FRM一級分析（附詳細(xì)解釋）
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課程詳情
以下5道是為了考察的同學(xué)對于一級的內(nèi)容是否掌握牢固的一種形式，大家可以先坐下，后面有答案可以詳細(xì)解答的哦。
1. 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. $.
B. $.
C. $.
D. $.
2. 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.
3. 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.
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 and 4.
B. Increase the allocations to assets 1 and 2 and decrease the allocations to assets 3 and 4.
C. Increase the allocations to assets 2 and 3 and decrease the allocations to assets 1 and 4.
D. Increase the allocations to assets 1 and 4 and decrease the allocations to assets 2 and 3.
4. Calculate the estimated default frequency (EDF) for a KMV credit risk model using the data given below (all figures in millions). Assets Liabilities Market valueBook valueStandard deviationof returns
A. 11.5.
B. 27.4.
C. 34.5.
D. 57.9.
5. Suppose the payoff from a merger arbitrage operation is $5 million if successful, -$20 million 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
怎么樣，大家覺得自己考得如何，下面是這五道題的答案和解析，趕快來對照一下吧。
1. 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) x 0.95) = - 16,299.
2. 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.
3. Answer: D
A is incorrect. Asset 3 should be decreased since it has the lowest marginal return-to-marginal risk ratio.
B is incorrect. Asset 4 should be increased since it has the highest marginal return-to-marginal risk ratio.
C is incorrect. Asset 4 should be increased since it has the highest marginal return-to-marginal risk ratio.
D is 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.
4. Correct answer: A
The distance between the current value of the assets and the book value of the liabilities
== 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.
5. 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.
