FRM Part I · FRM Exam Part I · Measures of Financial Risk
A bank estimates ES at the 97.5% level using 1,000 equally weighted historical simulation losses. The ten largest losses (USD million) are 9, 8, 7, 6, 5.5, 5, 4.5, 4, 3.5, 3, and the 11th to 25th largest losses average USD 2.2 million. The 26th largest loss is USD 2.0 million. What is the 97.5% ES?
The 97.5% ES is the average of the 25 worst losses. The top ten sum to 55.5 million and the next fifteen sum to 33 million, giving 88.5 million, divided by 25 equals USD 3.54 million.
- AUSD 3.64 millionCorrect
- BUSD 5.55 million
- CUSD 2.00 million
- DUSD 4.10 million
Explanation
The tail holds 2.5% of 1,000 = 25 losses. Sum of top ten = 9+8+7+6+5.5+5+4.5+4+3.5+3 = 55.5. Losses 11-25 are 15 observations averaging 2.2, totalling 33. Total = 88.5; divided by 25 = 3.54. Recheck: 88.5/25 = 3.54, so the correct figure is USD 3.54 million, which is not among the options.
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