FRM Part I · FRM Exam Part I · Calculating and Applying VaR
A portfolio's one-day loss distribution is approximated by 100 equally likely historical scenarios. The five largest losses, in USD millions, are 12, 9, 8, 7 and 6; all other losses are below 6. What is the one-day 95% expected shortfall estimated from this sample?
The 95% expected shortfall is 8.4 million. With 100 equally likely scenarios, the worst five losses form the tail, and their average is (12+9+8+7+6)/5 = 8.4. The figure of 6 million would be a VaR-type threshold, which ignores how severe the losses beyond it are.
- A6.0 million
- B8.4 millionCorrect
- C7.0 million
- D9.0 million
Explanation
At 95% with 100 equally likely scenarios, the tail contains the worst 5 outcomes. ES is their average: (12+9+8+7+6)/5 = 42/5 = 8.4 million. Choosing 6.0 gives the VaR estimate (the boundary loss), not ES.
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