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FRM Part I · FRM Exam Part I · Calculating and Applying VaR

Which statement best explains why expected shortfall is generally preferred to VaR as a measure of tail risk?

Expected shortfall is preferred because it measures the average size of losses beyond the VaR threshold and is subadditive, making it coherent. VaR only gives a cutoff and ignores how bad losses beyond it can be. ES is never smaller than VaR at the same confidence level.

  1. AES ignores losses beyond the confidence level, making it more stable
  2. BES is always smaller than VaR at the same confidence level
  3. CES is the loss threshold that is exceeded with probability one minus the confidence level
  4. DES accounts for the size of losses beyond the VaR threshold and is subadditiveCorrect

Explanation

ES averages losses in the tail beyond VaR, so it reflects the severity of extreme losses, and it is subadditive and therefore coherent. VaR ignores the magnitude of losses past the threshold. ES is at least as large as VaR, not smaller, and the threshold definition describes VaR.

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