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

A risk manager is comparing Value at Risk (VaR) and Expected Shortfall (ES) at the 97.5% confidence level for a portfolio. Which statement about ES is correct?

Expected Shortfall is the average loss conditional on the loss exceeding the VaR at the same confidence level. It therefore captures the tail beyond the VaR threshold and is at least as large as VaR, unlike VaR, which only gives the threshold itself.

  1. AES is the average loss conditional on the loss exceeding the VaR at the same confidence levelCorrect
  2. BES is the loss level that is exceeded with probability 2.5% and no more information about the tail
  3. CES is always smaller than VaR at the same confidence level
  4. DES ignores the shape of the tail beyond the VaR threshold

Explanation

ES is the expected loss given that the loss is at least as large as VaR at the chosen confidence level. Because it averages losses in the tail, it is never smaller than VaR. The second option describes VaR itself, not ES.

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