[ 2009 FRM ] Medium Practice Exam 2 Q1-5

1. Given the following 30 ordered simulated percentage returns of an asset, calculate the VaR and expected shortfall (both expressed in terms of returns) at a 90% confidence level.

-16, -14, -10, -7, -7, -5, -4, -4, -4, -3, -1, -1, 0, 0, 0, 1, 2, 2, 4, 6, 7, 8, 9,11, 12, 12, 14, 18, 21, 23

A. VaR (90%) = 10, Expected shortfall = 14

B. VaR (90%) = 10, Expected shortfall = 15

C. VaR (90%) = 14, Expected shortfall = 15

D. VaR (90%) = 18, Expected shortfall = 22

2. The result of the linear regression is: Y = 0.10 - 0.50 X with a correlation coefficient R = (-0.90). The fraction of the variance of Y attributable to X is equal to:

A. (-0.90)

B. (+0.90)

C. (+0.81)

D. (-0.50)

3. Which of the following statements is the most accurate about the relationship between a normal distribution and a Student's t-distribution that have the same mean and standard deviation?

A. They have the same skewness and the same kurtosis.

B. The Student's t-distribution has larger skewness and larger kurtosis.

C. The kurtosis of a Student's t -distribution converges to that of the normal distribution as the number of degrees of freedom increases.

D. The normal distribution is a good approximation for the Student's t-distribution when the number of degrees of freedom is small.

4. Which one of the following statements about the normal distribution is NOT accurate?

A. Kurtosis equals 3.

B. Skewness equals 1.

C. The entire distribution can be characterized by two moments, mean and variance.

D. The normal density function has the following expression:

5. Suppose an existing short option position is delta-neutral, but has a gamma of negative 600. Also assume that there exists a traded option with a delta of 0.75 and a gamma of 1.50. In order to maintain the position gamma-neutral and delta-neutral, which of the following is the appropriate strategy?

A. Buy 400 options and sell 300 shares of the underlying asset.

B. Buy 300 options and sell 400 shares of the underlying asset.

C. Sell 400 options and buy 300 shares of the underlying asset.

D. Sell 300 options and buy 400 shares of the underlying asset.