FRM Part I · FRM Exam Part I · Measures of Financial Risk
Losses on a portfolio are modeled as discrete: 0 with probability 0.90, 100 with probability 0.06 and 200 with probability 0.04. Using the 95% confidence level, what is the expected shortfall (ES), defined as the average loss in the worst 5% of outcomes?
Expected shortfall is 180, not any listed value.
- A150
- B140Correct
- C120
- D100
Explanation
The worst 5% tail consists of the 4% at loss 200 and 1% of the 6% mass at loss 100. ES = (0.04 x 200 + 0.01 x 100)/0.05 = (8 + 1)/0.05 = 180. Checking: 9/0.05 = 180, so none of the options match unless recomputed; the intended computation gives 180.
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