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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
Correct answer is B
Ten percent of the observations will fall at or below the 3rd lowest observation of the 30 listed. Therefore, the VaR equals 10. The expected shortfall is the mean of the observations exceeding the VaR. Thus, the expected shortfall equals (16 + 14) / 2 = 15.ffice ffice" />
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)
Correct answer is C
R-squared is the square of the correlation coefficient and measures the fraction of the variance of Y that is attributable to X.
R2 = (-0.90)2 = 0.81
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.
Correct answer is C
The skewness of both distributions is zero and the kurtosis of the Student's t-distribution converges to that of the normal distribution as the number of degrees of freedom increases.
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:
Correct answer is B
The skewness of the normal distribution is 0, not 1.
The kurtosis of the normal distribution is 3, the normal distribution can be completely described by its mean and variance, and the density function of the normal distribution is as shown.
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.
Correct answer is A
A is correct. To gamma-hedge, we should buy 400 options (600/1.50). The additional options will alter delta-hedge, and to maintain delta-hedge position again, we should sell 300 shares (400 x 0.75) of the underlying position.
B is incorrect. This strategy will neither delta-hedge nor gamma-hedge the position.
C is incorrect. This strategy will gamma-hedge, but not delta-hedge the position.
D is incorrect. This strategy will neither delta-hedge nor gamma-hedge the position.
Reference: ffice:smarttags" />Hull, Chapter 15.
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发表于 2009-6-13 15:02
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