FRM Part I · FRM Exam Part I · Common Univariate Random Variables
A risk analyst models a portfolio's loss as uniform on [0, 200] (USD millions). What is the 95% VaR and the 95% expected shortfall (the average loss given the loss exceeds VaR)?
VaR is 190 and expected shortfall is 195. The 95th percentile of a uniform on [0, 200] is 0.95 x 200 = 190, and the tail beyond it is uniform on [190, 200], whose mean is the midpoint 195.
- AVaR 190; ES 195Correct
- BVaR 190; ES 200
- CVaR 195; ES 197.5
- DVaR 180; ES 190
Explanation
The 95th percentile is 0.95 x 200 = 190. Losses beyond VaR are uniform on [190, 200], so their conditional mean is the midpoint, 195. Option VaR 195 wrongly uses 200 minus 5 rather than 5% of the range.
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