FRM 2016 PART 1Revision Course

FOUNDATIONS OF RISKMANAGEMENTFRM 2016 Part 1 Revision Course

RISK MANAGEMENT-A HELICOPTER VIEW

Reading: The Essentials of Risk Management, 2nd Edition (Crouhy, Galai and Mark; McGraw-Hill, 2014)

1. Definitions:a. Risk: Uncertainty regarding future lossesb. Risk Management: Sequence of activities aimed at reducing or eliminating potential lossesc. Risk Taking: Active assumption of incremental risk to generate incremental gainsd. Economic Capital: Capital required to cover potential lossese. Expected Loss: Loss that may happen in normal course of businessf. Unexpected Loss: Loss that may happen outside of normal course of business

2. Risk Management Processa. Identify Risksb. Quantify and Estimate Exposurec. Develop Risk mitigation strategy (Avoid, Transfer, Mitigate, Assume)

3. Challenges with Risk Mitigation Process:a. For risk management to be beneficial, risk must be sufficiently dispersed in the economyb. Risk Management can be thought of as a zero sum game

4. Risk Classification:

Risk

Market

Credit

Liquidity

Operational

Legal &Regulatory

Strategicand

Business

> Interest Rate> Equity Price> Foreign Exchange> Commodity

> Default> Bankruptcy> Downgrade> Settlement

> Funding Liquidity> Trading Liquidity

> Fraud, Error> IT, HR, Admin

CORPORATE RISK MANAGEMENT-A PRIMER

Reading: The Essentials of Risk Management, 2nd Edition (Crouhy, Galai and Mark; McGraw-Hill, 2014)

1. Disadvantages of Hedginga. Most hedging theories assume perfect capital markets and no transaction costs or taxesb. Derivative pricing is not likely to reflect all risk factorsc. All hedging strategies will incur some compliance costs such as for accounting and disclosure

2. Advantages of Hedginga. Reducing volatility of future cash flows helps with cost of capitalb. May result in operational improvements like locking in a costc. Derivatives like IRS may be cheaper than buying insurance

3. Hedging Decisions (Board’s Role)a. Communicate the firms risk appetite qualitatively and quantitativelyb. Ensure that goals stated are actionable and clear; goals are balanced between debt holders and

shareholdersc. Risk management goals need to be definitive in terms of time lines

4. Mapping Risks: Risks should be mapped to risk categories identified in the previous chapter5. Hedging Operational and Pricing Risks

a. Pricing Risk: Cost of inputs is locked using forwards or futuresb. Foreign Exchange Risk: Revenue hedging or balance sheet exposures can be managed using forwards. It

needs to take into account the cost of hedging as well as revenue, exchange rate volatility andcorrelations

c. Interest Rate Risk: Goal is to control net exposure to unfavorable movements in Interest rates.6. Static vs. Dynamic Hedging: Static hedging entails initial one time creation of a hedge. Dynamic hedging requires

continuous adjustments to hedge position. Static is less expensive and time consuming but may not remain aperfect hedge

7. Instruments: Exchange traded instruments cover only certain underlying and are standardized. OTC instrumentsare privately traded between a bank and a firm and can be customized. OTC are less liquid and more difficult toprice.

8. Hedging operational risk covers items on the income statement while hedging financial risks covers items on thebalance sheet.

CORPORATE GOVERNANCE AND RISK MANAGEMENT

Reading: The Essentials of Risk Management, 2nd Edition (Crouhy, Galai and Mark; McGraw-Hill, 2014)

1. Definitions:

a. Agency Risk: Management has incentives to take greater risks in order to achieve higher remuneration

b. Risk Appetite: Reflects the tolerance of the firm i.e. how much risk can be pursued by a firm

2. Corporate Governance-Best Practices

a. Board should have majority of independent members

b. Board should be aware of agency risks

c. Board should maintain independence from management

3. Risk management-Best Practices

a. Board should demand substance over form i.e. economic performance over accounting performance

b. Board should setup an ethics committee

c. Board must provide approval to all major transactions

d. Board should have a risk committee in place

e. Risk committee must be separate from Audit committee

4. Risk Advisory Director: Risk Advisory Director would be a board member who is a risk specialist who attends

Risk and Audit committee meetings

5. Compensation Committee: Existence of agency risks necessitates board to implement a compensation

committee

WHAT IS ERM?Reading: Enterprise Risk Management: From Incentives to Control, 2nd Edition (James Lam; John Wiley & Sons, 2014)

1. Definitions:a. ERM: An integrated and centralized framework for risk managementb. Risk: Potential events that may affect the entity or achievement of entities objectives

2. Advantages of ERM:a. Integration of Risk Organization: Factors in the interdependence of risksb. Integration of Risk Transfer: Leads to consistent and better risk reporting, prevents over-hedging of risksc. Integration of Business Process: Improved business performance through RAROC (Risk Adjusted Rate of

Capital)3. Functions of CRO:

a. Reports to CEO or CFOb. Dotted line to Boardc. Provides leadership for ERMd. Develops policies including Risk appetite, on measuring and quantifying risks, setting risk limits and

developing risk systems4. ERM Framework Components

ERM

CorporateGovernance

LineManagement

PortfolioManagement

Risk TransferRisk Analytics

DataResources

StakeholderManagement

GOVERNANCE, RISK MANAGEMENT & RISK TAKING

Reading: René Stulz, “Governance, Risk Management and Risk-Taking in Banks,” Finance Working Paper 427/2014,June 2014.

1. Definitions:

a. Good Risk: Risk which increase value of a firm.

2. Optimal Rating: If rating is AAA, banks have to give up many valuable risky projects. By targeting a specific

probability of default (e.g. For A rating, probability of default is 0.08%) the bank can achieve its desired level of

risk. This is also the framework recommended.

3. Risk Appetite:

a. It should specify the firm level VaR

b. VaR limits should depend on profitability of the risk taking unit

c. Marginal unit of risk should have the same expected profit across all units

4. Issue with granular limits of risk:

a. More granular limits for risk taking units make it harder for risk taking units to accumulate large un-

monitored pockets of risk. It also makes it more difficult to take advantage of good opportunities

without negotiation for relaxation of limits

b. Less granular limits help with taking advantage of good opportunities but can result in making it harder

to monitor risks

FINANCIAL DISASTERS

Reading: Financial Disasters (Chapter 4, Steve Allen, Financial Risk Management: A Practitioner’s Guide to ManagingMarket and Credit Risk, 2nd Edition (New York: John Wiley & Sons, 2013))

1. Chase Manhattan and Drysdale Securities: Misleading or misreporting risks

In three months of 1976, Drysdale Government Securities, a newly founded subsidiary of an established firm, succeeded

in obtaining unsecured borrowing of about $300 million by exploiting a flaw in the market practices for computing the

value of U.S. government bond collateral. This unsecured borrowing exceeded any amount Drysdale would have been

approved for, given that the firm had only $20 million in capital. To save time and effort, borrowed securities were

routinely valued as collateral without accounting for accrued coupon interest. By seeking to borrow large amounts of

securities with high coupons and a short time left until the next coupon date, Drysdale could take maximum advantage

of the difference in the amount of cash the borrowed security could be sold for (which included accrued interest) and

the amount of cash collateral that needed to be posted against the borrowed security (which did not include accrued

interest). Drysdale used the borrowed money to take outright positions in bond markets. When the traders lost money

on the positions they put on, they lacked cash with which to pay back their borrowings. Drysdale went bankrupt, losing

virtually all of the $300 million in unsecured borrowings. Chase Manhattan absorbed almost all of these losses because it

had brokered most of Drysdale’s securities borrowings.

2. Kidder Peabody: Misleading or misreporting risks

Between 1992 and 1994, Joseph Jett, head of the government bond trading desk at Kidder Peabody, entered into a

series of trades that were incorrectly reported in the firm’s accounting system, artificially inflating reported profits.

When this was ultimately corrected in April 1994, $350 million in previously reported gains had to be reversed. A flaw

in accounting for forward transactions in the computer system for government bond trading failed to take into account

the present valuing of the forward. This enabled a trader purchasing a cash bond and delivering it at a forward price to

book an instant profit. Over the period between booking and delivery, the profit would inevitably dissipate, since the

cash position had a financing cost that was unmatched by any financing gain on the forward position. Although Jett’s

trades had not resulted in any actual loss of cash for Kidder, the announcement of such a massive misreporting of

earnings triggered a substantial loss of confidence in the competence of the firm’s management by customers and

General Electric, which owned Kidder. In October 1994, General Electric sold Kidder to PaineWebber, which dismantled

the firm.

3. Barings: Misleading or misreporting risks

The incident involved the loss of roughly $1.25 billion due to the unauthorized trading activities during 1993 to 1995 of a

single, relatively junior trader named Nick Leeson. Leeson, who was supposed to be running a low‐risk, limited return

arbitrage business for Barings in Singapore, was actually taking increasingly large speculative positions in Japanese

stocks and interest rate futures and options. He disguised his speculative position taking by reporting that he was taking

the positions on behalf of fictitious customers. By booking the losses to these nonexistent customer accounts, he was

able to manufacture fairly substantial reported profits for his own accounts, enabling him to earn a $720,000 bonus in

1994. The size of the losses relative to Barings Bank’s capital along with potential additional losses on outstanding trades

forced Barings into bankruptcy in February 1995.

4. Allied Irish Bank: Misleading or misreporting risks

John Rusnak, a currency option trader in charge of a very small trading book in AIB’s Allfirst First Maryland Bancorp

subsidiary, entered into massive unauthorized trades during the period 1997 through 2002, ultimately resulting in $691

million in losses. Rusnak was supposed to be running a small arbitrage between foreign exchange (FX) options and FX

spot and forward markets. He was actually running large outright positions and disguising them from management. He

invented imaginary trades that offset his real trades, making his trading positions appear small. He persuaded back‐

office personnel not to check these bogus trades. He obtained cash to cover his losses by selling deep‐in‐the‐money

options, which provided cash up front in exchange for a high probability of needing to pay out even more cash at a later

date, and covered up his position by offsetting these real trades with further imaginary trades. He entered false

positions into the firm’s system for calculating value at risk (VaR) to mislead managers about the size of his positions.

5. Union Bank of Switzerland: Misleading or misreporting risks

This incident involves losses of between $400 million and $700 million in equity derivatives during 1997, which appear to

have been exacerbated by lack of internal controls. A loss of $700 million during 1998 was due to a large position in

long‐Term Capital Management (LTCM). Less is known about the UBS disaster than the other incidents discussed in this

chapter. Even the size of the losses has never been fully disclosed. Considerable controversy exists about whether the

1997 losses just reflected poor decision making or unlucky outcomes or whether an improper control structure led to

positions that management would not have authorized. The 1998 losses were the result of a position that certainly had

been approved by the UBS management, but evidence suggests that it failed to receive adequate scrutiny from the

firm’s risk controllers and that it was not adequately disclosed to the SBC management that took over the firm.

6. Société Générale: Misleading or misreporting risks

In January 2008, Société Générale reported trading losses of $7.1 billion that the fi rm attributed to unauthorized activity

by a junior trader, Jérôme Kerviel. Kerviel took very large unauthorized positions in equities and exchange‐traded

futures, beginning in July 2005 and ending when his concealment of positions was uncovered in January 2008. His

primary method for concealing these unauthorized positions was to enter fictitious transactions that offset the risk and

P&L of his true trades. The fictitious nature of these transactions was hidden mostly by creating transactions with

forward start dates and then, relying on his knowledge of when control personnel would seek confirmation of a forward‐

dated trade, canceling the trade prior to the date that confirmation would be sought (Kerviel had previously worked in

the middle office of the firm, which may have provided him with particular insight into the actions of control personnel).

The large loss severely damaged Société Générale’s reputation and required it to raise a large amount of new capital.

7. Long Term Capital Management(LTCM): Liquidity Risk

the basic investment philosophy of LTCM, which was to locate trading opportunities that represented what the partners

believed were temporary disruptions in price relationships due to short‐term market pressures, which were almost

certain to be reversed over longer time periods. To take advantage of such opportunities, they needed to know they had

access to patient capital that would not be withdrawn if markets seemed to be temporarily going against them. This also

helped to explain why LTCM was so secretive about its holdings. These were not quick in‐and‐out trades, but long‐term

holdings, and they needed to prevent other firms from learning the positions and trading against them. Dependence on

short‐term swings in valuation represented a potential Achilles’ heel for LTCM’s long‐term focused investment strategy.

Because the firm was seeking opportunities where market pressures were causing deviation from long‐run relationships,

a strong possibility always existed that these same market pressures would push the deviation even further. LTCM

wouldthen immediately need to come up with cash to fund the change in market valuation. This would not be a problem

if some of the trades were moving in its favor at the same time as others were moving against it, since LTCM would

receive cash on upswings in value to balance having to put up cash on downswings (again, the same structure as

exchange‐traded futures). However, if many of its trades were to move against it in tandem, LTCM would need to raise

cash quickly, either from investors or by cutting positions. In the actual events of August and September 1998, this is

exactly what led to LTCM’s rapid downfall. The initial trigger was a combination of the Russian debt default of August,

which unsettled the markets, and the June 1998 decision by Salomon Brothers to liquidate proprietary positions it was

holding, which were similar to many of those held by LTCM. The LTCM fund’s equity began to decline precipitously from

$4.1 billion as of the end of July 1998, and it was very reluctant to cut positions in a turbulent market in which any large

position sale could easily move the valuations even further against it. This left the option of seeking new equity from

investors. LTCM pursued this path vigorously, but the very act of doing so created two perverse effects. First, rumors of

LTCM’s predicament caused competitors to drive market prices even further against what they guessed were LTCM’s

positions, in anticipation of LTCM being forced to unload the positions at distressed prices. Second, to persuade

potential investors to provide new money in the midst of volatile markets, LTCM was forced to disclose information

about the actual positions it held. As competitors learned more about the actual positions, their pressure on market

prices in the direction unfavorable to LTCM intensified. By 2000, the fund had been wound down with the 14 creditors

having recovered all of the equity they had invested and having avoided any losses on the LTCM positions they had held

at the time of the bailout. This outcome lends support to two propositions: LTCM was largely right about the long‐term

values underlying its positions, and the creditors were right to see the primary problem as one of liquidity, which

required patience to ride out.

8. Metallgesellschaft (MG): Basis Risk

In 1992, an American subsidiary of MG, Metallgesellschaft Refining and Marketing (MGRM), began a program of

entering into long‐ term contracts to supply customers with gas and oil products at fixed costs and to hedge these

contracts with short‐term gas and oil futures. The futures being used to hedge were exchange‐traded instruments

requiring daily cash settlement. The long‐term contracts with customers involved no such cash settlement. So no matter

how effective the hedging strategy was, the consequence of a large downward move in gas and oil prices would be to

require MGRM to pay cash against its futures positions that would be offset by money owed to MGRM by customers

who would be paid in the future. In 1993, when a large decrease in gas and oil prices had resulted in funding needs of

around $900 million, the MG parent responded by closing down the futures positions, leaving unhedged exposure to gas

and oil price increases through the customer contracts.

9. Bankers Trust: Conduct of customer business

BT was sued by Procter & Gamble (P&G) and Gibson Greetings. Both P&G and Gibson claimed that they had suffered

large losses in derivatives trades they had entered into with BT due to being misled by BT as to the nature of the

positions. These were trades on which BT had little market or credit risk, since it had hedged the market risk on them

with other derivatives and there was no credit issue of P&G or Gibson being unable to pay the amount they owed. it was

quite clear that the exact nature of the structures hadn’t been tailored to meet client needs, why had BT utilized so

complex a design? The most probable reason was that the structures were designed to be complex enough to make it

difficult for clients to comparison shop the pricing to competitor firms. However, this also made the clients highly

dependent on BT on an ongoing basis. If they wanted to unwind the position, they couldn’t count on getting a

competitive quote from another firm.

10. JPMorgan, Citigroup and Enron: Conduct of customer business

Enron sold oil for future delivery, getting cash, and then agreed to buy back the oil that it delivered for a fixed price. So,

in effect, no oil was ever delivered. When you canceled out the oil part of the trades, what was left was just an

agreement for Enron to pay cash later for cash it had received up front—in practice, if not in legal terms, a loan. The

advantage to Enron was that it did not have to report this in its public statements as a loan, making the firm appear

more desirable as an investment and as a borrower. JPMorgan Chase and Citigroup were Enron’s principal

counterparties on these trades. In the end, they agreed to pay a combined $286 million for “helping to commit a fraud”

on Enron’s shareholders.

CREDIT CRISIS OF 2007Reading: Risk Management and Financial Institutions (3rd Edition, John Wiley and Sons, 2012)

1. Definitions:a. Subprime Mortgage: Mortgages that are considered to be higher risk than traditional mortgages and are

given to borrowers with weak credit historyb. ARM (Adjustable Rate Mortgage): Initial rates on loans are very low and then increases during later

yearsc. Liar Loans: Applicants information were not vetted to be accurated. NINJA Borrower: No Income No Job No Asset borrowerse. Securitization: Process of pooling cash flows into a large pool and dividing the pool into smaller units for

selling these units to investorsf. Loan to Value Ratio: Ratio of mortgage amount to appraised value of home)g. Asset Backed Security(ABS): Financial security created through securitization from the cash flows of

assets like mortgages, auto loans etc. i.e. loans backed by assetsh. Regulatory Arbitrage: Banks that originate, securitize and sell their mortgages were also investors in

these assets. These assets were considered as trading assets and had very low capital requirements2. Credit Crisis of 2007

a. Lenders started giving more subprime loans (on profit motives and govt. prodding) to borrowers whowere earlier not eligible for home loans

b. This started increasing the housing prices giving comfort to banks on loans as they were backed byassets increasing in value

c. Banks started rolling out ARM to induce more subprime customers to purchase homes further fuellingprices

d. Banks started securitizing these loans and selling to investors, creating regulatory arbitragee. To find more investors, securitized assets were re-securitized, creating higher rated ABS CDO as

compared to original CDO albeit with higher riskf. As ARM rates got reset, investors started defaulting on home loans, causing large supply and low

demand for houses, which in turn caused house prices to crash. As house process crashed, manyinvestors found it prudent to let banks foreclose the house in place of paying the full mortgage whichwas of significantly higher value, further eroding housing prices

g. ABS and ABS CDO started defaulting causing a widening credit spread and eventual bankruptcy of banksor government bailouts

3. Structure of ABS:a. Senior Tranche, Mezzanine Tranche and Equity Trancheb. Mezzanine tranches were further re-securitized for profit motives

RISK MANAGEMENT FAILURES

Reading: René Stulz, “Risk Management Failures: What are They and When Do They Happen?” Fisher College of BusinessWorking Paper Series, (Oct 2008)

1. Large loss is not a risk failure: Deciding whether to take a known risk is not a decision for risk managers. The

decision depends on the risk appetite of an institution. However, defining the risk appetite is a decision for the

board and top management. That decision is at the heart of the firm’s strategy and of how it creates value for its

shareholders. A decision to take a known risk may turn out poorly even though, at the time it was made, the

expectation was that taking the risk increased shareholder wealth and hence was in the best interest of the

shareholders. As long as the risks were understood, it was not a Risk management failure. E.g. LTCM

2. How Risk management can fail: Two types of mistakes can be made in measuring risk: Known risks can be mis-

measured and some risks can be ignored, either because they are unknown or viewed as not material. Once

risks are measured, they have to be communicated to the firm’s leadership. A failure in communicating risk to

management is a risk management failure as well. Types of Risk Management failures can be classified as: A)

Mis-measurement of known risks. B) Failure to take risks into account. C) Failure in communicating the risks to

top management. D) Failure in monitoring risks. E) Failure in managing risks. F) Failure to use appropriate risk

metrics.

3. Risk Communication Failure: Risk management has to provide timely information to the board and top

management that enables them to make decisions concerning the firm’s risk and to factor the firm’s risk in their

decisions. In order for the board and the top management to understand the risk situation of the firm, this

situation has to be communicated to them in a way that they can understand properly. E.d Subprime

Communication being complex

4. Failure in monitoring and managing risks: Risk management is responsible for making sure that the firm takes

the risks that it wants to take and not others. As a result, risk managers must constantly monitor the risks the

firm is taking. E.g. Complex exposures to derivatives which invalidate even daily MTM

5. Risk Metrics: Relying on historical data alone for models and prediction of future values would not have helped

in cases such as LTCM. Also, VaR does not show catastrophic losses. Even if it predicts with 99% confidence that

losses would not exceed certain amount, it does not say how bad the loss 1% of the time can be. VaR also losses

meaning if there is market illiquidity as it assumes complete liquidity in market. Most existing models do no

capture crisis scenarios and how to survive such scenarios.

STANDARD CAPMReading: The Standard CAPM (Chapter 13, Edwin J. Elton, Martin J. Gruber, Stephen J. Brown and William N. Goetzmann,

Modern Portfolio Theory and Investment Analysis, 9th Edition (Hoboken, NJ: John Wiley & Sons, 2014)).

1. Standard CAPM: Standard Capital Asset Pricing Model provides a way to calculate an asset’s expected return

based on its level of systematic (Market) risk which is measured by Beta (β).

E(Rp) = Rf + βp (Rm - Rf)

E(Ri)=Expected Return on Asset i, Rf = Risk Free Rate, Rm = Return on Market portfolio and βi = Systematic Risk of Individual asset i2. Assumptions of CAPM:

a) Investor can borrow and lend at risk free rate of return; b) All investors have same expectations of Risk and Return; c)

There is only a single period; d) There are no taxes or transactions costs

3. CML (Capital Market Line): The line connecting the risk free asset and Market portfolio.

The CML equation is very similar to the CAPM equation.E R = R + σwhere the slope is the Sharpe Ratio of Market Return. Note that for the Sharpe

Ratio of an individual security, you need to replace Rm with Ri and

correspondingly change σm with σi in the bracket portion of the equation.

4. Beta (Systematic Risk of an Asset): Beta, also called the systematic risk of an asset, is defined as the level of risk

for which an investor must be compensated for an individual security. The Beta is defined as the slope of the

SML and can be approximated as β ≈ σ σ . The actual formula for Beta is by

a. β = .b. where Covariance p,m = (ρp,m x σp x σm)

Risk Premium

PORTFOLIO PERFORMANCE MEASUREMENT

Reading: Applying the CAPM to Performance Measurement: Single-Index Performance Measurement Indicators (Section4.2 from Noel Amenc and Veronique Le Sourd, Portfolio Theory and Performance Analysis (West Sussex, England: John

Wiley & Sons, 2003))

1. Treynor Ratio: The Treynor Ratio is used to analyze whether portfolio risk is being appropriately rewarded. It is

given as (by re-arranging the terms of CAPM, term on the right of equation is Treynor Ratio):

a. E(R ) – R =( ) –

b. It is more appropriate for comparing a well-diversified portfolio as it uses systematic risk(βi)

2. Sharpe Ratio: The Sharpe ratio is defined as reward to variability ratio. It is defined asS = E(R ) – Rσa. Since this measure is based on the total risk, it enables the relative performance of portfolios that are

not very diversified to be evaluated, because the unsystematic risk taken by the manager is included in

this measure.

3. Jensen’s Alpha: It is defined as the differential rate of return on the portfolio compared to expected return as

per CAPM. It is defined as:= – [ + ( − )]a. The equation in the square brackets is that of CAPM or E(Ri). Testing for statistical significance of α can

give us whether the returns are due to luck or not

4. Tracking Error: Tracking error (Te) is the Standard Deviation of αp over a period of time. It is used to analyze

benchmarked funds and the fund manager is required to keep the tracking error below a minimum threshold.

5. Information Ratio: It allows us to check that the risk taken by the manager, in deviating from the benchmark, is

sufficiently rewarded. It is given as αp/ Te

6. Sortino Ratio: It is same as Sharpe ratio except that we replace Rf with some other minimum return Rmin. It is

given as E(Rp) – Rmin) / σp (σp only includes those values which are below the minimum return level)

APTReading: Arbitrage Pricing Theory and Multifactor Models of Risk and Return (Chapter 10, Zvi Bodie, Alex Kane, and Alan

J. Marcus, Investments, 9th Edition (New York: McGraw-Hill, 2010))

1. Multifactor Models: In CAPM, β summarized all the systematic risk due to all macro/micro variables. We can

decompose this into multiple factors, where β for each factor will measure specific factor risk. A general form of

multifactor models is given as:

a. E(Rp) = Rf + βpn (Factorn) + βpj (Factorj)+…2. Law of One Price: It states that if two assets are equivalent in all economically relevant respects, then they

should have the same market price. The Law of One Price is enforced by arbitrageurs.

3. APT(Arbitrage Pricing Theory): APT is a multifactor model, wherein we use different portfolios and their

sensitivity to market returns i.e. it is based on arbitrage theory

a. E(Rp) = Rf + βpn (E(Rn) - Rf) + βpj (E(Rj) - Rf) + …Where E(Rn) – Rf is the risk premium of that factor and βin is the sensitivity of i to that portfolio factor

4. Relationship between CAPM and APT: CAPM can be considered a special case of APT with just one factor i.e.

the Market Risk variable encapsulates all other factors.

5. Issues with APT: APT does not mention which factors are to be chose to approximate the systematic risk. Also,

it assumes that no arbitrage opportunities exist. It also makes other assumptions like CAPM that Unsystematic

risk can be completely diversified.

6. Passive and Active Investment Management:

a. Passive: It attempts to track an index as closely as possible by holding only a fraction of all securities in

the index. Fine tuning factors in APT can help achieve this

b. Active: It attempts to beat the benchmark by speculating on the future values of different factors in APT

and constructing portfolio accordingly

7. Fama-Fench Three Factor Model: One famous multifactor model is the Fama-Fench model. The model is stated

as Rp = Rf + βpm Rm + βpSMB SMB + βpHML HML

a. Where SMB is Small Minus Big (the return of a portfolio of small stocks in excess of the return

on a portfolio of large stocks. ) and HML is High Minus Low (the return of a portfolio of stocks

with a high book-to-market ratio in excess of the return on a portfolio of stocks with a low

book-to-market ratio)

INFORMATION RISK

Reading: Information Risk and Data Quality Management (Chapter 3, Anthony Tarantino and Deborah Cernauskas, RiskManagement in Finance: Six Sigma and Other Next Generation Techniques (Hoboken, NJ: John Wiley & Sons, 2009))

1. Impact of Poor Quality Data: Financial (Operating Costs), Confidence (Org. trust), Satisfaction (Customer),

Productivity (Workload), Risk (Credit Assessment), Compliance

2. Causes of Data Error: Data Entry errors, Missing Data, Duplicate records, Inconsistent Data, Nonstandard

formats, complex data transformations, Failed Identity Management process, Incorrect or misleading metadata

3. Key dimensions of Data Quality: Accuracy (Real to Model), Completeness, Consistency, Reasonableness

(expectations within operational context), Currency (Degree to which information is current), Uniqueness,

Semantic Consistency (Same meaning of data), Format Conformance and others.

4. Data Governance, Data Quality Inspection and Data Validation:

a. Data Governance: Operational data governance is the manifestation of the processes and protocols

necessary to ensure that an acceptable level of confidence in the data effectively satisfies the

organization’s business needs.

b. Data Validation: The data validation process reviews and measures conformance of data with a set of

defined business rules.

c. Data Inspection: Data inspection processes are instituted to measure and monitor compliance with data

quality rules. They are ongoing processes.

5. Data Quality Scorecard: Complex data quality metrics can be accumulated for reporting in a scorecard in one of

three different views: by issue, by business process, or by business impact.

a. Data Quality issues view: Evaluating the impacts of a specific data quality issue across multiple business

processes. Used for prioritizing tasks for diagnosis and remediation

b. Business Process view: Operational managers overseeing business processes may be interested in a

scorecard view by business process.

c. Business Impact view: Business impacts may have been incurred as a result of a number of different

data quality issues originating in a number of different business processes. This reporting scheme

displays the aggregation of business impacts rolled up from the different issues across different process

flows

EFFECTIVE DATA AGGREGATION AND RISK REPORTING

Reading: Principles for effective data aggregation and risk reporting (Basel Committee on Banking SupervisionPublication, January 2015)

1. Definitions:

a. Risk Data Aggregation: Defining, gathering and processing risk data according to the bank’s riskreporting requirements to enable the bank to measure its performance against its risk tolerance/appetite.

2. Benefits of Data Aggregation

a. Increased ability to anticipate problemsb. Enhanced ability to identify alternativesc. Improved resolvability in event of stress or failured. Enhanced ability to make strategic decisions

3. Governance Principle (Principle 1): Risk data aggregation should be a part of banks overall risk managementframework.

4. Data Architecture and IT (Principle 2): Bank should design, build, and maintain data architecture and ITinfrastructure which fully supports its risk data aggregation capabilities and risk reporting practices

5. Principles 3-6 specify standards and requirements for effective risk data aggregation. Banks should ensure thatthe data is accurate and has integrity (Principle 3), is complete (Principle 4), is timely (Principle 5), and isadaptable to the end user (Principle 6)

6. Principles 7-11 specify standards and requirements for effective risk reporting practices. Risk reports should beaccurate (Principle 7), comprehensive (Principle 8), and clear and useful (Principle 9). Principle 10 states thatreports should be “appropriately frequent” (i.e., frequency depends on the role of the recipient—boardmembers need reports less frequently than risk committee members). Reports should be distributed to relevantparties in a timely fashion while maintaining confidentially (Principle 11)

GARP CODE OF CONDUCT

Reading: GARP Code of Conduct, 2010

1. Code of Conduct:

a. Integrity and Ethical Standards: Act

professionally, ethically and with Integrity in all

dealings. Maintain independence of thought and

direction. Do not knowingly misrepresent facts,

details relating to analysis etc. Be mindful of

cultural differences regarding ethical behavior and

customs

b. Conflict of Interest: Disclose actual or potential

conflict of interest to all affected parties

c. Confidentiality: Do not use confidential

information for personal benefit

d. Responsibilities: No overstating the accuracy or

certainty of results or conclusions. Disclose limits

of specific knowledge and expertise

e. Adherence to best practices: Execute work in a manner that is independent from interested parties.

Make distinction between fact and opinion.

2. Violations of Code: Violation(s) of this Code by may result in, among other things, the temporary suspension or

permanent removal of the GARP Member from GARP’s Membership roles, and may also include temporarily or

permanently removing from the violator the right to use or refer to having earned the FRM designation or any

other GARP granted designation, following a formal determination that such a violation has occurred.

Principles

Integrity

Ethical Standards

Conflicts ofInterest

Confidentiality

Standards

Responsibilities

Adherence

QUANTITATIVE ANALYSISFRM 2016 Part 1 Revision Course

PROBABILITIES

Reading: Probabilities (Chapter 2, Michael Miller, Mathematics and Statistics for Financial Risk Management (Hoboken,NJ: John Wiley & Sons, 2012))

1. Definitions:

a. Random Variable: An uncertain quantity or number

b. Outcome: An observed value of a random variable

c. Event: A single or set of outcomes

d. Mutually Exclusive: Event that both cannot happen at the same time

e. Exhaustive Events: Events that include all possible outcomes

2. Discreet Random Variable (DRV): Random variable for which the number of possible outcomes can be counted

and for each possible outcome there is a measurable and positive probability e.g. Money

3. Continuous Random Variable (CRV): Random variable for which number of possible outcomes is infinite. The

probability of any single value is zero. E.g. Time

4. Joint Probability: Probability that two events will both occur. It is denoted as P(AB) i.e. Probability of event A

and B and is calculated as P(AB) = P(A/B) x P(B) where P(A/B) is read as probability of A given B and is called

Conditional Probability

5. Addition Rule: P(A or B) = P(A) + P(B) – P(AB) Note: The word “and” indicates multiplication i.e. Joint probability

and “or” indicates addition i.e. addition rule

6. Bayes Theorem: P(A B⁄ ) = P(B A⁄ ) x P(A)P(B)7. Probability Density Function (PDF): Denoted as f(x), it is used to generate probability that outcomes of a

continuous variable lie within a particular range of outcomes. Remember that in a continuous distribution,

probability of any particular outcome is zero.

8. Cumulative Density Function (CDF): Defines a random variable x that takes a value less than or equal to a

specific value.

9. Discrete Uniform Random variable: Probabilities of all variables is equal

BASIC STATISTICS

Reading: Basic Statistics (Chapter 3, Michael Miller, Mathematics and Statistics for Financial Risk Management(Hoboken, NJ: John Wiley & Sons, 2012))

1. Definitions:

a. Variance: Variance is defined as the expected value of the difference between the variable and its mean

squared. σ2 = E[(X-µ)2]

b. Standard Deviation: Square root of variance is called Standard Deviation (σ)

c. Return of portfolio with 2 assets : Average value of return e.g. if there are two portfolios with returns as

r1 and r2 with weights as w1 and w2, then mean return of portfolio is r = (w1xr1) + (w2xr2) . Note that

w1+w2=1 always

d. Variance of Portfolio with 2 assets: σ2 = (w1x σ 1)2 + (w2x σ 2)2 + 2ρ1,2w1w2 σ 1 σ 2

e. Covariance: Covariance is analogous to variance, but instead of looking at the deviation from the mean

of one variable, we are going to look at the relationship between the deviations of two variables.

i. Covx,y = E[(X-µx)2] x E[(Y-µy)2] or Covx,y = ρx,vσxσy

f. Correlation is ρ in the above equation. Correlation has the nice property that it varies between −1 and

+1

2. Skewness: Skew refers to the extent to which the distribution are not symmetrical.

3. Kurtosis: Degree to which a distribution is peaked than a normal distribution. Average Kurtosis for a normal

curve is 3.

a. Skewness is degree 3 and Kurtosis is degree 4. Skewness = Σ(Xi-µ)3

σ3 n

b. Kurtosis is Σ(Xi-µ)4

σ4 n

DISTRIBUTIONS

Reading: Bayesian Analysis (Chapter 4, Michael Miller, Mathematics and Statistics for Financial Risk Management(Hoboken, NJ: John Wiley & Sons, 2013))

1. Definitions:

a. Parametric Distribution: A parametric distribution can be described by a mathematical function. E.g.

Normal Curve

b. Non-parametric distribution: A nonparametric distribution cannot be summarized by a mathematical

formula. In simplest form, a nonparametric distribution is just a collection of data. E.g. Historical data

2. Uniform Distribution, Bernoulli Distribution, Binomial Distribution

Uniform Distribution Bernoulli Distribution Binomial Distribution

A binomial distribution can be

thought of as a collection of

Bernoulli random variables. If we

have two independent bonds and

the probability of default for both

is 10%, then there are three

possible outcomes: no bond

defaults, one bond defaults, or

both bonds default

Probability between points aand b is equal and is zero atevery other point

A Bernoulli random variable is

equal to either zero or one. E.g.

coin toss. µ = P and σ = P(1-P)

3. Poisson distribution: The Poisson distribution is often used to model the occurrence of events over time. E.g.

the number of bond defaults in a portfolio or the number of crashes in equity markets.

Where n is the number of default events and λ is the

constant rate of decay.

4. Normal Distribution: It is more common to refer to the normal distribution as the Gaussian distribution. The

distribution is described by two parameters, µ and σ; µ is the mean of the distribution and σ is the standard

deviation. Because a linear combination of normal distributions is also normal, standard normal distributions are

the building blocks of many financial models. When a normal distribution has a mean of zero and a standard

deviation of one, it is referred to as a standard normal distribution. The skew of a normal distribution is always

zero. The kurtosis of a normal distribution is always 3. Z = (x-µ)/σ

5. Lognormal Distribution: If a variable has a lognormal distribution, then the log of that variable has a normal

distribution. Unlike the normal distribution, which ranges from negative infinity to positive infinity, the

0

20

40

60

0 1

Count of X

lognormal distribution is undefined, or zero, for negative values. Using lognormal distribution, we avoid returns

lower than -100%.

6. Students –t Distribution, Chi Square, F-Test

Students T Chi Square F Test

Used when n <30 in place ofnormal distribution

Used to test if Variance of a

normally distributed population is

equal to some value

Used to compare equality of 2

variances.

Z = (x-µ) * √n/ σ χ2 = [(n-1)σActual2]/ σHypo2 F = σ12/ σ22

BAYESIAN ANALYSIS

Reading: Bayesian Analysis (Chapter 6, Michael Miller, Mathematics and Statistics for Financial Risk Management(Hoboken, NJ: John Wiley & Sons, 2013))

1. Bayes Theorem: Bayes theorem for two variables is defined as P (A/B) = ( / ) ( )( )a. The numerator of the above is same P(AB) which is same as P(A|B) P(B)

b. Unconditional probabilities are given as P(A) and P(B)

c. Bayes’ theorem provides a framework for determining the probability of one random event occurring

given that another random event has already occurred.

HYPOTHESIS TESTING

Reading: Hypothesis Testing (Chapter 5, Michael Miller, Mathematics and Statistics for Financial Risk Management(Hoboken, NJ: John Wiley & Sons, 2012))

1. Sample Mean and Sample Variance: As n gets larger, the sample mean (ẍ) approaches the population mean (µ).

The sample standard deviation is given by σs = σ / √n and variance is σs2.

2. I.I.D(Independent and Identically Distributed Variables): If each random variable has the same probability

distribution as the others and all are mutually independent, then they are said to be i.i.d. Observations in a

sample are often assumed to be effectively i.i.d. for the purposes of statistical inference.

3. Confidence Interval: It is a range of values within which the actual value of the parameter will lie, given the

probability of 1-α where α is called the significance level. The calculation of confidence interval is as follows:

ẍ ± (Reliability factor x Standard Error) where reliability factor is the Z value and Standard Error is σs = σ / √n

Note: For the entire population, replace ẍ with µ and σs with σ

4. Hypothesis Testing: It is a statistical assessment of a statement or idea regarding the population. A hypothesis is

a statement about the value of a population parameter developed for the purpose of testing a theory or belief.

a. Null Hypothesis (Ho): Generally the hypothesis which the researcher wants to reject.

b. Alternate Hypothesis (HA): Hypothesis which is true if we are able to reject the null hypothesis.

5. Two tail test or One tail test:

If Ho is µ = µHypo Use a two tail test

Reject Ho if test statistic > upper critical or < lower critical valuesIf Ho is µ ≤ µHypoUse a one tail test

If Ho is µ ≥ µHypo

6. CHEBYSHEV’S Inequality: For a random variable, X, with a standard deviation of σ, the probability that X is

within n standard deviations of µ is less than or equal to 1/n2. For a given level of variance, Chebyshev’s

inequality places an upper limit on the probability of a variable being more than a certain distance from its

mean. For a given distribution, the actual probability may be considerably less. Take, for example, a standard

normal variable. Chebyshev’s inequality tells us that the probability of being greater than two standard

deviations from the mean is less than or equal to 25%. Used when we do not know the distribution of the

variable.

CORRELATIONS AND COPULAS

Reading: Risk Management and Financial Institutions (3rd edition, Pearson Prentice Hall, 2012)

1. Definitions:

a. Correlation and Covariance: Measure linear relationship between the co-movements over time.

Correlation is between -1 to 1 and Covariance is between -∞ to ∞

b. ρ . = ,c. Independent Variables: Where one variable does not impact the probability distribution of another

variable

d. Copula creates a joint probability distribution between two or more variables while maintaining their

individual marginal distributions

2. EWMA (Exponentially Weighted Moving Average): Gives current observations more weight that previous

observations.

a. Cov = λ Cov + (1 − λ)X Yb. Covariance of an asset with itself is the same as Variance i.e. Covx = Varx = σ2x

3. GARCH(1,1) [Generalised Autoregressive Conditional Heteroskedasticity]:

a. Cov = γ V + β Cov + α X Y ; in the equation α+β+γ=1 always. Also, ω = γ V4. Copula: Steps for finding the correlation between two marginal distributions:

a. Plot each marginal distribution to a normal distribution (Percentile wise)

b. Assume that the two Normal distributions are bivariate normal and calculate correlation

c. Gaussian Copula: Maps marginal distribution to a standard normal distribution

d. Student’s t Copula: Maps to Student’s t distribution

e. Multivariate Copula: For more than two variables like Factor Copula models

5. Tail Dependence: Student’s t distribution exhibits better tail values than Gaussian distribution as during times of

stress, most of the tail values are similar like in Student’s t distribution thus its better at determining correlations

6. Positive-semidefinite matrix: A matrix is positive-semidefinite if it is internally consistent. The covariance matrix

of a one factor model is positive-semidefinite. One factor model also requires N estimates for correlations where

each variable N is correlated to factor F

LINEAR REGRESSION

Reading: Linear Regression with One Regressor (Chapter 4, James Stock and Mark Watson, Introduction toEconometrics, Brief Edition (Boston: Pearson Education, 2008))

1. Definition: Regression analysis has the goal of measuring how change in one variable, called ‘Dependent’, can

be explained by changes in one or more variables called ‘Independent Variables’. The parameters of an equation

indicate relationship. A generic form of an equation is: Y = Bo + B1X1 + ε where Bo is called Intercept, B1 is called

Slope, X1 is the independent variable and ε is error term.

2. Properties of Linear Regression:

a. Independent variables (X) enter into the equation without any transformation such as X2 or √x

b. Dependent variable (Y) is a linear function of parameters but does not require that there be linearity in

variables

3. OLS (ordinary Least Squares): It is a method to determine the values of B0 and B1 in the above equation. Themethod tries to minimize the sum of squares of error term i.e. Σ (Yi-B0-B1Xi)2 or Σ (εi)2 . OLS computes the valuesof the parameters B1 as : Σ (xi - ẍ)(yi - ӯ)

Σ(xi - ẍ)2

4. Coefficient of Determination: The coefficient of determination (R2) measures the goodness of fit. It isinterpreted as % of variation in the dependent variable explained by the independent variable. Note that R2 =SSR/SST

5. SST, SSR and SSE:a. SST: Sum of Squares total is the sum of squares of predicted values from their averageb. SSR(ESS): Sum of square regression, also known as Explained sum of squares of deviation from its

average

SINGLE REGRESSOR HYPOTHESIS

Reading: Regression with a Single Regressor: Hypothesis Tests and Confidence Intervals (Chapter 5, James Stock andMark Watson, Introduction to Econometrics, Brief Edition (Boston: Pearson Education, 2008))

1. Slope Hypothesis Test:

a. A frequently asked question is whether an estimated slope coefficient is statistically different from zero

i.e H0: B1= 0 and HA: B1 ≠ 0.

b. The confidence interval for the regression coefficient is given by B1 ± (tstat x σB1) where B1 is the mean of

slope coefficient, σB1 is standard error of slope and tstat is a two-tailed t test with degrees of freedom (df)

as n-2.

c. Alternatively, we might also use the t-test to determine if the slope is equal to some hypothesized value

(BHypo). The critical value is given by tcritical = (B1-BHypo)/ σB1. If the value of tcritical is not in the ranges above,

we reject H0.

d. For testing whether an independent variable explains the variation in the dependent variable, the

hypothesis test is whether slope is zero

2. Dummy Variable: An independent variable, binary in nature, is called a dummy variable. They are assigned

values of 0 or 1

3. Homoskedasticity & Heteroskedasticity:

a. If the variance of the residuals(ε) is constant across all observations in the sample, the regression is

Homoscedastic

b. If variance of the residual(ε) increases as independent variable increases, then its called Conditional

Heteroskedasticity

4. OLS as unbiased estimator: OLS places no restrictions on conditional variance of the residual term thus OLS

remains unbiased and consistent despite the residual term

5. Gauss-Markov Theorem: It states that in a linear regression model in which the errors have expectation zero

and are uncorrelated and have equal variances, the best linear unbiased estimator (BLUE) of the coefficients is

given by the ordinary least squares (OLS) estimator. Here residual is assumed to be homosekadastic and .

Limitations of theorem are:

a. In economic applications, residual or error terms are heteroskedastic

b. Under certain conditions, other estimators are more efficient than OLS

MULTIPLE REGRESSOR

Reading: Linear Regression with Multiple Regressors: Hypothesis Tests and Confidence Intervals (Chapter 6, James Stockand Mark Watson, Introduction to Econometrics, Brief Edition (Boston: Pearson Education, 2008))

1. Omitted Variable Bias: An omitted variable bias is present when

a. Omitted variable is correlated with the movement of the independent variable

b. Omitted variable is a determinant of the dependent variable

2. Multiple regression takes more than one independent variable (x), thus equation is of the form: Y = B0 + B1X1 +

B2X2 + B3X3+…+ BnXn + ε

3. Assumptions of Multiple regression:

a. ε has a mean of zero

b. X1, X2, X3,…,Xn are i.i.d

c. Large outliers are unlikely

d. No perfect multicollinearity

4. Standard Error of Regression (SER): It measures the standard deviation of the error term.

5. Goodness of Fit: R2 is not a good measure of goodness of fit as it increases with increase in the number of

independent variables. Thus, it overestimates regression accuracy. To overcome this bias, we use adjusted R2

which is given as: RAdj2 = 1 – [(n-1)(1-R2)]/(n-k-1) where n is the number of observations and k is number of

independent variables.

a. Note that RAdj2 ≤ R2

6. Multicollinearity: It refers to the condition that two or more variables or linear combination of the independent

variables in a multiple regression are highly correlated with each other. If correlation is perfect, then OLS

estimation is not possible.

a. Test is to check If R2 value is high but t-test shows that none of the independent variable are significant,

then multicollinearity exists

MULTIPLE REGRESSOR HYPOTHESIS

Reading: Hypothesis Tests and Confidence Intervals in Multiple Regression(Chapter 7, James Stock and Mark Watson,Introduction to Econometrics, Brief Edition (Boston: Pearson Education, 2008))

1. Hypothesis Testing:

a. The t-statistic used for the single regressor can also be used here.

b. The df changes to n-k-1in place of n-1

2. P-values: The p-values are the smallest level of significance for which the null hypothesis can be rejected.

a. Decision: p < α; reject H0

b. For statistical significance, we can either use the confidence interval or the p-values. Both will result in

the same decision being taken

3. Joint Hypothesis Testing: It sets two coefficients as zero i.e. H0 = B1 = 0 and B2 = 0. HA is that one of them is not

zero. If even one of them is not equal to zero, we can reject the null hypothesis. For joint hypothesis testing, we

always use the F-Test

a. F-test is always one tail test with F = SSR / k

SSE / (n-k-1)

b. The df in numerator is k and df in denominator is n-k-1

c. The F-value obtained is tested against the critical one tail value

d. Rejection indicates that at least one of the values is not equal to 0

4. Specification Bias: It refers to the fact that slope coefficients and other statistics for a given variable are usually

different in simple regression when compared to multiple regression of the same coefficients.

5. Model Misspecifications:

a. Functional Form:

i. Important variables are omitted

ii. Variable should be transformed

iii. Data is improperly pooled

b. Correlation with Error Term

i. Lagged dependent variable is taken as independent

ii. Function is used as independent variable

MODELING AND FORECASTING TREND

Reading: Elements of Forecasting (4th edition, Cengage Learning, 2006)

1. Definitions:

a. Mean squared Error: Statistical measure computed as sum of squared residuals divided by total number

of observations.MSE = ∑where e = y − ỳ (i.e. Observed – Expected)

b. Data Mining: As more variables are included in regression equation, the model is at the risk of over-

fitting the in-sample data. This is data mining

c. Asymptotic Efficiency: Property that chooses a regression model with one-step ahead forecast error

variances closest to the variance of the true model.

2. The regression model with the smallest MSE is also the model with smallest sum of squared residuals and

highest R2

3. Bias with MSE

a. There is a problem of data mining with MSE

b. S2 measure is an unbiased estimate of MSE because it corrects for degrees of freedom∑

c. S2 ranks the models the same way as adjusted R2

4. Model Selection Criteria

a. Penalty factors for S2 is (T/T-k); for AIC(Akaike information criterion) is e(2k/T) and for SIC(Schwarz

information criterion) is T(k/T)

b. SIC has the highest penalty factor but AIC has asymptotic efficiency (as defined above). SIC is not

asymptotic efficient

c. SIC is the most consistent criteria

CHARACTERIZING CYCLES

Reading: Elements of Forecasting (4th edition, Cengage Learning, 2006)

1. Definitions:

a. Time Series: A set of observations for a variable over successive periods of time

b. Autoregressive: Past values are used to predict future values

c. Covariance Stationary: Mean, Variance and Covariance do not change over time

d. Autocovariance Function: Tool used to quantify stability of the covariance

e. White Noise Process: A time series with zero mean, constant variance and no serial correlation is

referred to white noise

f. Q statistic: Used to measure the degree to which autocorrelations vary from zero and whether white

noise is present in the data set

g. Box-Pierce Q Statistic: Reflects magnitude of the correlations as it uses the sums squared

autocorrelations

h. Ljung-Box Q Statistic: Replaces the sum of squared autocorrelations with weighted sum of squared

autocorrelations

i. World’s Theorem: Evaluates covariance stationary as pre-requisite for time series modelling

MODELING CYCLES: MA, AR AND ARMAReading: Elements of Forecasting (4th edition, Cengage Learning, 2006)

1. MA(1)[Moving Average First Order Process]: It is a linear regression of the current values of time a time series

against both the current and previous unobserved white noise error terms which are random shocks. It is

defined as: y = ε + θεa. It has a mean of zero and a constant error term

b. The autocorrelation cutoff (ρ) is zero for any value beyond the first error term and can be computed asρ =2. MA(q) process: It increases the lagged terms to q and all other values after that have zero autocorrelation.

3. AR(1) [Autoregressive First Order]: It is specified in the form of a variable regressed against itself in the lagged

form. It is given as: y = ε + ϕya. The absolute value of the coefficient must be less than 1 i.e. |φ|<1

b. Yule Walker: ρ = ϕc. Moving averages exhibit autocorrelation cut-off while Auto regressive series exhibit autocorrelation

decay but never become zero

4. AR(p): It increases the lagged terms to p in the AR series

5. ARMA(Autoregressive Moving Averages): It combines MA and AR models and is defined as:

a. y = ε + θε + ϕyb. The autocorrelations decay gradually like in AR process

c. We can have ARMA(p,q) model which is p terms of AR and q terms of MA

d. This model enables modeling of more complex observations as compared to MA or AR processes

VOLATILITIES & CORRELATION

Reading: Estimating Volatilities and Correlations (Chapter 22, John Hull, Options, Futures, and Other Derivatives, 8thEdition (New York: Pearson Prentice Hall, 2012))

1. EWMA: Exponentially Weighted Moving Average (EWMA) is a method for calculating volatility (σ). The weights

in the method are exponentially declining, i.e. the nearest volatility has the maximum weight. It is given as:

σn2 = λσn-1

2 + (1-λ) µn-12 where λ is the rate of decay, µ is the return on a day and σ is standard deviation.

a. Large values of λ will minimize the effect of daily percentage returns, whereas low values will tend to

increase the effect of the same.

2. GARCH(1,1): Generalized Autoregressive Conditional Heteroskedasticity (GARCH) is another method for

calculation of volatility. It incorporates a long run value of variance apart from the variables above.

a. σn2 = ω + αµn-1

2 + βσn-12 where ω = ϒ VL and VL = ω/(1-α-β) thus ϒ = 1-α-β

b. For stability, we require that (α+β) < 1 always.

c. The EWMA can be thought as a special case of GARCH where ϒ=0, β= λ and α=(1- λ)

d. An implicit assumption of GARCH is that variance tends to return to its long term mean level.

e. α+β is also called the persistence i.e. the rate at which volatility will revert to its long term mean

3. Maximum Likelihood Method: It is a method used to calculate the parameters in GARCH

SIMULATION METHODS

Reading: Chapter 13, Chris Brooks, Introductory Econometrics for Finance, 3rd Edition (Cambridge, UK: CambridgeUniversity Press,2014)

1. Steps for Monte Carlo Simulation

a. Specify the DGP (Data Generating Process) and generate the data

b. Do the regression and calculate the test statistic

c. Save the statistic or parameter of interest

d. Go back to step 1 and repeat N times

2. Sampling Error in Monte Carlo: If we run the same simulation twice, we are likely to get different values for the

parameter of interest. There are two methods to reduce the sampling error in Monte Carlo:

a. Antithetic Variables: Take complement of a set of random numbers and run a parallel simulation

b. Control Variates: Employ a similar variable whose outcomes are known and simulate it with parameter

3. Bootstrapping: Random sampling with replacement i.e. the original value is not taken out for the next round.

a. Disadvantages: If there are outliers, they may impact the conclusions of the test. Use of bootstrap

implicitly assumes that data are independent of each other.

4. Pseudo-random draws: Computer generated random number draws.

5. Disadvantages of Simulation

a. It might be computationally expensive

b. Results might not be precise

c. Results are hard to replicate

d. Results are experiment specific

FINANCIAL PRODUCTSFRM 2016 Part 1 Revision Course

INTRODUCTION TO DERIVATIVES

Reading: Futures and Options (Chapters 1,2,3, The Institute for Financial Markets, Futures and Options (Washington, DC:The Institute for Financial Markets, 2011))

1. Definitions:

a. Options: The right to buy or sell an asset at an exercise price, but not an obligation

b. Forward: Specifies the price and quantity of an asset to be delivered sometime in the future. There is no

standardization and is traded over the counter (OTC)

c. Futures: A standardized contract specifying the price and quantity of an asset to be delivered in the

future. It is legally binding and standardized in terms of quality, quantity, delivery time and location.

Typically traded over an exchange

d. Market Maker: An individual who maintains bid and offer prices in a given security

e. Open Interest: Total number of long positions/short positions in a futures contract

f. Tick Size: Minimum price fluctuation for a contract is referred to as the tick size

g. Basis: The difference between the spot price and futures price. As maturity date nears, the basis

converges to zero

h. Margin: Cash or highly liquid collateral placed in an account to ensure that any trading losses will be

met. MTM is the procedure to adjust margin account daily

i. Initial Margin: Amount to open a futures account

ii. Maintenance Margin: Minimum balance after which the margin call is triggered

iii. Variation Margin: Amount to bring back the margin account to initial margin level

i. Clearing House: It acts as an intermediary in futures transaction. It guarantees the performance of

parties to each transaction.

j. Long the Basis: Long cash/asset position is hedged using short positions in futures

k. Short the Basis: A short position in an asset which is hedged using a long position in futures.

l. Exchange for Physicals (EFP): A method by which opposite parties of a futures contract that has

underlying cash commodities aim to close out their positions simultaneously

HEDGING STRATEGIES

Reading: Hedging Strategies Using Futures (Chapter 3, Hull, Options, Futures, and Other Derivatives, 8th Edition))

1. Hedge: A way to mitigate/ reduce the risk

a. Short Hedge: It involves a short position in futures contracts. Appropriate if you already own the asset

and expect to sell it sometime in the future.

b. Long Hedge: It involves taking a long position in futures contracts. Appropriate if you know you will

have to purchase an asset in the future.

c. Benefits of Hedge:

i. Can avoid sharp rise or fall in an asset price

ii. Help reduce volatility

d. Disadvantages of Hedge:

i. Can lead to a negative outcome i.e. Reduction in profits

ii. Hedging assumes that individual investors need a company to hedge and are incapable of doing

it themselves

2. Basis Risk: The price of the underlying asset may not move perfectly with the hedge

3. Cross Hedging: Occurs when underlying asset and hedge asset are different. E.g. Airline hedging Jet Fuel with

Standard Oil futures.

4. Minimum Variance Hedging: We account for imperfect relationship between spot and futures prices by

calculating an optimal hedge ratio. It is given as : HR = ρs,f x σs/σf where ρs,f is the coefficient of correlation

between spot and futures price.

a. Hedge effectiveness is measured by R2 where independent term is change in futures and dependent

term is change in spot prices.

5. Hedging with Stock Index Futures: No. of Contracts = βP x [Vp/Vf] where βP is the Beta of the portfolio and Vp is

the value of portfolio and Vf is the value of futures contract. Note that Vf = Futures Price x Contract Multiplier

a. If we wish to reduce the systematic risk of the portfolio, and our target Beta is (β*) then No. of contracts

= (β* - βP) x [Vp/Vf]

i. If above value is negative, we sell futures contracts. If positive, we buy futures contracts

6. Tailing the Hedge: A hedger may over-hedge if the daily settlement is not properly accounted for. To correct for

possibility, we can implement a trailing hedge strategy where no. of contracts x (short to futures ratio)

7. Rolling the Hedge: If the expiry of the futures contract is earlier, we need to roll the hedge.

MECHANICS OF FUTURES MARKET

Reading: Mechanics of Futures Market (9th edition, Pearson, 2014)

1. Definitions:

a. Futures: Exchange traded obligations to buy or sell a certain amount of an underlying at specified date

and price

b. Open interest: Total amount of long positions in a given contract

c. Tick Size: Minimum price fluctuation for the contract

d. Basis: Difference between the spot price and futures price. As maturity nears, basis converges to zero

e. Margin: Cash or highly liquid collateral placed in an account to ensure any trading loss will be met

f. Maintenance Margin: Minimum margin required to retain futures position

g. Variation Margin: Amount needed to get the account back to initial margin after receiving a margin call

due to margin falling below maintenance margin amount

h. Clearing House: guarantees that trades in the futures market will be honored

i. Collateralization: MTM feature for OC market where any loss at the end of the day is settled in cash

INTEREST RATES

Reading: Interest rates (Chapter 4, Hull, Options, Futures, and Other Derivatives, 8th Edition))

1. Definitions:

a. Treasury Rates: Govt. borrowing in own currency

b. LIBOR: Funding of large international bank activities

c. Repo Rates: Implied rate on repurchase agreements

2. Risk Free Rate: Treasury rates are often considered benchmarks for Risk free rates. Aa these are too low (due to

regulatory environment), most derivative traders use LIBOR rates for short-term risk free rate

3. Compounding Rates: An investment of A, earning an annual rate of R, compounded m times annually for n years

has a Future Value(FV) of A x (1 + R/m) mn

a. If the compounding is continuous, then FV = AeRn

b. If we want to convert discrete compounding to continuous compounding Rm = m(eRc/m – 1) where Rm is

rate of compounding for m times per year and Rc is the continuously compounded rate.

4. Spot Rates (Zero Rates): Spot rates are rates that correspond to zero-coupon bond yields. They are appropriate

discount rates for a single cash flow at a particular future time or maturity (e.g. Bootstrap method of calculation)

5. Forward Rates: They are interest rates implied by the spot curve for a specific future period. Given as (R2T2-

R1T1/T2-T1)

6. FRA (Forward Rate Agreement): It is a forward contract obligating two parties to agree to a certain interest rate

applying to a principal amount during a specified future time.

a. The value of the FRA is

i. Rk is earned: A (Rk-Rf) (T2-T1) e-R2

T2

ii. Rk is paid: A (Rf-RK) (T2-T1) e-R2

T2

7. Bond Duration: The average time until the cash flows on the bond are received. For a zero coupon bond, it is

time to maturity.

a. Duration is a linear estimate and as yield change grows in size, we need to add convexity to reduce

estimation error.

8. Term Structure Theory:

a. Expectations: Long term rates reflect expected future short term rates

b. Market Segmentation: No particular relation between short and long term rates

c. Liquidity Preference: Long term interest rates are always higher than short term rates

FORWARD AND FUTURE PRICES

Reading: Determination of Forward and Future Prices (Chapter 5, Hull, Options, Futures, and Other Derivatives, 8thEdition))

1. Formulae:

a. F = SerT where F is Forward Price and S is spot price. R is risk free rate

b. F = (S-I) erT where I is any income at present value

c. F = Se(r-q)T where q is the dividend yield

d. F= (S+u) erT where u is storage costs

e. F = Se(r+u)T where storage costs are in % terms

f. F = Se(r-rf)T where r-rf is the rate difference between domestic and foreign currency

g. F = Se(r+u-y)T where y is convenience yield

2. For a consumption asset, there may sometimes be a benefit to owning the underlying asset today compared to

owning the asset sometime in the future. The convenience yield is brought in to balance the equation

3. Backwardation: If F < S, then it is normal backwardation. For this to happen, there must be significant benefit to

holding the asset

4. Contango: If F > S, then it is normal contango. There are no benefits to holding the asset now.

INTEREST RATE FUTURES

Reading: Interest Rate Futures (Chapter 6, Hull, Options, Futures, and Other Derivatives, 8th Edition))

1. Day Count Conventions: There are 3 different day count conventions for calculating accrued interest(AI)

a. AI = Coupon x (no. of days from last coupon/ no. of days in coupon period)

Name Convention

US T-Bonds Actual no. of days from last coupon/ actual no. of days in coupon period

US Corp. or Municipal Bonds 30/360

US T-Bills Actual no. of days from last coupon/360

2. T-Bonds Quotes: T-Bonds are quoted relative to $100 par amount in dollars and 32nds. The quoted price (Clean

Price) is not the same as the cash price of the T-Bond. Cash Price = Quoted Price+ AI

a. E.g. If quoted price is 95-16, it means quoted price is $95.50

3. Discount Rate: T-Bills with $100 face value with n-days to maturity and a cash price of Y is quoted as

a. Discount Rate = (360/n)(100-Y)

b. E.g. If price of T-Bill is quoted as 8, it means rate of interest is 8% per annum for 360 days

4. T-Bond Futures: In this contract, any government bond that has more than 15 years to maturity on the first day

of the delivery month and is not callable within 15 years from that day can be delivered.

a. Cash = (Quoted Futures Price x Conversion Factor) + AI

b. The conversion factor for a bond is set equal to the quoted price the bond would have per dollar of

principal on the first day of the delivery month on the assumption that the interest rate for all maturities

equals 6% per annum (with semiannual compounding)

5. Cheapest-to-Deliver: The CTD = Quoted Price – (Quoted Futures Price x Conversion Factor)

a. Finding CTD requires searching between a large number of bonds.

i. When yields are < 6%, low coupon and long maturity bonds are CTD

ii. When yield curve is upward sloping, CTD bonds tend to have longer maturities

6. Eurodollar Futures: Eurodollar is a US dollar deposited outside US in a US or foreign bank. The Eurodollar

interest rate is the rate of interest earned on Eurodollars deposited by one bank with another bank. It is

essentially the same as the London Interbank Offered Rate (LIBOR). A three-month Eurodollar futures contract is

a futures contract on the interest that will be paid (by someone who borrows at the Eurodollar interest rate) on

$1 million for a future three-month period.

a. The contract is designed so that a one-basis-point (0.01) move in the futures quote corresponds to a

gain or loss of $25 per contract

b. The contract price is defined as 10,000 [100 – 0.25(100-Q)] where Q = 100-R and R is rate in day of

settlement

7. Duration based Hedging Strategies: It aims to create a combined position that does not change with change in

yields. A minus sign indicates that futures position is opposite of the original position.

a. No. of contracts = (-P x DP)/(F x DF) where P is portfolio value, DP is Duration of portfolio, F is Futures

value and DF is duration of futures contract

SWAPS

Reading: Swaps (Chapter 7, Hull, Options, Futures, and Other Derivatives, 8th Edition))

1. Interest Rate Swap: An interest rate swap is an agreement between two parties to exchange interest payments

based on a specified principal over a period of time. Some other types of swap include:

a. Equity Swap: Equity return with an interest rate

b. Commodity Swap: Fixed for floating on an avg. commodity price

c. Volatility Swap: One party pays a fixed volatility and another pays realized volatility

d. Currency Swap: Principal and interest in one currency is swapped for principal and interest in another

currency

2. Problems with Comparative Advantage: It assumes that a company can borrow at a floating rate over the entire

life of the swap.

3. Valuing an Interest Rate Swap: Value of a swap when it is initiated is zero.

a. As bonds: If one has a long position in floating rate note, then Vswap = BFloating - BFixed

i. Value of a floating rate bond is worth the notional principal immediately after an interest

payment

b. As FRA: Calculate individual forward rates, and then discount for floating cash flow.

4. Credit Risk: Whenever one side of the swap has positive value, credit risk is created as the other party may

default.

Refer to class instructions for actual calculations.

STOCK OPTIONS

Reading: Properties of Stock Options (Chapter 10, Hull, Options, Futures, and Other Derivatives, 8th Edition))

1. Summary of Effects:

Factors European Call European Put

Stock Price (S)

Strike Price (X)

Time to Expiry (T)

Volatility (σ)

Risk Free Rate (r)

Dividend (D)

2. Upper and Lower Bounds:

a. For a European Call Option:

i. (0, S0 - Xe-rt) ≥ C ≤ S0

b. For a European Put Option:

i. (0, Xe-rt - S0) ≥ P ≤ Xe-rt

3. Put-Call Parity: It is important to note that exercise prices on the put and the call, exercise date are all same.

Then C-P = S0 - Xe-rt

a. If this relationship is violated, it results in arbitrage opportunity

b. Also, S0 – X ≤ C - P ≥ S0 - Xe-rt

4. America Call: An American call in never exercised early for a non-dividend paying stock. Of the dividend is large

enough to forego the interest, only then we will exercise an American Call option

TRADING STRATEGIES

Reading: Trading Strategies involving options (Chapter 11, Hull, Options, Futures, and Other Derivatives, 8th Edition))

1. Covered PUT and CALL:

a. Covered PUT: If we have a long security and a long put, we have a protective put. The downside is

capped

b. Covered CALL: If we short a call option and long security, we have a covered call. It is used to generate

cash if the stock price does not move beyond the exercise price.

2. Spreads: They combine similar options to create a desired payoff profile. The differences are either strike price

or time expiration.

a. Bull Spreads: Buy a call with low strike price and

sell a call with high strike price. It benefits if price

remains in a narrow range. A bear spread is an

exact opposite and benefits from falling prices.

3. Butterfly Spread:

a. Buy two call options with low and high strike price; sell two call

options with medium strike price. The strategy benefits with prices

remaining in the range of written calls.

4. Other Spreads:

a. Calendar Spreads: Created by transacting in two options with the same strike price but different

expiration period. Profits come if prices remain in a small range. Sell short-dated option and buy a long

dated option.

b. Diagonal Spread: Similar to calendar options, can have different strike prices and expiration periods

c. Box Spreads: A combination of bull call spread and put bear spread. The payoff always remains the

same.

5. Combinations: They are strategies involving both calls and puts. They bet on volatility.

a. Straddle: A long straddle is created by buying one

put and one call option with the same strike price

and expiration. A short straddle is when we sell a put

and call with same strike price. This strategy is

profitable if there is a strong movement in either

direction.

c. Strips and Straps: A strip involves

purchasing 2 put options and 1 call

option with the same strike price

and expiration. A strip is betting on

a stock price fall. Straps are

opposite of strips.

b. Strangle: Same as straddle, but options

purchased are out of money. You need a

very string movement in either direction

for profit.

EXOTIC OPTIONS

Reading: Exotic Options (Chapter 25, Hull, Options, Futures, and Other Derivatives, 8th Edition)

Option Description

Forward Start Options that begin their existence sometime in the future e.g. ESOP’s

Compound Option Options on options. E.g. Call on call, Call on Put, Put on Call and Put on Put

Chooser Option After a certain time has elapsed, the owner may choose whether the option is call or

put

Barrier Options Their existence depends on whether the underlying asset price reaches a certain barrier

level over the life of the option. Down and Out: Option ceases to exist if the underlying

asset price hits a barrier level. Down and In: Option comes into effect only after hitting

the barrier level

Binary Options Options pay a set price if the asset value is above the strike price. Cash or Nothing: Fixed

amount is paid if the asset is above the strike price. In BSM, N(d2) gives this probability.

Asset or Nothing: Pays the value of the stock during the initiation of the contract if the

stock price ends up above the strike price

Lookback Options Payoff depends on the maximum or minimum price of the asset during the life of the

option

Shout Options Fix one price on the day of the shout and then choose between this price or price during

expiry

Asian Options Payoff is based on the average price of the security over life.

Exchange Option Exchange one asset for another e.g. one currency with another

Basket Options Options to purchase or sell a basket of securities

1. Volatility Swaps: Involves exchange of volatility based on a notional principal amount

2. Vega: Sensitivity of an option price to volatility. It is always positive but becomes negative for barrier options

3. Packages: Usually consist of selling one instrument and buying another so that initial cost is zero

4. Non-standard American Options:

a. Bermuda Option: Early exercise is restricted to certain dates

COMMODITY FORWARDS

Reading: Commodity Forwards and Futures (Chapter 6, Robert McDonald, Derivatives Markets, 3rd Edition (Boston:Addison-Wesley, 2013))

1. Definitions:

a. Storage Costs: The cost of storing a physical item such as corn or copper can be large relative to its

value.

b. Carry Markets: A commodity for which the forward price compensates a commodity owner for costs of

storage is called a carry market

c. Lease Rate: The short-seller of an item may have to compensate the owner of the item for lending. For

commodities, a short seller may have to make a payment, called a lease payment, to the commodity

lender (Can be thought of as dividend yield).

d. Convenience Yield: The owner of a commodity in a commodity-related business may receive

nonmonetary benefits from physical possession of the commodity. Such benefits may be reflected in

forward prices and are generically referred to as a convenience yield.

2. Cash and Carry Arbitrage: It consists of buying the commodity, storing/ holding the commodity, and selling the

commodity at a future price when contract expires. A profit is generated if futures is overpriced.

3. Commodity Spread: It results from a commodity that is an input in the production process of other

commodities. Crude oil can be converted into Gasoline & Heating oil. This process is called cracking and

difference in prices is called crack spread. E.g Spread 5-3-2 mean 5 gallons of oil being converted into 3 gallons

of Gasoline and 2 gallons of heating oil

4. Basis Risk: Basis risk is a generic problem with commodities because of storage and transportation costs and

quality differences.

5. Strip vs. Stack hedge:

a. Strip Hedge: We engage in a strip hedge when we hedge a stream of obligations by offsetting each

individual obligation with a futures contract matching the maturity and quantity of the obligation.

b. Stack Hedge: With a stack hedge, we enter into futures contracts with a single maturity, with the

number of contracts selected so that changes in the present value of the future obligations are offset by

changes in the value of this “stack” of futures contracts. When the near-term contract matures, we

reestablish the stack hedge by going long contracts in the new near month. This process of stacking

futures contracts in the near-term contract and rolling over into the new near-term contract is called a

stack and roll.

6. Weather Derivatives: Contracts that make payments based upon realized characteristics of weather.

7. Synthetic Commodities: We can create a synthetic commodity by combining a commodity forward contract and

a zero-coupon bond. Enter into a long commodity forward contract at the price F and buy a zero-coupon bond

that pays F at time T

Formulae seen in Chapter 4 apply here. Refer Chapter 4, Module 3 for formulae

FOREIGN EXCHANGE RISK

Reading: Foreign Exchange Risk (Chapter 14, Anthony Saunders and Marcia Millon Cornett, Financial InstitutionsManagement: A Risk Management Approach, 7th Edition (New York: McGraw-Hill, 2011))

1. Financial Exposure: A banks actual exposure to any given currency can be measured by its net position in that

currency. Net Position = (FX Assets – FX Liabilities) + (FX Bought – FX Sold)

2. Hedging:

a. On balance sheet hedging: Achieved when an institution has matched maturity and currency foreign

asset liability book

b. Off balance sheet hedging: The institution enters into a forward contract. Any forward position taken

would not appear on the balance sheet; it would appear as a contingent off-balance-sheet claim.

3. Interest rate parity: The discounted spread between domestic and foreign interest rate equals the percentage

spread between forward and spot exchange rates. Hedged dollar returns on foreign investment should be equal

to return on domestic investment. As shown earlier, F = Se(r-rf)t

4. Multi-currency foreign asset liability: Since currencies are less than perfectly correlated, diversification across

several asset and liability markets can potentially reduce portfolio risk as well as cost of funds

5. Nominal Rate: The interest rate before taking inflation into account. It is given as:

a. Nominal Rate = (1 + Real Interest Rate) (1 + Inflation Rate)

CENTRAL COUNTERPARTIES - INTRODUCTION

Reading: Jon Gregory, Central Counterparties: Mandatory Clearing and Bilateral Margin Requirements for OTCderivatives (West Sussex, UK: John Wiley & Sons, 2014).

1. Definitions:

a. Counterparty Risk: Possibility that a counterparty may not meet its contractual obligations when due

b. Mutualisation: One counterparties losses are dispersed throughout the market

2. OTC Derivatives:

a. Over-the-counter derivatives are derivative trades between two parties. They are illiquid and have non-

standard or exotic features.

b. Counter party risk in OTC trades creates systemic risks as trading volume in OTC market are dominated

by a relatively small number of large derivative counter parties. When a counterparty defaults, there is a

need to replace the underlying trades, and in an aftermath of a large default, this is highly problematic

3. Regulatory changes after the crisis:

a. Dodd-Frank Act and European Market Infrastructure Regulation required all standard OTC derivatives to

be cleared through Central Clearing Parties (CCP)

4. CCP:

a. A CCP is a buyer to every seller and vice versa. The original counterparty to a trade now represents no

direct risk. The CCP becomes the new counterparty.

b. Roles of CCP:

i. Sets standards for clearing members

ii. Takes responsibility for clearing all positions of a defaulting member

iii. Maintains financial resources like Margins and Mutualisation fund

5. Drawbacks of CCP:

a. OTC derivatives are illiquid, long-dated and complex compared to exchange traded derivatives and

hence are a challenge

b. CCP’s clearing OTC products will become systemically important themselves creating a moral hazard

during times of distress

c. CCP’s introduce more costs

d. Mutualisation means all members are treated in the same way. Most credit-worthy members may see

less advantage of their stronger credit quality.

EXCHANGES, OTC DERIVATIVES, DPCS & SPVS

Reading: Chapter 2. Exchanges, OTC Derivatives, DPCs and SPVs, Jon Gregory, Central Counterparties: MandatoryClearing and Bilateral Margin Requirements for OTC derivatives (West Sussex, UK: John Wiley & Sons, 2014).

1. Definitions:

a. Margining: Exchange members receiving and paying cash or other assets against gains and losses in

their positions (variation margin) and providing extra coverage against losses in case they default (initial

margin)

b. Netting: Offsetting of contracts to reduce exposure

c. Clearing Rings: Group of three or more participants will ring out offsetting positions

2. OTC vs Exchange Traded:

Exchange Traded OTC

Terms of Contract Standardised (Size, Strike etc.) Flexible & Negotiable

Maturity Standard Maturities Negotiable & Non-standard

Liquidity Very Good Limited or Poor

Credit Risk Guaranteed by CPP Bilateral

3. OTC Derivatives Class:

a. Interest Rate, Foreign Exchange, Equity, Commodity, Credit

BASIC PRINCIPLES OF CENTRAL CLEARING

Reading: Chapter 3, Basic Principles of Central Clearing, Jon Gregory, Central Counterparties: Mandatory Clearing andBilateral Margin Requirements for OTC derivatives (West Sussex, UK: John Wiley & Sons, 2014).

1. Definitions:

a. Clearing: Period between execution and settlement of a transaction

b. Novation: Replacement of one contract with one or more contracts.

c. Bifurcation: Cleared and non-cleared trades can cause volatile cash flows for customers

2. Advantages and Disadvantages of CPP:

a. Advantages:

i. CCP reduces interconnectedness within financial markets and hence can lessen impact of

insolvency of a participant

ii. CCP can provide more transparency on positions of members

iii. Multilateral Offsetting: Offsetting of multiple overlapping positions between market participants

iv. Loss Mutualisation

b. Disadvantages:

i. As CPP is the centre of the hub and spoke system, its failure can be catastrophic to the system

ii. Ca increase margins in times of volatility and increase systemic risks

iii. Disincentives to have good counterparty risk measures

3. Margining:

a. Variation Margin: Covers the net change in market value of the members’ positions

b. Initial Margin: Additional amount which is charged at trade inception and is designed to cover worst

case close out costs. It does not depend on the credit rating of the member.

c. Margin requirements of CCP’s are generally much stricter than in bilateral derivatives market. Thus

central clearing imposes significantly higher costs via margin requirements

4. Novation and Netting

RISK CAUSED AND FACED BY CCP’SReading: Chapter 14, Risks Caused by CCPs: Risks Faced by CCPs, Jon Gregory, Central Counterparties: Mandatory

Clearing and Bilateral Margin Requirements for OTC derivatives (West Sussex, UK: John Wiley & Sons, 2014).

1. Default Loss Events: Default of a clearing member and possibility of knock on effects

a. Default/ Distress of other members: Default correlations between members are high

b. Failed Auctions: Imposing losses on members for failed auctions increases financial distress

c. Reputational: Remedying a clearing member default may involve relatively extreme loss allocation which

can be seen as unfair by members

2. Non-default Loss Events:

a. Fraud

b. Operational: Business disruption due to system failures

c. Legal: Losses due to litigation or claims

d. Investment: Losses from investments of cash and securities held as margin

3. Model Risk:

a. Significant exposure to model risks through margining requirements especially initial margin

requirements

b. Models impose linearity i.e. Initial margins increase in proportion to the position

4. Liquidity Risk:

a. CCP must try to optimise investment of some of the financial resources they hold without taking

excessive credit and liquidity risks

b. Basel 3 leverage ratio increases the capital requirements for banks as it includes gross notional centrally

cleared OTC derivatives

5. Other Risks

a. Forex Risks

b. Concentration risk

CORPORATE BONDS

Reading: Corporate Bonds (Chapter 12, Frank Fabozzi, The Handbook of Fixed Income Securities, 8th Edition (New York:McGraw-Hill, 2012))

1. Indentures: The promises of corporate bond issuers and the rights of investors who buy them are set forth in

great detail in contracts generally called indentures. A corporate trustee is a bank or trust company with a

corporate trust department and officers who are experts in performing the functions of a trustee

(representative of the interests of bondholders).

2. Corporate Debt Maturity: A bond’s maturity is the date on which the issuer’s obligation to satisfy the terms of

the indenture is fulfilled. On that date, the principal is repaid with any premium and accrued interest that may

be due.

3. Types of Interest:

a. Straight Coupon Bond

b. Zero Coupon Bond (zero-coupon bonds pay only the principal portion at some future date)

c. Floating Rate Note

4. Zero Coupon Bond:

a. The difference between the face amount and the offering price when first issued is called the original-

issue discount. The rate of return depends on the amount of the discount and the period over which it

accretes.

b. Because there is no coupon to reinvest, there isn’t any reinvestment risk

5. Security Bonds:

a. Mortgage Bonds: A mortgage bond grants the bondholders a first-mortgage lien on substantially all its

properties

b. Collateral Trust Bonds: They pledge stocks, notes, bonds, or whatever other kinds of obligations they

own. These assets are termed collateral(or personal property)

c. Equipment Trust Certificates: Collateral is the equipment (E.g Rolling Stock in rails)

d. Debenture Bonds: Unsecured bonds are called Debentures.

6. Credit Risk: It can be classified as Credit Default Risk and Credit Spread Risk.

a. Credit Default: A default on payment by the issuer.

b. Credit Spread: The credit spread is the difference between a corporate bond’s yield and the yield on a

comparable-maturity benchmark Treasury security

OVERVIEW OF MBS MARKET

1. Fixed Rate MBS Pooling:

2. Trade in MBS: Fixed rate pass through securities trade in the following manner:

a. Pre-identified pool trade (Specified Pool): The identity and balance of pools is known at the time the

trade is consummated.

b. To be announced: It involves identifying the security (e.g. Fannie Mae 6.0%) and establishing the price.

Actual pools identity are revealed just before settlement. The attributes are defined by BMA (Bond

Market Association). It only exists for fixed rate markets in agency pools

c. Stipulated Trade: Similar to TBA, except pool characteristics are provided in greater detail

3. Dollar Roll: A dollar roll transaction occurs we an MBS market maker buys positions for one settlement and at

the same time, sells those same positions for another month

Fees paid to agenciesto insure the loan

Servicer Fee

Amount in excess ofdesired coupon

Loan 1 Loan 2

RATING AGENCIES

Reading: The Rating Agencies (Chapter 6, John B. Caouette, Edward I. Altman, Paul Narayanan, and Robert W.J. Nimmo,Managing Credit Risk, 2nd Edition (New York: John Wiley & Sons, 2008))

1. Role of Rating Agencies: Rating agencies specialize in evaluating the creditworthiness of debt securities issued

by corporate, financial, structured finance, municipal, and sovereign obligors, and by evaluating the general

creditworthiness of the issuers themselves.

2. Ratings: In rating long-term debt, each agency uses a system of alphanumeric letter grades that locate an issuer

or issue on a spectrum of credit quality from the very highest (AAA/Aaa meaning an extremely strong capacity to

meet financial commitments) to the very lowest (C/D meaning there has been a payment default). Each letter

grade has three notches (Fitch and S&P use +and−modifiers, Moody’s uses numerical modifiers 1, 2, 3)

a. Investment Grade: All debt rated BBB/Baa or above is considered to be of investment-grade quality,

while issues rated BB/Ba or below are viewed as speculative or noninvestment grade.

3. Rating Process: In evaluating credits issuers and obligations, the rating agencies use many of the same tools

normally applied by equity analysts; but their approach is focused on a longer time horizon than short-term

earnings and performance forecasts.

4. Rating and Regulators: The relationship between regulators and ratings agencies is deep and often ambiguous.

The regulators are attracted to the high quality, the independence, and very widespread acceptance of the

rating agency opinions on credit quality. On the other hand, they are concerned about putting so much reliance

on the agencies over whose activities they have no control. For the agencies, the use of their opinions by the

regulators is an important validation of their work.

5. Trends:

a. Other factors like liquidity becoming more important and credit rating agencies don’t just focus on

repayment capability

b. Clear process set to become NRSRO by US after Enron.

VALUATION & RISK MODELSFRM 2016 Part 1 Revision Course

VOLATILITY IN VARReading: Quantifying Volatility in VaR Models (Chapter 2, Linda Allen, Jacob Boudoukh and Anthony Saunders,

Understanding Market, Credit and Operational Risk (Oxford: Blackwell Publishing, 2004))

1. Deviation from Normal Returns:a. Fat Tails: A fat-tailed distribution is characterized by having more probability weight (observations) in its

tails relative to the normal distribution.b. Skewed: A skewed distribution in our case refers to the empirical fact that declines in asset prices are

more severe than increases. This is in contrast to the symmetry that is built into the normal distributionc. Unstable: Unstable parameter values are the result of varying market conditions, and their effect, for

example, on volatilityd. Unconditional return: On any given day we assume the same distribution exists, regardless of market

and economic conditionse. Conditional returns: Different market conditions may cause the mean and variance of the return

distribution to change over time.2. Regime-switching: A regime switching volatility model assumes different market regimes exist with high or low

volatility. The conditional distribution of returns are always normal with a constant mean but either have highvolatility or low volatility.

3. VaR methods:a. Historical:

i. Parametric (Delta Normal Method: [E(R) – Zασ]Vp ]ii. Non-parametric (Historical Simulation)

iii. Hybridb. Implied Volatility: Uses derivative pricing models and current derivative prices in order to impute an

implied volatility without having to resort to historical data4. Return Aggregation: Under the assumption that asset returns are jointly normal, the return on a portfolio is also

normally distributed. Using the variance–covariance matrix of asset returns we can calculate portfolio volatilityand VaR

5. Implied Volatility as future of Volatility: Take the at-the-money (ATM) implied volatility from puts and calls andextrapolate an average implied, over different maturity periods.

a. The most important reservation stems from the fact that implied volatility is model dependent6. Time Conversion: VaR Year = VaR Daily x √Days at the same significance level

VAR AT WORK

Reading: Putting VaR to Work (Chapter 3, Linda Allen, Jacob Boudoukh and Anthony Saunders, Understanding Market,Credit and Operational Risk (Oxford: Blackwell Publishing, 2004))

1. Linear Derivative: A derivative is defined as linear when the relationship between an underlying and the

derivative is linear in nature (E.g. Futures). The Delta (Change in price of future to change in price of underlying)

must be constant for all levels of the factor, but not necessary equal to 1.

2. Non-linear Derivative: Primary example is an Option. The price change in option for at-the-money options are

different than for out-of or in0the-money options.

3. VaR for Linear Derivatives: VaR for linear derivative is given as: VaRDerivative = Delta x VaRUnderlying

4. Option Delta-Gamma: Bond Duration and Convexity is the same as Option Delta and Gamma. Both

approximations are based on Taylor series. The series is not useful for callable bonds.

5. Correlations during Crisis: In times of crisis, the correlations increase substantially and strategies that rely on

low correlations fall apart. Diversifications benefits also fail. A simulation using Monte Carlo is not capable of

predicting scenarios during the time of crisis as the correlation between factors changes during crisis

6. WCS(Worst Case Scenario): It extends the VaR by estimating the extent of loss given an unfavorable event. In

contrast to VaR, WCS focuses on the distribution of the loss during the worst trading period.

MEASURES OF FINANCIAL RISK

Reading: Measures of Financial Risk (Chapter 2, Kevin Dowd, Measuring Market Risk, 2nd Edition(West Sussex, England:John Wiley & Sons, 2005))

1. Mean Variance framework: It assumes that return distributions are elliptical distributions (like Normal)

a) Use of standard deviation as a risk measurement quantity is not appropriate for non-normal distributions

2. Value at Risk: VaR is an estimate of loss that can occur with a given confidence interval. Recall that Delta Normal

VaR is μ – Zσ which requires a confidence interval (a limitation of VaR). VaR also increases with increase in

holding period (another limitation). It also does not tell the investor the amount of actual loss expected

3. Coherent Risk Measures:

a) Monotonicity: A portfolio with greater returns will have less risk

b) Subadditivity: The risk of a portfolio is at most equal to the risk of assets within the portfolio

c) Positive homogeneity: Size of a portfolio will affect the size of its risk

d) Translation Invariance: Risk of a portfolio is dependent upon the assets of the portfolio

4. Expected Shortfall: Its the mean percent loss among the returns falling below q-percentile. It gives us the

magnitude of loss expected.

a) VaR does not satisfy the property of subadditivity and hence is not a coherent measure of risk

b) ES satisfies all coherent properties

5. Spectral Risk Measures: A more general risk measure is the risk spectrum. It measures the weighted averages of

return quantiles from the loss distribution

a) Weights are set equal in ES for all quantiles below q

b) For Var, weight is 1 for q - quantile and 0 for everything else

BINOMIAL TREES

Reading: Binomial Trees (Chapter 12, Hull, Options, Futures, and Other Derivatives, 8th Edition))

1. Binomial Trees: A useful and very popular technique for pricing an option involves constructing a binomial tree.

This is a diagram representing different possible paths that might be followed by the stock price over the life of

an option. The underlying assumption is that the stock price follows arandom walk. In each time step, it has a

certain probability of moving up by a certain percentage amount and a certain probability of moving down by a

certain percentage amount. In the limit, as the time step becomes smaller, this model is the same as the Black–

Scholes–Merton model.

2. Steps in valuing an Option:

a. u = eσ√t and d = 1/u

b. p = (ert – d)u – d

c. C = e-rt [ Fu.p + (1-p)Fd ]

d. C = e-rt [Fu.p2 + (1 – p)2 Fd + p(1-p)Fud ]

3. As the t becomes small, the binomial model becomes the Black-Scholes Model

4. Variations:

a. If there is a dividend yield, formula for p at ert changes to e(r-q)t

b. If there is a currency, formula for p at ert changes to e(rdomestic-rforeign)t

c. If there is a futures, which is costless to enter and risk-neutral, then ert is replaced by 1

Calculate u and d. U is the Up-move and d is the down move

P is the probability of up move. This is done for the first step only

Call price C, Fu is the payoff from the up move and Fd is the payofffrom the down move

Fud is the payoff at middle step. This is for atwo-step binomial tree

BLACK SCHOLES MERTON

Reading: The Black-Scholes-Merton Mode (Chapter 14, Hull, Options, Futures, and Other Derivatives, 8th Edition))

1. Lognormal Property of Stock Prices: It assumes that percentage changes in stock prices are normally distributed

over a short period of time. A variable that has a lognormal distribution can take any value between zero and

infinity. the continuously compounded rate of return per annum is normally distributed with mean µ - (σ2/2) and

standard deviation σ/√t

2. Assumptions of BSM:

a. The stock price follows the process developed with µ and σ constant.

b. The short selling of securities with full use of proceeds is permitted.

c. There are no transactions costs or taxes. All securities are perfectly divisible.

d. There are no dividends during the life of the derivative.

e. There are no riskless arbitrage opportunities.

f. Security trading is continuous.

g. The risk-free rate of interest, r, is constant and the same for all maturities

3. The BSM pricing formula:

The variables c and p are the European call and European put price, S0 is the stock price at time zero, K is the

strike price, r is the continuously compounded risk-free rate,σ is the stock price volatility, and T is the time

to maturity of the option.

GREEK LETTERS

Reading: The Greek Letters (Chapter 18, Hull, Options, Futures, and Other Derivatives, 8th Edition))

1. Naked Option: A naked position occurs when one party sells a call option or purchases a put option without

owning the underlying asset.

2. Greek Letters:

Letter Symbol Comparison

Delta Δ Change in option price vs. change in underlying security

Gamma Γ Change in Delta vs. change in underlying security

Theta θ Change in option price vs. change in maturity

Vega Change in option price vs. change in volatility

Rho ρ Change in option price vs. change in interest rate

3. European Call and Put:

a. Delta of an European call option is N(d1) from the BSM model

b. Delta of an European put is N(d1) – 1

4. Delta-Neutral Hedging:

a. No. of Options = (No. of Shares/ Delta of Option).

b. The delta hedging works only for small changes in the underlying security.

c. Portfolio Delta is the weighted average of all the Delta of each security

5. Gamma Neutral Hedging: Gamma neutrality provides protection against larger movements in this stock price

between hedge rebalancing. We can make a portfolio Delta, Gamma and Vega Neutral.

BOND PRICES, DISCOUNT FACTORS

Reading: Prices, Discount Factors, and Arbitrage (Chapter 1, Bruce Tuckman, Fixed Income Securities, 3rd Edition(Hoboken, NJ: John Wiley & Sons, 2011))

1. Law of One Price: Absent confounding factors (e.g., liquidity, special financing rates, taxes, credit risk), two

securities (or portfolios of securities) with exactly the same cash flows should sell for the same price.

2. STRIPS: Zero coupon bond issued by US Treasury are called STRIPS (separate trading of registered interest and

principal securities). They are created when a coupon bond is presented to the treasury. The bond is stripped

into two components 1) Principal(P-STRIPS) and 2) Coupon(C-STRIPS)

a. STRIPS have more sensitivity to interest rates than coupon bonds

b. Longer term tend to trade cheap and shorter term tend to trade rich

3. Replicating Bond Portfolio:

a. B = F1 x y% + F2 x (y+x)% + F3 x (x+y+z)%

b. Set all initial F1 and F2 to zero ad solve for F3 first. Then solve backwards.

SPOT, FORWARD AND PAR RATES

Reading: Spot, Forward and Par Rates (Chapter 2, Bruce Tuckman, Fixed Income Securities, 3rd Edition (Hoboken, NJ:John Wiley & Sons, 2011))

1. Discount Rates from Swap Rates:

a. Swap rates represent bond coupon payments and swap notional amount represents the bonds par

value.

b. [ 100 + r ] x Discount Rate = 100 for 6 month

c. [ r ]Discount6 Month + [ 100 + r]Discount1Year = 100; we insert 6 month rate as calculated above

2. STRIPS Price: STRIPS Price can be used to calculate Discount factors. Discount Factor = (STRIPS Price/100) for a

given maturity. Also, to calculate SPOT rate, we can use the calculator functions.

3. Forward Rates: Forward Rates are rates that will apply starting at a future date.

a. Spot1Year2= Spot6Month x ForwardRate6Month

4. Par Rate: The rate at which the current value of bond is same as par value. A swap rate is the same as par rate.

5. Bond Prices and Maturity:

a. Bond prices tend to increase with maturity when coupon rates are above relevant forward rates

b. If short term rates are more than forward rates, shorter investment rolled over will outperform longer

investments

6. Flattening and Steepening:

a. A normal yield curve is where forward rates are higher than short term rates, so the curve has positive

slope.

b. A flat curve has all interest rates at similar levels

c. An inverted yield curve is where long term rates are smaller than short term rates

d. Flattening of yield curve means spread between short and long term rates has narrowed

e. Steepening of yield curve means spreads have increased

RETURNS, SPREADS AND YIELDS

Reading: Returns, Spreads and Yields (Chapter 3, Bruce Tuckman, Fixed Income Securities, 3rd Edition (Hoboken, NJ: JohnWiley & Sons, 2011))

1. Definitions:

a. Gross realized return for a bond is its total return over life i.e. (End- Beginning)/Beginning

b. Net realized return is its gross realized return – per period financing cost. To calculate realized return for

a bond over multiple periods, we must keep track of rates at which coupon are reinvested.

2. Bond Spread: Difference between bond market price and bond price according to the term structure of interest

rates. Used to determine if bond is trading cheap or rich relatively

3. Yield to Maturity: It is the discount rate that will equate all the future cash flows of the bond to its current

market price. It can also be viewed as realized return assuming that all coupons are reinvested at YTM. If rates

are in BEY(Bond Equivalent Yield), then divide it by two to get semiannual rate.

4. Perpetuity: Cash flows are received indefinitely and there is no principal payment as the perpetuity does not

end. It is valued as PVPerpetuity = Coupon/YTM

5. Carry-Roll-Down: It account for price changes due to interest rate movements from the original term structure

to an expected structure.

ONE FACTOR RISK METRICS

Reading: One-Factor Risk Metrics and Hedges (Chapter 4, Bruce Tuckman, Fixed Income Securities, 3rd Edition (Hoboken,NJ: John Wiley & Sons, 2011))

1. DV01: DV01 means change in fixed income security’s value for every 1 basis point (0.01%) change in interest

rates. It is also known as PVBP i.e. the price value of basis point. DV01 = - [Change in Bond Value/ (10000 x

change in yield)]. The DV01 is preceded by a negative sign because when rates decline, price increases.

2. Hedge Ratio: [DV01 of Instrument/ DV01 of Hedging Instrument] x Value of Position.

3. Duration: A bond price volatility is a function of its coupon, maturity and initial yield. Duration captures all these

variables in a single measure.

a. Macaulay Duration: Bonds interest rate sensitivity based on time in years until promised cash flows

arrive.

b. Modified Duration: It is given as Macaulay Duration/(1+YTM)

c. Effective Duration: (BV-Δy – BV+Δy)/(2 x BV0 x Δy)4. DV01 and Duration: DV01 = Duration x 0.0001 x Bond Value

5. Convexity: Duration is a linear estimate and is good for small changes in interest rates. As rate changes grow

larger, we need to adjust for convexity also. Convexity measures curvature relationship between bond yield and

price.

a. Convexity = (BV-Δy + BV+Δy - 2BV0)/(BV0 x Δy2)

b. Change in Bond Price % = [-duration x Δy x100] +[ 0.5 x convexity x Δy2 x 100]

c. Negative Convexity: A callable bond has an effective price cap at the call price. Thus curve exhibits

negative convexity

6. Portfolio:

a. Duration is the weighted average of all individual durations

MULTIFACTOR RISK METRICS

Reading: Multi-Factor Risk Metrics and Hedges (Chapter 5, Bruce Tuckman, Fixed Income Securities, 3rd Edition(Hoboken, NJ: John Wiley & Sons, 2011))

1. Issues with One-factor:

a. Assumes that term structure shifts in parallel fashion

2. Key Rate Exposures:

a. Key Rate makes an assumption that all rates can be determined as a function of a few key rates e.g. US

Treasury 2 years, 5 years, 10 years and 30 years bonds.

b. Calculations:

i. DV01KeyRate = -1 x Δ BV

10,000 Δ yK

ii. DurationKeyRate = -1 x Δ BV

BV Δ yK

3. Partial 01: It will measure change in value of portfolio from 1 basis point change in fitted rate(Swap Rate Curve)

and subsequent refitting of curve. Swap curves are refitted daily using par rates and short term money market/

future rates.

4. Forward 01: Computed by shifting forward rate curve over several regions of the term structure one region at a

time after the term structure is divided into several regions/ buckets

COUNTRY RISK: DETERMINANTS, MEASURES &IMPLICATIONS

Reading: Aswath Damodaran, Country Risk: Determinants, Measures and Implications - The 2015 Edition (July 14,2015)

1. Definitions:

a. Discontinuous Risk: Government policies that change infrequently (like in authoritarian regimes) but can

be difficult to protest

b. Continuous Risk: Government policies change as government changes

2. Country Risks

a. Corruption and Side Costs: Corruption is like an implicit tax on income that reduces ROI

b. Physical Violence

c. Nationalisation/ Expropriation Risk: Some business like Mines are more prone to appropriation

d. Legal Risks: Legal system needs to be effective (Enforcing laws in fair manner) and efficient (dispose

matter quickly)

3. Measures of Country Risk

a. Degree of indebtness: Measured as government debt to GDP

b. Pension/ Social Service commitments

c. Revenue/ Inflows to Government and stability of revenues

d. Political Risk

4. Why local currency defaults happen?

a. Gold Standard: Prior to 1971, currency had to be backed by Gold and thus could not be freely printed

b. Shared Currency: Greece could not print Euros to fulfil its debt obligations

5. Implications of Default:

a. Negative impact on GDP by 0.5% to 2%

b. Long term borrowing costs rise and impacts sovereign ratings

c. Export oriented industries are harmed due to possible trade retaliation

d. Defaults make banking system fragile

e. Increases likelihood of political change

EXTERNAL & INTERNAL RATINGS

Reading: External and Internal Ratings (Chapter 2, Arnaud de Servigny and Olivier Renault, Measuring and ManagingCredit Risk(New York: McGraw-Hill, 2004))

1. External Ratings: They convey information about either a specific instrument, called an issue specific rating or

information about the entity that issued the instrument called the issuer credit rating. They are one-dimensional

and rating scales are uniform

a. S&P uses ratings of AAA, AA, A, BBB, BB, B, CCC, CC, C and D. Anything above BBB is investment grade

and below BB is non-investment grade. D means default

b. Moody’s uses Aaa, Aa, A, Baa, Ba, B, Caa, Ca and C. Ratings of Baa and above are investment grade.

2. Ratings Transition Matrix: It shows the frequency of rating change or default over a given time period.

a. Probability of default increases with time.

b. Ratings are designed to be stable over business cycles.

c. Interpreting ratings may vary depending upon the industry but not much based on geography

3. Internal Ratings: Ratings used by banks for their internal calculations.

a. At-the point approach: Short term credit score which varies through the business cycles

b. Through-the cycle: Score over a longer horizon using more qualitative information. Tends to be more

stable over cycles

c. Pro-cyclical effect of ratings: After economic trough has been reached, bank may downgrade a company

poised for recovery with use of additional credit from bank.

d. For creating an internal transition matrix, it is important to back-test the rating system

4. Internal Rating system bias:

a. Time horizon bias (Using at the point or through the cycle)

b. Homogeneity Bias (non-consistent ratings)

c. Principal-Agent Bias

d. Information Bias(Insufficient information)

e. Criteria Bias (Unstable criteria)

f. Backtesting bias (Incorrect linking of system to default rates)

g. Distribution Bias(Incorrect model)

h. Scale Bias(Ratings are unstable over time)

CAPITAL STRUCTURE IN BANKS

Reading: Capital Structure in Banks (2nd edition, Shroeck, 2002)

1. Definitions:

a. Probability of Default(PD): Likelihood that borrower will default

b. Exposure at Default(EAD): Remaining exposure at default

c. Loss given Default (LGD): Likely percentage loss if a borrower defaults. It is also (1 - Recovery Rate)

d. Expected Loss(EL): Defined as expected deterioration in asset quality and is given as PD x EAD x LGD

e. Unexpected Loss: Variation in the expected loss amount.

i. It is given as UL = EAD × (PD × σ ) + (LGD × σ )2ii. σ = PD × (1 − PD)

f. Economic Capital: Estimated reserves required for dealing with Unexpected loss

2. Portfolio Expected Loss: Sum of expected losses of each asset is the expected loss of the portfolio. It is simply

given as EL = ∑ (PD × EAD × LGD )3. Portfolio Unexpected Loss: UL = ∑ ∑ UL × UL × ρ2

OPERATIONAL RISK

Reading: Operational Risk (Chapter 20, John Hull, Risk Management and Financial Institutions, 3rd Edition(Boston:Pearson Prentice Hall, 2012))

1. Regulatory capital: Three types of methods to determine regulatory capital are:

a) Basic Indicator: 15% of banks annual gross income over a 3 year period

b) Standardized approach: Eight business lines with different factors

c) Advanced measurement approach: Banks VaR measure at 99.9% confidence

2. Operational Risk: Basel Committee segregates operational risk into seven types namely Business Practices,

Internal Fraud, External Fraud, Damage to physical assets, process management, System failures, emplyment

practices.

3. Definitions:

a) Loss Frequency: Number of losses over a specific period of time (Poisson Distribution)

b) Loss Severity: Value of financial loss suffered (Lognormal Distribution)

c) Convolution: Combining frequency and severity (Monte Carlo Simulation)

d) RCSA(Risk and Control Self Assessment): Survey managers directly responsible for Risk Management

e) Power Law: EVT used to evaluate nature of tails of a given distribution

f) Moral Hazard: Presence of insurance causes the company to take more risks

g) Adverse selection: An insurance company cannot identify good or bad firm