Chapter 1 - Fundamental Risk Concepts

2009/2010 FINANCIAL RISK MANAGER (FRM) LEVEL I HANDBOOK

Alan Anderson, Ph.D. Western Connecticut State University

ECI Risk Training http://www.frmtraining.com

(c) ECI Risk Training 2009 2

CHAPTER 1: FUNDAMENTAL RISK CONCEPTS 1.1 RISK Risk refers to uncertainty over future events, such as stock prices, the level of interest rates, GDP growth, the repayment of loans by a borrower, etc. that can impact the solvency of an organization. 1.2 TYPES OF RISK Risk can be classified as follows:

• market risk o interest rate risk o commodity price risk o foreign exchange risk o equity price risk

• credit risk • operational risk

1.2.1 MARKET RISK Market risk refers to the possibility of losses due changes in economic variables such as interest rates, commodity prices, exchange rates and equity prices. 1.2.1.1 INTEREST RATE RISK Interest rate risk refers to the possibility that financial assets will decline in value due to an adverse change in interest rates. For example, the prices of bonds and interest rates are inversely related; therefore, rising interest rates lead to capital losses for bondholders. 1.2.1.2 COMMODITY PRICE RISK A commodity is a good that has highly standardized properties; some examples are:

• oil • gold • copper • sugar • salt


• wheat • orange juice • pork bellies

Commodities can be classified as hard (non-perishable) commodities and soft (perishable) commodities. Precious metals and industrial metals are examples of hard commodities, while agricultural products and energy are examples of soft commodities. Commodity price risk refers to the possibility that losses will occur due to adverse changes in commodity prices; for example, costs of production rise when oil prices rise, leading to reduced profits for a corporation. 1.2.1.3 FOREIGN EXCHANGE RISK Foreign exchange risk refers to the possibility that losses will occur due to changes in the strength of a currency. For example, if a U.S. firm earns profits denominated in British pounds, the dollar value of these profits will decline if the dollar strengthens (appreciates) against the pound. 1.2.1.4 EQUITY PRICE RISK Equity price risk refers to the possibility that losses could result from changes in equity (stock) prices. For example, if an insurance company holds a broad-based portfolio of common stocks, a decline in stock prices could make it difficult for the company to honor its obligations to its policyholders. 1.2.2 CREDIT RISK Credit risk refers to the possibility that losses will occur due to deterioration in the ability of the obligor (borrower) to make promised interest and principal payments in a timely manner. For example, if a bank holds corporate bonds in its investment portfolio, the possibility of default by these bonds is classified as credit risk. 1.2.3 OPERATIONAL RISK Operational risk refers to the possibility of losses due to a failure of internal processes, people, systems and external events. Sources of operational risk include fraud, human error, computer system failures, power failures, property damage due to fires or natural disasters, etc.


1.2.4 ENTERPRISE RISK MANAGEMENT (ERM) Enterprise risk management (ERM) refers to the integration of market, credit and operational risk into a coherent framework. The objective of ERM is to explicitly consider the interaction among these types of risk, instead of considering each type of risk in isolation. 1.3 OTHER TYPES OF RISK Other important types of risks include:

• liquidity risk • legal (regulatory) risk • business risk • strategic risk • reputation risk

1.3.1 LIQUIDITY RISK The liquidity of an asset refers to the ease of exchanging it for other goods or assets. For example, money is the most liquid asset; checking deposits are also highly liquid. Stocks and bonds are less liquid, since they must be sold through specialized brokers; this entails transactions costs, such as bid-ask spreads. In addition, selling stocks and bonds is relatively time-consuming compared with more liquid assets such as money. Examples of highly illiquid assets are: real estate, art, jewelry and gold coins. Valuing these assets can be difficult, since they have unique characteristics and are bought and sold infrequently. Further, the time required to sell these assets can be significant. Liquidity risk can be classified as:

• funding liquidity risk • asset liquidity risk

Funding liquidity risk refers to the possibility that sources of short-term funding will be restricted in the future, making it difficult or costly for a firm to meet its liabilities in a timely manner. For example, a corporation may find that its bank has restricted its lines of credit, making it difficult to meet short-term obligations such as payroll. Asset liquidity risk refers to the possibility that it will be difficult to carry out a financial transaction without incurring a significant cost. For example, if a bank holds a risky


corporate bond in its portfolio, it could be difficult to sell the bond without incurring significant transactions costs due to the thin market for the bond. 1.3.2 LEGAL (REGULATORY) RISK All financial transactions take place within a given country’s regulatory environment. The risk that this environment will change in an adverse way is known as legal or regulatory risk. An example of this would be unfavorable changes in tax laws. 1.3.3 BUSINESS RISK Business risk refers to the different types of uncertainties confronting a corporation, such as the quantity of a product to produce, the amount of advertising to use, the type of funding to use, etc. 1.3.4 STRATEGIC RISK Strategic risk refers to the possibility of losses due to poor decision-making, faulty implementation of business decisions, etc. For example, if a corporation decides to compete in a new market, the possibility of failure would be classified as strategic risk. 1.3.5 REPUTATION RISK Reputation risk refers to the chance that losses will occur as a result of damage to a firm’s public image. For example, a product recall could reduce consumer confidence in a firm, leading to a reduction in its sales. 1.4 ASSET PRICING MODELS: THE CAPM The Capital Asset Pricing Model (CAPM) explains the relationship between risk and expected returns for equities. The CAPM classifies all risk as:

• systematic (market) risk • non-systematic (firm-specific) risk

One of the key insights of the CAPM is that a security’s expected return does not reflect non-systematic risk, since this can be eliminated in a well-diversified portfolio. In a well-diversified portfolio, non-systematic risks will partially or totally offset each other. As a result, in an efficient market, no investor can expect to be rewarded for bearing non-systematic risk. Therefore, the expected return to a security depends only on systematic risk.


The CAPM is based on several restrictive assumptions:

• investors are risk averse and seek to maximize the expected utility of their wealth • all information is costless and available simultaneously to all investors • all investors have an identical investment horizon • investors may borrow or lend unlimited amounts at the risk-free rate of interest • there are no taxes or transactions costs; all assets trade and are infinitely divisible • all investors have identical expectations

According to the CAPM, there is a linear relationship between the expected return to a stock and its risk. Risk is defined by the CAPM as the uncertainty of a stock’s returns relative to those of the market portfolio. The market portfolio is defined as a portfolio containing all assets in the economy, weighted by their market capitalization. In order to implement the CAPM model, the returns to the market portfolio can be estimated with a proxy, such as the Standard and Poor’s 500 index. According to the CAPM, a security’s expected return is a function of its contribution to the risk of a well-diversified portfolio. This contribution is measured by the security’s sensitivity to systematic or market risk, as indicated by its beta: where: Var(rM) = the variance of the excess returns to the market portfolio Cov(ri, rM) = the covariance between the excess returns to stock i and the

market portfolio The excess return to a stock is the difference between the return to the stock and the risk-free rate of interest; i.e., the yield on Treasury securities. Excess return is also known as a risk premium. A risk premium is the compensation investors require in order to buy a risky asset instead of the risk-free asset. Since the risk-free rate is a known constant, its covariance with the market portfolio is zero. Therefore, its beta is also zero. The beta of the market portfolio equals one, since beta measures the risk of an asset relative to the market portfolio. Based on the CAPM assumptions, the model predicts that all investors will choose to hold a combination of the market portfolio (M) and the risk-free asset. Investors will allocate their portfolio to the market portfolio and the risk-free asset based on their degree of risk aversion. A risk-averse investor requires compensation for bearing risk; a risk-

βi =

Cov(ri ,rM )Var(rM )


neutral investor requires no compensation for bearing risk, while a risk-seeking investor would accept a lower return in exchange for bearing risk. 1.4.1 THE CAPM EQUATION According to the CAPM, the expected return to a stock is: E(ri) = rf + βi[E(rM) – rf] where: E(ri) = expected return to stock i rf = risk-free rate of interest βi

= beta of stock i E(rM) = expected return to market portfolio EXAMPLE Suppose that the risk-free rate is 3%, while the expected return to the market portfolio is 10%. Assume that Ford stock has a beta of 2.1, IBM stock has a beta of 1.4 and GM stock has a beta of 0.9. According to the CAPM, the expected return to each stock is determined as follows:

FORD: E(ri) = rf + βi[E(rM) – rf] =.03 + (2.1)[.10 - .03] =.177= 17.7% IBM: E(ri) = rf + βi[E(rM) – rf] =.03 + (1.4 )[.10 - .03] =.128 = 12.8% GM: E(ri) = rf + βi[E(rM) – rf] =.03 + (0.9 )[.10 - .03] =.093 = 9.3%

1.4.2 THE CAPITAL MARKET LINE (CML) The capital market line (CML) shows the relationship between the expected return to a stock and the risk of the stock, measured by the standard deviation of its returns. The Capital Market Line is tangent to the efficient frontier, which represents the set of all assets where the expected return is maximized for a given level of risk. The intercept of the Capital Market Line is the risk-free rate since its standard deviation is zero. The Capital Market Line is illustrated in the following diagram:


The slope of the CML represents the gain in expected return that can be achieved by bearing more risk. The steeper the CML, the more favorable is the tradeoff between expected return and risk. The Capital Market Line touches the efficient frontier at a single point: the market portfolio (M). The equation of the CML is: Choosing to invest on the CML gives investors the highest possible return per unit of risk; therefore, one of the implications of the CAPM is that all investors will choose a combination of the market portfolio and the risk-free asset. The allocation between the two assets will be determined by an investor’s degree of risk aversion. Highly risk-averse investors will place most or all of their funds in the risk-free asset; less risk-averse investors will place a larger proportion of their funds in the market portfolio. Investors can achieve positions that are riskier than the market portfolio by short-selling the risk-free asset (i.e., borrowing) to invest more in the market portfolio.

E(ri ) = rf +σ i

E(rM ) − rfσM

⎡

⎣⎢

⎤

⎦⎥


1.4.3 THE SECURITY MARKET LINE (SML) The security market line (SML) shows the relationship between the expected return to a stock and its beta (i.e., systematic risk). The SML is a graph of the CAPM equation. Using the data from the previous example (Ford, IBM and GM stock), the following SML can be constructed:

In equilibrium, all stocks will be on the SML; any stock that is not on the SML is considered to be mispriced. In an efficient market, the prices of these stocks will adjust quickly until they return to the SML. Any stock that is above the SML is underpriced relative to the CAPM, since its expected return exceeds the value predicted by the CAPM. As a result, investors will buy the stock, which raises its price and reduces its expected return. Similarly, any stock that is below the SML is overpriced. Investors will sell the stock, reducing its price and raising its expected return.


EXAMPLE If the stock of the XYZ corporation has a beta of 2.1, it should have an expected return equal to that of Ford (17.7%). Suppose instead that its expected return is 20%; this indicates that the price of the stock is too low. In an efficient market, investors will buy XYZ stock, which will raise its price and lower its expected return until it returns to the SML. EXAMPLE If the stock of the ABC corporation has a beta of 2.1, it should have an expected return equal to that of Ford (17.7%). Suppose instead that its expected return is 16.0%; this indicates that the price of the stock is too high. In an efficient market, investors will sell ABC stock, which will lower its price and raise its expected return until it returns to the SML. 1.4.4 MARKET EFFICIENCY The CAPM model is based on the assumption of efficient capital markets. The three basic forms of market efficiency are:

• weak • semi-strong • strong

If markets are weakly efficient, then all securities prices reflect their own past values. With the semi-strong form of market efficiency, securities prices reflect all publicly available information, including past prices. With the strong form of market efficiency, securities prices reflect all information, both public and private. The CAPM is based on the assumption of strong market efficiency. 1.5 MEASURES OF PERFORMANCE Several measures of the relationship between risk and return for an asset or portfolio are commonly used, including:

• the Sharpe Ratio • the Treynor Ratio • Jensen’s Alpha • the Information Ratio • the Sortino Ratio


1.5.1 THE SHARPE RATIO The Sharpe Ratio is defined as: where: E(rp) = expected portfolio return rf = risk-free rate σP = portfolio standard deviation The Sharpe Ratio indicates the expected excess return to an asset per unit of total risk, as measured by the standard deviation of returns. 1.5.2 THE TREYNOR RATIO The Treynor Ratio is defined as: where: βP = portfolio beta The Treynor Ratio indicates the expected excess return to an asset per unit of systematic risk, as measured by beta. This measure works best for diversified portfolios. 1.5.3 JENSEN’S ALPHA Jensen’s alpha is defined as: αi = E(ri) - rf - βi[E(rM) – rf] This represents deviations from the expected returns predicted by the CAPM model. In equilibrium, Jensen's alpha equals zero. Jensen’s alpha is used to determine if a portfolio manager is adding value relative to the returns from a passive investment strategy. Jensen’s alpha can be generalized as follows: α = E(rP) - E(rB)

E(rp ) − rfσ p

E(rp ) − rfβ p


where: E(rP) = expected return to a portfolio E(rB) = the expected return to a benchmark asset or portfolio Jensen's alpha provides a measure of an investment manager's skill, as follows:

α > 0: superior return α = 0: normal return α < 0: inferior return

Since alpha can be zero by pure chance, a hypothesis test can be performed to determine if alpha is significantly different from zero. In this case, the null hypothesis is that alpha equals zero; the alternative hypothesis is that alpha is different from zero: H0: α = 0 H1: α ≠ 0 The test statistic is: where: sα = the standard error of alpha As a rule of thumb, if the test statistic exceeds 2, then the null hypothesis is rejected in favor of the alternative hypothesis that alpha is positive. If the test statistic is less than -2, then the null hypothesis is rejected in favor of the alternative hypothesis that alpha is negative. Otherwise, the null hypothesis that alpha equals zero cannot be rejected. 1.5.4 THE INFORMATION RATIO The information ratio equals the difference between the expected return to a portfolio and the expected return to a benchmark, (portfolio active return), divided by the tracking error: The information ratio measures the expected return of an active portfolio manager relative to a benchmark divided by the risk taken. The information ratio can be used to

IR =E(rP ) − E(rB )σ (rP − rB )

t =α − 0Sα


compare the performances of two portfolio managers; a higher the value of the information ratio indicates a superior performance. The statistical significance of the information ratio can be tested with the following test statistic: where: IR = information ratio SIR = standard error of information ratio where: t = number of years 1.5.5 THE SORTINO RATIO The Sortino Ratio is defined as: where: rmin = minimum acceptable return (target return) SVmin = the semi-variance of the returns below rmin The semi-variance is computed in the same way as the variance except that returns greater than or equal to rmin are discarded. 1.6 TRACKING ERROR Tracking error is the standard deviation of the difference between the returns to a portfolio and the returns to a benchmark: TE = σ(rP - rB)

E(rP ) − rminSVmin

t =IRSIR

SIR ≈1t


where: TE = tracking error rP = portfolio returns rB = benchmark portfolio returns Tracking error may be thought of as the standard deviation of Jensen’s alpha over time; it shows how closely a portfolio’s returns match a benchmark portfolio. Tracking error is typically higher for actively managed portfolios than for passively managed portfolios. 1.7 ASSET PRICING MODELS: MULTFACTOR MODELS Newer models have extended the CAPM to include multiple risk factors; these are known as multifactor models. With a multifactor model, the expected return to a stock is decomposed into several risk factors and the sensitivities of the stock’s returns to these factors: E(ri) = αi + βi1f1 + βi2f2 + βi3f3 + .... + βiKfK + εi where: fk = risk factor k αi = a constant βik = the sensitivity of stock i’s returns to factor k εi = non-systematic risk 1.7.1 ARBITRAGE PRICING THEORY (APT) Arbitrage pricing theory (APT) is a multifactor version of the CAPM. The APT model can be written as: The risk factors are macroeconomic factors that apply to all assets in the economy, such as GDP, inflation rates, exchange rates, commodity prices, etc. A closely related type of multifactor model is known as the empirical model, where the risk factors are specific to an individual asset, such as its dividend yield, market capitalization, earnings, leverage, etc.

E(ri ) − rf = βikk=1

K

∑ fk


1.7.2 EXPLICIT VS. IMPLICIT MODELS With an explicit multifactor model, the factors are identified in advance; the sensitivities are estimated from historical data. With an implicit multifactor model, both the identity of the factors and the sensitivities are taken from historical data; the factors are determined through a statistical procedure known as factor analysis. 1.8 RISK MANAGEMENT FAILURES One of the main objectives of risk management is to correctly measure the risks faced by an organization. This process can lead to errors if risks are not measured correctly or if they are not measured at all. Another key objective of risk management is to properly communicate results to senior management. Risk management is also charged with ensuring that the risks taken by an organization are consistent with the risk appetite of senior management. This includes making decisions about which projects to accept and reject as well as hedging strategies. Overall, the six basic types of risk management failures are:

1) incorrect measurement of known risks 2) failure to take relevant risks into account 3) failure to communicate risks to senior management 4) failure to properly monitor risk 5) failure to properly manage risk 6) failure to properly measure risk

1.9 CASE STUDIES Over the past twenty years there have been several well-publicized cases of huge losses due to the failure to follow proper risk management procedures. These include:

• Metallgesellschaft • Sumitomo • Long-Term Capital Management • Barings

1.9.1 METALLGESELLSCHAFT (MGRM) In 1993, Metallgesellschaft (MGRM) admitted that its energy group had lost $1.5 billion from forward contracts on oil. MGRM was originally a metals producer; later, it became involved in risk management services. MGRM committed to sell oil (at prices set in


1992) every month for up to ten years through forward contracts on 160 million barrels. These contracts contained an embedded option in which the counterparty could terminate early if the shortest term New York Mercantile Exchange (NYMEX) oil futures contract was greater than the price of the forward contract. MGRM would then be required to pay one-half of the difference to the counterparty. This was beneficial to buyers who were in financial trouble or no longer needed the oil. MGRM used “stacked” futures to hedge their risk; all contracts were short-dated, not spread across maturities. MGRM took long positions in these futures contracts and entered into energy swaps as the payer of fixed energy prices and receiver of floating energy prices. The massive volume of trading relative to the size of the market ensured that it would be difficult to unwind their positions; the positions left MGRM vulnerable to liquidity risk. When oil prices fell, the short-dated futures contracts required large margin calls that MGRM couldn’t meet. The market was originally in normal backwardation, which occurs when the spot price is greater than the futures price. The futures curve is downward-sloping; i.e., futures prices decline as their maturity increases. It then switched to contango, which occurs when the futures price is greater than the spot price. The futures curve is upward-sloping; i.e., futures prices rise as their maturity increases. This causes “rollover” losses for the long futures position as short-dated hedges mature and are replaced with progressively more expensive contracts. Ultimately, the failure to anticipate this funding risk is what brought down MGRM. 1.9.2 SUMITOMO In June 1996, Sumitomo Corp. announced that it had lost over $2 billion due to unauthorized copper trading by Yasuo Hamanaka. Yasuo Hamanaka was the firm’s chief copper trader; his strategy involved illegal manipulations of the copper market through extremely large purchases or sales. Hamakana kept two sets of records of his trades, so that he could show profits to Sumitomo’s accountants while racking up huge losses. Since Hamanaka appeared to be making sizable profits for Sumitomo, his actions were not closely scrutinized, making Sumitomo management at least partially responsible for this debacle. 1.9.3 LONG-TERM CAPITAL MANAGEMENT (LTCM) John Meriwether, Myron Scholes and Robert Merton were the principals of LTCM. LTCM was able to use the reputation of its principals to borrow 100% of any collateral that it posted, then use the proceeds to borrow more; this enabled LTCM to leverage its investments to a level of 25-1. Bets were placed on “convergence trades.” In 1998, LTCM bet that the spread between U.S. Treasuries and emerging markets bonds would narrow as investors sought higher yields. Losses started in August 1998 following


the Russian debt moratorium; as the spread between U.S. Treasuries and other securities widened, more collateral was required to cover mounting losses. By September 1998, LTCM’s capital was down to $4 billion, but their total notional exposure was about $1 trillion. Although LTCM had stress-tested its portfolios, the change in correlations was so dramatic that their models did not predict what actually happened. Ultimately, LTCM was bailed out by a consortium of banks arranged by the Fed. The major problems at LTCM included: 1) Not enough attention was paid to stress-testing, gap risk and liquidity risk;

insufficient attention paid to size of notional positions, despite relatively small net positions was still risky since the price of notional principal can change in unpredictable ways.

2) Counterparties were too generous with their funding to LTCM 3) Supervision – the SEC and the New York Stock Exchange underestimated the risk

of LTCM 1.9.4 BARINGS Barings Bank became insolvent in 1995 as a result of the activities of a rogue trader named Nick Leeson. Leeson was the head derivatives trader at the bank’s newly-formed Singapore office. Leeson was also in charge of the back office; as a result, he was able to hide his losses in the phantom client account #88888. He also used falsified records to cover up his losses. Due to mounting margin calls, the scheme unraveled, forcing Leeson to confess to losses of about $1.3 billion. The strategies employed by Nick Leeson consisted mainly of long futures positions on the Japanese stock market and Japanese government bonds, which were partially funded by short options positions. Nick Leeson held a sizeable long position in Nikkei 225 futures; the Nikkei 225 is the most widely-followed index of the Japanese stock market. This position was held in anticipation of a recovery by the Japanese stock market; instead, partially due to the Kobe earthquake in January 1995, the Japanese stock market continued to slump. This triggered massive margin calls, requiring progressively more funding from London. One of the strategies employed by Nick Leeson was to set up short straddles on Nikkei 225 futures and use the premiums to partially offset the mounting margin calls from his rapidly increasing long Nikkei 225 futures position. A short straddle consists of a written call and a written put on the same asset with the same maturity and the same strike price. This position is profitable only if the price of the underlying asset remains within a narrow range.


Combining a short straddle with a long position in the underlying asset creates a position equivalent to a short put with more risk on the downside. In Nick Leeson’s case, his need for more funding led him to write multiple straddles for each long futures contract that he held. This led to the creation of an “iceberg”, a riskier version of a short straddle; as a result, the position would only be profitable if the Nikkei 225 remained within a very narrow range of prices. Any movement outside of this range would lead to extremely large losses. Nick Leeson also employed a strategy of “doubling.” Each time the Nikkei 225 fell, Nick doubled his long exposure on the theory that he would make up past losses as soon as the Nikkei 225 recovered. He also hoped that massive purchases of Nikkei 225 futures would drive up the Japanese stock market. This type of strategy is also known as the “gambler’s ruin” strategy, since capital can be wiped out very quickly. Ultimately, the inability to finance growing margin calls put an end to Nick Leeson’s trading in early 1995. Nick Leeson lost over $1 billion, causing the collapse of Barings bank. This earned him a jail sentence of six and a half years, while Barings was sold to the Dutch bank ING for one pound. 1.10 GARP CODE OF CONDUCT The GARP Code of Conduct consists of several principles of professional conduct and ethical standards for the risk management profession. GARP members are expected to display professional integrity and ethical conduct, avoid conflicts of interest and respect confidentiality. GARP members are also expected to exhibit the highest possible standards of professional skills and engage in best risk management practices.


CHAPTER 1 KEY CONCEPTS 1) Risk can be broadly classified as market risk, credit risk and operational risk. Market risk can be further subdivided into: interest rate risk, commodity price risk, foreign exchange risk and equity price risk. 2) The Capital Asset Pricing Model (CAPM) postulates that the expected return to a stock depends on the risk-free rate of interest, the expected return to the market portfolio and the risk of the stock, as measured by beta. Beta is defined as: This is the covariance between the excess returns to the stock and the market portfolio divided by the variance of the excess returns to the market portfolio. The excess return to a stock equals its actual return minus the risk-free rate of interest. The CAPM equation is E(ri) = rf + βi[E(rM) – rf]. 3) According to the CAPM, all non-systematic (firm-specific) risk can be eliminated in a well-diversified portfolio; therefore, investors can only expect to be compensated for bearing systematic (market) risk. 4) One of the implications of the CAPM is that all investors will choose to invest their wealth in a combination of the market portfolio and the risk-free asset. 5) The Capital Market Line (CML) shows the relationship between the expected return to a stock and its risk, as measured by the standard deviation of its returns. The CML is tangent to the efficient frontier, which shows all stocks that offer the highest rate of return for a given level of risk. 6) The Security Market Line (SML) shows the relationship between the expected return to a stock and its risk, as measured by beta. The SML is linear and represents the equilibrium expected return for all stocks based on their betas. 7) Several measures of portfolio performance have been developed. These include the Sharpe Ratio, the Treynor Ratio, Jensen's Alpha, the Information Ratio and the Sortino Ratio. The Sharpe Ratio equals:

βi =

Cov(ri ,rM )Var(rM )

E(rp ) − rfσ p


This is the expected excess return to a stock divided by its risk, as measured by the standard deviation of its returns. The Treynor Ratio is: This is the expected excess return to a stock divided by its risk, as measured by beta. Jensen's Alpha is defined as: αi = E(ri) - rf - βi[E(rM) – rf] This equals the deviation from the predictions of the CAPM model. It can be interpreted as a measure of the value added by a portfolio manager. The Information Ratio equals This represents the expected return to an active portfolio manager relative to the risk of the portfolio as measured by the standard deviation of the returns in excess of a benchmark. The Sortino Ratio equals This represents the expected return to an active portfolio manager relative to a minimum acceptable return divided by risk as defined by the semivariance of returns below the minimum acceptable level. 8) Tracking error is a measure of the standard deviation of excess returns relative to a benchmark. This is used to determine how closely a portfolio replicates a benchmark.

E(rp ) − rfβ p

IR =E(rP ) − E(rB )σ (rP − rB )

E(rP ) − rminSVmin


9) Multifactor models, such as Arbitrage Pricing Theory (APT) have been developed to extend the CAPM to include multiple sources of risk. 10) Several risk management failures have occurred in recent years, including Metallgesellschaft (MGRM), Sumitomo, Barings and Long-Term Capital Management (LTCM). MGRM adopted a hedging strategy based on the assumption that markets would remain in normal backwardation; when markets switched to contango, massive losses resulted for MGRM. Sumitomo lost over $2 billion in unauthorized copper trading due to a rogue trader who was able to hide his losses. Similarly, Barings Bank became insolvent due to massive losses by Nick Leeson, who both traded and ran the back office in Singapore for Barings. Long-Term Capital Management (LTCM) suffered catastrophic losses due to an unanticipated emerging markets crisis coupled with an inability to liquidate its positions in a timely fashion.


CHAPTER 1 PROBLEMS 1. The Capital Asset Pricing Model a. postulates a linear relationship between a stock’s expected return and standard deviation b. shows that the expected return to a stock depends on non-systematic risk c. defines beta as the covariance between the excess returns to a stock and the market portfolio relative to the standard deviation of the market portfolio d. none of the above 2. According to the CAPM, if the risk-free rate of interest is 3% and the expected return to the market portfolio is 5% and the expected return to the stock is 8%, a. the beta is 1.0 b. the beta is 2.0 c. the beta is 2.5 d. the beta is 0 3. The Sharpe ratio equals: a. the expected excess return to an asset divided by its beta b. the expected return to an asset divided by its beta c. the expected excess return to an asset divided by its standard deviation d. the beta divided by the expected return to an asset 4. Which of the following is true? I. The Sortino ratio is defined in terms of the semivariance of the returns to an asset II. A positive value of Jensen’s alpha indicates that a portfolio manager has underperformed the market III. The Information Ratio equals the expected return to a portfolio divided by its tracking error a. I and II b. I only c. II only d. I and III only 5. Metallgesellschaft a. used “stacked” forward contracts to hedge their risk b. used payer swaptions to hedge their risk c. used energy swaps as the fixed rate payer to hedge their risk d. used energy swaps as the floating rate payer to hedge their risk


6. Which of the following is true? a. if the spot price exceeds the futures price of a commodity, the market is in contango b. if the spot price exceeds the futures price of a commodity, the market is in normal backwardation c. if the spot price exceeds the futures price of a commodity, the market is in inverted backwardation d. none of the above 7. One of the strategies pursued by Nick Leeson at Barings was: a. taking short futures positions on the Nikkei 225 b. setting up short strangles on Nikkei 225 futures contracts b. setting up long straddles on Nikkei 225 futures contracts d. none of the above 8. The Treynor ratio is: a. the expected excess return to an asset divided by its beta b. the expected return to an asset divided by its beta c. the expected excess return to an asset divided by its standard deviation d. the beta divided by the expected return to an asset 9. Long-Term Capital Management a. bet that the spread between Treasury yields and emerging markets yields would widen b. suffered massive losses as a result of the 1997 Asian crisis c. was bought out by Goldman Sachs d. none of the above 10. Arbitrage pricing theory (APT) a. is a special case of the CAPM b. can be used to predict future arbitrage opportunities c. is one of the earliest option pricing models d. none of the above


CHAPTER 1 SOLUTIONS 1. D 2. C The CAPM model is: E(ri) = rf + βi[E(rM) – rf] Rearranging algebraically, βi = [E(ri) - rf ] / [E(rM) – rf] rf = 0.03 E(rM) = 0.05 E(ri) = 0.08 βi = [E(ri) - rf ] / [E(rM) – rf] = (0.08 - 0.03) / (0.05 - 0.03) = 0.05/0.02 = 2.5 3. C 4. B 5. C 6. B Normal backwardation occurs when the spot price is greater than the futures price, and futures prices decline with maturity. Contango occurs when the spot price is less than the futures price, and futures prices rise with maturity. 7. D 8. A 9. D 10. D

Chapter 1 - Fundamental Risk Concepts

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