金融风险管理师FRM考试+Answer

1. EXAMPLE 12.1: FRM EXAM 2000—QUESTION 78What feature of cash and futures prices tends to make hedging possible?a. They always move together in the same direction and by the same amount.b. They move in opposite directions by the same amount.c. They tend to move together, generally in the same direction and by the same amount.d. They move in the same direction by different amounts.----------------------------------------------------------------------------------ANSWERExample 12.1: FRM Exam 2000—Question 78c) Hedging is made possible by the fact that cash and futures prices usually move in the same direction and by the same amount.----------------------------------------------------------------------------------2. EXAMPLE 12.2: FRM EXAM 2000—QUESTION 79Under which scenario is basis risk likely to exist?a. A hedge (which was initially matched to the maturity of the underlying) is lifted before expiration.b. The correlation of the underlying and the hedge vehicle is less than one and their volatilities are unequal.c. The underlying instrument and the hedge vehicle are dissimilar.d. All of the above are correct.----------------------------------------------------------------------------------ANSWERExample 12.2: FRM Exam 2000—Question 79d) Basis risk occurs if movements in the value of the cash and hedged positions do not offset each other perfectly. This can happen if the instruments are dissimilar or if the correlation is not unity. Even with similar instruments, if the hedge is lifted before the maturity of the underlying, there is some basis risk.----------------------------------------------------------------------------------3. EXAMPLE 14.1: FRM EXAM 1999—QUESTION 64Under what circumstances is it appropriate to scale up a VAR estimate from a shorter holding period to a longer holding period using the square root of time?a. It is never appropriate.b. It is always appropriate.c. When either mean reversion or trend are present in the historical data series.d. When neither mean reversion nor trend are present in the historical data series.----------------------------------------------------------------------------------ANSWERExample 14.1: FRM Exam 1999—Question 64d) The presence of either mean reversion or trend (or time variation in risk) implies a different distribution of returns for different holding periods.----------------------------------------------------------------------------------4. EXAMPLE 14.2: FRM EXAM 1998—QUESTION 5Consider a portfolio with a one-day VAR of $1 million. Assume that the market is trending with an autocorrelation of 0.1. Under this scenario, what would you expect the two-day VAR to be?a. $2 millionb. $1.414 millionc. $1.483 milliond. $1.449 million----------------------------------------------------------------------------------ANSWERExample 14.2: FRM Exam 1998—Question 5c) Knowing that the variance is V(2-day) = V(1-day) [2 + 2ρ], we find VAR(2-day) = VAR(1-day)√(2 + 2ρ) = $1√(2 + 0.2) = $1.483, assuming the same distribution for the different horizons. ----------------------------------------------------------------------------------5. EXAMPLE 16.1: ABSOLUTE AND RELATIVE RISKAn investment manager is given the task of beating a benchmark. Hence, the risk should be measureda. In terms of loss relative to the initial investmentb. In terms of loss relative to the expected portfolio valuec. In terms of loss relative to the benchmarkd. In terms of loss attributed to the benchmark----------------------------------------------------------------------------------ANSWERExample 16.1: Absolute and Relative Riskc) This is an example of risk measured in terms of deviations of the active portfolio relative to the benchmark. Answers a) and b) are incorrect because they refer to absolute risk. Answer d) is also incorrect because it refers to the absolute risk of the benchmark.----------------------------------------------------------------------------------6. EXAMPLE 16.2: PENSION LIABILITIESThe AT&T pension plan reports a projected benefit obligation of $17.4 billion. If the discount rate decreases by 0.5%, this liability will increase by $0.8 billion. Based on this information, the liabilities behave like aa. Short position in the stock marketb. Short position in cashc. Short position in a bond with maturity of about 9 yearsd. Short position in a bond with duration of about 9 years----------------------------------------------------------------------------------ANSWERExample 16.2: Pension Liabilitiesd) We can compute the modified duration of the liabilities asSo, the liabilities behave like a short position in a bond with a duration around nine years. Answers a) and b) are incorrect because the liabilities have fixed future payoffs, which do not resemble cash flow patterns on equities nor cash. Answer c) is incorrect because the duration of a bond with a nine-year maturity is less than nine years. For example, the duration of a 6% coupon par bond with nine-year maturity is seven years only.----------------------------------------------------------------------------------A pension plan reports $12 billion in assets and $10 billion in present value of the benefit obligations. Future pension benefits are indexed to the rate of inflation. To immunize its liabilities, the plan shoulda. Invest $12 billion of assets in fixed-coupon long-term bondsb. Invest $10 billion of assets in fixed-coupon long-term bondsc. Invest $10 billion of assets in cashd. Invest $10 billion of assets in Treasury Inflation-Protected Securities----------------------------------------------------------------------------------ANSWERExample 16.3: Pension Immunizationd) Immunization occurs when assets are invested so as to perfectly hedge changes in liabilities. So, the amount to invest is $10 billion, which is the value of liabilities.In this case, we are told that the pension payments are indexed to the rate of inflation. Because the liabilities are tied to inflation, immunization requires that the assets should react in a similar way to inflation. This can be achieved with Treasury inflation-protected securities (TIPS).----------------------------------------------------------------------------------8. EXAMPLE 17.1: LEVERAGE AND HEDGE FUNDSA hedge fund with $100 million in equity is long $200 million in some stocks and short$150million in others. The gross and net leverage are, respectively,a. 2.0 and 0.5b. 2.0 and 1.5c. 3.5 and 0.5d. 3.5 and 1.5----------------------------------------------------------------------------------ANSWERExample 17.1: Leverage and Hedge Fundsc) The gross leverage is (200 + 150)/100 = 3.5. The net leverage is (200 ? 150)/100 = 0.5.----------------------------------------------------------------------------------9. EXAMPLE 17.2: HEDGING AND RETURNSContinuing with the previous question, assume the stock market went up by 20%last year. Ignore the risk-free rate and idiosyncratic risk, and assume the average beta of both long and short positions is one. Over the same period, the return on the fund should bea. 20%b. 15%c. 10%d. 5%----------------------------------------------------------------------------------ANSWERExample 17.2: Leverage and Returnsc) The net ret urn on the stock portfolio is (βL$200 ? βS$150) × 20%. With betas of 1, this is $10 million. Given that the equity is $100 million, the rate of return is 10%. The rate of return is less than the market because most of the exposure to the market is hedged.----------------------------------------------------------------------------------10. EXAMPLE 17.3: FRM EXAM 2004—QUESTION 2A relative value hedge fund manager holds a long position in Asset A and a short position in assetB of roughly equal principal amounts. Asset A currently has a correlation with asset B of 0.97. The risk manager decides to overwrite this correlation assumption in the variance-covariance based VAR model to a level of 0.30. What effect will this change have on the resulting VAR measure?b. It decreases VAR.c. It has no effect on VAR, but changes profit or loss of strategy.d. Do not have enough information to answer.----------------------------------------------------------------------------------ANSWERExample 17.3: FRM Exam 2004—Question 2a) Because the position is both long and short, high correlation implies low risk.Conversely, lowering correlation increases risk.----------------------------------------------------------------------------------11. EXAMPLE 18.1: FRM EXAM 2000—QUESTION 36Settlement risk in foreign exchange is generally due toa. Notionals being exchangedb. Net value being exchangedc. Multiple currencies and countries involvedd. High volatility of exchange rates----------------------------------------------------------------------------------ANSWERExample 18.1: FRM Exam 2000—Question 36a) Settlement risk is due to the exchange of notional principal in different currencies at different points in time, which exposes one counter party to default after it has made payment. There would be less risk with netted payments.----------------------------------------------------------------------------------12. EXAMPLE 18.2: FRM EXAM 2000—QUESTION 85Which one of the following statements about multilateral netting systems is not accurate?a. Systemic risks can actually increase because they concentrate risks on the central counterparty, the failure of which exposes all participants to risk.b. The concentration of risks on the central counterparty eliminates risk because of the high quality of the central counterparty.c. By altering settlement costs and credit exposures, multilateral netting systems for foreign exchange contracts could alter the structure of credit relations and affect competition in the foreign exchange markets.d. In payment netting systems, participants with net-debit positions will be obligated to make a net settlement payment to the central counter- party that, in turn, is obligated to pay those participants with net credit positions.----------------------------------------------------------------------------------ANSWERExample 18.2: FRM Exam 2000—Question 85b) Answers c) and d) are both correct. Answers a) and b) are contradictory. A multilateral netting system concentrates the credit risk into one institution. This could potentially create much damage if this institution fails.----------------------------------------------------------------------------------13. EXAMPLE 18.3: FRM EXAM 2002—QUESTION 130You have granted an unsecured loan to a company. This loan will be paid off by a single payment of $50 million. The company has a 3% chance of defaulting over the life of the transaction and your calculations indicate that if they default you would recover 70% of your loan from the bankruptcy courts. If you are required to hold a credit reserve equal to your expected credit loss, how great of a reserve should you hold?b. $750,000c. $1,050,000d. $1,500,000----------------------------------------------------------------------------------ANSWERExample 18.3: FRM Exam 2002—Question 130a) The expected credit loss (ECL) is the notional amount times the probability of default times the loss given default. This is $50,000, 000 × 0.03 × (1 ? 70%) = $450,000.----------------------------------------------------------------------------------14. EXAMPLE 18.4: FRM EXAM 2003—QUESTION 17An investor holds a portfolio of $100 million. This portfolio consists of A- rated bonds ($40 million) and BBB-rated bonds ($60 million). Assume that the one-year probabilities of default for A-rated and BBB-rated bonds are 3% and 5%, respectively, and that they are independent. If the recovery value for A-rated bonds in the event of default is 70% and the recovery value for BBB-rated bonds is 45%, what is the one-year expected credit loss from this portfolio?a. $1,672,000b. $1,842,000c. $2,010,000d. $2,218,000----------------------------------------------------------------------------------ANSWERExample 18.4: FRM Exam 2003—Question 17c) The expected lossis----------------------------------------------------------------------------------15. EXAMPLE 18.5: FRM EXAM 1998—QUESTION 38Calculate the probability of a subsidiary and parent company both defaulting over the next year. Assume that the subsidiary will default if the parent defaults, but the parent will not necessarily default if the subsidiary defaults. Also assume that the parent has a one-year probability of default of 0.50% and the subsidiary has a one-year probability of default of 0.90%.a. 0.450%b. 0.500%c. 0.545%d. 0.550%----------------------------------------------------------------------------------ANSWERExample 18.5: FRM Exam 1998—Question 38b) Since the subsidiary defaults when the parent defaults, the joint probability is simply that of the parent defaulting.----------------------------------------------------------------------------------16. EXAMPLE 18.6: FRM EXAM 1998—QUESTION 16A portfolio manager has been asked to take the risk related to the default of two securities A andB. She has to make a large payment if, and only if, both A and B default. For taking this risk, she will be compensated by receiving a fee. What can be said about this fee?a. The fee will be larger if the default of A and of B are highly correlated.b. The fee will be smaller if the default of A and of B are highly correlated.c. The fee is independent of the correlation between the default of A and of B.d. None of the above is correct.----------------------------------------------------------------------------------ANSWERExample 18.6: FRM Exam 1998—Question 16a) The fee must re?ect the joint probability of default. As described in Equation (18.7), if defaults of A and B are highly correlated, the default of one implies a greater probability of a second default. Hence the fee must be higher.----------------------------------------------------------------------------------17. EXAMPLE 18.7: FRM EXAM 1998—QUESTION 42A German bank lends €100 million to a Russian bank for one year and receives €120 million worth of Russian government securities as collateral.Assuming that the one-year 99% VAR on the Russian government securities is €20 million and the Russian bank’s one-year probability of default is 5%, what is the German bank’s probability of losing money on this trade over the next year?a. Less than 0.05%b. Approximately 0.05%c. Between 0.05% and 5%d. Greater than 5%----------------------------------------------------------------------------------ANSWERc) The probability of losing money is driven by (i) a fall in the value of the collateral and (ii) default by the Russian bank. If the two events are independent, the joint probability is 5%× 1% = 0.05%. In contrast, if the value of securities always drops at the same time the Russian bank defaults, the probability is simply that of the Russian bank’s default, or 5%.----------------------------------------------------------------------------------18. EXAMPLE 18.8: FRM EXAM 2000—QUESTION 51A portfolio consists of two (long) assets ￡100 million each. The probability of default over the next year is 10% for the first asset, 20% for the second asset, and the joint probability of default is 3%. Estimate the expected loss on this portfolio due to credit defaults over the next year, assuming 40% recovery rate for both assets.a. ￡18 millionb. ￡22 millionc. ￡30 milliond. None of the above----------------------------------------------------------------------------------ANSWERExample 18.8: FRM Exam 2000—Question 51a) The three loss events are(i) Default by the ?rst alone, with probability 0.10 ? 0.03 = 0.07(ii) Default by the second, with probability 0.20 ? 0.03 = 0.17(iii) Default by both, with probability 0.03The respective losses are￡100×(1 ? 0.4) × 0.07 = 4.2,￡100×(1 ? 0.4) × 0.17 = 10.2,￡200×(1 ? 0.4) × 0.03 = 3.6,for a total expected loss of ￡18 million.----------------------------------------------------------------------------------19. EXAMPLE 18.9: FRM EXAM 2004—QUESTION 46Consider an A-rated bond and a BBB-rated bond. Assume that the one-year probabilities of default for the A- and BBB-rated bonds are 2% and 4%, respectively, and that the joint probability of default of the two bonds is 0.15%. What is the default correlation between the two bonds?a. 0.07%b. 2.6%c. 93.0%d. The default correlation cannot be calculated with the information provided.----------------------------------------------------------------------------------ANSWERExample 18.9: FRM Exam 2004—Question 46b) From Equation (18.7), the default correlation is----------------------------------------------------------------------------------20. EXAMPLE 19.1: FRM EXAM 1998—QUESTION 5Which of the following events is not a “credit event”?a. Bankruptcyb. Calling back a bondc. Downgradingd. Default on payments----------------------------------------------------------------------------------ANSWERExample 19.1: FRM Exam 1998—Question 5b) Calling back a bond occurs when the borrower wants to re?nance its debt at a lower cost, which is not a credit event.----------------------------------------------------------------------------------21. EXAMPLE 19.2: FRM EXAM 2003—QUESTION 100What is the lowest tier of an investment-grade credit rating by Moody’s?a. Baa1b. Ba1c. Baa3d. Ba3----------------------------------------------------------------------------------ANSWERExample 19.2: FRM Exam 2003—Question 100c) Baa3 is the lowest investment-grade rating for Moody’s.----------------------------------------------------------------------------------22. EXAMPLE 19.3: FRM EXAM 2004—QUESTION 27You are considering an investment in one of three different bonds. Your investment guidelines require that any bond you invest in carry an investment- grade rating fromat least two recognized bond rating agencies. Which, if any, of the bonds listed below would meet your investment guidelines?a. Bond A carries an S&P rating of BB and a Moody’s rating of Baa.b. Bond B carries an S&P rating of BBB and a Moody’s rating of Ba.c. Bond C carries an S&P rating of BBB and a Moody’s rating of Baa.d. None of the above.----------------------------------------------------------------------------------ANSWERExample 19.3: FRM Exam 2004—Question 27c) The lowest investment-grade ratings are BBB and Baa.----------------------------------------------------------------------------------23. EXAMPLE 19.4: FRM EXAM 2002—QUESTION 110If Moody’s and S&P are equally good at rating bonds, the average default rate on BB bonds by S&P will be lower than the average default rate on bonds rated by Moody’s asa. Baa3b. Ba1c. Bad. Ba3----------------------------------------------------------------------------------ANSWERExample 19.4: FRM Exam 2002—Question 110d) The BB rating by S&P is similar to a Ba rating by Moody’s. A BB bond will have lower default rate than a bond rated lower. Hence, the answer is the next lowest rating category by Moody’s. ----------------------------------------------------------------------------------24. EXAMPLE 19.5: FRM EXAM 2004—QUESTION 34In Altman’s credit-classification model, the higher the z-score:a. The lower the default risk of the borrower.b. The higher the default risk of the borrower.c. The lower the recovery rate from debt instruments.d. The z-score indicates neither the default risk of the borrower nor the recovery rate of debt instruments.----------------------------------------------------------------------------------ANSWERExample 19.5: FRM Exam 2004—Question 34a) The z-score is a positive function of variables such as earnings, which are negatively related to default risk. So, a higher z-score is associated with lower default risk.----------------------------------------------------------------------------------25. EXAMPLE 20.1: FRM EXAM 2004—QUESTION 38Assume the one-year Treasury bill’s yield is 2.9%. Ford’s one-year zero coupon bond has a yield to maturity of 5.6%. Assuming zero recovery, what is Ford’s implied probability of default?b. 2.6%c. 2.7%d. 5.6%----------------------------------------------------------------------------------ANSWERExample 20.1: FRM Exam 2004—Question 38b) Using Equation (20.3), the risk-neutral default probability π is given by(1 +y?) = (1 + y)[1 ? π(1 ? f )],wh ere y? is the corporate yield, y is the Treasury yield,and f is the recovery rate.Thus, π = 1 ? (1 + y)/(1 + y?) = 1 ? 1.029/1.056 = 2.56%.----------------------------------------------------------------------------------26. EXAMPLE 20.2: FRM EXAM 2002—QUESTION 96A loan of $10 million is made to a counterparty whose expected default rate is 2% per annum and whose expected recovery rate is 40%. Assuming an all-in cost of funds of LIBOR for the lender, what would be the fair price for the loan?a. LIBOR + 120bpb. LIBOR + 240bpc. LIBOR - 120bpd. LIBOR + 160bp----------------------------------------------------------------------------------ANSWERExample 20.2: FRM Exam 2002—Question 96a) The credit spread should be y?? y = π(1 ? f ).Thus, π(1 ? f ) = 2%(1 ? 40%) = 1.2%. The spread over LIBOR should be 120 bp.----------------------------------------------------------------------------------27. EXAMPLE 21.1: FRM EXAM 2002—QUESTION 93Which transaction does not result in a long-term credit risk for party A?a. Party A makes an unsecured loan to party B.b. Party A is a ?xed-price receiver in an interest rate swap from party B.c. Party A buys a call option on September wheat from party B.d. Party A sells a put option on the S&P 500 index to party B.----------------------------------------------------------------------------------ANSWERExample 21.1: FRM Exam 2002—Question 93d) Selling an option does not create credit exposures, because the premium has been received up front and the option can only create a future liability.----------------------------------------------------------------------------------28. EXAMPLE 21.2: FRM EXAM 2004—QUESTION 8Your company has reached its credit limit to Ford, but Ford is insisting that your ?rm provide them some increased protection in the event a major project they are undertaking results in some unforeseen liability. Ignoring settlement risk and assuming option premiums are paid immediately at the time of the transaction, which of these strategies will not give rise to increased credit exposure to Ford?a. Selling a costless collar to Fordb. Buying an option from Fordc. Selling an option to Fordd. None of the above----------------------------------------------------------------------------------Example 21.2: FRM Exam 2004—Question 8c) This is the only answer that involves truly selling an option, which has no credit exposure. A collar involves the sale and purchase of an option.----------------------------------------------------------------------------------29. EXAMPLE 21.3: FRM EXAM 2003—QUESTION 38How does the credit exposure of a long OTC put option on XYZ stock change when the stock price decreases?a. It increases.b. It decreases.c. It does not vary with underlying stock price.d. There is no credit exposure on long options.----------------------------------------------------------------------------------ANSWERExample 21.3: FRM Exam 2003—Question 38a) As the stock price decreases, the option becomes more in-the-money, so it has greater exposure.----------------------------------------------------------------------------------30. EXAMPLE 21.4: FRM EXAM 2001—QUESTION 84If a counterparty defaults before maturity, which of the following situations will cause a credit loss?a. You are short euros in a one-year euro/USD forward FX contract and the euro has appreciated.b. You are short euros in a one-year euro/USD forward FX contract and the euro has depreciated.c. You sold a one-year OTC euro call option, and the euro has appreciated.d. You sold a one-year OTC euro call option, and the euro has depreciated.----------------------------------------------------------------------------------ANSWERExample 21.4: FRM Exam 2001—Question 84b) Being short an option creates no credit exposure, so answers c) and d) are false.With the short forward contract, a gain will be realized if the euro has depreciated.----------------------------------------------------------------------------------31. EXAMPLE 22.1: FRM EXAM 2004—QUESTION 9If an investor holds a ?ve-year IBM bond, it will give him a return very close to the return of the following position:a. A ?ve-year IBM credit default swap on which he pays ?xed and receives a payment in the event of defaultb. A ?ve-year IBMcredit default swap onwhich he receives ?xed andmakes a payment in the event of defaultc. A ?ve-year U.S. Treasury bond plus a ?ve-year IBM credit default swap on which he pays ?xed and receives a payment in the event of defaultd. A ?ve-year U.S. Treasury bond plus a ?ve-year IBM credit default swap on which hereceives ?xed and makes a payment in the event of default----------------------------------------------------------------------------------ANSWERExample 22.1: FRM Exam 2004—Question 9d) A long corporate bond position is equivalent to a long Treasury bond position plus a short CDS. ----------------------------------------------------------------------------------32. EXAMPLE 22.2: FRM EXAM 2002—QUESTION 88A credit default swap is an instrument that can be characterized best as:b. A swap that can only be valued against non–investment-grade debt securitiesc. An option to sell defaulted securities at par value to a third party in exchange for a seriesof ?xed cash ?owsd. Any swap that defaults to a third-party guarantor should a party to the swap ?le for bankruptcy protection----------------------------------------------------------------------------------ANSWERExample 22.2: FRM Exam 2002—Question 88c) CDS are options to exchange securities at par value even if their market value is less, due to a credit event.----------------------------------------------------------------------------------33. EXAMPLE 22.3: FRM EXAM 1999—QUESTION 122A portfolio manager holds a default swap to hedge an AA corporate bond position. If the counterparty of the default swap is acquired by the bond issuer, then the default swapa. Increases in valueb. Decreases in valuec. Decreases in value only if the corporate bond is downgradedd. Is unchanged in value----------------------------------------------------------------------------------ANSWERExample 22.3: FRM Exam 1999—Question 122b) This is an interesting question that demonstrates that the credit risk of the underlying asset is exchange for that of the swap counterparty. The swap is now worthless; if the underlying credit defaults, the counterparty will default as well (since it is the same).----------------------------------------------------------------------------------34. EXAMPLE 22.4: FRM EXAM 2000—QUESTION 39A portfolio consists of one (long) $100 million asset and a default protection contract on this asset. The probability of default over the next year is 10% for the asset and 20%for the counterparty that wrote the default protection.The joint probability of default for the asset and the contract counterparty is 3%. Estimate the expected loss on this portfolio due to credit defaults over the next year with a 40% recovery rate on the asset and 0% recovery rate for the counterparty.a. $3.0 millionb. $2.2 millionc. $1.8 milliond. None of the above----------------------------------------------------------------------------------。