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　　16. 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.
　　Correct answer： C
　　Probability (no default in Portfolio I) = (1-0.1%)^100 =90.48%. Probability (no defaultin Portfolio II) = (1-0.5%)^20 =90.46%. Notes：1The question does not ask you to compute expected loss， so you do not need to know the recovery rates.2Even 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.
　　17. 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.
　　B. I and III only.
　　C. II and IV only.
　　D. III and IV only.
　　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.
　　18. 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.
　　Correct answer： D
　　D 首先，由于此项政策的推出，必定导致交易员选择风险较小的资产进行投资其次，为了不受到惩罚或者希望的到根据新政策规定的提供的更多的报酬的目的，交易员必定控制自己的风险低于VaR limit，导致VaR limit被高估了。
　　19. 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.
　　Correct answer： C
　　Since this is a one-tailed test with a 0.01 significance level the critical Z value is 2.33.
　　20. Bank Z， a medium-size bank， uses only operational loss data from internal records to model its loss distribution from operational 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 of the following statements is correct？
　　A. The estimated loss distribution likely accurately represents Bank Z‘s real risk because the records are accurate and complete.
　　B. The estimated loss distribution likely overtakes bank Z’s real risk because many incidences in the past were likely “one off.”
　　C. The estimated loss distribution likely is the best estimate of Bank Z‘s real risk because there is no better loss data for the bank than its own.
　　D. The estimated loss distribution likely understates Bank Z’s real risk because the bank has not experienced a huge loss.
　　Correct answer： D
　　D 由于该公司的Loss Distribution近似于一个Uniform distribution，可以推测该公司损失的次数比较小，且大小相近或相似，其原因大致可归类于数据选取的偏差，原因可能是由于公司刚成立不久，数据量不够大，还没有经历过比较极端巨大的损失所造成的。
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