FRM Part I · FRM Exam Part I · Measures of Financial Risk
A portfolio's one-day losses have 50 equally likely scenarios. The four worst losses (USD thousands) are 120, 100, 80 and 60, and the fifth worst is 40. What is the one-day 92% expected shortfall, using the average of the worst 8% of scenarios?
The ES is USD 90 thousand. The worst 8% of 50 scenarios is four outcomes, and their losses of 120, 100, 80 and 60 average 90 thousand.
- AUSD 40 thousand
- BUSD 90 thousandCorrect
- CUSD 100 thousand
- DUSD 72 thousand
Explanation
8% of 50 scenarios is 4 scenarios, which are the four worst losses. ES = (120 + 100 + 80 + 60) / 4 = 360 / 4 = 90. Using 100 would average only the top two losses, and including the 40 would give 80 for five scenarios, which is the wrong tail size.
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