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FRM Part I · FRM Exam Part I · Measures of Financial Risk

A bank computes 99% VaR from 1,000 historical daily losses. The tail losses beyond VaR are the 10 largest observations, with the sum of those 10 losses equal to USD 31.0 million. Which statement about the 99% expected shortfall estimate is correct?

The 99% expected shortfall is USD 3.10 million. One percent of 1,000 observations is 10 tail losses, and ES is their average, so USD 31.0 million divided by 10. The sum is not ES, and ES normally exceeds VaR.

  1. AES is USD 3.10 million, the average of the 10 tail lossesCorrect
  2. BES is USD 31.0 million, the sum of the tail losses
  3. CES is USD 0.31 million, the sum divided by 100
  4. DES equals VaR because both use the same tail

Explanation

1% of 1,000 is 10 observations. ES is the average loss in the tail, 31.0/10 = USD 3.10 million. Summing overstates it, and ES is generally larger than VaR, not equal.

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