2007年FRM真题及答案

1、1. You are the new CFO of Global Insurance Inc. You have asked a task force to report to you on how to structure an enterprise risk management program (ERM) with the objective of ensuring that your firm has the optimal level of risk for its level of capital. The task force has made the following rec

2、ommendations. Which recommendation would hinder your ERM program from achieving its objective?a. Management should estimate the amount of capital required to support the risk of its operations given the firms target rating.b. Management should allocate the amount of capital determined to support the

3、 risk of its operations with the objective that units with better accounting performance receive more capital.c. Management should measure firm-level risk by aggregation risks across the firm consistently.d. Management should first determine the firms risk appetite and the general rules for capital

4、allocation.2. Which of the following statements regarding hypothesis testing is incorrect?a. Type II error refers to the failure to reject the null hypothesis when it is actually false.b. Hypothesis testing is used to make inferences about the parameters of a given population on the basis of statist

5、ics computed foe a sample that is drawn from that population.c. All else being equal, the decrease in the chance of making a Type I error comes at the cost of increasing the probability of making a Type II error.d. The p-value decision rule is to reject the null hypothesis if the p-value is greater

6、than the significance level.3. Your firms fixed-income portfolio has interest-only bonds(IO), callable corporate bonds, inverse floaters, noncallable corporate bonds. Your boss wants to know which of the following securities can lose value as yields decline.a. Callable corporate onlyb. Inverse float

7、er onlyc. IO and callable corporate bondd. IO and noncallable corporate bond4. You are asked by your boss to estimate the exposure of a hedge fund to the S&P 500. Though the fund claims to mark to market weekly, it does not do so and marks to market once a month. The fund also does not tell inve

8、stors that it simply holds an Exchange Traded Fund (ETF) that is indexed to the S&P 500. Because of the claims of the hedge fund, you decide to estimate the market exposure by regressing weekly returns of the fund on the weekly return of the S&P 500. Which of the following correctly describe

9、s a property of your regression estimates?a. The intercept of your regression will be positive, showing that the fund has positive alpha when estimated using an OLS regression.b. The beta will be misestimated because hedge fund exposures are nonlinear.c. The beta of your regression will be one becau

10、se the fund holds the S&P 500.d. The beta of your regression will be zero because the fund returns are not synchronous with the S&P 500 returns.5. You are an analyst at Bank Alpha. You were given the task to determine whether under Basel II your bank can use the simplified approach to report

11、 options exposure instead of the intermediate approach. Which of the following criteria would your bank have to satisfy in order for it to use the simplified approach?a. The bank writes options, but its options trading is insignificant in relation to its overall business activities.b. The bank purch

12、ases and writes options and has significant option trading.c. The bank solely purchases options, and its options trading is insignificant in relation to its overall business activities.d. The bank purchases and writes options, but its option trading is insignificant.6. The Potential Future Exposure

13、(PFE) model can be used toi. calculate economic and regulatory capital.ii. quantify credit risk.iii. calculate market risk.iv. determine the appropriate stochastic process of a credit portfolio.a. iii and iv onlyb. i and iii onlyc. i, ii, and iii onlyd. i, ii, and iv onlyThe following mini-case scen

14、ario applies to both question 7 and 8.7. On January 1, a risk manager observes that the one-year continuously compounded interest rate is 5% and storage costs of a commodity product A is USD 0.05 per quarter (payable at each quarter end). He further observes the following forward prices for product

15、A:·March USD 5,35·June USD 5.90·September USD 5.30·December USD 5.22Given the following explanation of supply and demand for commodity product A, how would you best describe its forward price curve form June to December?a. Backwardation as the supply of product A is expected to d

16、ecline after summer.b. Contango as the supply of product A is expected to decline after summer.c. Contango as there is excess demand for product A in early summer.d. Backwardation as there is excess demand for product A in early summer.8. What is the annualized rate of return earned on a cash-and-ca

17、rry trade entered into in March and closed out in June?a. 9.8%b. 8.9%c. 39.1%d. 35.7%9. Which of the following is characteristic of ”crowded trades”?a. As spreads narrow, traders have lower economic incentives to increase leverage levels in order to achieve comparable returns.b. The aggregate volume

18、 of trades in the market(s) is such that traders can simultaneously exit from their positions without significantly impacting prevailing prices.c. Until traders seek to unwind positions, crowded trades are often characterized by a dampening of volatilities and an increase in perceived liquidity meas

19、ures, leading to misleadingly low risk calculations in conventional VaR (including liquidity-adjusted VaR) and other risk models.d. A single large party enters into correlated trading strategies across one or more markets.10. The price of a three-year zero coupon government bond is 85.16. The price

20、of a similar four-year bond is 79.81. What is the one-year implied forward rate form year 3 to year 4?a. 5.4%b. 5.5%c. 5.8%d. 6.7%11. Suppose you are given the following information about the operational risk losses at your bank.Frequency distributionSeverity DistributionProbabilityFrequencyProbabil

21、itySeverity0.500.6USD 1,0000.310.3USD 10,0000.220.1USD 100,1000What is the estimate of the VaR at the 95% confidence level, assuming that the frequency and severity distributions are independent?a. USD 100,000b. USD 101,000c. USD 200,000d. USD 110,00012. A risk manager estimates daily variance()usin

22、g a GARCH model on daily returns():Assume the model parameter values are =0.005, =0.04, =0.94. The long-run annualized volatility is approximatelya. 13.54%b. 7.94%c. 72.72%d. 25.00%13. In pricing a first-to-default credit basket swap, which of the following is true, all else being equal?a. The lower

23、 the correlation between the assets of the basket, the lower the premium.b. The lower the correlation between the assets of the basket, the higher the premium.c. The higher the correlation between the assets of the basket, the higher the premium.d. The correlation between the assets has no impact on

24、 the premium of a first-to default credit basket swap.14. To control risk-taking by traders, your bank links trader compensation with their compliance with imposed VaR limits on their trading book. Why should your bank be careful in tying compensation to the VaR of each trader?a. It encourages trade

25、r to select positions with high estimated risks, which leads to an underestimation of the VaR limits.b. It encourages trader to select positions with high estimated risks, which leads to an overestimation of the VaR limits.c. It encourages trader to select positions with low estimated risks, which l

26、eads to an underestimation of the VaR limits.d. It encourages trader to select positions with low estimated risks, which leads to an overestimation of the VaR limits.15. Bank Z, a medium-size bank, uses only operational loss data from internal records to model its loss distribution from operational

27、risk events. The bank reviewed its records, and, after confirming that they were complete records of its historical losses and that its losses could be approximated by a uniform distribution, it decided against using external loss data to estimate its loss distribution. Based on that decision, which

28、 of the following statements is correct?a. The estimated loss distribution likely accurately represents Bank Zs real risk because the records are accurate and complete.b. The estimated loss distribution likely overtakes bank Zs real risk because many incidences in the past were likely “one off.”c. T

29、he estimated loss distribution likely is the best estimate of Bank Zs real risk because there is no better loss data for the bank than its own.d. The estimated loss distribution likely understates Bank Zs real risk because the bank has not experienced a huge loss.16. Which of the following is not an

30、 accurate statement regarding the purchase of insurance by banks for covering operational risk-related losses?a. Insurance for operational risk events can be very expensive.b. Insurance companies do not have any comparative advantage in bearing or measuring operational risk and thus make poor risk m

31、anagement partners for banks.c. The presence of moral hazard in insurance leads to numerous contracting terms that restrict and condition the insurance and that make the insurance less valuable for banks.d. Policy limits often limit insurance coverage to levels well below the catastrophic levels for

32、 which banks actually need protection.17. The skew of a lognormal distribution is alwaysa. positive.b. negative.c. 0.d. 3.18. Consider two stocks, A and B. Assume their annual returns are jointly normally distributed, the marginal distribution of each stock has mean 2% and standard deviation 10%, an

33、d the correlation is 0.9. What is the expected annual return of stock A if the annual return of stock B is 3%?a. 2%b. 2.9%c. 4.7%d. 1.1%19. If stock returns are independently, identically, normally distribution and the annual volatility is 30%, then the daily VaR at the 99% confidence level of a sto

34、ck market portfolio is approximatelya. 2.41%b. 3.11%c. 4.40%d. 1.89%20. Two years ago, a pass-through mortgage-backed security based on newly originated 30-year mortgages had a weighted average interest rate of 7%. The pass-through was stripped into an interest-only (IO) bond and a principal-only (P

35、O) bond. Today, rates on newly originated mortgages are 5%. Which of the following statements is true about the value of these bonds?a. The value of the IO has increased because the lower interest rates increase the present value of the cash flows to the IO investors and the prepayments include the

36、interest that would have been paid had the homeowners followed the scheduled payments.b. The value of the PO has increased because the lower interest rates increase the present value of the cash flows to the PO investors receive cash earlier than previously expected.c. The value of the IO has decrea

37、sed because the lower prepayments mean the cash flows are delayed.d. The value of the PO has increased because the prepayments have fallen since the first two years and the lower interest rate increases the present value of the payments to the PO investors.21. Synthetic collateralized debt obligatio

38、n (CDO) tranches are structured securities whose performance depends on the number of defaults in a portfolio of credit default swaps (CDS) .A typical synthetic CDO with an equity, mezzanine, senior tranche, and super senior tranche is shown below. Each of the tranches receives a contractual spread

39、in exchange for absorbing losses in the portfolio. For instance, the equity tranche receives a 1,250 bps running spread in exchange for absorbing losses form 0% to 3%.CDO tranche size and structureTrancheSizeNotional (in millions USD)Spread over LIBOREquity0%-3%3%3012.50%Mezzanine3%-6%3%302.50%Senio

40、r6%-9%3%300.90%Super Senior9%-100%91%9100.20%Which of the following statements is correct?a. The equity tranche holder is short a call option with a strike price of USD 30 million written on the value of the portfolio of CDS.b. The super senior tranche holder is short a put option with a strike pric

41、e of USD 90 million written on the value of the portfolio of CDS.c. The mezzanine tranche holder is short a put option with a strike price of USD 60 million written on the value of the portfolio of CDS.d. The senior tranche holder is long a put option with a strike price of USD 60 million written on

42、 the value of the portfolio of CDS.22. Which of the following sentences best describes the volatility smile in equity options?a. Actual volatility is higher for in-the-money options than for out-of-the-money options, possibly because the volatility is stochastic for longer maturity options. b. Impli

43、ed volatility derived from the Black-Scholes model is higher for in-the-money options than for at-the-money-options, possibly because the Black-Scholes model assumes there are jumps in underlying equity prices.c. Implied volatility derived from the Black-Scholes model is higher for out-of-the-money

44、options than for at-the-money-options, possibly because the Black-Scholes model assumes constant volatility.d. Implied volatility derived from the Black-Scholes model is higher for at-the-money options than for in-the-money options, possibly because the Black-Scholes model assumes constant volatilit

45、y.23. Consider the following homogeneous reference portfolio in a synthetic collateralized debt obligation: ·Number of reference entities: 100 ·Credit default swap (CDS) spread: 150 bps ·Recovery rate in case of default: 50%Assume that defaults are independent. On a single name the an

46、nual default probability is constant over five years and obeys the relation: CDS Premium = (1- Recovery rate) * Annual Default ProbabilityWhat is the expected number of defaulting entities over the next five years, and which of the following tranches would be entirely wiped out (loses 100% of the pr

47、incipal invested) by the expected number of defaulting entities?a. 14 defaults and a 3% - 14% tranche would be wiped outb. 3 defaults and a 0% - 1% tranche would be wiped outc. 7 defaults and a 2% -3% tranche would be wiped outd. 14 defaults and a 6% -7% tranche would be wiped out24. A hedge fund ma

48、nager has to choose a risk model for a large “equity market neutral” portfolio. Many of the stocks held are recent IPOs. Among the following alternatives, the best is a. A single index model with no specific risk, estimated over the last year. b. A diagonal index model with idiosyncratic risk, estim

49、ated over the last year. c. A model that maps positions on industry and style factors. d. A full covariance matrix model using a very short window.25. You are given the following information about firm A:·Market value of asset at time 0 = 1000·Market value of asset at time 1 = 1200·Sh

50、ort-term debt = 500·Long-term debt = 300·Annualized asset volatility = 10%According to the KMV model, what are the default point and the distance to default at time 1?Default PointDistance to Defaulta.8003.33b.6507.50c.6504.58d.5005.8326. Consider a portfolio consisting of USD 10 million o

51、f Intel shares and USD 5 million of GE shares. The returns on the two stocks have a bivariate normal distribution with a correlation of 0.3. The daily return volatility of Intel and GE is 2% and 1%, respectively. The standard deviation of daily changes in the value of the Intel position is USD 0.2 m

52、illion, and the standard deviation of daily changes in the value of the GE position is USD 0.05 million. The daily VaR at the 99% confidence level is USD 0.5131 million. What is the incremental daily VaR of the portfolio for a small increase in the position on Intel shares over a one-day horizon at

53、99% confidence level? a. USD 0.0455 million b. USD 2.275 millionc. USD 0.0453 million d. USD 0.0195 million27. As an approximation, it is true that a. Default swap spread = return of a risky bond return of a risk-free bond. b. Default swap spread = return of a risky bond + return of a risk-free bond

54、. c. Default swap spread = return of a risky bond * (1- return of a risk-free bond.) d. Default swap spread = return of a risky bond * return of a risk-free bond.28. The information ratio of the Sterole US Fund for 2006 against the S&P500, its benchmark index, is 1. For the same time period, the

55、 funds Sharpe ratio is 2, the fund has tracking error of 7% against the S&P 500, and the standard deviation of fund returns is 5%. The risk-free rate in the US is 4%. Calculate the return for the S&P 500 during the time period. a. 11% b. 14% c. 5% d. 7%29. An investment bank uses the Exponen

56、tially Weighted Moving Average (EWMA) technique with of 0.9 to model the daily volatility of a security. The current estimate of the daily volatility is 1.5%. The closing price of the security is USD 20 yesterday and USD 18 today. Using continuously compounded returns, what is the updated estimate o

57、f the volatility? a. 3.62% b. 1.31% c. 2.96% d. 5.44%30. Your bank has chosen to use the advanced Internal Rating Based Approach under Basel II. The bank is contemplating a large securitization of low-quality loans that are currently on its balance sheet. You are concerned about whether the securitization will provide you with regulatory capital relief. Which one of the following approaches would be the most efficient in reducing the banks regulatory capital?a. The