FRM一级练习题(4)

FRM一级练习题（4）

1、How do you create a long butterfly spread strategy and what is its main use?

A. Buy a call and buy a put with different strikes. Long butterfly strategies are used in volatility trading.

B. Buy a call and buy a put with the same strike. Long butterfly strategies are used in directional trading.

C. Buy a l ow strike call. Buy a high strike call. Sell two midstride calls. Long butterfly strategies are used in volatility trading.

D. Sell a l ow strike call and buy two or more high strike calls. Sell a high strike put; buy two or more l ow strike puts. Long butterfly strategies are used in directional and volatility trading.

2、You are asked to estimate the VaR of an investment in Big Pharma Inc. The company's stock is trading at $23 and has a daily volatility of 1.5%. Using the delta-normal method, the VaR at the 95% confidence level of a l ong position in at-the-money put on this stock with a delta of –0.5 over a one-day holding period is cl osest to which of the foll owing choices?

A. $0.40

B. $0.28

C. $0.57

D. $2.83

3、Assume that portfolio daily returns are independently and identically normally distributed. Sam Neil, a new quantitative analyst, has been asked by the portfolio manager to calculate portfolio VaRs for 10-, 15-, 20-, and 25-day periods. The portfolio manager notices something amiss with Sam's cal culations. Which one of foll owing VaRs on this portfolio is inconsistent with the others?

A. VaR(10-day) = USD 316M

B. VaR(15-day) = USD 465M

C. VaR(20-day) = USD 537M

D. VaR(25-day) = USD 600M

4、A portfolio is l ong stock A and short stock B. The stock A position has an annual VaR of USD 20 million and the stock B position has an annual VaR of USD 30 million, assuming that the distributions of price changes for both stocks are normal. If the annual VaR of the total portfolio is USD 40 million, the correlation between stock A and stock B is cl osest to:

A. - 0.25

B. 0.25

C. 0.5

D. - 0.5

5、An investor is long a short-term at-the-money (ATM) put option on an underlying portfolio of equities with a notional value of USD 100,000. If the 95% VaR of the und erlying portfolio is 10.4%, which of the foll owing statements about the VaR of the option position is correct?

A. The VaR of the option position is slightly more than USD 5,200 when second-order terms are considered.

B. The VaR of the option position is slightly more than USD 10,400 when second-order terms are considered.

C. The VaR of the option position is slightly less than USD 5,200 when second-ord er terms are considered.

D. The VaR of the option position is slightly less than USD 10,400 when second-order terms are considered.

6、A five-year corporate bond paying an annual coupon of 8% is sold at a price refl ecting a yield to maturity of 6%. One year passes and the interest rates remain unchanged. Assuming a flat term structure and hol ding all other factors constant, the bond's price during this period will have:

A. Increased.

B. Decreased.

C. Remained constant.

D. Cannot be determined with the data given.

7、Sam Ho's manager was worried about the volatility in interest rates and, d esiring steady income, was looking at perpetuities. Perpetuities are bonds that pay a steady coupon forever. Sam Ho's manager was keen on a USD 1.0 million face value perpetuity bond yielding 5.50% with a coupon of 6.50% paying every six months. Sam Ho's manager was in a hurry and asked Sam to quickly cal culate the price of the bond expressed per USD 100 of face value of the bond.

The price is closest to:

A. 84.61

B. 100.95

C. 108.95

D. 118.18

8、From the time of issuance until the bond matures, which of the foll owing bonds is most likely to exhibit negative convexity?

A. A putable bond

B. A callable bond

C. An option-free bond selling at a discount

D. A zero-coupon bond

9、Which of the foll owing statements is incorrect, given the foll owing one-year rating transition matrix?

From/To (%) AAA AA A BBB BB B CCC/C D Non

Rated

AAA 87.4 7.37 0.46 0.09 0.06 0.00 0.00 0.00 4.59

AA 0.6 86.65 7.78 0.58 0.06 0.11 0.02 0.01 4.21

A 0.05 2.05 89.96 5.50 0.43 0.16 0.03 0.04 4.79

BBB 0.02 0.21 3.58 84.13 4.39 0.77 0.19 0.29 6.14

BB 0.04 0.08 0.33 5.27 75.73 7.36 0.94 1.20 9.06

B 0.00 0.07 0.20 0.28 5.21 72.95 4.23 5.71 11.36

CCC/C 0.08 0.00 0.31 0.39 1.31 9.74 46.83 28.83 12.52

A. BBB l oans have a 4.08% chance of being upgraded over one year.

B. BB loans have a 75.73% chance of staying at BB over one year.

C. BBB l oans have a 95.92% chance of being d owngrad ed over one year.

D. BB l oans have a 18.56% chance of being d owngraded over one year.

10、An analyst is doing a study on the effect on option prices of changes in the price of the underlying asset. The analyst wants to find out when the deltas of calls and puts are most sensitive to changes in the price of the underlying. Assume that the options are European and that the Black-Scholes formula holds. An increase in the price of the underlying has the largest absolute value impact on delta for:

A. Calls d eep in-the-money and puts deep out-of-the-money

B. Deep in-the-money puts and calls

C. Deep out-of-the-money puts and calls

D. At-the-money puts and calls

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