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Assume that an operational process has a 5% probability of creating a material loss and, otherwise, no material loss is experienced (i.e., Bernoulli). If the material loss occurs, the severity is normally distributed with a mean of $4 million and standard deviation of $2 million. What is the 95% expected shortfall?

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A) $0.71 million

B) $3.29 million

C) $4.00 million

D) $7.29 million

答案：C

解析：ES = E(L | L > VaR). In this case, the 95% ES is the expected loss conditional on the loss occurring, which coincides with the mean of the normal distribution.

Arisk manager uses the past 480 months of correlation data from the Dow Jones IndustrialAverage (Dow) to estimate the long-run mean correlation of common stocks and the mean reversion rate. Based on historical data, the long-run mean correlation of Dow stocks was 34%, and he regression output estimates the following regression relationship: Y = 0.215 - 0.77X. Suppose that inApril 2014, the average monthly correlation for all Dow stocks was 33%. What is the estimated one-period autocorrelation for this time period based on the mean reversion rate estimated in the regression analysis?

A) 23%

B) 26%

C) 30%

D) 33%

答案：A

解析：The autocorrelation for a one-period lag is 23% for the same sample. The sum of the mean reversion rate (77% given the beta coefficient of -0.77) and the one-period autocorrelation rate will always equal 100%.

Suppose mean reversion exists for a variable with a value of 30 at time period t–Assume that the long-run mean value for this variable is 40 and ignore the stochastic term included in most regressions of financial data. What is the expected change in value of the variable for the next period if the mean reversion rate is 0.4.

A) -10

B) -4

C) 4

D) 10

答案：C

解析：The mean reversion rate, α, indicates the speed of the change or reversion back to the mean. If the mean reversion rate is 0.4 and the difference between the last variable and long-run mean is 10 (= 40 – 30), the expected change for the next period is 4 (i.e., 0.4*10 = 4)

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