Five questions are listed in the FRM weekly test. Notice that the test is designed for candidates who have spent at least 200 hours for FRM part 1 program.
　　1. Which of the following statements are true with regard to a 3-year Bermuda put option?
　　I.          A lower bound on its price is the price of a 3-year European put option.
　　II.       A lower bound on its price is the price of a 3-year American put option.
　　III.     It is likely to outperform both European and American put options as the price of the underlying rises.
　　A.      I only
　　B.       II only
　　C.       II and III
　　D.      III only
　　2. Consider two portfolios: Portfolio I consists of 100 bonds, each rated AAA, all weighted equally; and Portfolio II consists of 20 bonds, each rated A, all weighted equally. The 1-year default probabilities of AAA and A bonds are 0.1% and 0.5% respectively in this country. Assume that the event of default on any bond is independent of default on others.
　　Which one of the following statements is TRUE?
　　A.      The probability of observing no default in Portfolio I is lower than in Portfolio II.
　　B.       The probability of observing no default in Portfolio I is higher than in Portfolio II.
　　C.       The probability of observing no default in Portfolio I is roughly the same as Portfolio II.
　　D.      Insufficient information, we need to know the recovery rates.
　　3. Which of the following statements describe a property of bond convexity? Convexity:
　　I.          increases as yields increase.
　　II.       increases with the square of maturity.
　　III.     measures the rate of change in duration.
　　IV.     increases if the coupon on a bond is decreased.
　　A.    II and III only.
　　A.      I and III only.
　　B.       II and IV only.
　　C.       III and IV only.
　　4. 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 trader 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 leads 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.
　　5. An analyst wants to test whether the mean spending by tourists coming to a holiday resort is equal to or less than $2,000 with a 1 percent level of significance. He finds that the average spending by 16 tourists is $2,200 and the standard deviation of the population is $400. The critical value of the Z statistic for this study is:
　　A.      1.65.
　　B.       -1.96.
　　C.       2.33.
　　D.      2.58.
　　Answer：
　　1. Correct answer: A
　　The Bermuda put option allows multiple opportunities to exercise. Therefore, its price must be higher than that of a European put option (which allows exercise only at maturity) but less than that of American put option (which allows exercise at any point before maturity).
　　2. Correct answer: C
　　Probability (no default in Portfolio I) = (1-0.1%)^100 =90.48%.
　　Probability (no default in Portfolio II) = (1-0.5%)^20 =90.46%.
　　Notes:
　　The question does not ask you to compute expected loss, so you do not need to know the recovery rates.  Even though both portfolios have the same probability of not defaulting, the loss in the event of a single default will be much lower in case of portfolio I than portfolio II. In this question, you are not concerned with it. Hence the answer is counter-intuitive.
　　3. Correct answer ：A
　　Convexity is inversely related to yield and is directly related to the coupon rate on a bond. Convexity is the second derivative of price with respect to yield, which means that convexity measures the rate of change in duration. Convexity increases with the square of maturity.
　　4. Correct answer: D
　　首先，由于此項政策的推出，必定導致交易員選擇風險較小的資產(chǎn)進行投資；其次，為了不受到懲罰或者希望的到根據(jù)新政策規(guī)定的提供的更多的報酬的目的，交易員必定控制自己的風險低于VaR limit，導致VaR limit 被高估了。
　　5. Correct answer: C
　　Since this is a one-tailed test with a 0.01 significance level the critical Z value is 2.33.
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