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

price of 20. All calls and puts, including the ones used in creating the box spread, have the same expiration date. What strategy exploits an arbitrage opportunity, if any?

A. Short one put, short one unit of spot, buy one call, and buy six units of box spread.

B. Buy one put, short one unit of spot, short one call, and buy four units of box spread.

C. Buy one put, buy one unit of spot, short one call, and short six units of box spread.

D. There are no arbitrage opportunities.

7、The yield curve is upward sloping. You have a short T-bond interest rate futures position. The following bonds are eligible for delivery:

Bonds Spot Price Conversion Factor Coupon Rate

A 102 14320.98 4%

B 1061932 1.03 5%

C 9812320.95 3%

The futures price is 10317/32 and the maturity date of the contract is September 1. The bonds pay their coupon amount semiannually on June 30 and December 31. With these data, the cheapest-to-deliver bond is:

A. Bond A

B. Bond B

C. Bond C

D. Insufficient information

8、Which of the following statement(s) is/are true with respect to basis risk?

1. Basis risk arises in cross-hedging strategies but there is no basis risk when the underlying asset and hedge asset are identical.

2. Short hedge position benefits from unexpected strengthening of basis.

3. Long hedge position benefits from unexpected strengthening of basis.

A. 1 and 2

B. 1 and 3

C. 2 only

D. 3 only

9、A company has raised a five-year loan of JPY 1 billion at LIBOR to take advantage of lower interest rates. The loan is hedged through an OTC cross-currency swap with a market maker. They have hedged the principal by selling USD against JPY @ 100 and hedged the interest payments by paying a fixed USD interest rate of 3.5%

and receiving JPY LIBOR. Which of the following holds true about the value of the swap?

A. If the USD five-year rate rises to 4% and USD-JPY rate remains constant, the value of the swap decreases.

B. If the USD five-year rate remains constant while USD-JPY rate rises to 105, the value of the swap is unchanged.

C. If the USD five-year rate falls to 3% while USD-JPY rate remains constant, the value of the swap increases.

D. If the USD five-year rate falls to 3% while USD-JPY rate rises to 105, the value of the swap decreases.

10、The first step in country risk analysis (CRA) is to pick a set of variables that may be important in explaining rescheduling probabilities. Among the variables listed here, which one is most likely to be negatively related to the probability of rescheduling?

A. Debt service ratio (DSR)

B. Import ratio (IR)

C. Investment ratio (INVR)

D. Variance of export revenue (VAREX)

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