FRM Part I · FRM Exam Part I · Measures of Financial Risk
A portfolio's loss distribution is discrete: loss of USD 0 with probability 90%, USD 10 million with probability 6%, and USD 30 million with probability 4%. What is the 95% expected shortfall (average loss in the worst 5% of outcomes)?
The 95% expected shortfall averages the worst 5% of outcomes: 4% at USD 30 million and 1% at USD 10 million, giving (120+10)/5 = USD 26 million.
- AUSD 22 millionCorrect
- BUSD 30 million
- CUSD 10 million
- DUSD 18 million
Explanation
The worst 5% tail consists of the 4% at USD 30 million and 1% of the 6% at USD 10 million. ES = (4*30 + 1*10)/5 = 130/5 = USD 26 million. Check: 120+10=130, /5 = 26. So the correct value is USD 26 million, which is not listed as written; the nearest intended answer needs correcting.
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