“a bank is a place that will lend you money if you can prove that you don’t need it.”

Saunders & Cornett, Financial Institutions Management, 4th ed.

1

“A bank is a place that will lend you money if you can prove that

you don’t need it.”Bob Hope


2

Why New Approaches to Credit Risk Measurement and

Management?

Why Now?


3

Structural Increase in Bankruptcy• Increase in probability of default

– High yield default rates: 5.1% (2000), 4.3% (1999, 1.9% (1998). Source: Fitch 3/19/01

– Historical Default Rates: 6.92% (3Q2001), 5.065% (2000), 4.147% (1999), 1998 (1.603%), 1997 (1.252%), 10.273% (1991), 10.14% (1990). Source: Altman

• Increase in Loss Given Default (LGD)– First half of 2001 defaulted telecom junk bonds recovered

average 12 cents per $1 ($0.25 in 1999-2000)

• Only 9 AAA Firms in US: Merck, Bristol-Myers, Squibb, GE, Exxon Mobil, Berkshire Hathaway, AIG, J&J, Pfizer, UPS. Late 70s: 58 firms. Early 90s: 22 firms.


4

Disintermediation

• Direct Access to Credit Markets– 20,000 US companies have access to US

commercial paper market.– Junk Bonds, Private Placements.

• “Winner’s Curse” – Banks make loans to borrowers without access to credit markets.


5

More Competitive Margins

• Worsening of the risk-return tradeoff– Interest Margins (Spreads) have declined

• Ex: Secondary Loan Market: Largest mutual funds investing in bank loans (Eaton Vance Prime Rate Reserves, Van Kampen Prime Rate Income, Franklin Floating Rate, MSDW Prime Income Trust): 5-year average returns 5.45% and 6/30/00-6/30/01 returns of only 2.67%

– Average Quality of Loans have deteriorated• The loan mutual funds have written down loan value


6

The Growth of Off-Balance Sheet Derivatives

• Total on-balance sheet assets for all US banks = $5 trillion (Dec. 2000) and for all Euro banks = $13 trillion.

• Value of non-government debt & bond markets worldwide = $12 trillion.

• Global Derivatives Markets > $84 trillion.• All derivatives have credit exposure.• Credit Derivatives.


7

Declining and Volatile Values of Collateral

• Worldwide deflation in real asset prices.– Ex: Japan and Switzerland– Lending based on intangibles – ex. Enron.


8

Technology

• Computer Information Technology– Models use Monte Carlo Simulations that are

computationally intensive

• Databases– Commercial Databases such as Loan Pricing

Corporation– ISDA/IIF Survey: internal databases exist to

measure credit risk on commercial, retail, mortgage loans. Not emerging market debt.


9

BIS Risk-Based Capital Requirements

• BIS I: Introduced risk-based capital using 8% “one size fits all” capital charge.

• Market Risk Amendment: Allowed internal models to measure VAR for tradable instruments & portfolio correlations – the “1 bad day in 100” standard.

• Proposed New Capital Accord BIS II – Links capital charges to external credit ratings or internal model of credit risk. To be implemented in 2005.


10

Traditional Approaches to Credit Risk Measurement

20 years of modeling history


11

Expert Systems – The 5 Cs

• Character – reputation, repayment history• Capital – equity contribution, leverage.• Capacity – Earnings volatility.• Collateral – Seniority, market value & volatility of

MV of collateral.• Cycle – Economic conditions.

– 1990-91 recession default rates >10%, 1992-1999: < 3% p.a. Altman & Saunders (2001)

– Non-monotonic relationship between interest rates & excess returns. Stiglitz-Weiss adverse selection & risk shifting.


12

Problems with Expert Systems

• Consistency– Across borrower. “Good” customers are likely to be

treated more leniently. “A rolling loan gathers no loss.”

– Across expert loan officer. Loan review committees try to set standards, but still may vary.

– Dispersion in accuracy across 43 loan officers evaluating 60 loans: accuracy rate ranged from 27-50. Libby (1975), Libby, Trotman & Zimmer (1987).

• Subjectivity– What are the optimal weights to assign to each factor?


13

Credit Scoring Models

• Linear Probability Model• Logit Model• Probit Model• Discriminant Analysis Model• 97% of banks use to approve credit card

applications, 70% for small business lending, but only 8% of small banks (<$5 billion in assets) use for small business loans. Mester (1997).


14

Linear Discriminant Analysis – The Altman Z-Score Model

• Z-score (probability of default) is a function of:– Working capital/total assets ratio (1.2)

– Retained earnings/assets (1.4)

– EBIT/Assets ratio (3.3)

– Market Value of Equity/Book Value of Debt (0.6)

– Sales/Total Assets (1.0)

– Critical Value: 1.81


15

Problems with Credit Scoring

• Assumes linearity.• Based on historical accounting ratios, not market

values (with exception of market to book ratio).– Not responsive to changing market conditions.

– 56% of the 33 banks that used credit scoring for credit card applications failed to predict loan quality problems. Mester (1998).

• Lack of grounding in economic theory.


16

The Option Theoretic Model of Credit Risk Measurement

Based on Merton (1974)

KMV Proprietary Model


17

The Link Between Loans and Optionality: Merton (1974)

• Figure 4.1: Payoff on pure discount bank loan with face value=0B secured by firm asset value.– Firm owners repay loan if asset value (upon

loan maturity) exceeds 0B (eg., 0A2). Bank receives full principal + interest payment.

– If asset value < 0B then default. Bank receives assets.


18

Using Option Valuation Models to Value Loans

• Figure 4.1 loan payoff = Figure 4.2 payoff to the writer of a put option on a stock.

• Value of put option on stock = equation (4.1) = f(S, X, r, , ) whereS=stock price, X=exercise price, r=risk-free rate, =equity

volatility,=time to maturity. Value of default option on risky loan = equation (4.2) =

f(A, B, r, A, ) whereA=market value of assets, B=face value of debt, r=risk-free

rate, A=asset volatility,=time to debt maturity.


19

$ Payoff

Assets0 A1 B A2

Figure 4.1 The payoff to a bank lender


20

$ Payoff

Stock Price (S)0

X

Figure 4.2 The payoff to the writer of a put option on a stock.


21

Problem with Equation (4.2)

• A and A are not observable.• Model equity as a call option on a firm. (Figure 4.3)• Equity valuation = equation (4.3) =

E = h(A, A, B, r, )

Need another equation to solve for A and A:

E = g(A) Equation (4.4)

Can solve for A and A with equations (4.3) and (4.4) to obtain a Distance to Default = (A-B)/ A Figure 4.4


22

Value ofAssets (A)

Value ofEquity (E)

($)

B

L

A1 A20

Figure 4.3 Equity as a call option on a firm.


23

B$80m

A$100m

t0 t1 Time(t)

Default Region

A

A

Figure 4.4 Calculating the theoretical EDF


24

Merton’s Theoretical PD

• Assumes assets are normally distributed.• Example: Assets=$100m, Debt=$80m, A=$10m• Distance to Default = (100-80)/10 = 2 std. dev.• There is a 2.5% probability that normally

distributed assets increase (fall) by more than 2 standard deviations from mean. So theoretical PD = 2.5%.

• But, asset values are not normally distributed. Fat tails and skewed distribution (limited upside gain).


25

Merton’s Bond Valuation Model

• B=$100,000, =1 year, =12%, r=5%, leverage ratio (d)=90%

• Substituting in Merton’s option valuation expression: – The current market value of the risky loan is

$93,866.18– The required risk premium = 1.33%


26

KMV’s Empirical EDF

• Utilize database of historical defaults to calculate empirical PD (called EDF):

• Fig. 4.5

Number of firms that defaulted within a year with asset values of 2 from Empirical EDF = B at the beginning of the year Total population of firms with asset values of 2 from B at the beginning of the year

50 Defaults Empirical EDF = Firm population of 1, 000 = 5 percent


27

5%

EmpiricalEDF

Figure 4.5default (DD): A hypothetical example.Empirical EDF and the distance to

0 Distanceto Default

(DD)

ProprieteryTrade-Off

2


28

Accuracy of KMV EDFsComparison to External Credit Ratings

• Enron (Figure 4.8)• Comdisco (Figure 4.6)• USG Corp. (Figure 4.7)• Power Curve (Figure 4.9): Deny credit to

the bottom 20% of all rankings: Type 1 error on KMV EDF = 16%; Type 1 error on S&P/Moody’s obligor-level ratings=22%; Type 1 error on issue-specific rating=35%.


29

12/96 06/97 12/97 06/98 12/98 06/99 12/99 06/00 12/00 06/01

20 CCCCC

B

KMV EDF Credit Measure

Source: KMV.

Agency Rating

BB

BBB

A

AA

AAA

151075

2

1.0

.5

.20

.15

.10

.05

.02

Figure 4.6 KMV expected default frequency TM and agency rating for Comdisco Inc.

12/96 06/97 12/97 06/98 12/98 06/99 12/99 06/00 12/00 06/01

20 CCCCC

B

KMV EDF Credit Measure Agency Rating

BB

BBB

A

AA

AAA

151075

2

1.0

.5

.20

.15

.10

.05

.02

Source: KMV.

Figure 4.7 KMV expected default frequency TM and agency rating for USG Corp.


30

Monthly EDF™ credit measure

Agency Rating


31

1009080706050

Percent of Population Excluded

40302010

100

90

80

70

60

50

40

30

20

10

00

Figure 4.8

Source: Kealhofer (2000).

agency ratings (1990-1999) for rated U.S. companies.KMV EDF Credit Measure vs.

EDF Power

S&P Company Power

S&P Implied Power

Moodys Implied Power


32

Problems with KMV EDF

• Not risk-neutral PD: Understates PD since includes an asset expected return > risk-free rate.– Use CAPM to remove risk-adjusted rate of return. Derives risk-neutral

EDF (denoted QDF). Bohn (2000).

• Static model – assumes that leverage is unchanged. Mueller (2000) and Collin-Dufresne and Goldstein (2001) model leverage changes.

• Does not distinguish between different types of debt – seniority, collateral, covenants, convertibility. Leland (1994), Anderson, Sundaresan and Tychon (1996) and Mella-Barral and Perraudin (1997) consider debt renegotiations and other frictions.

• Suggests that credit spreads should tend to zero as time to maturity approaches zero. Duffie and Lando (2001) incomplete information model. Zhou (2001) jump diffusion model.


33

Term Structure Derivation of Credit Risk Measures

Reduced Form Models: KPMG’s Loan Analysis System and Kamakura’s Risk Manager


34

Estimating PD: An Alternative Approach

• Merton’s OPM took a structural approach to modeling default: default occurs when the market value of assets fall below debt value

• Reduced form models: Decompose risky debt prices to estimate the stochastic default intensity function. No structural explanation of why default occurs.


35

A Discrete Example:Deriving Risk-Neutral Probabilities of Default

• B rated $100 face value, zero-coupon debt security with 1 year until maturity and fixed LGD=100%. Risk-free spot rate = 8% p.a.

• Security P = 87.96 = [100(1-PD)]/1.08 Solving (5.1), PD=5% p.a.

• Alternatively, 87.96 = 100/(1+y) where y is the risk-adjusted rate of return. Solving (5.2), y=13.69% p.a.

• (1+r) = (1-PD)(1+y) or 1.08=(1-.05)(1.1369)


36

Multiyear PD Using Forward Rates

• Using the expectations hypothesis, the yield curves in Figure 5.1 can be decomposed:

• (1+0y2)2 = (1+0y1)(1+1y1) or 1.162=1.1369(1+1y1) 1y1=18.36% p.a.

• (1+0r2)2 = (1+0r1)(1+1r1) or 1.102=1.08(1+1r1) 1r1=12.04% p.a.

• One year forward PD=5.34% p.a. from:

(1+r) = (1- PD)(1+y) 1.1204=1.1836(1 – PD)

• Cumulative PD = 1 – [(1 - PD1)(1 – PD2)] = 1 – [(1-.05)(1-.0534)] = 10.07%


37

16%

14%

10%

8%

1 Yr. 2 Yr. Time to Maturity

SpotYield

Zero-CouponTreasury Bond

A Rated Zero-Coupon Bond

B Rated Zero-Coupon Bond

11.5%

13.69%

Figure 5.1 Yield curves.


38

The Loss Intensity Process

• Expected Losses (EL) = PD x LGD

• If LGD is not fixed at 100% then:(1 + r) = [1 - (PDxLGD)](1 + y)

Identification problem: cannot disentangle PD from LGD.


39

Disentangling PD from LGD• Intensity-based models specify stochastic functional

form for PD.– Jarrow & Turnbull (1995): Fixed LGD, exponentially

distributed default process.– Das & Tufano (1995): LGD proportional to bond values.– Jarrow, Lando & Turnbull (1997): LGD proportional to debt

obligations.– Duffie & Singleton (1999): LGD and PD functions of

economic conditions– Unal, Madan & Guntay (2001): LGD a function of debt

seniority.– Jarrow (2001): LGD determined using equity prices.


40

KPMG’s Loan Analysis System

• Uses risk-neutral pricing grid to mark-to-market

• Backward recursive iterative solution – Figure 5.2.

• Example: Consider a $100 2 year zero coupon loan with LGD=100% and yield curves from Figure 5.1.

• Year 1 Node (Figure 5.3):– Valuation at B rating = $84.79 =.94(100/1.1204) + .01(100/1.1204)

+ .05(0)

– Valuation at A rating = $88.95 = .94(100/1.1204) +.0566(100/1.1204) + .0034(0)

• Year 0 Node = $74.62 = .94(84.79/1.08) + .01(88.95/1.08)

• Calculating a credit spread:

74.62 = 100/[(1.08+CS)(1.1204+CS)] to get CS=5.8% p.a.


41

0 1 2 3

Time

4D

C

B

B RiskGrade

A

Figure 5.2 The multiperiod loan migrates overmany periods.


42

Period 1Period 0

Figure 5.3 Risky debt pricing.

Period 2

$100 A Rating

$100 B Rating

$85.43

$67.14$80.28

$0 Default

5%5%

0.34%

94%

94%

1%5.66%

94%

1%


43

Noisy Risky Debt Prices• US corporate bond market is much larger than equity

market, but less transparent• Interdealer market not competitive – large spreads and

infrequent trading: Saunders, Srinivasan & Walter (2002)• Noisy prices: Hancock & Kwast (2001)• More noise in senior than subordinated issues: Bohn

(1999)• In addition to credit spreads, bond yields include:

– Liquidity premium– Embedded options– Tax considerations and administrative costs of holding risky debt


44

Mortality Rate Derivation of Credit Risk Measures

The Insurance Approach:

Mortality Models and the CSFP Credit Risk Plus Model


45

Mortality Analysis

• Marginal Mortality Rates = (total value of B-rated bonds defaulting in yr 1 of issue)/(total value of B-rated bonds in yr 1 of issue).

• Do for each year of issue.• Weighted Average MMR = MMRi =

tMMRt x w where w is the size weight for each year t.


46

Mortality Rates - Table 11.10

• Cumulative Mortality Rates (CMR) are calculated as:– MMRi = 1 – SRi where SRi is the survival rate defined as

1-MMRi in ith year of issue.– CMRT = 1 – (SR1 x SR2 x…x SRT) over the T years of

calculation.– Standard deviation = [MMRi(1-MMRi)/n] As the number

of bonds in the sample n increases, the standard error falls. Can calculate the number of observations needed to reduce error rate to say std. dev.= .001

– No. of obs. = MMRi(1-MMRi)/2 = (.01)(.99)/(.001)2 = 9,900


47

CSFP Credit Risk Plus Appendix 11B

• Default mode model• CreditMetrics: default probability is discrete (from

transition matrix). In CreditRisk +, default is a continuous variable with a probability distribution.

• Default probabilities are independent across loans.• Loan portfolio’s default probability follows a

Poisson distribution. See Fig.8.1.• Variance of PD = mean default rate. • Loss severity (LGD) is also stochastic in Credit

Risk +.


48

Default Rate

BBB Loan

Credit Risk Plus

CreditMetrics

Possible Path of Default Rate

Time Horizon

Default Rate

BBB Loan

Possible Pathof Default Rate D

BBB

AAA

Time Horizon

Figure 8.1Comparison of credit risk plusand CreditMetrics.


49

Frequencyof Defaults

Distribution ofDefault Losses

Severityof Losses

Figure 8.2 The CSFP credit risk plus model.


50

Distribution of Losses

• Combine default frequency and loss severity to obtain a loss distribution. Figure 8.3.

• Loss distribution is close to normal, but with fatter tails.

• Mean default rate of loan portfolio equals its variance. (property of Poisson distrib.)


51

Probability

Model 1

ActualDistributionof Losses

Losses

Figure 8.3 Distribution of losses with defaultrate uncertainty and severity uncertainty.


52

Probability

ExpectedLoss

EconomicCapital

99thPercentileLoss Level

Loss0

Figure 8.4 Capital requirement under the CSFPcredit risk plus model.


53

Pros and Cons

• Pro: Simplicity and low data requirements – just need mean loss rates and loss severities.

• Con: Inaccuracy if distributional assumptions are violated.


54

Divide Loan Portfolio Into Exposure Bands

• In $20,000 increments.• Group all loans that have $20,000 of

exposure (PDxLGD), $40,000 of exposure, etc.

• Say 100 loans have $20,000 of exposure.• Historical default rate for this exposure

class = 3%, distributed according to Poisson distrib.


55

Properties of Poisson Distribution

• Prob.(n defaults in $20,000 severity band) = (e-mmn)/n! Where: m=mean number of defaults. So: if m=3, then prob(3defaults) = 22.4% and prob(8 defaults)=0.8%.

• Table 8.2 shows the cumulative probability of defaults for different values of n.

• Fig. 8.5 shows the distribution of the default probability for the $20,000 band.


56

.008

.05

.168

.224

Defaults

843210

Figure 8.5 Distribution of defaults: Band 1.


57

Loss Probabilities for $20,000 Severity Band

Table 8.2 Calculation of the Probability of Default, Using the Poisson Distribution N Probability Cumulative Probability 0 0.049787 0.049789 1 0.149361 0.199148 2 0.224042 0.42319 3 0.224042 0.647232 . 7 0.021604 0.988095 8 0.008102 0.996197


58

Economic Capital Calculations

• Expected losses in the $20,000 band are $60,000 (=3x$20,000)

• Consider the 99.6% VaR: The probability that losses exceed this VaR = 0.4%. That is the probability that 8 loans or more default in the $20,000 band. VaR is the minimum loss in the 0.4% region = 8 x $20,000 = $160,000.

• Unexpected Losses = $160,000 – 60,000 = $100,000 = economic capital.


59

0

0.25

0.15

0.05

0.1

0.2

0

Amount of Loss in $

ExpectedLoss

EconomicCapital

UnexpectedLoss

350,000400,000250,000300,000160,000200,00060,000 100,000

Figure 8.6 Loss distribution for single loan portfolio —severity rate = $20,000 per $100,000 loan.


60

0

0.25

0.15

0.05

0.1

0.2

0

Amount of Loss in $

350,000400,000250,000300,000150,000200,00050,000 100,000

Figure 8.7 Single loan portfolio — severity rate = $40,000per $100,000 loan.


61

Calculating the Loss Distribution of a Portfolio Consisting of 2 Bands:

$20,000 and $40,000 Loss Severity

Aggregate Portfolio (Loss on v = 1, Loss on v = 2) Loss ($) in $20,000 units Probability 0 (0,0) (.0497 x .0497) 20,000 (1,0) (.1493 x .0497) 40,000 [(2, 0) (0,1)] [(.224 x .0497) + (.0497 x.1493)] 60,000 [(3, 0) (1, 1)] [(.224 x .0497) + (.1493)2] 80,000 [(4, 0) (2,l) (0, 2)] [(.168 x.0497) + (.224 x.1493) + (.0497x.224)]


62

Add Another Severity Band

• Assume average loss exposure of $40,000

• 100 loans in the $40,000 band

• Assume a historic default rate of 3%

• Combining the $20,000 and the $40,000 loss severity bands makes the loss distribution more “normal.” Fig. 8.8.


63

0

0.120

0.060

0.020

0.040

0.080

0.100

0.000

Amount of Loss in $

350,000400,000250,000300,000150,000200,00050,000 100,000

Figure 8.8 Loss distribution for two loan portfolios withseverity rates of $20,000 and $40,000.


64

Oversimplifications

• The mean default rate was assumed constant in each severity band. Should be a function of macroeconomic conditions.

• Ignores default correlations – particularly during business cycles.


65

Loan Portfolio Selection and Risk Measurement

Chapter 12


66

The Paradox of Credit

• Lending is not a “buy and hold”process.

• To move to the efficient frontier, maximize return for any given level of risk or equivalently, minimize risk for any given level of return.

• This may entail the selling of loans from the portfolio. “Paradox of Credit” – Fig. 10.1.


67

Return

The EfficientFrontier

A

B

C

Risk0

Figure 10.1 The paradox of credit.


68

Managing the Loan Portfolio According to the Tenets of Modern Portfolio Theory

• Improve the risk-return tradeoff by:– Calculating default correlations across assets.– Trade the loans in the portfolio (as conditions

change) rather than hold the loans to maturity.– This requires the existence of a low transaction

cost, liquid loan market.– Inputs to MPT model: Expected return, Risk

(standard deviation) and correlations


69

The Optimum Risky Loan Portfolio – Fig. 10.2

• Choose the point on the efficient frontier with the highest Sharpe ratio:– The Sharpe ratio is the excess return to risk

ratio calculated as:

p

fp rR


70

Return (Rp)rf

A

BD

C

Risk (p)

Figure 10.2 The optimum risky loan portfolio


71

Problems in Applying MPT to Untraded Loan Portfolios

• Mean-variance world only relevant if security returns are normal or if investors have quadratic utility functions.– Need 3rd moment (skewness) and 4th moment

(kurtosis) to represent loan return distributions.

• Unobservable returns– No historical price data.

• Unobservable correlations


72

KMV’s Portfolio Manager

• Returns for each loan I:– Rit = Spreadi + Feesi – (EDFi x LGDi) – rf

• Loan Risks=variability around EL=EGF x LGD = UL– LGD assumed fixed: ULi = – LGD variable, but independent across borrowers: ULi =

– VOL is the standard deviation of LGD. VVOL is valuation volatility of loan value under MTM model.

– MTM model with variable, indep LGD (mean LGD): ULi =

)1( EDFEDF

22)1( ii EDFiVOLLGDEDFiEDFi

222 )1()1( iii VVOLEDFiEDFiVVOLLGDEDFiEDFi


73

Correlations

• Figure 11.2 – joint PD is the shaded area.GF = GF/GF

GF =

• Correlations higher (lower) if isocircles are more elliptical (circular).

• If JDFGF = EDFGEDFF then correlation=0.

)1()1(

)(

FFGG

FGGF

EDFEDFEDFEDF

EDFEDFJDF


74

Firm F

Firm G

Firm F’sDebt Payoff

100

100(1-LGD)

Market Valueof Assets - Firm G

Market Valueof Assets - Firm F

Face Value of Debt

Figure 11.2 Value correlation.

“a bank is a place that will lend you money if you can prove that you don’t need it.”

Documents

credit derivatives

internal model of credit

loan valuesaunders cornett

credit markets20

credit exposure

market risk amendment

bob hopesaunders cornett

external credit ratings