FRM一级模拟题（3）
1、Currently, shares of ABC Corp. trade at $100. The probability of the price increasing by $10 is 30% and the probability of the price decreasing by $10 is 70%. What is the mean and standard d eviation of the price after two days?
A.Mean: 70; standard d eviation: 11.3
B.Mean: 70; standard d eviation: 12.9
C.Mean: 92; standard d eviation: 11.3
D.Mean: 92; standard d eviation: 12.9
2、Which of the foll owing statements about stress testing are true?
(1). Stress testing can complement VaR estimation in helping risk managers identify crucial vulnerabilities in a portfolio.
(2). Stress testing all ows users to include scenarios that did not occur in the l ookback horizon of the VaR data but are nonetheless possibl e.
(3). A drawback of stress testing is that it is highly subjective.
(4). The inclusion of a large number of scenarios helps management better und erstand the risk exposure of a portfolio.
A. 1 and 2 only.
B. 3 and 4 only.
C.1, 2, and 3 only.
D.1, 2, and 3 only.
3、Unexpected loss (UL) represents the standard deviation of losses, and expected l oss (EL) represents the average losses over the same time horizon. Further d efine LGD as l oss given default, and EDF as expected default frequency. Which of the foll owing statements hold(s) true?
(1). EL increases linearly with increasing EDF.
(2). EL is often higher than UL.
(3). With increasing EDF, UL increases at a much faster rate than EL.
(4). The l ower the LGD, the higher the percentage l oss for both the EL and UL.
A. 1 only
B. 1 and 2
C. 1 and 3
D. 2 and 4
4、There are many reasons why risk management increases sharehol der wealth. Which of the foll owing risk management policies is least likely to increase sharehol der wealth?
A.Hedging strategies to l ower probability of financial distress and bankruptcy.
B.Risk management policies designed to reduce the probability of debt overhang.
C.Well-d esigned compensation structure for managers that sets incentives for managers to take appropriate
risks.
D.Risk management policies designed to eliminate projects with high volatility.
5、Over the past year, the HIR Fund had a return of 7.8%, whil e its benchmark—the S&P 500 Index—had a return of 7.2%. Over this period, the fund's volatility was 11.3%, while the S&P 500 Ind ex volatility was 10.7% and the fund's tracking error was 1.25%. Assume a risk-free rate of 3%. What is the information ratio for the HIR Fund and for how many years must this performance persist to be statistically significant at a 95% confidence l evel?
A.0.480 and approximately 16.7 years
B.0.425 and approximately 21.3 years
C. 3.840 and approximately 0.2 years
D. 1.200 and approximately 1.9 years
6、The Liberty Fund, an actively managed mutual fund, uses the S&P 500 Index as its benchmark. The foll owing tabl e shows the returns of the fund and the benchmark over the past three years.
Year Liberty Fund S&P 500
2005 5.4% 4.9%
2006 16.7% 15.8%
2007 6.4% 5.5%
Calculate the cumulative active return over this three-year period.
A. 2.30%
B. 2.31%
C. 2.32%
D. 2.72%
7、Portfolio Q has a beta of 0.7, an expected return of 12.8%, and an equity risk premium of 5.25%. The risk-free rate is 4.85%. Cal culate Jensen's alpha measure for Portfolio Q.
A.7.67%
B. 2.70%
C. 5.73%
D. 4.27%
8、A bank entered into a 3-year interest rate swap for a notional amount of USD 250 million, paying a fixed rate of 7.5% and receiving LIBOR annually. Just after the payment was made at the end of the first year, the continuously compounded 1-year and 2-year LIBOR rates are 8% and 8.5%, respectively. The value of the swap at that time is cl osest to:
https://www.doczj.com/doc/b210790484.html,D 14 million
https://www.doczj.com/doc/b210790484.html,D –6 million
https://www.doczj.com/doc/b210790484.html,D –14 million
https://www.doczj.com/doc/b210790484.html,D 6 million
9、Which of the foll owing statements regarding Metallgesellschaft's failure is incorrect?
A.The futures and swap positions Metallgesellschaft entered into introduced significant credit risk for the
company.
B.An oil market move from a state of contango to normal backwardation and margin calls created a major
cash crunch for Metallgesellschaft.
C.Metallgesellschaft engaged in a stack-and-roll hedge, and as spot prices began to d ecrease more than
futures prices, roll over losses could not be recovered.
D.Because of the size of its position in heating and gasoline oil futures, Metallgesellschaft was exposed to
market liquidity risk and had difficulty liquidating its position.
10、The foll owing table from Fitch Ratings shows the number of rated issuers migrating between two ratings categories during one year. Based on this information, what is the probability that an issue with a rating of A at the beginning of the year will be d owngrad ed by the end of the year?
Year 0 Rating Year 1 Rating
AAA AA A BBB Default Total AAA 45 4 2 0 0 51 AA 3 30 4 3 2 42
A 2 5 40 2 3 52 BB
B 0 1 2 30 1 34 Default 0 0 0 0 0 0
A.13.46%
B.13.44%
C.9.62%
D. 3.85%
Answer and Explanation:
1、Mean = 9% (120) + 42% (100) + 49% (80) = 92
Variance = 9% (120 – 92)2 + 42% (100 – 92)2 + 49% (92 – 80)2 = 168
Standard deviation = 12.9
The other answer reverses the probabilities.
2、Statement 4 is incorrect—using too many scenarios gives a lot of unfiltered information and can hind er management's ability to understand the risk exposure.
3、Over the same fixed horizon, we have the foll owing equations:
EL = AE × LGD × EDF
UL = AE×
AE – adjusted exposure at d efault
1 is correct. EL increases linearly with increasing EDF.
2 is incorrect. EL is often l ower than UL(EL < UL).
3 is correct. UL increases much faster than EL with increasing EDF.
4 is incorrect. The l ower the LGD (the higher the recovery rate), the l ower the percentage loss for both EL and UL.
4、The first three are examples of where risk management can increase firm value. The last one is invalid because reducing volatility per se could just eliminate projects with extremely high payoffs.
5、Information ratio = (Return(portfolio) – Return(benchmark))/Tracking error = (0.078 – 0.072) / 0.0125 = 0.48. This is all the candidate really needs to get the right answer.
If we wish the result to be statistically significant at the 95% l evel, then we need the t-statistic to be within the 95% confid ence level, which is 1.96 at 95% (here we are looking at both tails so we take the inverse normal function at 0.975). If we let T be the length of the period, then T = (t-statistics/IR)2 = (1.96/0.48)2 = 16.7 years.
(A) Correct.
(B) Incorrect. 0.425 is the Sharpe ratio, and 21.3 = (1.96/0.425)2.
(C) Incorrect. 3.84 = (0.078 – 0.03)/0.125, and 0.2 = (1.645/3.84)2.
(D) Incorrect. 1.2 = (0.078 – 0.072)/(0.113 – 0.107), and 0.2 = (1.645/1.2)2.
6、Cumulative return of Liberty Fund = (1.054) * (1.167) * (1.064) – 1 = 30.87%
Cumulative return of S&P 500 = (1.049) * (1.158) * (1.055) – 1 = 28.16%
Cumulative active return = 30.87 – 28.16 = 2.72%
(A) Incorrect. Uses the sum of the differences.
(B) Incorrect. Uses the difference of the average annualized returns: (1 + 1.3087 ^ (1/3) – 1.2816 ^ (1/3)) ^ 3 – 1 = 2.31%.
(C) Incorrect. Uses the cumulative differences: (1 + (5.4% – 4.9%)) * (1 + (16.7% – 15.8%)) * (1 + (6.4% –
5.5%)) – 1 = 2.32%.
(D) Correct.
7、Jensen's alpha is defined by:
E(RP ) - RF = aP + bP(E(RM) - RF)
a P = E(RP ) - RF –
b P(E(RM) - RF)
= 0.128 – 0.0485 – 0.7 * (0.0525 + 0.0485 – 0.0485)
= 0.0427
(A) Incorrect. Forgets to subtract the risk-free rate for the excess market return.
(B) Incorrect. Forgets to multiply the excess market return by beta.
(C) Incorrect. Forgets to subtract the risk-free rate for both the excess market return and the excess portfolio return.
(D) Correct.
8、Fixed rate coupon = USD 250 million x 7.5% = USD 18.75 million
Value of the fixed payment = Bfix = 18.75e(–0.08) + 268.75e(–0.085 * 2) = USD 244.04 million
Value of the floating payment = Bfloating= USD 250 million. Since the payment has just been made, the value of the fl oating rate is equal to the notional amount.
Value of the swap = Bfloating – Bfix = USD 250 – USD 244 = USD 6 million
(A) is incorrect. Forgets the tenor of the second-year payment.
(B) is incorrect. Cal culates Bfix – Bfloating.
(C) is incorrect.
(D) is correct.
9、The answer is (B), since statement (B) is incorrect. An oil market move from a state of normal backwardation to contango and margin calls created a major cash crunch for Metallgesellschaft.
10、Total number of A-rated issuances = 52
Probability of A-rated issues to be d owngraded to BBB (P1) = 2/52 = 0.0385
Probability of A-rated issues to be d owngraded to Default (P2) = 3/52 = 0.0577
Probability of A-rated issues to be d owngraded in one year = P1 + P2 = 0.0962 = 9.62%
Thus (C) is the correct answer. All other options are wrong.
(A) is the number of upgrades from an A rating: (2 + 5)/52 = 13.46%.
(B) is the number of d owngrad es to an A rating: 2/51 + 4/42 = 3.92% + 9.52% = 13.44%.
(D) is the number of d owngrad es to BBB: 2/52 = 3.85%.
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