1. Suppose that the gain from a portfolio during a 6-month holding period is normally distributed with mean $12 million and standard deviation $18 million. What of the following is closest to the VaR for the portfolio with a 6-month time horizon and a 97.5% confidence level?

A.

-10

B.

-12

C.

-18

D.

-23.28

E.

None of the above

2. Suppose that for a one-year project all outcomes between a loss of $200 million and a gain of $350 million are equally likely. Which of the following is closest to the VaR for a one-year time horizon and a 95% confidence level?

A.

-$100 million

B.

-$120 million

C.

-$145.5 million

D.

-$172.5 million

E.

None of the above

3. Question 3 to 5 are based on the following information. Suppose there is a two-asset portfolio, consisting of Asset A and Asset B. The returns of both assets follow normal distribution. Asset A has an expected return of 12.5%, Asset B has an expected return of 2.5%. The standard deviation of the Asset A s return is 4.5%, and the standard deviation of the Asset B s return is 6.5%. The correlation coefficient ( ) of the two assets is 0.15. The market value of Asset A is 35% of the total portfolio. What is the expected return of this portfolio?

A.

1.25%

B.

2.50%

C.

2.75%

D.

3.15%

E.

None of the above

4. What is the standard deviation of the return of this portfolio?

A.

0.035

B.

0.047

C.

0.265

D.

0.318

E.

None of the above

5. What is the VaR of this portfolio at 1% left tail?

A.

-5.6%

B.

-6.2%

C.

-7.3%

D.

-8.2%

E.

None of the above

6. The spot price for gold is $1,550 per ounce. The risk-free interest rate is 3.5%. The futures price for gold for a 6-month contract on gold should be __________.

A.

$1,504.99

B.

$1,569.08

C.

$1,576.89

D.

$1,585.73

E.

None of the above

7. A butterfly spread is the purchase of one call at exercise price X₁, the sale of two calls at exercise price X₂, and the purchase of one call at exercise price X₃. X₁is less than X₂, and X₂is less than X₃by equal amounts (i.e., X₂- X₁= X₃- X₂), and all calls have the same expiration date.IfX₁=$10,X₂=$15,X₃=$20,what is the minimum and maximum payoff of this strategy?

A.

Minimum: 0; Maximum: $5

B.

Minimum: 0; Maximum: $10

C.

Minimum: 0; Maximum: $15

D.

Minimum: unlimited; Maximum: $5

E.

Minimum: unlimited; Maximum: unlimited.