept some prepayment and convexity risk for better spread; therefore they tend to prefer sequentials over PACs; 2 year sequential is a typical purchase

− Little convexity hedging is done, but delta hedging is common − Bank may have a spread bogey, but ALM and liquidity concerns tend to dominate − Some banks use FFIEC test, initially set up by US bank regulators but no longer required, which

restricts extension and call risk, checks that price changes due to ±300 bp interest rate shocks are less than 17%, and limits starting average life to 10 years

⎯ GSEs (24%) − Use OAS or comparison to collateral to determine cheapness and buy “cheap” CMOs − GSEs sometimes buy CMOs off certain hard to find collateral − FHLB operates more like a bank caring as much about yield, net interest margin and average life

profile as about relative value in OAS framework ⎯ Insurers


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− Buy CMOs across spectrum of regular tranches; P&C companies tend to buy shorter maturity tranches; life companies are looking for more structure to match liabilities and are more likely to purchase longer duration bonds

− In 1995 S&P devised a convexity test that penalized insurers for having negative convexity in their portfolios; served primarily to reduce mortgage holdings at some particularly large outlier firms that held lots of MBSs

⎯ Money managers − Any CMO is effectively an out of index bet for money managers since they are compared to

pass‐throughs; OAS analysis tends to be an important tool − Liquidity tends to be a bigger issue for money managers than for insurers

⎯ Pension funds – ERISA considerations sometimes keep pension funds from investing in mortgage derivatives although there is no obvious basis in ERISA case law for this fear

⎯ Hedge funds − May buy a CMO and hedge its cash flows over time using swaps and options, netting a spread

they hope to earn over time − Certain funds specialize in mortgage derivatives; issues will be pricing their inventory (since

bonds may not trade for months) and liquidity ⎯ Retail investors and regional dealers – companions are often sold via this channel; focus is on yield;

any broker who sells CMOs to retail investors must include disclaimers mandated by NASD In a crisis mortgage market may continue to trade via pass‐throughs but CMO market can lose liquidity and derivatives market can practically stop trading for some time7

Using Bloomberg Most CMO prices in Bloomberg are inaccurate

7 We saw this in 2007Q4 and 2008Q1


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Chapter 25: Non‐agency CMOs

Market and risk Non‐agency market is substantially smaller than agency market Non‐agency CMOs typically are created from collateral that is non‐conforming for GSEs ⎯ Jumbo loans ⎯ Alt‐A – limited documentation or otherwise below top credit; rates are higher than market so less

sensitive to interest rate moves A major sector of non‐agency market is backed by ARMs; by 2004 largest share of market was IO hybrid ARMs

In addition to credit risk, jumbo loans have worse prepayment characteristics; jumbo whole loan packages typically trade behind similar agency collateral by $0.75 to $1.25 per $100

Primary rating factors – property type, loan type and terms, geographic dispersion, loan size, loan seasoning, purpose of loan

Credit enhancement Non‐agency CMOs typically are structured into senior securities with AAA rating using some form of credit support, generally subordination ⎯ Losses are leveraged into small subordinate tranches, senior AAA tranches are paid principal and

interest before anything is paid to subordinated tranches and do not have to take losses until subordinate tranches are all gone

⎯ Credit enhancement of choice because issuer transfers credit risk completely to market in form of subordinated tranche buyers

⎯ Shifting interest redirects prepayments from subordinated class to senior class according to a formula to keep subordinated class large enough to absorb future losses, which shortens average life of senior class

⎯ Subordination is sometimes combined with other methods of credit enhancement, most typically excess spreads or reserve fund

Other internal credit enhancement methods are less typical today with exception of lower loan quality deals which still use over‐collateralization and/or excess spread ⎯ Excess spreads – some interest on deal is captured and used to pay off losses before any other

credit enhancement is used; leftover income may go to reserve fund or back to originator; works best if defaults occur later in loan life after reserve has been built up

⎯ Cash reserve fund – cash from underwriting profit is placed in escrow and used to pay off losses, used in coordination with excess spread and sometimes with a letter of credit

⎯ Over‐collateralization – excess collateral backs deal, defaults and losses must eat through excess collateral before there is risk to bonds; any collateral left when CMO is called or matures is returned to originator

External credit enhancements; vulnerable to credit downgrade of third‐party guarantor ⎯ Parent guarantee – issuer guarantees investor against credit losses, not popular ⎯ Letter of credit – financial institution provides guarantee on losses up to a certain amount;

vulnerable to downgrade of letter as well as collateral underperformance ⎯ Pool insurance – cover losses from defaults and foreclosures typically written for a dollar amount of

coverage that continues in force for life; some policies decline as pool seasons as long as credit


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performance is better than expected and rating agencies approve; additional insurance must be obtained to cover bankruptcy, fraud and special hazards

⎯ Bond insurance – typically not used as primary protection but to supplement other forms of credit enhancement

Subordinated tranches ⎯ Can run gamut from unrated to AAA “mezzanine” ⎯ For tranches rated A and higher cash flow characteristics are more important than credit

characteristics; defaults do not affect cash flow except in form of prepayment; subordinate class takes loss and senior class will receive principal as if prepayment had occurred

⎯ Often a subordinated tranche has better convexity and less prepayment risk than PAC bonds; often prohibited from receiving principal for some period of time for credit enhancement purposes and have relatively strict schedules for returning principal; designed to prevent subordination levels from falling too low and risking a credit downgrade

⎯ Percentage of subordinate bonds in deal is carefully managed over time through shifting percentage of principal that is paid to senior and subordinated bonds; in particular at first very little principal is allocated to subordinated bonds because delinquencies mount in first seven years, after defaults peak more principal is allocated to subordinated bonds; this affects cash flow of senior class even in absence of defaults

⎯ For tranches rated BBB and lower credit characteristics are more important than cash flow characteristics; also these bonds have much smaller size and less liquidity

⎯ Most non‐agency CMOs include an unrated first‐loss tranche; issuer often retains this tranche as a sign of its faith in structure8

Special collateral types with prepayment characteristics superior to typical jumbo loans ⎯ Reperforming loans – loans that were first originated by government agency and were seriously

delinquent but have been rehabilitated or modified; credit issues cause them to be less reactive to interest rate moves and hence desirable to investors from cash flow analysis standpoint

⎯ VA vendee – loans made at very high LTV up to 100% to non VA borrowers purchasing VA owned real estate (typically foreclosures); since starting with below market interest and very high LTV less sensitive to interest rate moves

⎯ Alt‐A loans – prepayments higher over time, not necessarily correlated with interest rates

Other issues Compensating interest ⎯ Prepayments received before EOM result in interest shortfall since borrower is not obligated to pay

interest once loan is paid off yet CMO deal is structured to pay interest on balance until EOM; in agency deals shortfall is made up by agency; in non‐agency deals there are several ways problem can be solved

⎯ Paid by servicer, originator or deal sponsor; often amount of interest in month is limited to fees taken in that month raising a small risk to investor

⎯ Can create CMO tranche that absorb interest shortfall risk or a WAC IO similar to regular IO except that coupon varies to absorb interest shortfall

Servicer and bankruptcy risk – CMO collateral is bankruptcy remote from issuer and originator, but there can be servicing risk if servicer has financial problems; if servicer goes bankrupt and servicing fee is too small bondholders may have to pay to transfer servicing on loans

8 We know how well this turned out in 2007


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Jumbo prepayments tend to behave differently than agency prepayments because larger loan size makes refinancing economical even for smaller interest rate changes and because jumbo borrowers tend to be more sophisticated

Non‐agency CMOs have wider WAC dispersion than agencies – WAC IOs can be created to absorb variability in coupons of underlying loans, payments will change as specific pools are paid off


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Chapter 26: Residential ABSs

Market development Home Equity Loans (HELs) – traditionally consisted of second mortgages, but now includes first mortgages with high LTV, home improvement loans, HELOCs, sub‐prime (B,C,D) mortgages ⎯ Proportion of first liens in pools is typically 90% ⎯ Cash out refis, rate/term refis, consolidate consumer debt, home improvements, education or

medical expenses ⎯ 2/28 and 3/27 ARMs are predominant products securitized

Residential ABS market grew rapidly in 1990s; outstanding in 2004 was $411B; new issuance in 2005 was $383B

On 1/1/2002 RBC rules gave AAA and AA ABSs a 20% risk weight, same as agencies During middle to late 1990s most lenders in this sector were independent finance companies; competition in falling interest rate environment of 1997 and 1998 led issuers to weaken underwriting standards, and firms that grew rapidly in this period were overly reliant on securitization; liquidity crunch in late 1998 forced many into bankruptcy; of top ten issuers at year‐end 1998 all but one (GMAC Mortgage) have exited

Of top ten issuers at year‐end 2003 listed six have imploded spectacularly in last year

Characteristics of sub‐prime borrowers General rule of thumb is that borrower needs credit score of 680+ to qualify as prime; 620‐680 is considered A‐; scores below 620 are squarely sub‐prime which is about 20% of population

Prepayment Prepayment rates differ in important ways from agencies which can provide a superior convexity, hence good diversification

Prepayment rates have a faster seasoning ramp and reach a higher steady state level than agency pools, similar for fixed and ARM collateral, so shorter average mortgage life ⎯ Baseline Home Equity Prepayment (HEP) curve ramps up to 20% CPR over 10 months ⎯ ARM collateral prepayments peak at 25‐30% after 12 months; prepayment spikes around 24

months for 2/28 and around 36 months for 3/27 when rate first resets ⎯ Prepayment penalties reduce prepayment rates by 8‐10% of baseline CPR

Major reason for faster prepayment rate is credit curing effect; less sensitive to interest rate swings and thus provide superior convexity and more stable average lives

Prepayment rates on sub‐prime pools are more stable than for conforming mortgage pools ⎯ Sub‐prime loans tend to have lower balances so incentive to refinance is more muted ⎯ Sub‐prime borrowers tend to have fewer refinancing alternatives

Relative value During most of 2000‐2003 yield differential between HELs and agencies was 20‐60 bp During 2002 when rates fell sharply and prepayment rates were accelerating yield on HELs actually moved inside yield on agencies due to greater variability of prepayments on agencies


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Chapter 27: CMBSs

Introduction Backed by mortgages on income producing property – multifamily housing, office buildings, industrial properties, warehouses, retail properties, hotels, health care facilities

Market growing rapidly in US and Europe Multi‐property single borrowers and multi‐property conduits (commercial lending entities that are established for sole purpose of generating collateral to securitized), fastest growing segment of CMBSs

Commercial loans are commonly locked out from prepayment for 10 years Counterbalancing reduced prepayment risk is increased default risk; commercial mortgages are non‐recourse loans – if there is a default lender looks to proceed from sale of property but has no recourse to borrower for any unpaid balance; lender must view each property as a stand‐alone business

CMBS Deal GMAC 1999‐C3 deal is an example of a sequential pay CMBS CMBS Ratings and Subordination Levels ⎯ Rating agency looks at Debt Service Coverage Ratio (DSCR, which is ratio of NOI to loan payments)

and LTV of underlying loans ⎯ Subordination is used to improve rating; most senior tranches are usually AAA

Prioritization of Payments ⎯ Any return of principal caused by amortization, prepayment or default is used to repay highest

priority outstanding tranches first; interest is paid to all tranches according to rules ⎯ Any losses are charged against principal balance of lowest rated outstanding tranche ⎯ Prioritization rules among most senior classes can get more complicated

Call Protection ⎯ Prepayment lockout ⎯ Prepayment penalties which decline as loan ages ⎯ Yield maintenance – borrower is required to pay a make whole penalty equal to difference between

PV of remaining loan cash flows and principal repayment; common in older deals but is less common in newer deals

⎯ Defeasance – calculated same as yield maintenance, but borrower invests in Treasuries to fulfill remaining cash flow structure; common in older deals but is less common in newer deals

⎯ Protection within CMBS structure due to sequential pay nature Timing of principal repayment ⎯ Commercial loans underlying CMBS deals are often balloon loans; if there is a change in quality of

underlying asset there is a danger that loan will not be refinanced which could result in default ⎯ To reduce loan failure risk at balloon date there are two types of loan provisions

− Internal tail – requires borrower to provide evidence that effort is underway to refinance, say one year prior to balloon date, and obtain refinancing commitment, say six months prior to balloon date

− External tail – maturity of CMBS deal is set longer than underlying loans which allows borrower more time to arrange financing while avoiding default on bonds


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Underlying Loan Portfolio Diversification ⎯ Spatial diversification reduces risk associated with regional drops in real estate ⎯ Diversification across property types

− Riskier loans demand higher coupon as well as higher DSCR and lower LTV − Least risky property types are apartment, office and retail properties

Cross‐Collateralization – properties that serve as collateral for individual loans are pledged against each loan by borrower; lender can also use cross‐default by calling every loan in pool if one defaults, prevents cherry picking by borrower

Loan Analysis – DSCR, LTV, maturity, prepayment lock type, etc; S&P Conquest also forecasts NOI and market value for each property

Stress Testing at Loan Level – Despite diversification, stress test should consider common variance (of NOI, etc) across all properties reflecting general economic conditions as well as common variance within property types and geographic regions

Historical Loan Performance – 2.73% of loans in rated transactions went into default; at low end were multi‐family (1.92%) and office (1.48%); at high end were hotels (11.15%) and health care (8.46%)

Factors that could make future experience better than historical experience ⎯ Prepayment lockouts are becoming more popular and are better at deterring prepayments than

yield maintenance provisions ⎯ Mortgage terms are becoming longer ⎯ Underwriting is getting better


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Chapter 30: Cash CDOs

Introduction Backed by diversified pool of investment grade corporate bonds, high yield bonds, emerging market bonds, residential MBSs, CMBSs, ABSs, REIT debt, US bank loans, special loans or distressed debt, foreign bank loans, or even other CDOs

A CDO is a way of creating securities with widely different risk characteristics from a portfolio of debt instruments9; provides a way of creating high quality debt from average or even low quality debt

Cash CDO are backed by pools of actual market debt instruments Distinguished based on motivation of sponsor ⎯ Balance sheet CDO – remove assets from balance sheet ⎯ Arbitrage driven CDO

− Gain a fee for managing CDO assets and capture a spread between return realized on collateral and interest paid on CDO

− Largest part of cash CDO sector − Cash arbitrage driven CDOs are further divided into cash flow and market value − Key as to whether it is economically feasible to create an arbitrage CDO is whether a structure

can offer a competitive return to equity tranche10 Structure ⎯ Tranches are (1) large senior tranches typically rated AAA or AA, (2) mezzanine tranches typically

rated A through B, and (3) subordinate unrated equity tranche which is small percentage of total principal

⎯ Cash flows come from coupons, maturing assets, asset sales ⎯ Creator of CDO normally retains equity tranche and sells remaining tranches in market ⎯ Typically most debt tranches are floating rate but CDO manager invested in fixed rate bonds; this

creates a mismatch; to deal with this problem rating agencies require CDO to use interest rate swaps to convert position

Cash Flow Transactions General considerations ⎯ Coupon interest payments, maturing principal and default recoveries provide top two tranches of

CDO with credit protection without active trading ⎯ Manager has trading restrictions to maintain quality of portfolio ⎯ There are three relevant periods in a CDO life

− Ramp‐up begins 2‐6 months before closing date and ends fewer than 6 months after − Reinvestment or revolving period when principal proceeds are reinvested in new collateral is

usually 5‐7 years long − Final period when holders are paid off

Distribution of income ⎯ Payments are made first to trustee and administrator and then to CDO manager ⎯ Once fees are paid, senior tranches are paid their interest ⎯ If senior coverage tests are passed then interest is paid to mezzanine tranches

9 Text has a worked out example of a cash CDO with which I am already familiar 10 Text pages 672-3 provide a numerical example of this


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⎯ If mezzanine coverage tests are passed then interest is paid to equity tranche ⎯ If either round of tests is failed then depending on structure and how severely tests failed available

income is used either to pay down senior tranche principal or to purchase more collateral ⎯ If senior tranches are paid off but mezzanine tests are failed then available income is used to pay

down mezzanine tranches Distribution of principal cash flow ⎯ If there is a shortfall in interest to senior tranches principal proceeds are used to make it up ⎯ During reinvestment period if coverage tests are passed principal cash flows are reinvested ⎯ Afterwards principal cash flows are used to pay down senior tranches first then mezzanine tranches

then equity tranche ⎯ If performance of equity class is above some threshold manager will often get a bonus

Restrictions on management: Coverage tests to ensure performance of collateral is sufficient to make payments ⎯ Lower seniority tranches have lower triggers on tests ⎯ Over‐Collateralization tests

− OC ratio for a tranche = Principal par value of collateral / Principal par value for tranche and all tranches senior to it

− Minimum is called over‐collateralization trigger, which is lower for less senior tranches ⎯ Interest Coverage test: IC ratio for a tranche = Scheduled interest due on collateral / Scheduled

interest for tranche and all tranches senior to it, with minimum established for each tranche Restrictions on management: Quality tests ⎯ Minimum collateral diversification

− Best known diversity score is Moody’s which reduces number of correlated assets to a smaller number of uncorrelated assets; each industry is assumed to have zero correlation with other industries, different issuers within an industry are assumed to have some correlation; securities from same issuer are treated as 100% correlated

− In order for a corporate debt back CDO to merit a high diversity score most industry groups must be represented; usually will include 20‐25 out of 33 industry groups

− General guideline is that no industry group can represent more than 8%; there is often an exemption for 2‐3 largest industry groups with concentration as high as 10‐12%

⎯ Minimum Weighted Average Rating Factor (WARF); S&P also requires strict percentage limits for lower rated assets

⎯ Maximum maturity ⎯ Minimum WAC and minimum weighted average spread

Market Value Transactions General considerations ⎯ Ability of CDO to realize proceeds from sale of assets to repay its debt provides CDO debt with

credit protection; manager must maintain or improve market value of collateral ⎯ Were used in cases of unpredictable collateral cash flows such as distressed debt, managers who

wanted more trading flexibility, and managers who wanted to invest in longer term securities; since accounting rules changed in 1990s no market value balance sheet CDOs have been issued

⎯ OC ratio for a tranche = Principal market value of collateral / Principal market value for tranche and all tranches senior to it

⎯ Cash flow deals are generally preferred, so market value deals have a higher spread Rating process


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⎯ Biggest risk is sudden decline in market value of collateral; thus rating agencies focus on price volatility and asset liquidity

⎯ Market value over‐collateralization tests require that market value multiplied by “advance rates” (factors obtained from Moody’s or Fitch cross tables based on asset type and credit rating) must be greater than or equal to debt outstanding; if not collateral sales and liability redemptions are required to bring ratios into compliance

⎯ Advance rates tables vary depending on maximum investment in any one issuer or in any one industry; assume 5% max in one issuer and 20% max in one industry

⎯ Fitch also requires quarterly minimum net worth test, which requires that 60% of original equity remains to protect senior tranche and 30% to protect subordinated tranche

Investment Principles for Managing a Portfolio of CDOs Rule 1 – Track records ⎯ There is good reason to be very skeptical about track records; they contain three biases – creation

bias, survivorship bias, size bias ⎯ Make sure firm and manager have track record with every asset included in CDO ⎯ Make sure firm has a disciplined consistent approach to investing which is followed in good times

and bad ⎯ Look at stability of firm and personnel ⎯ There is an assumption that dealers act as gatekeepers bringing only top‐notch performing

managers; this trust is to some extent misplaced as more firms wish to manage CDOs than there is dealer pipeline capacity and there are other considerations including relationship between dealer and manager and help that manager can provide in marketing deal and taking some equity

Rule 2 – Look at incentive structure ⎯ In most deals manager owns between 25% and 49.9% of equity (if manager owned 50% or more

entire deal would get consolidated on its balance sheet); manager has incentive to keep cash flow going to equity holders even if that works to detriment of bondholders and NAV of deal

⎯ Moody’s: Some managers are lax in righting a deteriorating portfolio, are tardy in treating a security as defaulted, buy deep discounted securities, or hold on to severely impaired securities

⎯ Incentive structure of CDO and performance of existing CDOs provides much more information than general track records of CDO managers

⎯ Some managers can be egregiously self‐serving; this can usually be spotted in huge deterioration of WARF or a big growth of assets with CCC ratings

Rule 3 – Asset Diversification ⎯ Collect CDOs backed by different types of collateral ⎯ Key for portfolio of CDOs is to hold different types of collateral; style or asset class is most

important factor in explaining investment returns ⎯ Buy a certain type of CDO when you believe underlying collateral is cheap

Rule 4 – Portfolio Diversification ⎯ Buying CDOs backed by different collateral creates your own diversification; do not necessarily

avoid CDOs with low diversity scores; even a CDO with low diversity score may increase diversity of a particular portfolio

⎯ Conversely deals with very high diversity scores may hurt diversification if they are substantially same style


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Chapter 31: Synthetic CDOs

Introduction Investor has economic exposure to pool of debt instruments but realized via credit derivatives; creator sells a portfolio of CDSs then passes default risk to tranche holders; income from CDSs is distributed to tranches in a way that reflects risk they bear

Three events led to creation and rapid expansion of synthetic market ⎯ Creation of a super‐senior tranche reduced cost of liabilities ⎯ Increased attention from rating agencies has given investors confidence ⎯ Development and standardization of CDS technology has allowed participants to communicate

more efficiently, acquire collateral faster and hedge more efficiently Advantages ⎯ More straightforward, flexible and efficient than cash CDOs ⎯ There are no fixed/floating or maturity mismatches ⎯ Currency mismatches are handled seamlessly without currency hedges ⎯ Quick and easy ramp‐up of collateral; greater collateral diversity

Growth and evolution of market Originated in 1997 so banks could lower regulatory capital 80% without removing loans from their balance sheets

In 2003 64% of deals were synthetic; many synthetic CDOs are now executed for arbitrage purposes; arbitrage CDOs ($500M‐$1B) are usually smaller than balance sheet CDOs ($1B‐$10B)

Synthetic CDOs from ground up In its simplest form a synthetic CDO is application of an unfunded CDS to a pool of reference credits; sponsor is buyer and investors are sellers of credit protection

To expand investor base and remove counterparty risk sponsors incorporated funding by Credit Linked Notes (CLNs) into framework; a SPE is created to provide a bankruptcy remote depository for high quality assets purchased with note proceeds

Many synthetic CDO transactions actually are a hybrid; a single highly rated investor typically a monoline insurer will invest in super‐senior AAA tranche in unfunded form and rest of liability is purchased by various investors in funded CLN or unfunded form

Super‐senior tranche frequently accounts for 85% of capital and carries a very low spread of 8‐15 bp Losses are passed on to investors in reverse order of priority although sometimes realization is at end of deal allowing noteholders to earn interest on entire amount of investmente

Settlement Mechanics Cash settlement is more common Valuation methodologies involve a bidding process (one or multiple rounds) and multiple bids, although sometimes it is just two bids one of which can be provided by sponsor

Moral hazard is higher with fewer bids so investors should seek transactions with more bids; market standard was at least five non‐affiliated bids on corporates and three on structured finance securities


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Chapter 44: Quantitative Management of Benchmarked Portfolios

Introduction Most fixed income portfolios today are managed relative to a benchmark; at one end are passive indexed funds that strive to match benchmark risk exposures as closely as possible and at other end are very active portfolios with high risk tolerance that freely maximize performance by investing outside benchmark; majority fall somewhere in between

Often an appropriate benchmark can be selected from wide array of existing indices; there are many cases when an existing index needs to be modified due to limitations; sometimes a new highly specialized index needs to be constructed; finally for some investors right benchmark may not even be a traditional total return market index

Selection and customization of benchmarks General consideration – It is not always possible to achieve investable, transparent, known‐in‐advance, diversified goals to same degree; first and foremost benchmark should be appropriate meaning there should not be any built‐in differences between benchmark and portfolio

Reflecting investor opportunity set and constraints ⎯ When an investment policy requires a duration target, changes weights of standard index

components, imposes a credit rating threshold, restricts security attributes (maturity, age, coupon, etc), or places limits on exposure (industries, countries, issuers, etc) then a standard index may not be appropriate

⎯ In all cases goal should be to keep benchmark as broad‐based and well‐diversified as possible while still meeting all requirements of investment policy

⎯ One widely used method to attempt outperformance is to invest outside benchmark, referred to as core‐plus; a case can be made for inclusion of frequently used core‐plus assets into benchmark; this presents additional opportunity to underweight such assets relative to benchmark

Targeting duration / cash flow profile ⎯ Portfolios are often managed by keeping duration equal to liability duration or by dedication; yet

actual investment policies can be quite liberal ⎯ An appropriate benchmark for such a portfolio could match sector and quality distribution of

underlying index while matching cash flow profile of liabilities ⎯ If target duration is not close to duration of any standard index benchmark may be constructed as a

blend of two indices ⎯ Things may get more complicated for portfolios containing a large proportion of securities with

embedded optionality, durations of such portfolios is likely to be unstable − Manager may engage in delta hedging to overcome convexity and keep duration constant; this

entails transaction costs obviously but also less obvious but potentially much more devastating whipsaw costs

− Delta hedging can be applied to benchmark to construct a constant duration index that provides a fairer benchmark for a delta‐hedged portfolio

Asset swapped indices ⎯ Some bank and insurer managers must manage portfolios to a short duration target for ALM

purposes but are free to exercise their credit skills in asset selection; leveraged investors often concentrate on credit exposure and minimize interest rate exposure by managing portfolio duration to short‐term LIBOR funding; in an environment of moderate credit spreads and low interest rates


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traditional total return managers are likely to keep durations very short while maintaining an overweight to spread sectors

⎯ Most straightforward way to create and maintain such exposures is to turn to floating rate market, but this may create unintended sector or issuer concentration

⎯ Manager would want to match diversified credit quality and sector exposure risks of broad index while simultaneously removing exposure to all Treasury key rate risk factors except desired key rate

⎯ To exercise their spread sector skills while minimizing interest rate exposure investors can buy fixed rate spread assets on an asset swap basis; gives investor opportunity to take spread sector exposure with little term structure risk

⎯ There are no indices of asset swaps performance; benchmark must represent a neutral spread sector allocation; one approach to creating such a benchmark starts with creation for each asset class of a mirror swap index that matches key rate duration profile of that asset class; then short position in these mirror swap indices are combined with long positions in corresponding asset class indices as well as with short term asset; customized benchmark must represent a neutral spread sector allocation

Book accounting based indices ⎯ For insurers and banks that are less concerned about short‐term market fluctuations, liabilities are

valued using book accounting so managers prefer to measure portfolio performance similarly using book return or book yield

⎯ Lately fixed income market has seen introduction of book accounting indices BOOKINs

Diversification issues in benchmarks General consideration – issuer specific risk is a serious concern even for users of very broad market indices; as of February 2004 top ten issuers in Lehman US Corporate Index accounted for 22% of overall market value

Issuer capped benchmarks – impose a maximum on market value weight of any issuer ⎯ Caps can be different for various credit ratings ⎯ Some redistribution rules can limit benefits of issuer capping by inadvertently introducing

unfavorable sector or quality risk exposures relative to uncapped index ⎯ This can be avoided by a quality/sector neutral redistribution rule ⎯ Another side effect is increase of weights of smaller issuers; raises concern that available supply

may not allow manager to match required allocation in benchmark index Swap based benchmarks ⎯ Swaps offer excellent liquidity, limited idiosyncratic risk and opportunity to capture some of long‐

term spread advantage of investing in non‐Treasuries ⎯ Swaps can be viewed as a yield curve for non‐specific high grade (Aa) credit spreads; this has

prompted some investors to consider swaps as return benchmarks ⎯ However returns on swaps are not directly observable in market; to create returns requires

developing a methodology relying on creation of hypothetical constant maturity swap securities from observable swap yield curve

⎯ A swap index can be constructed with any desired term structure from these “securities”; a manager with such a swap index as a benchmark is free to hold only those credits which he things will outperform; there is no pressure to have any exposure to larges issuers in market cap index

Downgrade tolerant benchmarks ⎯ For investment grade only indices, fallen angels are removed at end of downgrade month at

marginal price; in contrast a manager must find buyers and often has to hold fallen angels for at


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least several months until buyers can be found and price stabilizes; this makes index difficult to replicate especially during stressful markets

⎯ Benchmark can be modified to produce downgrade‐tolerant index that keeps fallen angels for a certain period of time after downgrade; magnitude of bias is small (around 1 bp)

⎯ If plan sponsors are willing to give managers time to ease out of downgraded issues they should give them at least six months to do so

Portfolio analysis relative to a benchmark General considerations ⎯ Managing a benchmarked portfolio may have a well defined and stable cycle, say monthly ⎯ Cycle may be functional rather than procedural, performed on ongoing basis as need arises and not

necessarily in a fixed order Analyzing portfolio risk: a cell‐based approach ⎯ Partition portfolio and benchmark into matrix of cells based on portfolio composition – quality,

industry/sector, duration ⎯ Amount of quality of information depend on appropriateness of chosen risk dimensions ⎯ Fundamental assumption behind this approach is that contribution of a given cell is a function of

magnitude of mismatch and weight of cell, which is not unreasonable ⎯ Simplicity is attractive, but there are two major problems

− Risk consequences of a particular mismatch depend not only on its apparent magnitude but also on its nature; e.g., a mismatch in spread duration of Aa financial is a very different risk prospect than of Baa telecom; experienced portfolio managers usually have a feel for more consequential mismatches even if only in a qualitative way

− Cross‐correlation among multiple sources of risk makes judging overall risk daunting; two mismatches in different cells with significant risk in isolation but with low or negative correlation and hence negligible joint risk; conversely a few mismatches that could be ignored individually may represent a serious risk if correlations are high; this problem is more difficult to compensate for with experience

Analyzing portfolio risk: multi‐factor risk models ⎯ Primary goal is to help managers structure portfolios with desired risk exposures relative to

benchmark; as such it is generally used ex post control tool but rather as an ex ante tool for portfolio structuring − Measure expected risk of return deviations in portfolios that track a benchmark − Form a reliable estimate of risk for active managers with a particular alpha target − There is a well established consensus among investment professionals on realistically

achievable levels of information ratio; 0.5 is quite high and 1.0 is practical upper limit; if as a result of policy constraints projected risk is estimated to be too low manager should make case for either relaxing constraints or revising alpha target

⎯ Separating systematic and non‐systematic components of default risk is quite difficult ⎯ Systematic risk is quantified using covariance matrix of small set of common risk factors ⎯ Non‐systematic risk is quantified by multiplying differences between portfolio and benchmark

concentrations by spread volatilities specific to given issuer or group ⎯ Two components of risk combine to produce key output, Tracking Error Volatility (TEV) ⎯ TEV = projected standard deviation of monthly return differentials between portfolio and

benchmark


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⎯ Provides common unit for many different sources of risk, enhancing comparisons and facilitating risk management

⎯ Reliance on historical observations generates criticism that correlations are unstable and depend on economic cycle; concerns have been shown to be exaggerated; for systematic risk time decay can be imposed on data series to give greater weight to more recent data; non‐systematic risk presents a bigger challenge due to large body of data needed

History based scenario analysis complements multi‐factor risk analysis ⎯ Managers may focus on most likely scenarios or unlikely but most adverse scenarios ⎯ It is very difficult to formulate scenarios that are consistent in both direction and magnitude along

many dimensions; solution is to use a historical covariance matrix to build scenarios; incorporate a few explicit forecasts and infer historically consistent realizations for all other factors

Attribution of portfolio performance relative to a benchmark ⎯ For multi‐currency portfolios analysis normally starts at global level where outperformance results

from two basic sources, unhedged exchange rate exposures and currency‐hedged exposures to different markets; then portfolio positions are segregated with each currency evaluated separately

⎯ Quantifying outperformance owing to differences in volatility exposures that affect embedded optionality requires a good term structure model and analytics to compute vega

Quantitative approaches to benchmark replication General considerations ⎯ Buying benchmark is often a reasonable tactic even for active managers

− In times when manager has no definite views on particular segments, matching index in those segments is sensible and safe

− Managers who have accrued significant outperformance before year is over switch to passive investing to preserve their gains

− Use for modeling purposes rather than direct investment, to eliminate model noise ⎯ Replication with actual cash securities

− In markets with high idiosyncratic risk, more important to match issuer distribution − Where systematic risks dominate, pay close attention to allocation along risk dimensions − Buying most securities in index practical only for few largest index funds; furthermore

appropriate only for portfolios that intend to remain neutral for a long time Stratified sampling ⎯ One attempts to match contribution of each important segment with a few securities

− In simplest case total market value weight of holdings in a segment is set to match index weight of that segment

− More often holdings are selected and scaled ∋ they match segment’s contribution to index duration

⎯ To improve tracking manager may target other characteristics, such as convexity or quality ⎯ Approach works quite satisfactorily in homogeneous markets, such as Treasuries or MBSs

− Lehman has matched Treasury curve with just six securities − For MBSs it may be sufficient to sample just three dimensions: program (GNMA, conventional,

15‐yr, balloon) seasoning, price (premium, cusp, discount) ⎯ Actual techniques while based on sampling get quite complicated; special rules may be used for

selecting bonds and for setting diversification in each segment; sampling may be performed within optimization

⎯ Matching some cells may be more critical than matching others due to volatility of cells


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⎯ Sampling based techniques ignore all‐important correlations between cells ⎯ Stratified sampling may be useful even in presence of a powerful risk model; it may alert manager

to structural mismatches ignored by model Tracking error minimization ⎯ Multi‐factor risk models usually provide more accurate estimates of portfolio risk than sampling

techniques ⎯ Can be augmented with optimization techniques by picking a set of bonds with minimum projected

tracking error against benchmark ⎯ Can be done in one step (model is a black box) or stepwise one transaction at a time leaving

manager in control; from practical standpoint stepwise may be preferable ⎯ At first adding securities reduces tracking error quickly, but gradually rate of decline slows;

explanation lies in systematic risk which is virtually gone at 30‐35 bond level ⎯ Multi‐factor models rely on historical experience, which may ignore a significant structural

mismatches that historically did not result in return volatility Replication with derivatives ⎯ Derivatives effectively reduce number of dimensions ⎯ Particularly useful in start up phases in which amount of money to invest is small ⎯ Treasury futures are widely used as a duration adjustment tool because of advantages of no

portfolio disruption, ease of establishing and unwinding positions, and low transaction costs ⎯ Lehman divides index into four maturity/duration cells and market value allocations and dollar

durations are matched with a combination of cash and an appropriate futures contract ⎯ Derivatives popular in portable alpha strategies, structure derivatives to replicate index and invest

cash outside index to gain alpha ⎯ For portfolios with very dynamic cash flows, replicating benchmark with exchange traded futures

may be preferred because of liquidity and low cost ⎯ Spread risk cannot be matched with Treasury futures and needs to be hedged separately; introduce

Eurodollar futures and swaps ⎯ Derivatives to replicate mortgage component plus CDSs reduces TEV below 10 bp/month; offers

two advantages over mortgage pools − Suitable for unfunded strategy since no cash outlay is required − Much simpler because monthly interest payments are principal paydowns are avoided

⎯ Can be employed to replicate broadest multi‐currency indices; single‐market components are replicated separately and then combined

Controlling issuer‐specific risk in portfolio General consideration – for broad indices benchmark issuer risk is much smaller than typical cash portfolio; swap markets provide viable means of getting credit exposure without acquiring actual securities

Sufficient diversification in credit portfolios ⎯ For a portfolio of a given number of bonds, how many bonds of each credit quality should be held

to achieve lowest tracking error due to downgrade risk? Optimal allocations were found to be rather heavily skewed in their diversification levels across qualities

⎯ When one takes into account volatility not caused by rating transitions, ratio tends to become less dramatic but still indicates use of smaller position limits in lower qualities


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⎯ Managers should consider costs associated with increasing number of issuers: (1) transaction costs increase, (2) overhead of monitoring more issuers, (3) forced to extend to issuers that are less highly regarded by portfolio’s analysts

Swaps as a total return investment ⎯ Lehman publishes swap indices whose returns are based on receive‐fixed swaps of various

maturities plus cash in three‐month LIBOR ⎯ In a steep yield curve environment swapping activities by corporations intensifies leading to

tightening of swap spreads unaccompanied by corresponding tightening of credit spreads; this diminishes value of swaps as credit proxy but promotes role of swaps as means to diversify systematic risk in total return portfolios

Quantitative methods for portfolio optimization Optimal Risk Budgeting with Skill ⎯ First step is to estimate explicitly or implicitly degree of reliance on each particular

recommendation which depends on perceived skill of those who made recommendation ⎯ Skill based historical simulations produced interesting conclusion, information ratios of very diverse

strategies were very similar for a given skill level; on risk‐adjusted basis nature of investment strategy plays a minor role

⎯ Fundamental law of active management (Grinold & Kahn) states that information ratio of an investment strategy is determined by two factors: (1) information coefficient based on correlation between predictions and realizations, (2) breadth or number of independent decisions made by strategy

Asset allocation for buy‐and‐hold investors ⎯ For total return investors who are not holding bonds to maturity dominant risks are spread

volatility, possible loss of liquidity, and downgrade ⎯ If total return investors expect high short term spread volatility they can drive spreads much wider

than would be justified by long term default risk alone; this action can work to benefit of long term credit investors unaffected by short term risks

⎯ Mean‐variance optimization generally is not suitable for buy‐and‐hold investors due to tail risk; central problem is trade‐off between current credit spreads and expected horizon defaults to decide when is credit cheap from buy‐and‐hold perspective

Tools for quantitative portfolio management Objective is to treat a wide range of asset classes within a single consistent framework without giving up too much accuracy ⎯ Security level analytics – cash flow projections, price spread conversion, duration and key rate

duration ⎯ Portfolio level analytics – multifactor risk model, portfolio risk and structure, portfolio optimization,

flexible performance attribution, maximum likelihood scenario analysis


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Chapter 47: Bond Immunization: An Asset/Liability Optimization Strategy

What is an immunized portfolio? Immunization is defined as locking in a fixed return over a specified horizon or generating a minimum future value at end of horizon ⎯ Reddington (actuary) defined immunization in 1952 as investment of assets in such a way that

existing business is immune to general change in interest rates ⎯ Fisher & Weil defined immunization in 1971 as portfolio value at end of holding period regardless of

course of rates being at least as large as it would be if rates stayed constant

Maturity matching: reinvestment problem Interest rates can be locked in for coupons and principal redemption; however interest on coupons cannot be locked

As holding period increases interest‐on‐coupon exerts a stronger influence; at 10 years it generally dominates

Since interest on coupons increases when rates increase and price of bond drops, it is still possible to lock in a return since changes offset each other

Single period immunization Most straightforward approach is to purchase zeros maturing on liability payment date If zeros have insufficient yield a portfolio of coupon bonds can be immunized to fund same single period payment iff three conditions are met ⎯ Duration of portfolio equals horizon ⎯ Market value of assets must be greater than PV of liabilities discounted at IRR ⎯ Dispersion of assets mush be slightly greater than dispersion of liabilities

− D = Σ(ti‐D)2PV(CFi) / ΣPV(CFi) Portfolio could be constructed in three ways ⎯ Barbell – incorporates greatest amount of yield curve risk ⎯ Ladder ⎯ Bullet – preferred because it incorporates least amount of yield curve risk

Rebalancing procedures As time passes single period immunized portfolio must be rebalanced so duration is reset to remaining life in planning period to ensure offsetting effects of capital gains with reinvestment return

Because duration is inversely related to both prevailing yields and coupon rate it may not be possible to immunize a portfolio beyond a certain number of years using only coupon securities

Multi period immunization It is possible to create multiple single period immunized portfolios to fund multiple‐period liability payouts

However calculating duration of multiple‐period liabilities is not straightforward; duration is derived using IRR, but IRR is not determinable unless we know precise portfolio, duration and dispersion

As a result construction of an immunized portfolio is an iterative process Absence of strict cash matching would introduce an element of market risk


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A multi‐period portfolio must be rebalanced whenever one of three conditions is violated; in particular durations will tend to wander whenever a liability payment comes due

Applications of immunization strategy Pensions ⎯ Single period immunization is generally employed as alternative to purchase of GIC

− Advantage of liquidity since it consists of marketable securities and GICs are not traded − Manager can take advantage of market opportunities by including securities or sectors that are

attractive on relative value basis ⎯ Multi period immunization is to fund schedule of expected benefit payouts to retired lives – sponsor

can lock in prevailing rates and possibly raise its actuarial interest assumption Insurance – because GIC, structured settlement and buyout assets and liabilities are segmented from general assets and liabilities, entire line of business can be immunized

Banks and thrifts use immunization to assist in management of asset/liability gap and ensure future duration matched growth of assets and liabilities; Technical Bulletin 13 mandated for thrifts that interest sensitivity of assets and liabilities be similar

Variations to immunization Combination matching or horizon matching is most popular variation ⎯ Duration matched with added constrain that it be cash matched in first few usually 5 years ⎯ Most of positive slope or inversion of yield curve tends to take place in first few years ⎯ Cost is slightly greater and swapping discretion is constrained

Contingent immunization is a blend of active management with lower floor return ensured ⎯ Floor return or safety net is a rate set below immunized rate, allowing managers discretion to

actively position their portfolios; if market moves against managers ∋ floor return is violated, managers commit to immunized portfolio to ensure floor return over remainder of horizon

⎯ Contingent immunization requires an abrupt change at moment floor return is violated; dynamic asset allocation (portfolio insurance) change in strategy is gradual

Immunized portfolios can also be created with futures to replicate interest sensitivity, options and CMO PACs to enhance returns, and swaps

Stochastic duration matching


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Chapter 48: Dedicated Bond Portfolios

Need for a broader asset/liability focus Dedicated bond portfolio matches monthly cash flows from a portfolio of bonds to a pre‐specified set of monthly cash requirements of liabilities, eliminating interest rate risk

Applications include pension benefit funding, defeasance of debt service, municipal funding of construction takedown schedules, structured settlement funding, GIC matching

Need for complete funding perspective is best illustrated by significant interest rate risk assumed by many insurers in early years of their GICs ⎯ Large number of 3‐7 year maturities were issued in positively sloped yield curve environment of

mid‐1970s and proceeds invested at higher rates in 10‐30 instruments ⎯ By pricing GICs on spread basis and investing in mismatched assets companies assumed rollover risk ⎯ As rates rose dramatically insurers were exposed to extreme disintermediation

Cash flow matching for pension funds Determining liabilities ⎯ For pension plans this is usually expected benefit payouts to closed block of current retirees;

frequently term vested participants are included as well ⎯ Some plans have extended dedication strategy to include “anticipated retirees”

Setting portfolio constraints ⎯ First step is setting portfolio constraints on sector, quality, issuer, lot size; A or better is a common

requirement ⎯ As a general rule mortgages are not desirable because of uncertain prepayment; some managers

allow PACs because they are protected within relatively wide bands; in protracted bull market of early 1990s even wide band PACs busted and sponsors were required to pay in to purchase new swap them for new instruments to protect integrity of portfolio

⎯ Care must be taken to select corporates that are call‐protected; low probability of credit downgrades is useful but not critical since integrity of cash flows is still preserved even with downgrades if there is no default

Reinvestment rate ⎯ Since timing of cash receipts does not always exactly match timing of disbursements, surplus funds

must be reinvested until next payout ⎯ More conservative reinvestment rates bias investment selection in favor of lower yielding securities

closer to liability payment dates and tighter cash flow match ⎯ More aggressive reinvestment dates bias investment selection in favor of higher yielding securities

but greater risk of not earning reinvestment rate ⎯ Current actuarial rates range from 5% to 8%

Selecting optimal portfolio ⎯ Optimal least cost portfolio is structured by restricting universe to some subset of credits ⎯ Three methods: stepwise solutions, linear programming, integer programming11 ⎯ Integer programming is most technically advanced and able to identify lower cost solution

Re‐optimizing a dedicated bond portfolio

11 Text provides a specific numerical example


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⎯ It was originally thought that once a dedicated portfolio was structured it should be managed passively but active management can be applied

⎯ A cash matched portfolio can be entirely re‐optimized on a periodic basis; if a new optimal portfolio can be found that is less expensive than existing one a cash takeout can be done

Active management of a dedicated bond portfolio ⎯ Bond‐for‐bond swaps can be undertaken to pick up yield or remove an undesirable credit ⎯ Active positioning in cheap sectors of market ⎯ Re‐optimize to improve duration matching or quality

Role of manager and dealer Portfolio optimization requires a database of bonds priced by traders; most money managers have access only to computer derived pricing; optimal solutions found on this basis may not be optimal when executed at market prices; dealers are best positions to execute an optimal portfolio owing to accurate pricing

Because dealers are not fiduciaries money managers are best suited to make active management decisions about sector positioning, call protection, spread forecasts, and credit

Table of Contents Benchmarks and Investment Management Chapter 9 ...................................................................................... 2 Performance Measurement Using Transfer Pricing........................................................................................... 4 Creating Value in Pension Plans ......................................................................................................................... 7 Real Estate Portfolio Management Process..................................................................................................... 10 From EMH to Behavioral Finance..................................................................................................................... 15 EMH and Its Critics ........................................................................................................................................... 18 Anomalies: Law of One Price in Financial Markets .......................................................................................... 22 Stocks for Long Run Chapter 7 ......................................................................................................................... 25 Derivatives Practices and Principles Recommendations ................................................................................. 28 Financial Dynamics of Insurance Industry Chapter 16..................................................................................... 32 IFRS Model Financial Statements and Disclosures Checklist (IAS 39).............................................................. 38 Longevity Bonds and other Mortality Linked Securities .................................................................................. 39 Handbook of Portfolio Management Chapter 20 ............................................................................................ 42 Handbook of Portfolio Management Chapter 21 ............................................................................................ 47 Specialty Guide on Economic Capital ............................................................................................................... 50 Overview of Investment Policy Statement in ALM Context............................................................................. 59

APMV Syllabus Study Notes 3 Study Notes© 2008 Alberto Dominguez

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Benchmarks and Investment Management Chapter 9

Fixed‐income benchmarks Unlike equities fixed income assets have closely specified cash flows and other properties that make them easy to classify into distinct groupings

Term, issuer type, currency, claim priority, call provisions, other characteristics form basis for index map; as a result mapping is not only possible but also relatively easy for bonds

Simply knowing name of benchmark provides a good clue as to what kinds of bonds are in it, and having a working understanding of duration, credit quality, prepayment provisions and other characteristics gives you most of what you need to know about that bond; of course a bond might have a misleading credit rating or be otherwise mis‐mapped

Corporations typically have only one class of equity but a number of different bond issues with different characteristics; there are a great many more bonds than stocks in market

Most large‐cap US equity portfolios have quite a few stocks in common, but bond portfolios with similar goals and attributes may not have any issues in common

Bond management is mostly science and individuals with mathematical training tend to be best

Capitalization weighting Cap weighted benchmarks have become standard for almost all asset classes including fixed income Practice originated with equities; extending it to fixed income securities makes benchmark construction easy but does not necessarily make benchmark a good investment ⎯ Theoretical argument that market portfolio of bonds is efficient is much more tenuous than it is for

equities − Offsetting claims exist in bond market that cause multiple counting of wealth − Controversy continues as to whether government bonds represent wealth − Each investor rather than holding cap weighted benchmark should seek duration and other

attributes that fit investor’s needs or liabilities ⎯ Most highly indebted companies get biggest benchmark weights (bums problem)

Cap weighted all inclusive benchmarks are useful for performance evaluation because active management against such a benchmark is a zero‐sum game

All‐inclusiveness has consequences for liquidity; many issues especially corporate issues are difficult to trade and price pressure effects are substantial; bond portfolio managers thus find tracking benchmarks through either sampling or full replication difficult

A bond index fund must be very large to track index well because of large number of bonds in benchmark and large order sizes required to get reasonably good execution (contrary to equity market where large orders tend to be expensive to trade)

Duration problem Duration structure of a cap weighted bond benchmark reflects duration preferences who are seeking to minimize their cost of debt capital, but investors are trying to maximize returns

Investors usually have specific time horizon preferences that make one duration more advantageous than another, and these preferences do not necessarily match those of issuers in aggregate

Optimal portfolio for an investor with no defined time horizon should not be set by matching duration of benchmark; duration is like a beta, exposure to interest rate factor; choice of duration or beta is an asset allocation decision based on investor’s risk tolerance


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In equities investors typically and most efficiently make decision by adjusting up or down proportion of equities in portfolio and not by holding low or high beta stocks; in fixed income adjusting duration of portfolio is much more practical than holding market duration portfolio and then levering duration up or down using cash or derivatives

Because issuers do not have to pay a great deal of premium to float long term issues given demand for such issues from pension funds and other investors with long term liabilities, duration extension does not provide much of a risk premium ⎯ In 1976‐2002 Lehman US Aggregate representing full spectrum of maturities outperformed

intermediate version of benchmark by only 15 bp while taking appreciably more risk; results slightly distorted by mortgage market

⎯ Comparing Lehman Brothers Government/Credit Index which does not include mortgages to its intermediate counterpart shows advantage of 30bp, still not enough to give it a higher Sharpe ratio

Many institutional investors have addressed these concerns by adopting intermediate duration benchmarks rather than broad market benchmarks

Bums problem Because corporate and sovereign issuers who manage to go deepest into debt have largest weights in a cap weighted benchmark, such a benchmark is not likely to be mean‐variance efficient

If you are tracking such a benchmark when someone issues a security you have to buy it in proportion to its cap even if security is only marginally of high enough quality to make it into benchmark and even if size of issue is inordinately large; such securities would seem to be most likely to be downgraded or to default

Although problem is probably best appreciated with corporates, international sovereign bond market provides a clear‐cut example; looking at 2003 Citigroup World Government Bond Index shows weight of Japan (which had been in 13‐year bear market involving multiple recessions) to be 35% (more than Italy, Germany and France combined); holding benchmark seems to be a bet on whatever country has most profoundly mismanaged its public finances

This bet sometimes works out well; in mid‐1960s Italy had an outsize weight and was a strong performer because it became a developed market and convergence on way to formation of euro caused yields to decline, but harmonization of Europe was a once in a lifetime event

Credit market growth and volatility A final issue arises from recent growth in size of credit market at a time when corporate bonds were individually becoming riskier; this has caused broad benchmarks to be riskier today than they were historically

Although very long term trend is displacement of corporate bonds by MBSs and ABSs, more recent trend is reduction of Treasury debt and increase in corporate issues

With $2.2 trillion of $5.0 trillion US corporate bond market having been downgraded in 2001 and 2002, absolute risk was at an all‐time high in fall of 2002

At same time that corporate bond exposure has made broad benchmarks riskier, many fixed income managers have begun trading bonds like equities instead of buying and holding to maturity as they did a generation ago ⎯ Managers regard their job as maximizing return subject to a penalty for active risk ⎯ Practice potentially in conflict with goals of fixed income investors who regard bonds as vehicles for

capital preservation and not total return


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Performance Measurement Using Transfer Pricing

Conceptual foundations of transfer pricing Transfer pricing in its simplest form is a means of assigning a price or charge for use of funds that are transferred internally within a company; concept has evolved into a tool that is used for measuring performance in a more effective manner

Use of multiple transfer pricing benchmarks to disaggregate performance of financial institution ⎯ Three benchmarks

− 1. Benchmark based on generic assets that have same duration and convexity as liabilities and have credit risk equal to credit or claims paying risk of liabilities

− 2. Benchmark based on generic assets that have same duration and convexity as assets that will be used in actual investment portfolio and have credit risk equal to credit or claims paying risk of liabilities

− 3. Benchmark based on generic assets that have same duration and convexity as assets that will be used in actual investment portfolio

⎯ Division of performance − Liability performance = Benchmark 1 – Actual return on liabilities; associated responsibilities are

product design/development and pricing, marketing skills and management of in‐force block − Asset performance due to interest rate risk = Benchmark 2 – Benchmark 1; associated

responsibilities are ALM and hedging skills − Asset performance due to credit risk = Benchmark 3 – Benchmark 2; associated responsibilities

are analysis of credit risk and recovery on defaulted assets − Asset performance due to security selection = Actual return on assets – Benchmark 3;

associated responsibilities are evaluation and selection of individual securities & assets and execution of trades

Incorporating transfer pricing benchmarks into various performance measures ⎯ Income measures

− Total Income = Income from assets – Payments on liabilities = Income from security selection + Income from credit risk + Income from interest rate risk + Product income

− Since income measures are generally short term book value based measures, their main value is to determine whether actual performance is on track with expectations

⎯ Market measures − Securities in asset portfolio can be marked to market on a routine basis and compared to

current market price of benchmark securities; this can provide information about performance of portfolio on risk‐adjusted basis

− Since market measures incorporate expectations of future income as well as current income, they are a better gauge of overall performance than income measures alone

Applications of transfer pricing in banking industry How transfer pricing rate is determined – three steps ⎯ Develop a curve of market rates at which funds can be bought or sold ⎯ Assign a transfer pricing rate to all bank liabilities; project cash flows for each liability product and

match them to yield at same duration; pricing rate equals overall yield ⎯ Assign a transfer pricing rate to all bank assets; bank assets may or may not match liabilities; in

order to assure both are priced correctly a pricing rate needs to be determined for all assets and


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liabilities separately; project cash flows for each asset and match them to yield at same duration; pricing rate equals overall yield

Organizational structure of banks with transfer pricing1 ⎯ All product lines and lending units are profit centers with matched assets and liabilities ⎯ Asset Liability Committee (ALC) manages any mismatches between loans to lending units and loans

from product lines; thus all mismatches are concentrated in this unit, which is closely affiliated with bank’s treasury unit which raises and lends fund to full short term funding gaps and can also rebalance risks through purchase or sale of hedges

⎯ Transfer pricing also facilitates measurement of product profitability in banking environment2 Benefits of transfer pricing to banks ⎯ Improved profitability analysis – Branch profitability measurement is significantly improved leading

to better analysis of continuing economic viability of individual bank branches ⎯ Benchmarking of asset performance – well‐defined risk‐adjusted targets are established ⎯ Isolation of asset/liability risks

Extension of transfer pricing to insurance industry Benefits of transfer pricing to insurers ⎯ Improved profitability analysis

− Product profitability measurement is significantly improved leading to better product pricing − Transfer pricing also facilitates comparison of actual product profitability vs expected

profitability at time of pricing; this results in better decision making regarding which product lines to expand and which to re‐price, reorganize or eliminate

− Branch profitability does not have same relevance in insurance industry; due to commission structure a large proportion of cost related to sale of new products is variable; although there may be some benefit from using transfer pricing gains from doing this are not likely to be as large as in banking industry

− Transfer pricing can improve measurement of product profitability which is currently difficult to separate from investment performance in absence of transfer pricing system

⎯ Benchmarking of asset performance − Transfer pricing helps establish a benchmark with a well‐defined risk‐adjusted target for

investment department or other lending units; it also facilitates measurement of actual asset performance on a risk‐adjusted basis; this should ultimately lead to better investment decisions and improved performance of asset portfolio over time

− Transfer pricing provides a viable investment alternative (e.g. buy benchmark) when return on actual assets do not match performance of benchmark over time

− Most insurers have few natural assets, so they have more flexibility to choose duration of their assets independent of their customers’ wishes and can match assets to liabilities even in absence of a transfer pricing system; nevertheless many insurers do not invest in assets that are precisely matched to liabilities and could therefore benefit from using transfer pricing to compare performance

⎯ Isolation of asset/liability risks

1 Study note p13 has a good example where performance of lending unit reflects only impact of credit decisions, performance of product line reflects only impact of product, and ALC reflects interest rate risk 2 Study note pp14-17 have a good example illustrating this by determining profitability of bank if it only issued deposits or if it only made loans


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− Transfer pricing can be used to concentrate all ALM risk in one unit and should therefore result in a more coordinated approach for managing this risk

− Separate measurement of impact from any residual mismatching of assets and liabilities and should better promote better risk management decisions over time

Organizational structure of insurers with transfer pricing – structure can be established to split investment line and product line; could also split asset performance into pieces for interest rate risk, credit risk, etc

Other implementation issues ⎯ What is proper market rate curve to use in context of insurance industry?

− While some flexibility may be warranted choice in general should reflect rates at which different areas of company could invest or borrow funds if they relied on external funding sources

− Because certain liability products involve long durations, it is necessary to choose a curve for which prices are available at long maturities

⎯ How to handle interest‐sensitive products – while cash flow matching is a reasonable approach for establishing benchmarks for non‐interest sensitive products benchmarks for interest sensitive products need to take account of duration and convexity of underlying products or investments

⎯ Organizational Issue / Political Question – Transfer pricing is only intended to measure impact of each function separately and does not necessarily require that these functions should be done by anyone different than areas that were doing them previously

⎯ Must take into account short term vs long term considerations


7

Creating Value in Pension Plans

Introduction Boots went from 75/25 to 100% bonds in July 2001 and reduced its annual fund management costs from £10M to £300K

Analysts, accountants and actuaries were critical of move; FE argues change would increase shareholder value by lowering taxes and risk

Sponsors should invest entirely in debt instruments that match expected payout structure of liabilities for two reasons ⎯ Capture full tax benefits of pre‐funding their pension obligations ⎯ Improve company’s overall risk profile by converting stock market risk where corporate

management has no comparative advantage into firm‐specific operating risk where it should Well funded plans are forced to pay for ones that default through PBGC

First principles FAS 87 averaging and amortizing returns, replacing actual returns with expected returns, encourages equity investing for pension plans by rewarding companies invested in equities without penalizing them for extra risk incurred

Fund assets and liabilities although not included on corporate balance sheets are corporate assets and liabilities; poor investment results create higher future funding requirements

In well‐functioning competitive markets higher expected return on stocks reflects their greater risk in such a way that risk‐adjusted expected returns of stocks and bonds are equal

Tax arbitrage Equities held by plan are tax‐neutral from point of view of shareholder, while bonds held by plan are taxed at shareholder rate rather than higher bond rate

Tepper arbitrage ⎯ Plan shifts $1 from stocks to bonds and shareholders simultaneously shift $(1‐tcorp) from bonds to

stocks in their personal portfolios, net gain to shareholders is equal to rbond(1 – tcorp)(tpers,bond – tpers,stock)

⎯ Using current tax rates, after tax value gain equals 16% of total bond return each year in perpetuity ⎯ Discounting this stream at after tax return on bonds we obtain an after tax free gain in PV terms of

$0.27 for every dollar of pension plan assets switched from stocks to bonds3 Black arbitrage ⎯ In 1980 Black presented a variation that can be executed by corporation to deliver value regardless

of portfolio strategies of individual shareholders ⎯ Plan shifts $1 from stocks to bonds and simultaneously issues $(1‐tcorp) of new bonds and

repurchases an equal amount of its outstanding stock net gain to shareholders is rbondtcorp(1‐tcorp)(1 – tpers,bond)

⎯ After tax value gain equals 19% of total bond return each year in perpetuity ⎯ Discounting we obtain an after tax free gain in PV terms of $0.32 for every dollar switched ⎯ Increase of $0.05 is attributable to gains from leverage at corporate level

3 This number differs substantially from results of problems on past exams (e.g. 2005-8V-19)


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Savings on cost of actively managing equities could easily increase shareholder value by another 5% of plan assets

Noting that pension plan leverage has been moved to balance sheet ∋ diversified equity has been replaced by firm’s own equity Black and Tepper point out that value gain occurs when assets are swapped inside pension plan; additional actions on corporate balance sheet are designed merely to highlight captured value for stockholders

Additional source of value but one less easily quantified is tightening of focus from general stock market risk to corporate operating risk; swap of stocks for bonds represents decision to increase capacity for risk bearing on operating side of business; management teams will agree that this is where they have a competitive advantage; investors will welcome such a move as a signal of management’s confidence in its ability to create more value by managing productive assets than by speculating on relative financial asset performance

Why did it take so long for leader to emerge and where are followers? When confronted by financial economics arguments, actuaries respond in two ways, both of which are inaccurate ⎯ Pension plans have longer time horizons than average investor; since shareholders own residual

interest in plans it makes no sense to impute anything other than shareholder risk preferences onto plan; if equity values do not reflect shareholder trade‐offs then whose trade‐offs do they reflect?

⎯ Price of long futures position on an equity‐bond swap is wrong4; if futures position is offered at a price other than 0 it is easy to show that arbitrage profits are available

Regardless of which period we look at average company would have been better off accessing higher stock returns by holding bonds in pension plan and redeeming its own stock which also outperforms bonds

Future salaries increases should not be treated as current liabilities, but even if we decided to treat them this way relationship between unanticipated inflation and equity returns is generally negative making equities a poor hedge

In addition to inventing liabilities that are neither legally binding nor representative of good financial reporting anticipating salary increases constitutes poor compensation management

Some pension fund managers mistakenly think that prudent man rule requires diversification among asset classes including equities

Change accounting and valuation In 2002 GE encouraged shareholders to defeat proposals to decouple executive compensation and pension income; in 2003 seeing FAS87 “income” turn to expense for first time in many years GE announced it will no longer tie executive compensation to pension earnings

Accounting changes recommended ⎯ Reporting assets and liabilities and changes thereto at market values will eliminate many distortions ⎯ Another step would be to separate financing results from operations ⎯ Liabilities should be valued on ABO basis without reference to future salary increases

UK FRS 17 eliminates smoothing features prevalent in US GAAP but still uses wrong measure for liabilities (including estimated future salary increases), does not go nearly as far as it should in

4 This isn’t just inaccurate; it’s singularly stupid; however, I can’t disagree with Gold as I saw it for myself in financial economics session at 2007 Employee Benefits Spring Meeting


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separating operating and financing elements of pension plan, and anticipates a risk premium in income statement

Economic cost of providing benefit is not a function of contributions or changes in reserves

Effects of a widespread switch to bonds End of equity cross‐ownership; pension plans own 10% of stock market cap Increase in corporate debt issuance would suggest increased exposure to market discipline, same effect as a leveraged recapitalization but without increased economic leverage; we should see benefits of improved managerial incentives traditionally associated with recapitalization but generally without financial distress costs associated with higher leverage

Corporate taxes would be saved across board, prompting an increase in other tax rates PBGC should have fewer calls

Conclusion By failing to consider their consolidated tax picture pension fund sponsors have sacrificed hundreds of billions of dollars in shareholder value

By transferring risk from pension fund to corporate balance sheet companies will be operating less like mutual funds and expressing a vote of confidence in their ability to operate more like stand‐alone pure play businesses their investors want


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Real Estate Portfolio Management Process5

Shift Old paradigm was firms using an asset‐by‐asset process; new paradigm is firms using a disciplined portfolio management process

Until recently asset‐by‐asset process dominated real estate portfolio allocation, construction and management; investment decision was based on individual property fundamentals and risk‐return relationship, sensitivity to local supply and demand market conditions, and market’s pricing of risk assets; portfolio allocation is determined by ad hoc selection of assets that meet singular property criteria; little or no consideration of how individual properties influence risk‐return relationship of entire portfolio

Portfolio management process concentrates on aggregation of individual properties that when combined into a portfolio exhibit certain risk‐return characteristics; asset‐by‐asset analysis remains an essential element but becomes an intermediate step in a larger process

Institutional investors made this shift for several reasons ⎯ Need to restore credibility lost in early 1990s commercial real estate industry collapse ⎯ Lower cost and increased availability of national, regional, local real estate market supply and

demand information; proliferation of low‐cost computer applications ⎯ Asset class competition for capital inflows ⎯ Increased sophistication of real estate professionals (MBA, PhD, CFA) ⎯ Application of financial technologies initially developed for stocks and bonds

Portfolio manager must understand limitations and applications of many analytical tools and techniques, and must recognize that judgment must be applied and used as a reality check at all times

Portfolio management process Two main forces have acted on portfolio management process ⎯ Technological advances and Modern Portfolio Theory (MPT) – Expected returns, variances,

correlations are constantly in flux; job of manager is to monitor and rebalance as needed keeping in mind that real estate transaction costs can be substantial

⎯ Growth of institutional assets under a fiduciary framework – Before ERISA real estate occupied a minuscule portion of institutional mixed asset portfolios; however many saw ERISA as a mandate to more completely diversify

Step 1 – Investor objectives and constraints General considerations ⎯ Before constructing or repositioning a portfolio it is essential to understand investor objectives and

constraints, and develop a formal investment policy that encompasses them ⎯ Managers often do not give investment policy attention it deserves; once initially developed, if at

all, it often becomes a dormant documents instead of communication tool it is meant to be Portfolio size and allocation to real estate What is required return? Is there a minimum that must be met? Should it be measured in nominal or real terms? Should for be mostly in current income or in long term capital gains?

Risk tolerance 5 Written in 1995


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⎯ Consider risk‐return characteristics of real estate property types ⎯ Investment policy of a conservative investor may specify relatively fixed percentages with little or

no market timing, fully leased properties, diversified and stable markets, and purchases without leverage

⎯ Should make sure risk and return expectations are in line Liquidity and time horizon requirements ⎯ Given inherent poor liquidity and lumpiness of real estate market it is essential to define liquidity

needs of portfolio and continually reassess cash requirements over extended time horizon ⎯ Allocate some funds to liquid real estate equity securities

Tax, legal, regulatory considerations

Step 2 – Real estate market conditions and expectations General consideration – Difficulty in obtaining high quality, inexpensive, consistent real estate market data; manager with access to relatively superior data has upper hand in beating market index

Market efficiency ⎯ At start managers must determine how they view question of how efficient market is ⎯ Active approach assumes low to moderate efficiency, mispriced market segments and properties

are worth seeking out, and over/under allocate in attempt to outperform index ⎯ Passive approach assumes moderate to high efficiency, mispriced segments and properties are not

worth seeking, and allocate to match broad market index ⎯ Given lesser quality and availability of data, few believe real estate market is efficient; attempts to

obtain excess returns seem appropriate; as market becomes relatively more efficient passive approaches will become more viable

Portfolio management approaches ⎯ Top‐down approach focuses on national market first, then regions and local markets that are

expected to outperform overall market, finally properties are selected ⎯ Bottom‐up approaches focuses on individual properties ⎯ Best is an interactive top‐down/bottom‐up approach ⎯ In real estate investor is to some degree directly responsible for management of asset

Asset selection approaches ⎯ Fundamental analysis assesses fundamentals to estimate amount and timing of cash flows along

with appropriate discount rate to apply to arrive at an estimate of value which is then compared to current market price

⎯ Technical analysis is less compatible with accepted real estate analytics Real estate market analysis ⎯ Real estate markets and potential risk factors

− National market – risks are inflation, industrial production, risk premia, term structure of interest rates, business cycle, federal taxes and regulations, fiscal and monetary policy; manager should determine sensitivity of portfolio to these systematic risk factors

− Regional market – risks are employment base and growth, demographic trends, income level and growth, vacancy rate; concept of region is evolving away from grouping of contiguous states to grouping of metropolitan areas based on respective economic concentrations even if they are in divergent parts of country

− Local market – risks are same as regional market, plus construction cost, space utilization rate, state and local taxes and regulations


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− Properties – risks are physical characteristics, location characteristics, lease characteristics, property management expertise, financing • If average lease term is shorter cash flows are more equity‐like and property is more

sensitive to local market, if average lease term is longer cash flows are more bond‐like and property is less sensitive to local market

• No two properties are alike, each has a different sensitivity to national, regional and local influences

⎯ Diversification can become a dominant force in determining portfolio allocation to property types and geographic locations

Market segmentation ⎯ Segments should constitute an aggregation of assets with high correlations of returns but low

correlations of returns to other segments ⎯ Some segments have been property type, geographic region, economic region, economic cluster,

metropolitan area employment growth, tenancy type, average lease rollover, land use density, property life cycle

⎯ Research sources are (1) a historical review of applicable data and literature, (2) interviews and discussions, and (3) creation of knowledge base through explanatory models

Tool 1 – Single or multi factor return factor model ⎯ Required rate of return – return investor requires to be fairly compensated for assuming risks of

asset or portfolio being acquired; has three components – rate of inflation, real riskless rate, risk premium; based on historical relationships which could be naïve

⎯ APT model includes four economic factors: (1) inflation, (2) industrial production, (3) risk premia, and (4) term structure of interest rates

⎯ Real estate managers may want to include influence of market cycles, employment growth, costs ⎯ Basic characteristics of good factor model

− Error term in ex post returns should not be correlated to model factors; if it is factors may suffer from multi‐collinearity

− Error term should not be correlated with return; if it is model may be missing a factor − Model should be parsimonious, few risk factors with a high R2

⎯ Several practical problems should be noted − Which factors should be used? Absence of a factor might seriously impair model − Developed using historical data, applying to future may be a leap of faith − Model assumes sensitivities will remain constant − Scenario/probabilistic approach is still needed to determine variances and covariances

⎯ Two potential uses − Assist in developing diversification or allocation strategy based on portfolio’s current

sensitivities and market factor expectations − Generate required inputs for each market segment for portfolio optimization

Tool 2 – Fundamental analysis ⎯ V0 = Σ CFn/(1+k)n = CF0(1+g1)/(1+k) + CF1(1+g2)/(1+k)2 + … + (k‐gN)CFN‐1(1+gN)/(1+k)N where (k‐gN) is

reversionary capitalization rate is intrinsic value, compare to market value ⎯ To determine a segment’s expected return one can build a pro forma income statement

Tool 3 – Scenario analysis and probabilistic forecasting ⎯ Today scenario analysis can be performed inexpensively; there is very little justification for

continuing to use old single‐point estimate approach ⎯ Process of thinking through scenarios adds to appreciation of intricacies and relationships


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⎯ Can extend market pro forma income statement into a probabilistic forecast Tool 4 – MC simulation is beneficial as it relies on forecasting to reflect uncertain future Portfolio optimization, reconciliation and judgment ⎯ As a tool to construct ex ante portfolios efficient frontier is only as good as its “fuzzy” inputs ⎯ Having used different tools manager must determine best inputs ⎯ Must use judgment, but multiple approaches should provide knowledge and insight ⎯ Real estate appraisers use three approaches to value reconciliation (cost, market, income)

Other optimization and MPT related problems ⎯ Results of MPT efficient frontiers depend on classification scheme used for segments; too broad will

mask important differences, too narrow will be overly cumbersome ⎯ If two assets offer nearly identical mean/variance characteristics but one is slightly more attractive,

optimization process will place very large allocation on it to virtual exclusion of other asset; common sense tells us uncertainty in inputs makes this foolish

Step 3 – Target portfolio determination Tangential intersection of investor’s risk‐return indifference curve and efficient curve represents portfolio with greatest possible utility for investor and gives us exact segment allocation

Rather than exact allocations, allocation ranges are used to (1) reflect uncertainty in inputs and (2) provide flexibility needed to properly manage property level investment decisions

Manager faces problem of balancing property’s existing position in market (leasing, capital improvements, property management changes) and market’s position within investment cycle ⎯ Allow portfolio to stray too far from designated allocation ranges and risk losing return, risk and

diversification benefits of target portfolio ⎯ Maintain understanding of properties and markets or run risk of generating lower returns due to

inopportune timing

Step 4 – Portfolio strategy determination Challenge becomes translating broad goals to be both definable and measurable Consistent with allocation ranges of target portfolio (where you want to be) and current and expected conditions of properties in current portfolio (where you are) must use repositioning analysis (testing alternatives) to choose best portfolio strategy

Implementation ⎯ Acquisition strategy – property type, location, size, age, lease structure, financing ⎯ Disposition strategy ⎯ Property management strategy for holds – market and property risk analysis, leasing objectives and

guidelines, operating and capital budgets Should complete development of each functional group’s strategy in conjunction with group to ensure buy in and proper execution

Step 5 – Monitoring and rebalancing General considerations and definitions ⎯ Need to monitor investor objectives/constraints and market conditions/expectations ⎯ Monitoring means analyzing and understanding change and its potential impact on portfolio ⎯ Rebalancing means modifying assets in portfolio to make them better fit changing needs

− Allocation changes between market segments − Category or emphasis changes within a market segment


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− Selling a property and replacing it with another of like kind Rebalancing costs ⎯ Costs of not trading include holding on to a property (1) that is overpriced and/or (2) that no longer

fits needs of investor ⎯ Costs of trading include commissions and associated fees and impact on market

Need to avoid psychological portfolio rebalancing due to fads or herd mentality

Step 6 – Portfolio performance measurement Adding value ⎯ Market allocation ⎯ Property selection ⎯ Diversification

Return measures can be historical or forecast ⎯ Russell/NCREIF

− Base = MVt‐1 + ½(CapitalImprovementt – PartialSalest) – 1/3INCt

− Rinc = INCt / Base − Rapp = [(MVt – MVt‐1) + PartialSalest – CapitalImprovementt] / Base − R = Rinc + Rapp

⎯ Cash‐on‐cash using average book cost: R = CFt / ½(BCt‐1 + BCt) ⎯ Cash‐on‐cash using market value: R = CFt / MVt‐1 ⎯ Capitalization Rate = NOIt / MVt‐1

Performance attribution ⎯ Russell/NCREIF ⎯ Plus/Minus impact of portfolio allocation deviating from benchmark portfolio ⎯ Plus/Minus impact of actual market segments against returns from benchmark segments

Role of portfolio manager Identifies investor objectives and constraints Analyzed market conditions Integrates investment policy with market conditions and converts them into target portfolio allocation ranges

Creates portfolio strategy, communicates its goals and objectives Monitors investor objectives/constraints and market conditions Measures and communicates portfolio performance Must also be an effective leader and manager to work with organization and/or vendors


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From EMH to Behavioral Finance

Excessive Volatility 1970s – EMH reached its height of dominance; academic finance has evolved a long way since 1980s were a time of important academic discussion of consistency of EMH with econometric time series properties of prices, dividends and earnings; of particular concern was whether stocks show excess volatility relative to what would be predicted by EMH; anomalies discovered in 1970s might be considered small departures from fundamental efficiency, but if most volatility in market was unexplained it would call into question entire EMH

EMH asserts that price Pt equals optimal forecast of expectation conditional on all information available at time t of PV of all future dividends Pt

*, and any surprising movements in market must have at their origin some new information about fundamental value ⎯ Pt* = Pt + Ut and Pt, Ut must be uncorrelated ⇒ forecast must have less variability than variable

being forecasted For period 1871‐2002 PV of future dividends behaves remarkably like a stable trend; in contrast price index gyrates wildly up and down around this trend, arguing against EMH

Marsh & Merton argued that dividends need not stay close to a trend and if managers smoothed dividends prices might be expected to shift more rapidly than dividends; as more general models that incorporated this were developed they tended to confirm that prices had more volatility than EMH could explain

West 1988 derived inequality that variance of innovations in prices must be less than variance of innovations in PV of dividends, which holds even when prices and dividends have infinite variances so long as variance of innovations is finite; variance of innovations in prices was 4‐20 times theoretical upper bound

Campbell 1991 indicated that variability conveyed information about future returns rather than future dividends

Allowing time‐varying interest rates in PV formula does little to support EMH; actual price is still more volatile than PV, especially for latest half century

In a model with discounting using marginal rates of substitution of consumption and deriving equations for stock returns in context of maximizing utility of consumption, PV of dividends has only a tenuous relation to actual stock prices and was not volatile enough to justify price movements

Hansen‐Jagannathan lower bound on volatility of marginal rate of substitution is exceeded in US unless risk aversion were implausibly high, which is regarded as an important anomaly

Recent research has provided evidence that even though aggregate stock market appears to be wildly inefficient individual stock prices show some correspondence to EMH and individual stock movements make more sense than do market movements; book‐to‐market value of US firms explains a substantial fraction (0.75‐0.80) of changes in future earnings; predictable variation is often larger than bubble component of stock prices

EMH for aggregate market has still never been supported by any study linking stock market fluctuations with subsequent economic fundamentals

Blossoming of Behavioral Finance General considerations – by end of 1980s academic finance had turned to other theories; behavioral finance developed because researchers had seen too many anomalies in EMH

Feedback models


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⎯ When speculative prices go up creating successes for some investors, this may attract public attention, promote word‐of‐mouth enthusiasm and heighten expectations for further price increases; talk attracts attention of “new era” theories and models that justify price increases; this in turn creates investor demand and generates another round of price increases; if feedback is not interrupted it produces a speculative bubble in which high expectations for further price increases support very high current prices; high prices are ultimately not sustainable and bubble eventually bursts

⎯ Feedback carries seeds of its own destruction; end of bubble may be unrelated to news or fundamentals; same feedback may also produce a negative bubble where downward price movements propel further downward price movements

⎯ Feedback theory is at least as old as Holland tulip mania (Anonymous 1637, MacKay 1841) ⎯ Feedback theory is very difficult to find expressed in finance or economics texts even today;

academic research has until recently hardly addressed it ⎯ Presence of feedback is supported by experimental evidence in finance

− Andreassen & Kraus 1988 showed people extrapolate past price changes − Smith et al 1988 created experimental markets that generated bubbles − Marimom et al 1993 generated bubbles if subjects preconditioned to expect bubbles − Daniel et al 1999 showed biased self‐attribution can promote feedback

⎯ Presence of feedback is also supported by cognitive psychology − Bem 1965 identified biased self‐attribution, whereby individuals attribute events that confirm

validity of their actions to their own high ability and events that disconfirm their actions to bad luck or sabotage

− Tversky & Kahneman 1974 showed people predict using representativeness heuristic, seeking match to most similar past pattern without attention to observed probability of matching pattern; people evaluate probability of uncertain event by degree to which it is (1) similar in essential properties to its parent population and (2) reflects salient features of process by which it is generated

− Tversky & Kahneman 1979 prospect theory suggests that individuals are roughly twice as upset by losses than they are pleased by equivalent gains and that investors are systematically overconfident in their ability to forecast future stock prices and corporate earnings

⎯ Feedback is also confirmed by obvious success of Ponzi schemes like Albania 1997 ⎯ It is widely thought that there is a problem with feedback theories because they would seem to

imply that speculative price changes are strongly serially correlated but stock prices approximately follow a random walk; in fact simple feedback models do not imply strong serial correlations − Shiller 1990 models demand for speculative assets as a distributed lag with exponentially

decreasing weights on past price changes plus other factors that affect demand; people react to price changes over months or years and not just recent prices

− Random walk is not fully supported by evidence and there has been more than a little momentum to stock prices; there is tendency for prices to continue in same direction over six months to a year but to reverse themselves over longer intervals

Smart money vs Ordinary investors ⎯ From a theoretical point of view it is far from clear that smart money has power to drive market

prices to fundamental values in presence of irrational investors ⎯ Goetzmann & Massa 1999 grouped Fidelity traders into momentum investors and contrarian

investors, and investors tended to stay as one or other rarely shifting between categories


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⎯ Since Miller 1977 research has focused on an important obstacle to smart money offsetting irrational investors – smart money may be unable to short shares; in some cases stocks are held primarily by zealots; an example is irrational pricing of 3Com spin‐off of Palm

⎯ High levels of short interest for individual stocks predicts low subsequent returns for them as expected, but predictability is weak; there is a significant errors‐in‐variables problem when using short interest as an indicator of cost of shorting, and there is no unambiguous way to understand which stocks are difficult to short or cost of shorting individual stocks

⎯ True cost of shorting is higher than explicit cost of borrowing shares because of psychological costs of shorting, especially unlimited loss potential and need to cover losing positions

⎯ Professional arbitrageurs will be loath to sell short a stock they believe is trading too high relative to its fundamental value when it is always possible that some greater fools may be willing to pay even more; they are quite likely to have short horizons since even temporary losses may induce their clients to withdraw their money

⎯ Shleifer & Vishny 1997 discuss possibility that arbitrage opportunities may fail to be eliminated and mispricings may widen if arbitrageurs are driven out by adverse market movements

⎯ Remarkably few shares are sold short; from 1977‐2000 NYSE short interest ranged from 0.14% to 1.91%; less than 2% of all stocks had short interest greater than 5%; it is hard to see how such a small amount of short selling could offset effect on prices of extra demand by irrational investors

Conclusion Fama 1998 found fault with behavioral finance for two basic reasons ⎯ Anomalies tended to be underreactions as often as overreactions; post‐event continuation of

abnormal returns is as frequent as post‐event reversals; there is no fundamental psychological principle that people tend to overreact so financial anomalies should not reveal such a principle either

⎯ Anomalies tended to disappear either as time passed or as methodology improved; many anomalies tend to disappear when exposed to different models for expected normal returns, different methods to adjust for risk or when different statistical approaches are used to measure them − Most fundamental anomaly of excess volatility has not been knocked down and in fact was

graphically reinforced by recent global boom/crash stock market − Moreover one would expect anomalies to sometimes disappear in irrational markets, it seems

peculiar to argue that irrational markets should display regular and lasting patterns While theoretical models based on EMH have their place as illustrations of an ideal world we cannot maintain them as accurate descriptors of actual markets


18

EMH and Its Critics

Introduction Intellectual dominance of EMH is far less universal, but paper concludes that stock markets are far more efficient and far less predictable than some recent academic papers would have us believe

Evidence is overwhelming that whatever anomalous behavior may exist it does not create portfolio trading opportunities that enable investors to earn extraordinary risk adjusted returns

Markets can be efficient even if stock prices exhibit greater volatility than can apparently be explained by fundamentals such as earnings and dividends6

A nonrandom walk down Wall Street Short term momentum ⎯ Lo & MacKinlay 1999 found that short‐run serial correlations are not zero and existence of too

many successive moves in same direction enable them to reject hypothesis that stock prices behave as true random walks; attributed to bandwagon effect

⎯ Lo et al 2000 found through nonparametric statistical techniques that some price signals used by technical analysts have some modes predictive power

⎯ Investors underreact to new information – if full impact of an important news announcement is only grasped over a period of time, stock prices will exhibit positive serial correlation

⎯ Several factors should prevent us from interpreting empirical results reported above as an indication that markets are inefficient − While stock market may not be a random walk, it is important to distinguish statistical

significance from economic significance; statistical dependencies giving rise to momentum are extremely small and are not likely to permit investors to realize extraordinary excess returns; momentum and relative strength strategies are not profitable because of transaction costs involved in their execution

− Evidence that bandwagon effects and underreaction to new information occur systematically7 is rather thin as surveyed by Fama 1998

− Many predictable patterns seem to disappear after they are published in finance literature, for example January effect

Long term return reversals ⎯ Fama & French 1988 found that 25‐40% of variation in long holding period returns can be predicted

in terms of negative correlation with past returns; Poterba & Summers 1988 found substantial mean reversion at long horizons; attributed to investor overreaction

⎯ Finding of mean reversion is not uniform across studies and is quite a bit weaker in some periods than others; strongest empirical results come from periods including Great Depression which may be a time with patterns that do not generalize well8

⎯ Fluck et al 1997 confirmed very strong statistical evidence of return reversals but not one that would enable investors to make excess returns

6 This is rather an odd interpretation of market efficiency; I disagree with this position and agree with Shiller’s position in his paper 7 It is unclear why we would expect these effects to occur systematically rather than erratically 8 Paper goes on to mention that stock mean reversion “could” result from interest rates which are known to be mean reverting but does not provide any evidence to support this supposition


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Seasonal and day‐of‐week patterns ⎯ January effect: Stock returns tended to be unusually high during first two weeks of year,

particularly for small cap stocks ⎯ Monday effect: French 1980 documented significantly higher Monday returns ⎯ There appear to be patterns in returns around turn of month as well as around holidays ⎯ There appear to be significant differences in average daily returns in foreign countries ⎯ These anomalies are not dependable and are very small relative to transaction costs

Predictable patterns based on valuation parameters Predicting future returns from initial dividend yield ⎯ As much as 40% of variance of future returns for market can be predicted on basis of initial dividend

yield of market index; works less well for individual stocks ⎯ These findings are not necessarily inconsistent with efficiency; dividend yields tend to be high when

interest rates are high ⎯ Dividend behavior of US corporations has changed over time; dividend yield may not be as

meaningful as in past Predicting market returns from initial P/E ratio ⎯ As much as 40% of variance of future returns for market can be predicted on basis of initial P/E ratio

of market index ⎯ However, based on results from this strategy in period 1987‐2002 we should take a very cautious

assessment of extent to which returns are predictable on this basis Other predictable time series patterns9 ⎯ Fama & Schwert 1977 found that short term interest rates were related to future stock returns ⎯ Keim & Stambaugh 1986 found that corporate bond spreads had some predictive power ⎯ Campbell 1987 found term structure of interest rates contained useful information for forecasting

stock returns

Cross‐sectional predictable patterns based on firm characteristics and valuation parameters

Size effect ⎯ Since 1926 small cap stocks in US have produced returns over 1 percentage point larger than large

cap stock returns; if beta is accepted as correct risk measurement statistic size effect indicates small stocks earn excess risk‐adjusted return

⎯ Fama & French 1993 suggest size may be a far better proxy for risk than beta, eliminating this anomaly

⎯ Some studies have been affected by survivorship bias Value stocks ⎯ Since 1960 studies have suggested that value stocks have higher returns than growth stocks; finding

is consistent with views of Graham & Dodd 1934 and Buffett; may be caused by investor willingness to overpay for growth

⎯ Fama & French 1993 concluded that size and book‐to‐market together provide considerable explanatory power for future returns and little additional influence can be attributed to P/E

9 Paper says this apparent predictability “may” reflect varying risk premium but does not provide any evidence; use of varying risk premium seems bogus to me in any event since it is used to explain away any excess return that does not fit neatly into whatever model is being presented


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⎯ These findings do not necessarily imply inefficiency; they may simply indicate failure of CAPM; book‐to‐market may reflect another risk factor that is priced into market; Fama & French argue that three‐factor asset pricing model is appropriate benchmark against which anomalies should be measured

Equity Risk Premium (ERP) puzzle ⎯ Another puzzle is existence of very large historical ERP inconsistent with actual risk of stocks ⎯ May be due to perceived equity risk being considerably higher during early years of period; US stock

market is almost unique in that it remained in continuous operation during period ⎯ One must be very careful to distinguish between expected risk premiums and such premiums

measured after fact10 Summarizing anomalies and predictable patterns ⎯ Any truly repetitive and exploitable pattern or irrationality that can be discovered will be arbitraged

away and self destruct; practitioners exploit it ∋ it becomes no longer profitable ⎯ Many predictable patterns that have been discovered may simply be spurious correlations as a

consequence of data mining ⎯ Published literature is biased in favor of reporting positive results rather than negative results or

confirmations of previous findings

Seemingly irrefutable cases of inefficiency Market crash of October 1987 could be ascribed to cumulative effect of a number of fundamental events unfavorable to equities11 ⎯ Yields on long term Treasury bonds increased from about 9% to almost 10.5% in two months

preceding mid‐October ⎯ Early in October Congress threatened to impose a merger tax that could well have made merger

activity prohibitively expensive and ended merger boom and SecTreas Baker threatened to encourage a further fall in value of dollar

Internet bubble of late 1990s – while it is now clear in retrospect that even market professionals were egregiously wrong there was certainly no obvious arbitrage opportunity available

Closed‐end funds sell at arguably irrational discounts from their NAVs; discounts have narrowed from historical averages for funds with assets traded in liquid markets; researchers have suggested discounts can largely be explained by fund management fees12

Palm spin‐off Other illustrations of irrational pricing (paper does not even attempt to refute these) ⎯ Co‐movement of MCI Corporation stock (MCIC) with unrelated closed‐end bond investment fund

MassMutual Corporate Investors (MCI) ⎯ Positive stock price reactions in 1998‐9 when non‐internet companies added dotcom to their

corporate titles

Performance of professional investors A remarkably large body of evidence starting with Jensen 1968 suggests that most professional investment managers (about ¾ in past decade) are not able to outperform index funds that buy and

10 Problem is that expected risk premia are not observable in market 11 So was the price “efficient” immediately before the crash or immediately after the crash? If both, then how? 12 What about when closed-end funds sell at a premium?


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hold broad market index portfolio such as S&P or Wilshire; median manager underperformed S&P500 by almost 2 percentage points over past 20 years


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Anomalies: Law of One Price in Financial Markets

Introduction Essential ingredients for violations of law of one price are (1) some agents must falsely believe there are real differences between two identical goods and (2) there have to be some impediments to prevent rational arbitrageurs from restoring equality of prices – can these conditions exist in financial markets?

Closed‐end funds Both discounts and premia of greater than 30% are commonly observed; rational justifications such as fees and expenses to justify discounts or superior stock picking ability to justify premia can at best justify small deviations

Late 1980s saw proliferation of country funds that trade on US exchanges; these often had much larger deviations than those observed in domestic funds; Spain and Germany funds had over a 100% premium; an extreme example is Taiwan Fund that had a 205% premium during early 1987 shortly after its start

Graham 1959 called this “an expensive monument erected to inertia and stupidity of stockholders” Differences may exist because it is difficult for arbitrageurs to short overpriced funds

ADRs ADRs can have prices different from value of underlying assets although in most cases they don’t have significant deviations since arbitrage is possible; however occasionally remarkable price discrepancies do exist particularly if there are barriers to buying foreign securities directly

Infosys ADR was trading at 136% premium to Indian shares; while in a segmented market it can be rational for same asset to have different prices in different markets, particularly due to diversification benefits it is dubious that this could justify such a large discrepancy

Twin shares – can stock market multiply by 1.5? Royal Dutch / Shell was one firm but had both Royal Dutch shares in Amsterdam and Shell shares in London; based on 1907 merger agreement Royal Dutch shares had a 60% interest in firm and Shell shares had 40%; therefore ratio of market value of Royal Dutch to market value of Shell should have been 1.513

This ratio varied considerably from its theoretical value, from 30% too low in 1981 to 22% too high in October 1998

LTCM had a $2.3B convergence trade on Royal Dutch / Shell for which it could find no takers when it entered financial distress

Both Royal Dutch and Shell had ADRs; thus to profit a US investor didn’t even need to trade in international markets, just short overpriced shares and buy underpriced shares and hold forever; of course in near term price disparity can wide producing losses to this strategy

Of course there is an even simpler way to keep prices lined up – investors should only buy cheaper version; why during 1990s when Royal Dutch was selling at a premium over Shell did US mutual funds own billions of dollars of Royal Dutch? A partial answer is that Royal Dutch was a member of S&P500 index

13 In 2005, after paper was written, Royal Dutch Shell’s corporate structure was integrated to eliminate this oddity


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Dual share classes Molex has two classes of stock with claims to identical dividends and cash flows but different voting rights; premium for voting stock had tended to range between 0 and 10%; in November 1999 S&P500 announced it was adding voting stock and premium rose from 12% to 24% and subsequently rose as high as 49% in March 2000; whatever value voting rights had it is hard to see why these rights would become more valuable because firm was included in S&P500

Corporate spinoffs – can stock market multiply by 1.5? In early 2000 3Com carved out 5% of Palm with rest to be distributed to 3Com shareholders (1.5 shares of Palm per share of 3Com) about six months later

On day of IPO 3Com was selling for $104 and Palm was offered at $38; Palm ended day at $95 after trading as high as $165 and 3Com fell to $82; this implied a value of ‐$60 for rest of 3Com’s assets which included $10 per share in cash; investors were willing to buy expensive shares of Palm rather than buy cheap Palm shares embedded in 3Com and get 3Com thrown in for free

This example is even more puzzling because there was a clear termination date; an arbitrageur would need only buy 1 share of 3Com, short 1.5 shares of Palm and wait six months; spin‐off depended on a favorable IRS ruling but this appeared highly likely; there was thus a strong incentive to short Palm

This was not an obscure corner of capital markets; it was a widely publicized IPO that attracted frenzied attention; nature of mispricing was so simple that even dimmest market participants grasped it; it even made USA Today in addition to WSJ and NYT

At one point 148% of floating shares of Palm had been borrowed, interest cost of borrowing Palm shares reached 35%, and puts on Palm became so expensive that put‐call parity failed to hold; zealots had won with Palm and had control over its price for time being

Other examples ⎯ Lamont & Thaler 2003 identified internet and telecom examples from 1996‐2000 ⎯ Graham 1923 noticed that although DuPont owned a substantial number of GM shares its market

cap was ∋ it had a stub value of about zero so he bought DuPont and shorted GM

Long term capital in a short term world Why aren’t arbitrageurs doing their job? Answer is that violations of law of one price do not generally create arbitrage opportunities, just good but risky bets

Risks are particularly large in situations without a specified terminal date; noise trader risk is risk that valuation disparity widens causing net worth of arbitrageur to fall; idea is that whatever irrational opinion caused noise traders to get excited or depressed could get worse before it gets better

Most prominent example is LTCM

Commentary For most securities that market needs to price there are no good substitutes so arbitrage cannot be relied upon to set prices correctly

What economists should really care about is whether markets are sending approximately correct signals to market participants in order to direct capital to its most productive uses

Special cases in this paper are interesting because they should be situations in which it is particularly easy for market to get things right; if market is flunking these no‐brainers what else is it getting wrong?


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During NASDAQ bubble approximately $7 trillion14 of wealth was created and then destroyed

14 This doesn’t include NYSE companies such as Lucent


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Stocks for Long Run Chapter 7

Introduction On 2/14/2000 Merrill Lynch Global Fundamental Equity Research Department published a report claiming that “new economy” called for “creative” valuation models because internet had unleashed a new alignment between businesses and humanity’s innate need to create

There is little historical evidence that periods of more rapid technological progress have had any permanent impact on earnings growth or stock prices

As long as sources of efficiency gains are not proprietary and can be replicated and used by other firms, excess profits will be competed away quickly in form of lower prices; history shows that ultimate beneficiary of technological change is always consumers

Corporate Profits and National Income Corporate profits long term average from 1929 to 2001 was 6.8%; although it fluctuates with business cycles it cannot grow faster than national income in long run

Limit on real per share earnings growth also puts a limit on return shareholders can expect from equity

Factors raising valuation ratios General considerations ⎯ Even if earnings growth does not increase there are several favorable factors that justify higher

valuation ratios for stock market as we enter new millennium; there is good reason to believe that many of these factors may be expected to persist over some time

⎯ Historically stocks have been undervalued delivering much higher returns than should be expected considering their long term risk; one possible explanation for rise in stock prices is that stocks have been bid up because investing public has finally recognized superiority of equities as long term investments

⎯ Of course past decade has not been only period when investors recognized “superiority” of common stocks as long term investments; in 1920s and 1960s investors bid up stock prices only to be hammered by Great Depression of 1930s and by 1970s respectively

Economy has become more stable – policymakers are able to avoid sharp swings in real output and inflation that in past made stocks far riskier investments; industrial production is much more stable, and stable service sector is a larger fraction of GDP

Transaction costs have dropped from 1% in 1975 to 0.18% today; this allows for efficient diversification; also stocks today are far more liquid than through most of past two centuries so valuation relative to earnings should rise

Taxes – a considerable and increasing part of a stock’s return is realized through capital gains and taxes on those gains are set at substantially lower levels than rates on other income; a further favorable tax‐related development is low inflation since capital gains taxes are calculated on nominal appreciation

Justified P/E ratios ⎯ If we take into account changes in inflation, taxes and transaction costs, higher P/E ratios are

justified than past historical average of 14‐15, perhaps as high as 27 based on 2001 factors ⎯ These three factors also explain major movements of market’s P/E ratio over past 50 years


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ERP ERP has been 5% from 1926 to 2001 and 3.5% over past 200 years Mehra & Prescott 1985 studied return data 1889‐1978 and claimed that economic models predicted that relative risk aversion parameter should be no larger than 10 which implied that either stock returns should be lower or Treasury returns should be higher or both; according to their studies an ERP as low as 1% could be justified

Bosland 1937 predicted that one consequence of knowledge of superior stock returns would be narrowing of ERP; Glassman & Hassett 1999 claimed that ERP should be 0 and that this should send DJIA to 36000

Although stocks may be as safe as bonds at long horizons they cannot be safer than new Treasury Inflation Protection Securities (TIPS) that are now yielding about 3.5% (and rose temporarily as high as 4.5% in March 2000) so stocks must yield more than this; how much more is an open question

Future Equity Returns A P/E ratio of 20‐25 would indicate real equity returns of 4‐5% There are a number of favorable factors ⎯ When market value of equity exceeds replacement cost of capital, Tobin’s Q > 1, and earnings yield

underestimates future returns ⎯ Past overinvestment in networking and telecommunications provides excess supply of capital that

lowers funding costs and increases future returns ⎯ Financial and intellectual capital flow into US economy from abroad seeking a safe haven, a factor

that boosts US equities ⎯ Given shift toward corporate form of ownership and away from partnerships and sole

proprietorships, one would have expected corporate profit share to increase yet it did not; hence total return to capital has declined; this leaves corporate profits with some room to grow as a share of national income

These factors should boost future real return on equities to about 6%, somewhat lower than 7% long run average return that stocks have yielded throughout history; this means future ERP is likely to be in 2‐3% range, about one half of level that has prevailed over past 70 years

Terrorism Composition of US output will be tilted toward increased military and security expenditures; this will reduce productivity growth because for firms security is considered an input into production process and is not included in GDP; increased security will raise price and lower quantity of final output produced

Immediately after 9/11/2001 terrorist attacks capital began flowing to security industry; even though their output may not find its way into GDP their market value increased; in general security using firms will lose earnings that security producing firms will gain

Terrorist attacks raised level of uncertainty; unpredictable consumer demand means less capital will be devoted to industries that require substantial investment; unpredictable corporate profits may cause investors to require a higher return on equity capital

However it is very hard to quantify increase in ERP if any; height of potential nuclear holocaust threat occurred in late 50s and early 60s, a decade of robust stock prices


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Age Wave To some forecasters all these issues are small potatoes compared to Age Wave; in past younger generations when reaching middle age usually had sufficient purchasing power to buy their parents’ assets; this time however there are not nearly enough generation Xers with sufficient wealth to absorb baby boomers’ substantial portfolios at current prices

Solution to age wave crisis ⎯ More rapid economic growth – one can compensate for dearth of numbers of generation Xers by

making them all better off ∋ they are able to buy abundant assets of baby boomers; Social Security figures indicate a 2% productivity increase is needed; most economists believe productivity can be boosted 1% but not 2%

⎯ Developing world can emerge as another answer – if their progress continues they will sell goods to baby boomers and thereby acquire buying power to purchase their assets; this is critically dependent on continued integration of world economies

Conclusion Although stocks may not match their impressive returns of past all evidence still indicates that they will significantly outperform fixed income investments over long run


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Derivatives Practices and Principles Recommendations

1. General Policy – Role of Senior Management Dealers and end users should use derivatives in a manner consistent with overall risk management and capital policies approved by their boards of directors. These policies should be reviewed as business and market circumstances change. Policies governing derivatives use should be clearly defined, including purposes for which these transactions are to be undertaken. Senior management should approve procedures and controls to implement these policies, and management at all levels should enforce them.

Valuation and Market Risk Management 2. Marking to Market – Dealers should mark their derivatives to market on at least a daily basis for risk management purposes

3. Market Valuation Methods – Derivatives portfolios of dealers should be valued based on mid‐market levels less specific adjustments, or on appropriate bid or offer levels. Mid‐market valuation adjustments should allow for expected future costs such as unearned credit spreads, close‐out costs, investing and funding costs, and administrative costs

4. Identifying Revenue Sources – Dealers should measure components of revenue regularly and in sufficient detail to understand sources of risk

5. Measuring Market Risk – Dealers should use a consistent measure to calculate daily market risk of their derivatives positions and compare it to market risk limits. ⎯ Market risk is best measured as VaR using probability analysis based upon a common confidence

interval (e.g. 2 standard deviations) and time horizon (e.g. 1 day exposure) ⎯ Components of market risk that should be considered across term structure include absolute price

or rate change (delta), convexity (gamma), volatility (vega), time decay (theta), discount rate (rho), and basis or correlation

6. Stress Simulations – Dealers should regularly perform simulations to determine how their portfolios would perform under stress conditions

7. Investing and Funding Forecasts – Dealers should periodically forecast cash investing and funding requirements arising from their derivatives positions

8. Independent Market Risk Management – Dealers should have a market risk management function with clear independence and authority to ensure that responsibilities are carried out ⎯ Development of risk limit policies and monitoring of transactions and positions for adherence to

these policies ⎯ Design of stress scenarios to measure impact of market conditions however improbable that might

cause market gaps, volatility swings, or disruptions of major relationships, or might reduce liquidity in face of unfavorable market linkages, concentrated market making, or credit exhaustion

⎯ Design of revenue reports quantifying contributions of various risk components and of market risk measures such as VaR

⎯ Monitoring of variance between actual volatility of portfolio value and that predicted by measure of market risk

⎯ Review and approval of pricing models and valuation systems used by front and back office personnel and development of reconciliation procedures if difference systems are used

9. Practices by End Users – As appropriate to nature, size and complexity of their derivatives activities, end users should adopt same valuation and market risk management practices that are recommended for dealers. Specifically they should consider regular marking to market their derivatives transactions


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for risk management purposes, periodically forecasting cash investing and funding requirements arising from their derivatives transactions, and establishing a clearly independent and authoritative function to design and assure adherence to prudent risk limits

Credit Risk Measurement and Management 10. Measuring Credit Exposure – Dealers and end users should measure credit exposure in two ways: (1) current exposure which is replacement cost or market value of derivatives transactions and (2) potential exposure which is an estimate of future replacement cost of derivatives transactions and should be calculated using probability analysis upon broad confidence intervals (e.g. 2 standard deviations) over remaining terms of transactions ⎯ Dealer or end user should ask two questions: (1) If counterparty defaults today what would it cost

to replace derivatives transaction? (2) If counterparty defaults in future what is a reasonable estimate of future replacement cost?

⎯ Current exposure is an accurate measure of credit risk that addresses first question; regular calculation of current exposure is a broadly accepted practice today

⎯ Most rigorous methods of potential exposure use either simulation analysis or option valuation models; often used to generate two measures: expected exposure and worst‐case exposure

11. Aggregating Credit Exposures – Credit exposures on derivatives and all other credit exposures to a counterparty should be aggregated taking into consideration enforceable netting arrangements; credit exposures should be calculated regularly and compared to credit limits ⎯ Current exposure is simply sum of negative exposures if netting applies (zero if netting does not

apply) and positive exposures ⎯ Potential exposure is more complicated as simply summing will in most casesdramatically overstate

actual exposure; straight summation fails to take into account transactions that offset each other or have peak potential exposures at different times; accurate calculation of potential exposure simulates entire portfolio

⎯ Dealers should monitor current exposure daily; can generally measure potential exposure less frequently

12. Independent Credit Risk Management – Dealers and end users should have a credit risk management function with clear independence and authority and with analytical capabilities in derivatives, responsible for (1) approving credit exposure measurement standards, (2) setting credit limits and monitoring their use, (3) reviewing credits and concentration of credit risk, and (4) reviewing and monitoring risk reduction arrangements ⎯ Credit risk management function should establish credit limits for counterparties consistent with

standards, conduct credit reviews before engaging in transactions with a counterparty, and should guide use of documentation and credit support tools

⎯ Credit limits and guidelines should ensure that only those potential counterparties that meet appropriate credit standards with or without credit support become actual counterparties

⎯ Credit risk management function should continually review creditworthiness and credit limits of counterparties

13. Master Agreements – Dealers and end users are encouraged to use one master agreement as widely as possible with each counterparty to document existing and future derivatives transactions including foreign exchange forwards and options; master agreements should provide for payment netting and close‐out netting using a fully two‐way payment approach ⎯ There is substantial scope for reducing credit risk by including foreign exchange forwards and

options along with other derivatives transactions


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⎯ Use of multiple agreements introduces risk of cherry‐picking and risk that right to net amounts might be delayed

⎯ Using full two‐way payments net amount calculated through netting provisions is due regardless of whether it is to or from defaulting party; benefits created about value of net position outweigh benefits under limited two‐way payment approach

14. Credit Enhancement – Dealers and end users should assess both benefits and costs of credit enhancement, collateral, margin and related risk reduction arrangements; where it is proposed that credit downgrades would trigger early termination or collateral requirements participants should carefully consider their own capacity and that of their counterparties to meet potentially substantial funding needs that might result

15. Promoting Enforceability Dealers and end users should work together on a continuing basis to identify and recommend solutions for issues of legal enforceability both within and across jurisdictions as activities evolve and new types of transactions are developed

Systems, Operations, Controls 16. Professional Expertise – Dealers and end users must ensure that their derivatives activities are undertaken by professionals in sufficient numbers and with appropriate experience, skill levels and degrees of specialization; these professionals include specialists who transact and manage risks involved, their supervisors and those responsible for processing, reporting and auditing activities

17. Systems – Dealers and end users must ensure that adequate systems for data capture, processing, settlement and management reporting are in place ∋ derivatives transactions are conducted in an orderly and efficient manner in compliance with management policies; dealers should have risk management systems that measure risks incurred in their derivatives activities including market and credit risks; end users should have risk management systems that measure risks incurred in their derivatives activities based upon their nature, size and complexity

18. Authority – Management of dealers and end users should designate who is authorized to commit their institutions to derivatives transactions

Accounting and Disclosure 19. Accounting Practices – Internal harmonization of accounting standards for derivatives is desirable; pending adoption of harmonized standards following accounting practices are recommended ⎯ Dealers should account for derivatives transactions by marking them to market taking changes in

value in income each period ⎯ End users should account for derivatives used to manage risks to as to achieve a consistency of

income recognition treatment between those instruments and risks being managed, thus if risk being managed is accounted for at cost (or in case of an anticipatory hedge not yet recognized) changes in value of qualifying risk management instrument should be deferred until a gain or loss is recognized on risk being managed; if risk being managed is marked to market with changes in value taken to income qualifying risk management instrument should be treated in a comparable fashion

⎯ End users should account for derivatives not qualifying for risk management treatment on a mark to market basis

⎯ Amounts due to and from counterparties should only be offset when there is a legal right to net or when enforceable netting arrangements are in place


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⎯ Where local regulations prevent adoption of these practices disclosure along these lines is nevertheless recommended

20. Disclosure – Financial statements of dealers and end users should contain sufficient information about their use of derivatives to provide an understanding of purposes for which transactions are undertaken, extent of transactions, degree of risk involved, and how transactions have been accounted for; pending adoption of harmonized accounting standards following disclosures are recommended: (1) information about management’s attitude to financial risks, how instruments are used, and how risks are monitored and controlled, (2) accounting policies, (3) analysis of positions at balance sheet date, (4) analysis of credit risk inherent in these positions, and (5) for dealers only additional information about extent of their activities in financial instruments

Legislators, Regulators, Supervisors 21. Recognizing Netting – Regulators and supervisors should recognize benefits of netting arrangements where and to full extent that they are enforceable and encourage their use by reflecting these arrangements in capital adequacy standards; specifically they should promptly implement recognition of effectiveness of bilateral closeout netting in bank capital regulations

22. Legal and Regulatory Uncertainties – Legislators, regulators and supervisors including central banks should work in concert with dealers and end users to identify and remove any remaining legal and regulatory uncertainties wrt (1) form of documentation required to create legally enforceable agreements, (2) capacity of parties such as governmental entities, insurers, pension funds and building societies to enter into transactions, (3) enforceability of bilateral closeout netting, multi‐branch netting and collateral arrangements in bankruptcy, and (4) legality and enforceability of derivatives transactions

23. Tax Treatment – Legislators and tax authorities are encouraged to review and where appropriate amend tax laws and regulations that disadvantage use of derivatives in risk management strategies; tax impediments include inconsistent and uncertain tax treatment of gains and losses on derivatives in comparison with gains and loses that arise from risks being managed

24. Accounting Standards – Accounting standards setting bodies should as a matter of priority provide comprehensive guidance on accounting and reporting of transactions in financial instruments including derivatives and should work towards international harmonization of standards on this subject; IAS committee should finalize its accounting standard on financial instruments


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Financial Dynamics of Insurance Industry Chapter 16

Introduction To serve cause of ALM it is essential for a performance measure to report profitability and risk exposures in a timely and market‐sensitive manner; to function as an early warning system it must give effects to changing market conditions

Traditionally insurers report earnings on a book‐value basis, compare portfolio rate with credited rate to measure spread earned by assets over liabilities, and measure manager performance compared to market; each of these measures serves a purpose; however upon close examination each by itself seems to suffer from one of two drawbacks or both ⎯ May be too stabilized by design for day‐to‐day management ⎯ May be too one‐dimensional to give integrated view of performance in today’s environment, does

not work well with embedded options, interest sensitive liabilities, derivatives Environment has become more complex and risk‐exposed ⎯ Assets: MBSs, CDOs ⎯ Liabilities: GICs, SPDAs, UL, closeouts, structured settlements ⎯ Portfolio management has increasingly relied on derivatives

Conventional approaches may not adequately reflect risk and return; a new integrated approach is needed – asset allocation, bond swaps, targeting duration, product pricing as well as testing alternative distributions and product mixes

To extent assets are marketable, they can be managed by standard approaches; mark to market for retrospective analysis; perform simulations for prospective analysis

Liabilities on other hand are by and large unmarketable; an insurer has no recourse; in event of poor asset performance an insurer cannot pay its policyholders or another insurer a distress price to unload liabilities; book value approaches are used for retrospective analysis; cash flow testing is used for prospective analysis

Total return approach, for prospective/retrospective analysis of ALM ⎯ Recognizes crucial connection between assets and liabilities via interest rate (C3) risk ⎯ Establishes internally consistent management system for assets and liabilities as well as for

prospective and retrospective analysis Description of approach ⎯ Value liabilities in a manner consistent with assets ⎯ Introduce measure that relates mark to market approach to initial pricing of liability ⎯ Provide return attribution methodology to identify effect of all risk sources on ALM ⎯ Implement cash flow testing in a manner consistent with total return analysis

Has broad applications to internal management – strategic and tactical decisions, management of assets and other resources; complements but does not replace standard measures

Differs from conventional approaches in way it captures economic gains and losses and attributes them to independent management actions

Total Return Approach Liability valuation ⎯ Marking liabilities to market like assets breaks new ground in a performance measure ⎯ Assets and liabilities share dependence of their economic values on level of interest rates; this

crucial link is what makes consistent valuation both a possibility and a requirement


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⎯ Credit risk is not a common thread since insurer has to perform, so market’s perception of requisite credit spread on liabilities has no bearing

⎯ Required spread − For a single‐premium contract with a fixed cash flow stream, required spread is spread over

Treasury spot curve by which discounted value of cash flow stream is equal to single premium at issue

− Once required spread is so determined it is held constant and used to mark liability to market by discounting remaining cash flows at prevailing Treasury spot curve plus calculated required spread

⎯ Hence liability value is equal to single premium at issue, final cash flow at maturity, and a market sensitive value in between; traditional book value accomplishes first two but not third objective; discounting cash flows at Treasury rates accomplishes second and third but not first objective

⎯ Despite label “market value” it should not be misconstrued as price that same liability would fetch in open market or price insurer would set today or liquidation value

⎯ Change in liability value has three components: (1) change in interest rates, (2) time value of money, (3) required spread

⎯ By maintaining a market value gain insurer is assured a surplus at maturity; by maintaining a book value gain there is no such assurance

⎯ A common alternative is to discount at Treasury spot curve, corresponding to zero required spread; a drawback is that this would lead to initial liability value in excess of premium, analogous to reserve strain that often arises in statutory accounting

⎯ Rather than putting up a market value loss up front to recover it later, methodology in effect amortizes strain over life of liability through use of required spread

⎯ If cash flows incorporate life contingencies, there will be changes in liability attributed to a 4th component – revisions to cash flow projections, which in practice should not materialize as often as first three

⎯ Required OAS – natural extension of required spread to products with embedded options − Consider an interest rate path generated by an arbitrage free model of Treasury yield curve

movements − Determine cash flow of option embedded bond along this path via a contingent claim model for

bonds − OAS is spread that equates fair value (average of PV of path specific cash flows along all interest

rate paths) to market price or net issue price of product − Required OAS in effect amortizes excess of liability’s riskless price over its actual price

Total Return and Total Required Return ⎯ Once we know how to mark to market periodically we have a way of measuring performance

retrospectively ⎯ Total Return on asset side is made up of income received and asset appreciation; Total Required

Return on liability side is made up of obligations discharged and change in value of remaining liabilities

⎯ Net profit on total return basis is total return minus total required return ⎯ Recommend a weekly determination of total return and total required return, accumulated

geometrically once a month; if return calculation is done more often cash flow incidence needs to be less precise

⎯ Prospective analysis


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− Start with a liability pricing model, an asset pricing model and a spectrum of interest rate scenarios

− If total return exceeds total required return at each point along each path, assets and liabilities are immunized

Return attribution ⎯ First define key rate durations; then from initial yield curve project forward yield curve for one

period (usually a week); consider deviation of actual yield curve from forward yield curve as represented by key rates

⎯ r = rf + ROAS – ΣDi,liabilityΔri + Expliability − If ROAS is revised to recognize experience gains/losses a term for ΔROAS is added

⎯ For assets r = rf + OAS – DOASΔOAS – ΣDi,assetΔri + R/C + PA – Expasset − R/C is rich/cheap rate relative to observed prices for actively traded assets − PA is a portfolio adjustment for securities traded in or out during period

⎯ Performance measurement and evaluation − rf is riskless rate on assets and liabilities; if both values are equal net profit is 0; if asset value

exceeds liability value this term gives riskless return on market surplus − Net profit from taking on Credit (C1) Risk = OAS – DOASΔOAS − Net profit from Pricing (C2) Risk = ‐ROAS; an inadequately priced product would lead to a high

ROAS which may be an unreachable goal; if a line of business truly becomes more successful in marketing we may expect to see increased sales with lower ROAS

− Net profit from taking on Duration (C3) Risk =15 ΣDi,assetΔri,asset – ΣDi,liabilityΔri,liability − Intraweek changes due to market risk = R/C + PA − Expenses = –(Expasset – Expliability)

⎯ Breakdown allows us to attribute change in market surplus to management actions from different sources

Applications Setting consistent goals in managing assets and liabilities ⎯ In a turbulent environment it may not be possible for total return to beat required return week

after week; however it may not be necessary; what total return approach gives insurer is a way of monitoring exactly where it is; within a tolerance level there is no need to make an adjustment if a temporary market condition is expected to reverse itself

⎯ If danger in book value accounting is complacency, danger in market value accounting is overreaction; hence one needs both types of accounting to strike a proper balance

There is an interdependence between prospective and retrospective analysis; maintaining consistency is an important part of developing a sound management tool

Tactical decision tool – if key rate durations are made available to asset managers each trade can be evaluated by its marginal contribution to ALM

Performance evaluation – return attribution pinpoints what each independent management action has contributed to change in net return ⎯ Positive result in rich/cheap rate indicates skill in bond selection ⎯ Positive result in duration return indicates skill in interest rate anticipation ⎯ Positive result in OAS return indicates skill in sector rotation16

15 Equation in study note is incorrect as it does not take into account possibility that rate changes could be different


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Supplementing conventional performance measures ⎯ What is good for public consumption is good for internal management, only internal management

needs more to provide early warning signals ⎯ If GAAP earnings, statutory earnings and market net return are tracked simultaneously over time,

market net return will better reveal economic undercurrents

SPDA Pricing procedure17 ⎯ Procedure starts with estimating Treasury spot yield curve and calibrating binomial lattice arbitrage‐

free term structure model ⎯ Then we randomly select interest rate paths within binomial lattice; along each path we start with

interest rates to get lapse rates and then SPDA cash flows at each point; average PV of path‐specific cash flows for entire random space defines model value

⎯ To search for ROAS we repeat above procedure by adding a constant spread to each path iteratively until spread is found to equate model value with net proceeds of SPDA

Analytic results ⎯ Comparative pricing analysis

− Rate responsive crediting strategy (α=0.7) vs stable crediting strategy (α=0.2) − Three lapse assumptions as multiples of arctan function: 150% (rate sensitive), 100% (normal),

50% (rate insensitive) − Results obtained were SPDA model price for zero ROAS, effective duration, convexity,

proportional price sensitivity to small change in ROAS, policyholder option cost, ROAS, and market index spread sensitivity

− Crediting strategy has significant effect on duration − Unlike MBSs whose prepayment function resembles our lapse function an SPDA need not have

a negative convexity; a key difference lies in fact that crediting strategy seeks to neutralize lapse behavior plus deterrent posed by surrender charge; as a result SPDA convexity is positive

− Average life is shorter for rate‐sensitive lapse function and longer for rate‐insensitive lapse function; average life is somewhat independent of crediting strategy

− Policyholder option value varies by crediting strategy, with rate responsive strategy SPDA offers negligible option value

− ROAS is higher for rate responsive crediting strategy ⎯ Total return analysis

− Interest rate component attributable to yield curve movements is small, which is no surprise in view of proximity in effective duration of assets and liabilities

− Liquidity/Credit Spread = OAS – ROAS, is also relatively small − Relative insignificance of Rich/Cheap term shows that bond selection is not an important

contribution to total return − Residuals, return components not explained by model, are negligibly small

Conventional approaches to performance measurement Statutory or GAAP investment income

16 Of course, it is also possible that these positive results are nothing but random accidents 17 Details of SPDA contract are given but they are not needed for this study note summary


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⎯ Inasmuch as an insurer’s public reporting basis is statutory/GAAP, book‐based statutory/GAAP investment income has a rightful role in guiding corporate policy and management decisions; for example in deciding dividend scale insurer should consider implications emanating from statutory/GAAP investment income

⎯ For day‐to‐day operational management investment income has a number of limitations − Book values do not reflect what assets are worth; not market sensitive − Until adoption of Interest Maintenance Reserve one can arbitrarily put earnings on books by

selectively harvesting capital gains − Investment income is not a very informative indicator without normalizing for size of asset base,

availability of investable funds, level of new money rates, and amount and timing of asset rollovers; not risk adjusted

− It is incomplete without a liability benchmark Earned Rate vs Credited Rate ⎯ This measure has certain advantages over previous one: (1) it is expressed as a rate so it is

automatically normalized for size, and (2) it uses credited rate as a liability benchmark ⎯ However it is still a book yield insensitive to market and not adjusted for call risk and credit risk;

cannot guide management decisions Nominal spread of Treasuries on new investments ⎯ Market values are used for performance measure for marginal investment decisions, by measuring

new money rates against Treasury rates ⎯ Works well for new money but it may leave out too much of a portfolio; also Treasuries may not be

an appropriate benchmark; finally new money rate as nominal yield can still grossly misstate prospective return since it is not adjusted for call risk and credit risk; cannot guide management decisions

Capital market indices and cash flow testing ⎯ Approach at forefront today is two‐fold: (1) money management conventions for performance

measurement, and (2) cash flow testing for risk analysis ⎯ Money management

− Most significant advantage is that asset manager goals are defined in familiar and standardized fashion, and manager is given a benchmark that is market‐sensitive and risk‐adjusted

− Main drawback is that indices do not represent insurer’s liability, and outperforming index is no safeguard against insolvency; cannot guide management decisions

⎯ Cash flow testing − Connects asset and liability performances − Depends on many assumptions (credit spread, default rates, call/prepayment functions,

crediting strategies, lapse rates, reinvestment policies); research leads to question of how many scenarios one should test, and as products and assets are becoming more complex there is to date no satisfactory answer to this question

Summary of what we should strive for in a performance measure, which conventional approaches fail to exhibit ⎯ Relate to management portfolio and pricing decisions to enhance firm value ⎯ Must be risk‐adjusted for all risks ⎯ Must be market sensitive ⎯ Assets and liabilities have to be evaluated concurrently and consistently


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Liability index Why build a liability index? ⎯ Replicates interest rate risk exposure of liabilities, which is most significant risk that is common to

assets and liabilities ⎯ Liability index represents connection between asset and liability performance; seeks to determine

Normal OAS (NOAS) while controlling all interest rate risks ⎯ Liability index is a communication vehicle between asset manager and line of business; if asset

managers are given just liabilities they will have to resort to individual methods and cannot be evaluated easily; if index is identified then manager has a well defined benchmark to outperform

Constructing a liability index ⎯ Should be customized ∋ sources of return are limited to those of liability, ROAS and interest rate risk ⎯ To replicate sources of interest rate risk we can create a portfolio with key rate durations identical

to liability; key rate duration immunization adequately controls interest rate risk ⎯ For ROAS term, we need to determine normal OAS for publicly traded bonds for comparison

− We should construct liability index by starting from some broad‐based index and changing portfolio composition only minimally to match key rate durations of liability

− To eliminate rich/cheap term include many securities so unsystematic price changes are diversified away

− To eliminate portfolio adjustment term calculate total return of liability index for each period and assume inflows/outflows occur at end of period after return calculated

⎯ Lally (1992) describes as a linear programming problem to maximize diversification of portfolio holdings, given asset constraints on effective duration, key rate durations, convexity and sector weights

⎯ r = rf + NOAS – DNOASΔNOAS – ΣDiΔri Applications of a liability index ⎯ Referee between asset performance and liability performance ⎯ Changes of net value of liability return are mainly normal return of index; this is result we want

analysis to show; we want to know under some basic assumptions what is normal in order to judge cost of funding liability

⎯ For comparison of factors affecting performance over time using cumulative returns

Conclusions Total return approach is conducive to day‐by‐day management actions and business decisions by providing timely and accurate information on each major factor contributing to performance

Has become practical only recently due to (1) accuracy of pricing models and (2) low cost intensive computer power; what was once prohibitive has now become compulsory


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IFRS Model Financial Statements and Disclosures Checklist (IAS 39)

Classification of financial assets IAS 39.45 – Entity may use descriptors or categorizations for its financial assets other than those defined in IAS 39 (financial assets at fair value through profit or loss, held to maturity investments, loans and receivables, available for sale financial assets) when presenting information on face of financial statements

Fair value hedges IAS 39.89A – For a fair value hedge of interest rate exposure of a portion of a portfolio of financial assets or financial liabilities requirement of IAS 39 may be met by presenting gain or loss attributable to hedged item either (a) in a single separate line item within assets for those repricing time periods for which hedged item is an asset or (b) in a single separate line item within liabilities for those repricing time periods for which hedged item is a liability ⎯ Presented next to financial assets or financial liabilities; amounts included in these line items shall

be removed from balance sheet when assets and liabilities to which they relate are derecognized

Adoption of standard before effective date IAS 39.103 – If entity has applied IAS 39 for a period beginning before 1/1/2005 it shall disclose that fact ⎯ An entity shall not apply IAS 39 before 1/1/2005 unless it also applies IAS 32 ⎯ Application for periods beginning on or after 1/1/2005 is required

IAS 39.104 – If on adoption of IAS 39 it is impractical to adjust opening balance of retained earnings at beginning of earliest year presented and all other comparative amounts as if IAS 39 had always been in use, entity shall disclose that fact and indicate extent to which information was restated

IAS 39.105 ⎯ For any financial instrument designated as available for sale when first applying IAS 39 entity shall

recognize all cumulative changes in fair value as a separate component of equity until subsequent derecognition or impairment

⎯ For any financial instrument designated as at fair value through profit or loss when first applying IAS 39 entity shall (a) restate financial asset or financial liability using new designation in comparative financial statements and (b) disclose fair value of financial assets or financial liabilities designated into each category and classification and carrying amount in previous financial statements


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Longevity Bonds and other Mortality Linked Securities

Stakeholders in markets for mortality linked securities Hedgers ⎯ Annuity providers stand to lose if mortality improves more than anticipated while life insurers stand

to gain, so they can hedge each other’s longevity risk ⎯ Life insurers can also hedge longevity risk by reinsuring or transferring it to capital markets

General investors – investment banks or hedge funds might be interested since it has low correlation with standard financial market risk factors and potentially positive alpha

Speculators who provide liquidity and arbitrageurs who eliminate pricing anomalies Government as insurer of last resort is potentially residual holder of longevity risk Regulators, security managers, organized exchanges and other stakeholders

Existing mortality linked securities Swiss Re mortality bond ⎯ In December 2003 Swiss Re issued a $400M 3 year life catastrophe bond to reduce its exposure to

catastrophic mortality deterioration ⎯ Coupon is LIBOR + 135 bp, but principal is unprotected and depends on a mortality index in US, UK,

France, Italy, Switzerland; principal is reduced 5% for every .01 increase in index above 1.3 times base 2002 level so becomes exhausted at 1.5 times base level

⎯ SPE invested principal in high quality bonds and swapped income stream for a LIBOR linked cash flow

⎯ Bond allowed Swiss Re to reassure rating agencies about its mortality risk management without taking on any credit risk exposure or using traditional reinsurance

⎯ Beelders & Calarossi 2004 estimated probability of attachment (q > 1.3q0) at 33 bp and probability of exhaustion at 15 bp; expected loss of 22 bp was much lower than 135 bp compensation offered so bond appears to be a good deal; however their figures are only estimates based on a model that ignores parameter uncertainty and plausible alternative parameter estimates can produce different values

⎯ In June 2004 bond was trading at LIBOR + 100 bp; in November 2005 it was trading at LIBOR + 123 bp possibly due to increased probability of a bird flu pandemic

⎯ Issue was fully subscribed and press reports suggest investors were happy with it; investors included pension funds who were attracted by coupon as well as hedging opportunity offered by fact that bond’s mortality risk was anti‐correlated with mortality risk associated with active plan members

⎯ In April 2005 Swiss Re issued a $362M 5 year life catastrophe bond with three tranches ($62M for B, $200M for C, $100M for D); principal is at risk if for any two consecutive years before maturity combined mortality index exceeds specified percentage of expected mortality level (120% for B, 115% for C, 110% for D)

EIB/BNP longevity bond ⎯ In November 2004 BNP announced a ₤540M long‐term longevity bond targeted at pension plans

and other annuity providers designed by BNP and issued by European Investment Bank; security was not well received, did not generate sufficient demand to be launched and in late 2005 was withdrawn for redesign


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⎯ Bond was a 25 year amortizing bond with initial coupon of ₤50M and subsequent coupons linked to a cohort survivor index based on realized mortality rates of English and Welsh males age 65 in 2002

⎯ Cash flows were priced at LIBOR – 35 bp but EIB’s curve was typically LIBOR – 15 bp, so investors were being asked to pay 20 bp to hedge their longevity risk

⎯ At a technical level, bond is actually made up of three components − Floating rate amortizing bond issued by EIB in euros − Cross‐currency interest‐rate swap in which EIB pays floating euros and BNP pays fixed sterling − Mortality swap between EIB and Partner Re in which EIB exchanges fixed sterling on expected

mortality for floating sterling on actual mortality ⎯ EIB and BNP have potential credit exposures to each other, BNP has exposure to Partner; investors

have exposure only to EIB (AAA rating) that must pay regardless of defaults ⎯ Attractive features

− Designed to help pension plans hedge exposure to longevity risk − Survivor index is based on a reliable and easily obtainable public source − Trends in national mortality should reasonably match trends in annuitant mortality

⎯ There seem to be a number of reasons for bond’s slow take‐up − 25 year horizon is less effective than a longer bond; bond might prove less effective hedge for

different age cohorts or for females; since March 2005 UK announced it will start to issue ultra long gilts longer than 25 years so this problem can be addressed by increasing maturity of longevity bond

− Amount of capital required is high relative to reduction in risk exposure; answer is to find ways of increasing gearing to provide same exposure to risk for a lower initial capital outlay

− Degree of model and parameter risk is high for a bond of this duration; this can be overcome after a small number of longevity bonds have been issued

− Level of basis risk may be too high relative to price being charged − Underlying index is calculated wrt central death rates rather than usual mortality rates; this can

be handled by using standard approximation

New mortality linked securities Longevity bond ⎯ Can be principal at risk or coupon at risk ⎯ Classical longevity bond – final payment is at death of last surviving member of cohort; provides a

better hedge than EIB/BNP type bond with a specified maturity ⎯ Zero coupon longevity bond – financially engineered by stripping classical longevity bonds ⎯ Geared longevity bonds and longevity spreads ⎯ Deferred longevity bonds

Mortality swap ⎯ Like reinsurance without distinctive legal restrictions on insurance ⎯ Can be arranged at lower transaction cost than a longevity bond issue and are more easily

cancelled; more flexible and can be tailor‐made to suit diverse circumstances ⎯ Can be one payment or multiple payment

Mortality futures ⎯ Annuity futures ⎯ Longevity futures – underlying can be longevity bond prices or survivor indices

Mortality options ⎯ Survivor caps and floors


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⎯ Annuity futures options ⎯ OTC options and embedded options ⎯ Mortality swaptions


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Handbook of Portfolio Management Chapter 20

Introduction Progressive contraction of spreads has provided incentive for extending into new asset classes to boost spreads; index providers have responded with increased coverage of those new markets

More investors have begun expressing return objectives and risk constraints in terms of deviations from their benchmarks; even for portfolios for which traditional market weighted indices are inappropriate insurers and banks have sought market‐based benchmarks for measuring risk and performance

To be effective quantitative analysis of a portfolio relative to an index requires that consistent pricing assumptions and models be applied to each security in both portfolio and benchmark

Basic steps in quantitative portfolio management relative to an index are ⎯ Formulate investment policy in terms of limits on allocation to asset classes, diversification and

liquidity requirements, asset/liability constraints and/or duration targets ⎯ Select a standard benchmark or create a customized benchmark if necessary ⎯ Profile a portfolio against its benchmark along multiple risk dimensions to compare allocations,

exposures, returns as well as identify intentional and unintentional exposures ⎯ Quantify risk exposures based on historical volatilities and correlations ⎯ Compare projected portfolio performance vs its benchmark under a set of scenarios ⎯ Establish a methodology for creating proxy portfolio and replicating benchmark return ⎯ Optimize portfolio subject to constraints on deviation from benchmark ⎯ Attribute achieved return to exposures taken

Investment Policy and Benchmarks Development of investment policy guidelines does not follow a set order ⎯ In many cases benchmark is selected first and investment policy is crafted to control risk that a

portfolio manager might take while trying to outperform benchmark; limits may be placed on type and allocations of out‐of‐index securities, concentration in individual issues and issuers, and on magnitude of allowed deviations from benchmark

⎯ In other cases investment policy constraints are dictated by asset/liabilities issues, regulatory requirements or liquidity considerations; in these situations a custom benchmark must be designed to offer an objective point of reference for performance; this is often case for insurers

Methodologies for benchmark customization ⎯ Narrowing definition to select a particular subset of standard index ⎯ Combining asset classes using weights that differ from market

For central banks which typically use duration target as a benchmark analytical methods can help optimize selection of duration target and make dynamic adjustments; analysis of historical Sharpe ratios along yield curve represent one approach to yield curve positioning

Insurers typically divide their portfolio along product lines with investment guidelines matched to expected liability stream of each product; this creates demand for benchmarks tailored to liability cash flows while maintaining advantages of using broad market weighted indices ⎯ One approach is to construct an optimized portfolio from universe of securities within investment

policy which is constrained to match liability cash flows as well as liquidity and diversification requirements


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⎯ Another approach is to construct a term structure of spreads based on all securities in investable universe and combine with Treasury yield curve to obtain yield curve reflective of chosen asset mix; liability cash flows can be modeled as a portfolio of zeros discounted along this curve

Measuring Portfolio Exposures vs a Benchmark Must first analyze composition of benchmark in detail (sector, quality, duration); in addition to aggregate statistics it is very important to know benchmark allocations and exposures along all relevant risk dimensions and profile them against portfolio

Amount of information derived from a profile depends on proper selection of risk dimensions and quantities compared within each cell

Heterogeneous risk axes might be particular useful for certain portfolios Return volatility for most fixed income portfolios is dominated by term structure risk; to control this risk at a basic level portfolio duration and convexity are compared to benchmark; a multi‐dimensional comparison of exposures along yield curve could be very helpful in evaluating term structure risk and creating curve‐neutral positions ⎯ One approach is to partition portfolio and benchmark into ranges of maturity, duration or average

life and compare within each range ⎯ Another is to generate and compare cash flow profiles for portfolio and benchmark aggregated to a

common set of time intervals ⎯ Finally portfolio and benchmark could be compared by their sensitivities to representative changes

in yield curve − Key rate durations, sensitivity to movements of a single point on spot curve − Forward rate durations, sensitivity to movements of points on forward curve − Principal component durations, sensitivity to historically likely shapes of yield curve movements

Quantifying Risk Comparison of allocations along each risk axis independently has two shortcomings ⎯ Does not indicate which mismatches are likely to contribute most to return deviations; greatest

mismatches are not necessarily those that carry most risk ⎯ Completely ignores any correlations that might exist between different risk axes

There are two approaches to quantifying return deviations between portfolio and benchmark ⎯ Multi‐factor risk analysis: attribute most of variance to a small set of systematic market risk factors

− Sensitivities of portfolio and benchmark to each factor are compared − Difference between sensitivities is multiplied by covariance matrix to give systematic risk − However common risk factors combined do not always explain full return variance − Unexplained part is non‐systematic risk and can be quantified separately − Systematic and non‐systematic risk are combined to produce annualized total tracking error,

standard deviation of difference between portfolio and benchmark; can be estimated ex ante or measured ex post

− Models are based on historical time series study of a set of risk factors; choice of factors is particular to each model implementation

− Model can be designed ∋ risk factors are not highly correlated ⎯ Asset allocation: divide market into a few asset classes and derive return, variances, and

covariances from historical data − Portfolio risk is calculated based on weight differentials relative to benchmark within each asset

class


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− Asset allocation approach is often used in multi‐currency portfolios − Optimization methods can be used to calculate efficient frontier of optimal allocations for

different levels of risk tolerance − Asset allocation approach works particularly well for assets with low correlation; for assets with

high correlation small changes in input expected returns can result in large changes in optimal allocations

Scenario Analysis Another view of risk involves comparison of projected portfolio and benchmark returns under a set of anticipated yield curve and spread scenarios; most common is parallel shift of Treasury yield curve, but it is important to consider other scenarios such as non‐parallel yield curve movements, changes in spread relationships, and changes in volatilities

Scenarios should be internally consistent Several mechanisms are used for horizon pricing of bonds for a changed yield curve: constant spread to par curve, constant zero volatility spread over forward curve, constant OAS over a lognormal tree of short rates

For MBSs, workout modes might include constant zero volatility spread and constant OAS over a set of MC interest rate paths

Common assumptions on timing of yield curve change include instantaneous change and linear phase‐in over all or part of horizon period

For portfolios with mixed currencies scenarios include curves in any currency as well as foreign exchange rates ⎯ Hedging costs can be derived from interest rate differentials between any two currencies ⎯ Investors are likely to have strong views for only a few variables; remaining variables can be derived

from historical data

Replicating Benchmark Returns: Proxy Portfolios Investors often look for index proxies, portfolios with a small number of securities that deviate minimally from returns of a target index

Proxies are of interest for two distinct purposes: direct passive investment and index analysis Practical method of matching index returns while containing transaction costs; can be used by passive investors or active investors with no strong view on market; also a portfolio can be analyzed against an index proxy using methods that would be impractical for an index of several thousand securities

Proxy portfolios can be built using cell matching, tracking error minimization, and/or matching index scenario results; replication can also be achieved using securities outside indices such as Treasury futures or by entering into an index swap or structured note

Cell Matching ⎯ Benchmark is profiled on an arbitrary grid reflecting risk dimensions along which allocation

decisions are made; index allocations to each cell are matched by one or more liquid and representative securities; duration and convexity of benchmark within each cell can be used as targets when purchasing securities to fill out cell

⎯ For MBS indices this produces proxy portfolios of 20‐25 securities which track indices of 600 MBS securities to within 3 bp/month

⎯ This technique can also be applied to replicate term structure exposure of any fixed income index using Treasury futures; it tracks Lehman Brothers Aggregate Index within 11 bp/month and Treasury Index within 7 bp/month


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Tracking Error Minimization ⎯ In context of multi‐factor model, systematic tracking error can be reduced by restructuring portfolio

so its risk characteristics more closely match index; optimal path is rarely obvious because each security contributes to many dimensions of risk; constrained quadratic optimization could be used to solve for best tracking portfolio with a given number of securities

⎯ Another very useful approach for reducing tracking error is gradient descent method, which ranks each security by sensitivity of tracking error to a change in its holding; from ranked list of transactions leading to largest reductions in tracking error manager is free to choose most practical ones

⎯ Minimization of tracking error proves to be particularly successful in creating indexed portfolios where systematic risks dominate; for example a proxy portfolio of 7 MBS passthroughs tracked Lehman Brothers MBS Index within 14 bp/year

⎯ Corporate proxy portfolios need more diversification due to higher issuer‐specific event risk Matching index scenario results – an indexed portfolio could be optimized for a desired objective such as yield or liquidity while being constrained in terms of deviation from its benchmark across a wide spectrum of scenarios; in order to give truly indexed portfolios it is very important to consider changes in market risk along any relevant dimension

Portfolio Optimization Credit analysis, relative value analysis, market analysis all participate in security selection process Examples of optimization objectives include minimum risk relative to a benchmark, maximum liquidity, minimum cost immunization, maximum yield, diversification bounds, and/or maximum outperformance of benchmark subject to constraint on underperformance

Could try to maximize performance in expected interest rate environment Should control transaction costs and maintain sufficient diversity

Explaining Achieved Returns General considerations ⎯ Identification of source of performance differences can help measure effects of various allocation

decisions within overall performance management process ⎯ Careful analysis of return surprises can help point out unintended portfolio characteristics that

should be corrected in future ⎯ Excess return over duration‐matched Treasuries separates out any returns due to differences in

yield curve exposures Approach 1 – Return attribution ⎯ Operates at level of individual security returns, seeks to attribute those returns to common market

influences analogous to risk factors ⎯ Four sources of changes in prices are passage of time, changes in yield curve, changes in volatilities

(only affect securities with embedded optionality), and changes in spreads; largest sources are passage of time and changes in Treasury yield curve

⎯ Security level results can be aggregated to analyze portfolio and benchmark separately or to compare them

⎯ Considerations in selecting model include intuitive clarity and computational accuracy Approach 2 – Performance attribution ⎯ Operates at portfolio level, seeks to analyze differences between portfolio and benchmark caused

by differences in allocation to various risk dimensions


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⎯ Allocation dimensions are selected and prioritized to reflect portfolio manager’s decision process, e.g. curve positioning, sector allocation, security selection

⎯ To attribute performance to portfolio management decisions our model attempts to answer two separate questions − Had portfolio earned within each market segment exact same return as index how much would

it differ in performance? This difference is attributable to high‐level allocation decision of weights assigned to each segment.

− How much extra return was achieved due to differences in returns within each market segment? This difference is attributable to security selection.

Conclusion Analytical tools need to keep up with new security structures introduced into marketplace Dynamic nature of many portfolios greatly complicates attribution of historical return by introducing a changing basis for returns and an extra source of deviation from benchmark

Quantitative portfolio analysis and management will play an increasing role in decision making process


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Handbook of Portfolio Management Chapter 21

Introduction Need for clarity leads us to define yield curve movements based on changes in bellwether yields; need for accuracy leads us to use full valuation approach to return attribution

Lehman Brothers model calculates each component of return using full OAS evaluation; has historically reported how a security contributes to total return, but return attribution model attempts to show why returns have been realized

Model breaks down returns into a practical set of components which correspond to strategies commonly used by portfolio managers

Components of Price Return Passage of time ⎯ Coupon ⎯ Accretion – due to convergence of bond price to par as it approaches maturity; positive for discount

bonds and negative for premium bonds; very important for zeros; calculated by holding yield constant while moving settlement date forward; for MBSs hold prepayment rate constant as well

⎯ Rolldown – results from predictable changes in yield as time elapses, reflecting change in bond’s placement along yield curve; if yield curve is positive yield decreases as bond approaches maturity

⎯ For bonds with embedded options, effect of option theta – for MBSs return can be strongly influenced by anticipated increase or decrease in prepayments following significant yield curve movements due to lag between refinancing incentive and actual prepayment activity

Yield curve movements – shift, twist, butterfly For bonds with embedded options, effect of changes in volatility Changes in spread

Model Implementation of Yield Curve Changes In an effort to make model as simple as possible yield curve movements are based on changes in Treasury yields which are directly observable and not on output of computational procedures such as principal component analysis or linear regression analysis

Returns associated with movement of yield curve can be decomposed into three basic shapes18 ⎯ Shift returns are produced by a parallel yield curve shift s = ¼(Δy2 + Δy5 + Δy10 + Δy30)

− Explains 88.2% of returns − Four point shift was selected as superior to three point shift (2,5,30 years) which may use too

sparse a representation of yield curve and five point shift (2,3,5,10,30) which over‐represents short end of yield curve

⎯ Twist returns are produced by a yield curve flattening or steepening centered at 5 years − 30 year yield moves by T/2 while 2 year yield moves by –T/2 ⇒ T = Δy30 ‐ Δy2 − Other choices are linear, two piece linear with pivot at 5 (one wing of twist is linear between 2

and 5 years and second wing is linear between 5 and 30 years), two piece linear with pivot at 10, and three piece linear with pivots at 5 and 10

18 These results differ from those discussed in Oxford Guide to Financial Modeling Chapter 5


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− Definitions with pivot at 5 years are clearly superior; three piece linear is only marginally better than two piece linear; explains 9.1% of returns

⎯ Butterfly returns are produced by middle of curve moving in opposite direction from wings − 30 year and 2 year yields move by B/3 while 5 year yield moves by ‐2B/3 ⇒ B = ½(Δy2 + Δy30) ‐

Δy5 − Results in modest improvements in explanatory power (1% of returns) but can be significant in

certain periods ⎯ Residual return or shape return are yield curve returns other than those explained by these three

types of yield curve changes; approximately 1.7% of returns

OAS Methodology Model constructs a sequence of stepwise changes by which BOM environment is transformed into EOM environment and re‐prices bond at each step using full OAS valuation; each component of price return is given by difference in prices obtained by successive valuations

Steps include items such as accretion, rolldown, shift, twist, butterfly, volatility Full valuation pricing methodology allows each component of return on a callable bond to be split into a bullet‐to‐maturity equivalent component and an optionality component; most accurate treatment possible for securities with curve dependent cash flows

Government and corporate bonds are priced using tree model; MBSs are priced using MC and prepayment model

Approach holds a clear advantage over methods that rely on BOM sensitivities and ignore fact that changes in yield curve can cause profound changes in risk characteristics of securities

Model Development and Validation Model measures month‐to‐month yield changes on BOM on‐run Treasuries Comparison with other models ⎯ Compare to (a) rolling bellwether method in which yield change is obtained by subtracting

beginning and ending yields of two different bonds in action months and (b) theoretical par curve method in which beginning and ending yields are those of hypothetical par coupon Treasuries derived from an off‐run spline model − Explanatory power is roughly equivalent to par curve and is more intuitive and accessible to

market practitioners − Performs significantly better than rolling bellwether which leads to large modeling errors in

certain months ⎯ Performance provides fit roughly equivalent to principal component analysis but is more intuitive

and accessible

Applications to Portfolio Management In passive portfolio management a good understanding of sources of return differences can help identify structural differences and suggest corrective action

In active portfolio management this understanding can help attribute returns to sector allocation, quality allocation, and security selection


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Model Results for Published Indices Time series analysis of components of index returns can help characterize risks inherent in different asset classes

Main source of return variance is shift return; sometimes 99% is explained by shift alone; slightly less dominant for indices concentrated at long or short end


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Specialty Guide on Economic Capital

Foreword, Introduction, Overview Group formed in Spring 2002, released guide in June 2003, work in progress Uses results of 2002 survey and group member experience Not intended to represent only best practices, rather current practices in common use

Executive Summary Topic is becoming mainstream, but a standard definition of EC is not readily available Common thread – sufficient surplus to cover adverse outcomes at a given level of tolerance over a specified time horizon – guide will use this as working definition

EC impacts many company business management and decision making processes ⎯ Company can be sliced into various product lines and companies can allocate capital to determine

lines in which to invest more or less ⎯ In M&A situation one supplemental method would be to look at EC in context of new organization ⎯ EC can be used to actively manage and measure risk across organization in an ERM or ALM context ⎯ Financial and management reporting ⎯ Product pricing using EC can be a useful way of comparing different lines while controlling risks by

using it to set tolerances and constraints ⎯ Incentive compensation and performance measurement can be based on EC

Possible approaches for calculating EC are numerous ⎯ Scenario based – full economic scenarios, certain stress test scenarios, random scenario generator ⎯ Other methods – RBC C3 Phase II, factor based tables, mean‐variance‐covariance models, option

pricing theory When more than one motivation or method exists, companies will find themselves with different required capital figures that need to be allocated ⎯ If regulatory and/or rating agency capital is higher than EC extra capital has to be allocated

somewhere while actively optimizing this difference ⎯ Top down or Bottom up

Banking industry has been focused on this topic longer so it may be beneficial to leverage their experience in developing best practices for insurance industry; actuaries should take lead in gathering information and addressing differences from banking industry so best practices can be shared and improved upon

International Association of Insurance Supervisors is currently discussing issue of determining “right” amount of capital

How do we define EC? Overview ⎯ EC is based on calculations specific to company’s risks while regulatory or rating agency capital are

based on industry averages that may or may not be suitable to any particular company ⎯ Three main alternative definitions demonstrate main themes

− Sufficient surplus to meet potential negative cash flows, reductions in value of assets, increases in value of liabilities at a given level of tolerance over a specified time horizon


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− Excess of market value of assets over fair value of liabilities required to ensure that obligations can be satisfied at a given level of tolerance over a specified time horizon

− Sufficient surplus to maintain solvency at a given level of tolerance over a specified time horizon Risk tolerance levels – several methods are common ⎯ Specified VaR percentile often related to financial strength rating of company – commonly used by

rating agencies ⎯ CTE – used in Canada and used for setting regulatory capital requirements under RBC C3 Phase II

starting in 2004 Risks covered ⎯ All risks faced by enterprise s/b considered ⎯ Interest rate (96%), pricing (93%), credit (92%), equity (91%), liquidity (86%), operational (79%) ⎯ Asset risks – currency, financing, real estate, ALM, reinvestment ⎯ Underwriting risks – model, fluctuations under pricing, spread, mortality and other contingencies,

concentration, unique sectors ⎯ Other risks mentioned – separate accounts, transfers, regulatory, political, tax, legislative,

economic, overall market security, strategic, marketing, diversification, growth, product, mismanagement, expense, sales, governance, audit, reputation, catastrophic, etc

⎯ Interaction among risks s/b considered by use of either multivariate distributions or correlation factors

⎯ While EC does not exclude any of these risks, guide focuses primarily on financial risks

Uses of EC Overview – types of capital are not independent; companies favor EC for several reasons ⎯ EC reflects underlying economics of business as opposed to political and rating agency conservatism ⎯ Regulatory and rating agency capital may actually not allow for some risks a company faces such as

interest rate guarantees, guaranteed surrender values, operational risks ⎯ Since regulatory capital varies by jurisdiction, if a large institution were to make decisions based on

regulatory capital it may have different strategies in different jurisdictions which would amount to running a number of smaller independent institutions and result in a forfeiture of gains from economies of scale

⎯ Opportunities to hedge difference between regulatory capital and EC through rule arbitrage between jurisdictions

⎯ EC can be compared across lines Survey feedback ⎯ Have you been using concept of EC? 45% yes, 55% no ⎯ Among those using, main reasons are to provide management with knowledge that risks are being

adequately managed (44%) and to better measure performance of different units (32%) ⎯ 64% anticipate same or greater significance in future ⎯ Heaviest users are in diversified financial institutions, followed by life & annuity writers; greater

acceptance and applications in non‐insurance financial world ⎯ Consultants use EC concepts less than insurer employees and are less likely to indicate anticipation

of greater use in future ⎯ Stock and mutual companies elicited surprisingly similar response patterns; however they use EC

for different purposes, stock companies to demonstrate risk management and mutual companies to identify excess capital

⎯ Larger companies tend to be more likely to use EC


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Applications ⎯ Determination of company or product risk profile

− Full risk profile will include information about short and long term exposure to large losses and to unacceptably high fluctuations in earnings as well as impact of specific stress and/or liquidity tests

− EC is one part of risk profile; can be used in other analysis, capital budgeting, setting limits − Results ∀ activities, products, businesses and in total can then be compared to assess reduction

in EC resulting from diversification ⎯ Capital budgeting

− Under a capital budgeting process each unit submits a long range financial forecast that includes level of projected profits as well as net amount of capital that either is needed or can be released

− Process will then focus on obtaining right mix of short and long term returns for capital needed ∀ set of business plans

− Insurance products normally consume capital at issue and release capital in subsequent years − Both new and existing products can be subjected to this discipline

⎯ Evaluation of required capital in M&A situations − Acquirers will look carefully as to whether they can afford to establish full EC of acquired

business in addition to maintaining their own EC − If multiple companies are evaluating a potential acquisition company having lower correlation

of risks with acquisition will have lowest marginal capital ⎯ Insurance product pricing

− Many companies use allocated capital in pricing process; difference between after tax returns on assets backing allocated capital and pricing hurdle rate is recognized as a cost

− Indirect approach – model recognizes establishment and later release of EC as an annual product flow; when annual distributable earnings are discounted at cost of capital rate this indirectly depresses results

− Direct approach – difference is determined directly and calculated either as an annual charge or as a percentage of PV

− Less common in health insurance; EC and cost of capital cannot easily be incorporated into loss ratio models

⎯ Risk tolerances and constraints − Useful way to limit risk when EC is responsive to actual variations in risk levels rather than just

business volume − Will sometimes apply only to specific lines − Situations are chosen for limits when they are seen as capital intensive

⎯ ALM − An objective of rebalancing may be to maintain or reestablish EC for a block at a target level,

usually as a percentage of liabilities − A goal might be to obtain highest projected profits for a block where EC is maintained at lowest

regulatory capital level allowed; could also determine if minimum regulatory capital is sufficient ⎯ Calculating RAROC

− Step 1 – overall required capital position of company must be determined − Step 2 – capital must be allocated to various lines and units − Step 3 – total company capital and allocated amounts must be reconciled


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− Typically a corporate area will calculate RAROC figures; communicating these results to operating areas is integral to be sure they understand target returns to which management expects products to perform

⎯ Performance measurement − A growing number of North America life insurers are implementing EV, traditionally using

regulatory or rating agency capital formulas − Increasingly companies are employing EC when calculating EV as these are deemed to be more

representative of company’s actual cost of capital − Some companies particularly multinationals incorporate stochastic analysis to better

understand costs of options and guarantees; actuarial literature references this type of enhanced EV as Economic Value

⎯ Incentive compensation − Very few companies reflect EC in their incentive compensation − In those cases incentive compensation is determined primarily from other measures and has an

adjustment based on range of acceptable ratios of actual capital to EC − In theory actual RAROC compared to target levels would make a more meaningful basis than

more common target dollar amounts of gain − A measure whose underlying calculations are understood by few and whose measurement

methodology is based on assumptions about future events may not be an appropriate basis for bonuses

⎯ Rating agency and regulator discussions − Monitoring and projection process of both regulatory and rating agency capital amounts can

serve as basis for a better understanding of how EC can be measured − Reconciling differences between external and internal EC measures can be cumbersome but is

necessary for management’s full understanding of how to evaluate company − No companies were found to have discussed their internal EC position with regulators, although

regulators and rating agencies are beginning to adopt EC methods − Recent trends

• RBC C3 Phase II – more complex, meaningful, realistic interest rate risk measurement • AM Best – Enterprise Risk Model to supplement its capital adequacy ratio • S&P Financial Product Capital measures required EC

− Main rationales for new models and methodologies • Increased sophistication of risk management practices at insurers • Failure of factor based approaches to properly deal with risks inherent in current products

and investment strategies • Inquiries from companies seeking quantitative recognition of risk management practices

including quality of their product structures • Pressure on companies to optimize their capital base

Tie‐in of EC to regulator / rating agency capital Motivation for regulatory / rating agency capital ⎯ Motivated primarily by solvency concerns; rating agencies are also concerned with financial

strength and general creditworthiness ⎯ Generally simplified methods such as factor approaches at levels appropriate for aggregate

industry, do not reflect specific risks of company


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⎯ Create overall constraint as to amount of capital held by firm; too little threatens ability of company to meet obligations; too much creates a drag on earnings

Recent developments at regulatory level ⎯ Number of articles recently detailing large losses and accelerated DAC amortization related to

equity driven products ⇒ better methods are required to value these lines and set capital requirements

⎯ RBC C3 Phase I and Phase II – using a company’s actual mix of business and running a broad range of stochastic scenarios will develop company‐specific distribution of risk exposures; enhance factor based models

⎯ NAIC Life RBC Working Group recommends using CTE

Current approaches to calculating EC Overview of EC calculation methods ⎯ General considerations

− Similar theoretical underpinnings, may be viewed as different paths to same goal − Some methods more complicated or more efficient in some situations − Not uncommon to see companies using different approaches for different lines or product types − Decision typically based on availability of data and resources as well as materiality of bloc

⎯ Full economic scenarios − Used where primary goal is to determine EC ∀ risks combined − Does not result in any explicit amount of EC attributable to any particular risk − Step 1 – Corporate provides a set of economic scenarios to all units − Step 2 – Each unit calculates operating income and surplus ∀ scenarios − Step 3 – Corporate aggregates results, ranks them and determines desired VaR or CTE − Companies using this method may allocate it to units using any reasonable approach − Another application is to calculate EC using differences between PV of Future Profits under

different scenarios ⎯ Stress test method

− Generally a highly adverse scenario is set as basis for determining EC − Straightforward, judgment usually plays a role in determining particular scenario to use − Can be used for a single aspect of risk, such as interest rate risk like New York 7 or mortality

catastrophe risk, or for a combination of risks ⎯ Factor tables

− Industry‐wide or company‐specific models are used to develop factors for various risk to which company is exposed

− Company activity is summarized into homogeneous segments − Risk units and factors are multiplied and summed to get gross EC − Adjustments are usually made for correlations to determine net EC − If company believes they have not been able to determine factors ∀ risks, calculated EC might

not be reduced − Using industry experience to determine factors will likely result in EC similar to US or Canadian

regulatory capital levels ⎯ Stochastic models – Scenario generator is used to create random scenarios, resulting capital needs

are ranked and EC is determined according to chosen rule − Univariate stochastic models – covariance adjustment is made outside model − Multivariate stochastic models – implicitly allow for covariances


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⎯ Scenario generator − Major economic risk is assumed to be a function of a random variable − Random number generator is used to populate time series − Function and parameters of function are chosen to fulfill a series of criteria often called stylized

facts − One stylized fact relates to relationship between results and market prices − Risk neutral – average PV of cash flows of some set of scenarios averaged over all scenarios

equals market price of those securities at time 0 − Real world – scenarios satisfy criteria that reflect modeler expectations: (a) historical average

over some predefined period, (b) average scenario reproduces initial conditions, or (c) scenarios reflected some expected future trend

⎯ Statistical methods – mean‐variance‐covariance model − Mean, variance and covariances of gains and losses is developed using a stochastic model or

other method − Normal distribution is assumed and EC is determined from normal tables

⎯ Credit risk methods – frequency and severity models − Usually based on historical studies for rating classes − Could assume companies within same sector have perfect correlation − Other model is Merton, which calculates probability of default based on stock price

⎯ Operational risk methods – frequency and severity models − Based on company and/or industry data − Since data is scarce, various techniques are used to incorporate “expert” opinions into data to

create quantitative results − SDEs, multiple regression, neural networks, systems dynamic simulations, Bayesian belief

networks, fuzzy logic ⎯ Option pricing theory

− Can be extremely effective in some situations including products where insured event can be assumed to occur at only a certain point in time

− Loss situation that attracts EC is reframed as an option, and option pricing models are used to back into EC amount

− If a company can develop a multivariate loss distribution EC could be set equal to CTE(x≥90%) – mean of distribution + provision for error in estimation of and deterioration of mean

⎯ Adjustments for correlation − Adjustments may be explicit or implicit − Depending on situation adjustments may be done at micro level or macro level − Micro adjustments involve determining covariances among and between each and every risk

factor at each level of risk, which requires a tremendous amount of data − Macro adjustments use broad correlation between risk types as basis for combining risks

Practical methods to calculate EC ⎯ Example 1 – Calculating EC from probability and economic cost of ruin

− Probability of ruin is probability that PV of liabilities will exceed assets at valuation date resulting in technical insolvency

− EC based on probability of ruin is determined by calculating additional assets needed to reduce probability to target specified by management


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− Both probability‐of‐ruin and VaR methods have advantage of being easy to understand and communicate; however both are inadequate for policy because they fail to consider severity of ruin

− Economic Cost Of Ruin is an enhancement of probability of ruin concept, although more prevalent in P&C arena

− ECOR is difference between what policyholders are promised and expected value of their post‐ruin benefits often expressed as percentage of policyholder reserves19

− ECOR is an improvement over probability‐of‐ruin and VaR methods but for some companies conceptual advantages may be outweighed by complexity, practicality

− This can be calculated by simulating assets and liabilities ⎯ Example 2 – another approach is to use change in after tax statutory PV of Future Profits

− Three different bases for dealing with profits • Profits retained – EC is amount of capital in addition to earned profits needed to assure

company meets EC criteria; generally used for cash flow testing and for regulatory definitions; most companies do not expect to leave profits in fund

• Profits released – EC is amount of capital needed after profits are paid to shareholders to assure company meets EC criteria; to generalize method you would have to define accounting basis used to develop amount of profits that would be released and then include those dividend cash flows in model; this would be more realistic but significantly more cumbersome particularly as accounting migrates to a higher dependence on stochastic calculations

• Paid as expected – EC is not particularly realistic since it implies a level of payout not directly related to earnings but can be used as an approximation to profits released; simply profits retained method less expected profits

− Demonstration of methodology • Using best estimate assumptions determine PVFP for block • For one assumption set e.g. mortality recalculate EV using an adverse assumption set • Difference is amount of EC needed to provide for adverse mortality for block • Because assumptions are defined deterministically measure of degree of confidence that

this level of EC provides is not available although a confidence level can be built into amount of change in assumption set

• Hybrid approach – standard deviations of mortality function can be developed from data underlying best estimate assumptions and adverse mortality assumption could then be defined based on degree of confidence desired and assumed probability distribution function

• Extending example, can do same thing for new money interest rate assumptions, asset default assumptions, etc

• Total EC required would be [ECmort2 + (ECdef + ECint)

2]½ • Extending hybrid approach to a theoretically correct EC calculation requires development of

means and standard deviations ∀ assumptions and correlations among assumptions • PVFP can be developed stochastically under numerous simulations; this has a major

obstacle to usefulness, amount of time needed is excessive today both in terms of computer runtime and programming/implementation time; if obstacles are overcome this will produce a good measure of true EC

19 Called Expected Policyholder Deficit in Study Note 146


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⎯ Example 3 – Calculating EC for a typical life insurer − EC = amount of capital needed to cover misestimation of mean, deterioration of mean,

statistical fluctuations − Parameters

• Adjust amount of capital to extent balance sheet assets and liabilities have provisions to cover EC items

• EC calculations should cover time period over which company has made guarantees or has exposure; 100 year time horizon has been selected

• EC will be set at 99th percentile of loss distribution of various risks taken together; covariance approximations will be used to achieve this objective

− Company develops one multivariate MC simulation model to determine mortality and lapse risks

− A second model gauges interest rate risk, for following reasons • Combining interest rate risk with mortality and lapse is a modeling challenge • Runtime increases significantly if three risks are analyzed together • Interest rate risk is by far most significant risk and they want to analyze it separately and

more rigorously − Study note p36 shows numerical results

Current approaches to allocation of EC Required Capital = larger of rating agency capital and regulatory capital Face Capital = Required Capital – EC Free Capital = Capital held over larger of required capital and EC Some companies equate Tier 1 capital to EC, Tier 2 capital to Face Capital, and Tier 3 capital to Free Capital

Allocating capital at enterprise level ⎯ Insurer must determine how to allocate diversification benefit to lines ⎯ Similarly company must determine how to allocate face capital if any across lines

− Hold fully in corporate • Advantages – simple, insulates lines from vagaries of required capital formulas • Disadvantage – could lead to over‐investment in lines that tie up excessive required capital

− Allocate using a marginal approach; calculate change in face capital that occurs if unit is removed and give negative of this change to unit with remainder allocated to corporate • Advantage – attempts to allocate true cost of capital for adding line • Disadvantages – complicated

− Allocate on a pro‐rata basis weighted by EC, by reserves, or by EC+reserves • Advantages – simple, allocates capital to units • Disadvantages – may allocate large amount of capital to lines that generate none and vice

versa − Calculate by treating each line as a mono‐line company, with any diversification benefit

allocated to corporate • Advantages – somewhat easier to understand than marginal approach, neither helps nor

hurts a given line due to presence of other lines • Disadvantage – may allocate large amount of capital to lines that add little required capital

due to diversification − Study note pp38‐9 provides a numerical example


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− In practice many companies that calculate EC in one of these ways typically charge lines for any capital held at corporate either implicitly based on difference in hurdle rates or explicitly by imposing a capital rent charge

Allocating EC to business segments ⎯ Having determined appropriate capital requirement at enterprise level to satisfy policyholder

interests, it is necessary to fairly attribute capital to each segment in a way that reflects its contribution to enterprise‐wide capital requirement

⎯ Several methods for attributing capital to units, differing by choice of risk measure − Attribute capital to units in proportion to PV of expected customer payments; each product is

assumed to contribute to risk of insolvency in proportion to economic value of commitment to customers and thus all products are assumed to involve same degree of risk; thus less risky products provide a capital subsidy to more risk products and resulting unfairness may result in business decisions that destroy economic value

− To attribute capital fairly, capital requirements must be determined in relation to risk of segments; it is often suggested that probability‐of‐ruin or VaR constraints be used to drive attribution; however both have a drawback because when two or more risky portfolios are combined capital based on these measures may incorrectly turn out to be more than sum of portfolios determined separately; this occurs when loss distributions are asymmetric and not correlated uniformly

− A refinement would be to use ECOR ratio to drive attribution ⎯ In any case attribution process requires completion of two steps

− Calculation of standalone capital requirements – expressed as a probability of default or ECOR ratio

− Allocation of diversification benefit to segments – derived by any one of several possible algorithms

⎯ Results can be highly sensitive to risk measure Allocation of EC for pricing purposes ⎯ Allocated at pricing model cell level, in theory using same methodology used to determine capital

for line ⎯ In practice this is rarely done; 2/3 of companies use simplified linear formulas rather than

simulation models or tail probabilities ⎯ Examples

− Life products = a∙NARt + b∙tVx or c∙NARt∙tqx + b∙tVx − Annuity products = d∙tV or e∙AccountValue − Health products = f∙Premiums

⎯ Factors are determined ∋ if they were applied to in‐force business total would equal EC for line − Factors a,c,f are usually determined from insurance risk portion of EC − Factors b,d,e are usually determined from credit and market risk portions of EC − Operational risk plus difference between total EC and sum of EC for risk types are commonly

allocated to factors as a gross‐up


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Overview of Investment Policy Statement in ALM Context

Why Is an Investment Policy Required An effective investment policy underscores link between investments and liabilities, sets out objectives and constraints, required under federal and many provincial jurisdictions

For insurers, marketing, actuarial, finance and investment areas must be involved and strong sponsorship by senior management is critical; for pension funds, coordination is required between sponsor or pension committee, actuary and investment manager; only through close cooperation is it possible to establish investment policies that fully reflect risk tolerance and return expectations

Investment policy can also be used as an educational tool for liability managers on investment objectives and constraints and for investment managers on benefit promises made to plan participants and policyholders and movement of resulting liabilities over time

Contents of Investment Policy It is helpful to segment assets and liabilities and create a policy for each segment as well as for total company; for insurers, a split could be made along par/non‐par, new money vs portfolio return products, policyholder vs shareholder funds; pension plans may be split between retired lives and active lives

Investment policy should contain: ⎯ Objective of business – could be stated as a tangible target such as an investment spread, a

measure of profitability or a real return objective; could also be stated more qualitatively as a statement on desired level and stability of performance of entire business.

⎯ Description of liabilities – should include expected short and long term growth of segment; should describe cash flow characteristics of liabilities in terms of predictability and size of contribution/premium income, benefit payments and expenses; should include a reference to sensitivity to inflation levels and movements in interest rates, as well as important aspects impacting cash flow such as embedded policyholder or plan member options, pricing horizon and interest costs

⎯ Risk tolerance of organization − It helps to start with an analysis of non‐investment risks inherent in product or plan along with

relative importance of product or plan performance to profitability of company − This will lead to a better understanding of segment’s ability to take credit, market, foreign

exchange, and interest rate risk on investment side − It is also important to take into consideration financial materiality of plan or segment to

company as well as financial stability of sponsor; risk tolerance could be related to capitalization level of company or surplus level of pension plan

⎯ Marketability/liquidity requirements − There should be a description of ability of policyholders/plan members to withdraw funds on

demand and at what cost: market value, book value or a modification of either − For insurers marketability could be required to meet unforeseen surrenders, large death

benefits, income tax and shareholder dividend payments − For pension funds may need to recognize potential for downsizing or restructure causing a

partial windup resulting in significant commuted values being paid out to terminating or retiring employees, commuted values offered to retirees, annuities purchased for a sizeable portion of


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retired population, negative outlook for industry and/or company, net cash flows out of fund, early retirement window with substantial early retirement subsidies including bridge benefits

− It is important to combine all segments to ensure combined portfolio is not holding excessive cash or short term investments at cost of giving up potential returns; cash requirements can be more effectively controlled at master trust or total portfolio level releasing some cash to be invested at a higher expected return

− Marketability or liquidity is a very significant risk for P&C companies; seasonality of premiums and claims creates potentially significant liquidity risks

⎯ Accounting, regulatory and tax rules that will have an impact on investments − Depending on surplus position of organization, MCCSR rules may greatly influence investment

strategy for a life company; impact of proposed asset mix on surplus position of company should be discussed; investment limits imposed by legislation

− For pensions, although a large surplus permits more risk to be assumed when viewed from a funding perspective since cash flow requirements can be smoothed through use of surplus, this risk posture could result in a volatile pension expense figure for company’s income statement; inability to access pension surplus for funding would significantly alter risk/reward trade‐off

− Taxable income items, in particular for P&C companies ⎯ Asset mix targets and permitted ranges

− Targets need to be set for liquidity, asset mix, matching measures based on ALM techniques adopted, credit risk and MCCSR

− End result is a policy portfolio which could then represent a long‐term asset mix for segment/plan, a risk‐free or risk minimizing portfolio, or a basis for analyzing manager’s performance

⎯ Portfolio management guidelines − Include targets for each asset type, quality constraints, portfolio management style − Address single borrower or industry exposure limits and authority limits, which assets are

permitted investments, asset/liability matching constraints ⎯ Performance goals and evaluation criteria

− It is important to differentiate between goals for fund and goals for manager; typically objectives would compare performance of each specific asset class with a passive index; ensure that specific index being utilized is appropriate given constraints and objectives of fund; use attribution analysis to break down value added

− Qualitative criteria should be used to monitor manager, such as adherence to policy, no change in investment style, sound management and investment process

− In some instances, performance objectives are more appropriately set by reference to internal liability requirements and not an external index for example new money annuity products; another objective could be performance of managers against their peers based on a sample of comparably managed funds with similar objectives and available discretion20; goals for fund could be based on real returns exceeding a minimum threshold

⎯ Procedures and authorities − Should clarify roles of board, investment committee, etc − Procedure for annual review and audit should be established and laid out − It is typical to include a section on standard authorization limits − Should refer to procedures related to credit control

20 Not desirable according to Managing Investment Portfolios Chapter 12


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Canadian Assets Short term – Treasury bills or bank paper with terms less than 1 year, source of liquidity Bonds ⎯ Government of Canada bonds, provincial and municipal bonds, issues by large public and private

enterprises ⎯ Can be a significant secondary source of liquidity complementing short‐term portfolio; large active

market will allow trading to take advantage of interest rate movements; available term can extend to 30 years even though 80% of issues are for 5 years or less

⎯ Very few callable bonds, less liquid strip bond market, new real return bonds Private placements – less liquid so higher yields, often have sinking funds Commercial/Industrial mortgages – not very liquid so large yield premium Residential mortgages – CMHC or MICC will insure if LTV > 75%; MBS market is growing, not liquid, significant spread

Preferred stock – more risky and less liquid than bonds, used a lot by P&C companies Common stock Real estate – very illiquid, life insurance accounting re‐appraises every three years Policy loans Futures, forwards, options, swaps

Liability Description from an Investment Perspective Analysis of insurance liabilities from investment perspective will focus on term and level of interest rate guarantees, predictability of cash flows, policyholder options, risk tolerance, impact of aggregating various liability types, pricing and rate crediting strategy, expected growth of business

Participating insurance ⎯ Importance of interest guarantee is that it implies protection of capital which in turn implies a

careful decision in asset mix targets between equities and debt ⎯ There should be a clear understanding of dividend policy which must then be translated into

investment terms ⎯ Following questions should be answered before determining appropriate asset mix and investment

management style: How large is par fund surplus and what is desired surplus ratio? How stable should ratio be in good times and in bad times? How quickly should performance of fund respond to market changes?

⎯ There must be positive cash flow generated from premium income and investments to pay for book value cashout option to guard against undue market risk

⎯ Differentiate between insurance liabilities, surplus, amounts left on deposit Spread products – nonpar life insurance, GICs, payout annuities, RRIFs ⎯ Market for spread products is very competitive; interest rate is a key competitive determinant; very

close link to investment strategy is therefore critical to proper pricing ⎯ Manage credit, liquidity, market risks; interest risk from time guarantee is made to when premium

received ⎯ Products differ in cash flow predictability; GICs fairly certain but life products are not

Group Life and Health – Benefit loss ratios are critical factor that will determine profitability of these businesses; however it is not possible to de‐link completely goals of business and goals of investment strategy; investments should match claim runoff; biggest focus on credit and liquidity risk

P&C – Unearned premiums are very short term but some mismatch, longer assets than liabilities, could be appropriate because of going concern of business; this is a common strategy when short end of yield


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curve is steep and expected to remain so; this strategy has its risks but expected rewards may justify risk when strategy is implemented and monitored appropriately; analyze historical seasonal pattern

Pension plans ⎯ Solvency liability – Since termination liabilities are determined using an interest rate comparable to

current annuity rates, they are sensitive to movement of long‐term yields; because of extremely long duration particularly for active members, fluctuation in liabilities can be significant; embedded options such as early retirement subsidies must be valued assuming option is exercised at most advantageous point for employee

⎯ Funding valuation – Ongoing liability, statutory limitations on assumptions; for flat dollar benefits or for retirees where no indexation is provided liabilities are similar to solvency valuation; benefits based on average earnings are inflation‐sensitive; any surplus that exists can be treated as a Reserve for Adverse Deviations; embedded options are normally valued based on reasonable assumptions

⎯ Accounting valuation (CICA) − Discount rate is management’s best estimate of long‐term expected returns − Impact of discount rate and sensitivity of liabilities is muted to extent that long‐term

expectations for investment returns change slowly; short‐term movements in interest rate levels generally will not immediately impact discount rate

− Liabilities may include benefits that are not guaranteed in plan document such as ad hoc increases for pensioners; therefore liabilities on accounting basis tend to be more inflation‐sensitive and theoretically representative of a realistic estimate

− A large surplus can increase potential volatility of pension expense for accounting purposes because of required methodology

⎯ Accounting valuation (FAS87) – discount rate is a settlement rate; liabilities will fluctuate with movement of long‐term interest rates from one valuation to next

⎯ Wind‐up − Settlement for retirees is purchase of insured annuities; risk assumed by plan is movement of

long‐term interest rates from wind‐up date to purchase date; this can be hedged to some extent by immunizing retired life reserve

− Active and TV members will have option of deferred annuity or commuted value; since it is not known which options members will elect, appropriate ALM process will require assumptions be made wrt percentages electing each option since a hedged portfolio will vary widely depending upon which options are elected

Surplus fund ⎯ Investment considerations will be determined by size of surplus relative to MCCSR, ability of

organization to readily raise capital, expected growth of company, dividend policy; dynamic solvency testing can give good insight

⎯ Because surplus fund usually requires less liquidity than other liabilities it is usual to invest in equities and long‐term investments such as strategic investments in new ventures

⎯ Dividends to shareholders are usually paid from surplus; a special consideration is to ensure that cash profit (as opposed to statutory profit) is sufficient to pay dividends

ALM Techniques for Interest Rate Management Cash flow matching – if achieved can eliminate interest rate risk ⎯ Serious drawbacks for most businesses


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− It is frequently impossible to accurately predict cash flows of assets and liabilities because of various options embedded on both sides such as surrenders and prepayments

− Even if cash flows could be predicted accurately, it would be very expensive to acquire a portfolio which would exactly mirror liability cash flow, and match constructed is generally only valid for current level of interest rates

⎯ However few ALM techniques will be effective without some cash‐flow matching; thus care should be taken to forecast cash flows and options as accurately as possible

Duration matching ⎯ Protects value of business against small parallel yield curve shifts ⎯ Disadvantages

− Often does not account for various options embedded in assets or liabilities; option‐adjusted duration could be utilized to alleviate problem

− Only works for small changes in interest rates; to understand implications of larger shifts in interest rates analysis must include convexity

− Only works for parallel yield curve shifts Scenario testing of assets, liabilities and investments under various interest rate scenarios; model parallel and non‐parallel shifts and exercise of options ⎯ Tackles all concerns of other techniques ⎯ Disadvantages

− Volume of assumptions required may mean model doesn’t reflect “real life” − We assume universe of possible changes is included in our set of future scenarios; if “real life” is

outside our analysis we could have put business at serious financial risk; careful selection of deterministic scenarios is crucial and should be communicated along with results of analysis; this is even more true of stochastic models which could convey a false sense of precision

Pension approaches utilize many of same techniques as life insurers; pension actuary must model expected return for equities to a much larger extent; emphasis on equities introduces significant complications since potential returns and results are biased by somewhat arbitrary nature of input parameters selected

Other (developing) techniques such as multivariate directional duration techniques

Role of Actuary Actuary must play key role in development of investment policy; ensure link between financial projections and investment decisions are solid; actuary is well suited to implement ALM analysis tools required to ensure risks are well managed

Investment management can add invaluable expertise and insight in identifying risks and solutions to these risks; partnership will be key to success


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