FRM Part I · FRM Exam Part I · Measures of Financial Risk
A portfolio's one-period loss is normally distributed with mean 0 and standard deviation 10 (in USD million). Using the normal distribution, the 99% VaR is 23.26 and the density at the 99% quantile gives z = 2.326 with phi(2.326) = 0.0267. What is the 99% expected shortfall (ES) in USD million, to the nearest 0.01?
The 99% expected shortfall is 26.70 million. For a normal loss with zero mean, ES equals sigma times the density at the quantile divided by one minus the confidence level: 10 times 0.0267 divided by 0.01.
- A26.70
- B23.26
- C29.23Correct
- D2.67
Explanation
For a normal loss, ES = sigma * phi(z)/(1-alpha) = 10 * 0.0267/0.01 = 26.7. Check: 0.0267/0.01 = 2.67, times 10 = 26.70. So the correct value is 26.70, which is option 0, not the others.
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