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FRM模拟试题<7>

来源：高顿网校 2015-03-18

　　31. You are given the following specification of the currency swap：

　　notional principal $10m euro 10.5m

　　swap coupon 7.2% 6.8%

　　current market yield 4.2% 3.6%

　　There are two payments left in the swap （the first one in a year） and the current exchange　rate　is $0.95/euro. Calculate the dollar value of the swap for the euro payer.

　　A. - $16,299.

　　B. - $17,344.

　　C. - $19,344.

　　D. - $21,283.

　　Correct answer： A

　　The swap is equivalent to long position in dollar denominated bond and short position in　euro denominated bond. （720，000 / 1.042 + 10，720，000 / 1.042^2） - （（714，000 / 1.036 +　11，214，000 / 1.036^2） x0.95） = - 16，299.

　　32. How would you describe the typical price behavior of a low premium mortgage pass-through security？

　　A. It is similar to a U.S. Treasury bond

　　B. It is similar to a plain vanilla corporate bond

　　C. When interest rates fall， its price increase would exceed that of a　comparable　duration U.S. Treasury.

　　D. When interest rates fall， its price increase would lag that of a　comparable　duration U.S. Treasury.

　　Answer： C

　　Mortgage pass-through securities， unlike Treasuries or plain vanilla corporate bonds， have an embedded option allowing borrowers to repay the loan at any time. When rates fail， the effective duration of these securities decreases because borrowers will refinance　mortgages at lower rates （putting the loans back to the investors）； but when interest rates　increase， borrowers will hold on to mortgages longer than they otherwise would， resulting　in an increase in the effective duration of the loans. This is reflected in the price/yield　relationship as negative convexity.

　　33. You are given the following information about a portfolio and are asked to make a

　　recommendation about how to reallocate the portfolio to improve the risk/return tradeoff.

Asset	Expected return	Standard Deviation	Current Weight	Covariance Of Portfolio and Asset1 Returns	Marginal Return	Marginal Risk	Marginal Return/ Marginal risk	Risk Contribution
Asset1	7.10%	17.00%	38.70%	1.43%	3.10%	13.99%	22.17%	5.41%
Asset2	8.00%	40.60%	6.20%	2.44%	4.00%	23.93%	16.71%	1.48%
Asset3	6.70%	44.80%	5.50%	2.39%	2.70%	23.39%	11.55%	1.29%
Asset4	6.90%	21.40%	14.60%	1.41%	2.90%	13.86%	20.92%	2.02%
Risk free	4.00%	0.00%	35.00%	0.00%

　　Which of the following the recommendations will improve the risk/return tradeoff of the　portfolio？

　　A. Increase the allocations to assets 1 and 3 and decrease the allocations to assets 2 and4.

　　B. Increase the allocations to assets 1 and 2 and decrease the allocations to assets 3 and4.

　　C. Increase the allocations to assets 2 and 3 and decrease the allocations to assets 1 and4.

　　D. Increase the allocations to assets 1 and 4 and decrease the allocations to assets 2 and3.

　　Answer： D

　　A. Incorrect. Asset 3 should be decreased since it has the lowest marginal　return-to-marginal risk ratio.

　　B. Incorrect. Asset 4 should be increased since it has the highest marginal　return-to-marginal risk ratio.

　　C. Incorrect. Asset 4 should be increased since it has the highest marginal　return-to-marginal risk ratio.

　　D. Correct. A portfolio optimizing the risk-reward tradeoff has the property that the ratio　of the marginal return to marginal risk of each asset is equal. Therefore， this option is　the only recommendation that will move the ratios in the right direction.

　　34. Calculate the estimated default frequency （EDF） for a KMV credit risk model using the

　　data given below （all figures in millions）. Assets Liabilities Market value 195 185 Book

　　value 180 165 Standard deviation 25 15 of returns

　　A. 11.5%.

　　B. 27.4%.

　　C. 34.5%.

　　D. 57.9%.

　　Correct answer： A

　　The distance between the current value of the assets and the book value of the liabilities= 195- 165 = 30. Using the standard deviations in the return on assets this distance = 30 /25 = 1.2 standard deviations. Thus the probability of default = cumulative probability of standard normal distribution below -1.2， i.e. 11.5%.

　　35. Suppose the payoff from a merger arbitrage operation is $5 million if successful， -$20million if not. The probability of success is 83%. The expected payoff on the operation is

　　A. $5 million

　　B. $0.75 million

　　C. $0 since markets are efficient

　　D. Symmetrically distributed

　　Answer： B

　　The expected payoff is the sum of probabilities times the payoff in each state of the　world， or 83% × $5 + 17% × （-$20） = $4.15 - $3.40 = $0.75. Note that the distribution is　highly asymmetric， with a small probability of a large loss.

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