1、ABC Bank believes that the underlying distribution of its loan returns should follow a normal distribution with a mean of 10 and a standard deviation of 3. The following table identifies tail VARs at different confidence levels. Assume the initial analysis uses five tail slices. Calculate the expected shortfall at the 97% confidence level and identify the effect on ES when the number of tail slices increases.
Confidence level Tail VAR
Expected Shortfall Increasing Slices
A. 4.117 ES increases
B. 4.117 ES decreases
C. 4.375 ES increases
D. 4.375 ES decreases
The expected shortfall calculation takes the average of the expected shortfalls at varying confidences in the tail region. Note that the tail VAR at 97% is not included in the calculation since ES is the average loss beyond 3% VAR. In addition, as the number of tail slices increases, the average ES will increase as the number of higher confidence tail VARs increases.
2、The VaR at a 99% confidence level is estimated to be 2.56 from a historical simulation of 1,000 observations. Which of the following statements is most likely true?
A.The parametric assumption of normal returns is correct.
B.The parametric assumption of lognormal returns is correct.
C.The historical distribution has fatter tails than a normal distribution.
D.The historical distribution has thinner tails than a normal distribution.
The historical simulation indicates that the 1% tail loss begins at 2.56, which is over 2.33 predicted by a standard normal distribution. Therefore, the historical simulation has fatter tails than a standard normal distribution.