FRM一级练习题(3)

FRM一级练习题（3）

1、For a sample of the past 30 monthly stock returns for McCreary, Inc., the mean return is 4% and the sample standard deviation is 20%. Since the population variance is unknown, the standard error of the sample is estimated to be:

S_X=(20%)/√30=3.65%

The related t-table values are (ti,j denotes the (100-j)th percentile of t-distribution value with i degrees of freedom):

t29,2.5=2.045

t29,5.0=1.699

t30,2.5=2.042

t29,5.0=1.697

A. [-3.453%, 11.453%]

B. [-2.201%, 10.201%]

C. [-2.194%, 10.194%]

D. [-3.464%, 11.464%]

2、Which of the following statements is incorrect regarding the volatility term structure predicted by a GARCH (1,1) model:

σt2=ω+αu t−12+βt−12,where α+β<1?

A. When the current volatility estimate is below the long-run average volatility, the GARCH (1, 1) model estimates an upward-sloping volatility term structure.

B. When the current volatility estimate is above the long-run average volatility, the GARCH (1, 1) model estimates a downward-sloping volatility term structure.

C. Assuming the long-run estimated variance remains unchanged, as the GARCH (1, 1) parameters αand βincrease, the volatility term structure predicted by the GARCH (1, 1) model reverts to the long-run estimated variance more slowly.

D. Assuming the long-run estimated variance remains unchanged, as the parameters αand βincrease, the volatility term structure predicted by the GARCH (1, 1) model reverts to the long-run estimated variance faster.

3、On November 1, Jimmy Walton, a fund manager of an USD 60 million U.S. medium- to large-cap equity portfolio, considers locking up the profit from the recent rally. The S&P 500 index and its futures with the multiplier of 250 are trading at 900 and 910, respectively. Instead of selling off his holdings, he would rather

hedge two-thirds of his market exposure over the remaining two months. Given that the correlation between Jimmy's portfolio and the S&P 500 index futures is 0.89 and the volatilities of the equity fund and the futures are 0.51 and 0.48 per year, respectively, what position should he take to achieve his objective?

A. Sell 250 futures contracts of the S&P

B. Sell 169 futures contracts of the S&P 500.

C. Sell 167 futures contracts of the S&P

D. Sell 148 futures contracts of the S&P 500.

4、On the over-the-counter (OTC) market there are two options available on Microsoft stock: a European put with a premium of USD 2.25 and an American call option with a premium of USD 0.46. Both options have a strike price of USD 24 and an expiration date three months from now. Microsoft's stock price is currently at USD 22 and no dividend is due during the next six months. Assuming that there is no arbitrage opportunity, which of these values is the closest to the level of risk free rate?

A. 0.25%

B. 3.52%

C. 1.76%

D. Cannot be determined, as one of the two options is an American option.

5、According to an in-house research report, it is expected that USDJPY (quoted as JPY/USD) will trade near 97 at the end of March. Frankie Shiller, the investment director of a house fund, decides to use an option strategy to capture this investment opportunity. The current level of the USDJPY exchange rate is 97 on February 28. Accordingly, which of the following strategies would be the most appropriate for the largest profit while the potential loss is limited?

A. Long a call option on USDJPY and long a put option on USDJPY with the same strike price of USDJPY 97 and expiration date.

B. Long a call option on USDJPY with strike price of USDJPY 97 and short a call option on USDJPY with strike price of USDJPY 99 and the same expiration date.

C. Short a call option on USDJPY and long a put option on USDJPY with the same strike price of USDJPY 97 and expiration date.

D. Long a call option with strike price of USDJPY 96, long a call option with strike price of USDJPY 98, and sell two call options with strike price of USDJPY 97, all of them with the same expiration date.

6、The price of a European call option at a strike of 120 is at 5, whereas a European put at the same strike is quoted at a price of 25, while the spot price is at 100. A box spread with strikes at 120 and 150 is quoted at a