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FRM Part II · FRM Exam Part II · Estimating Market Risk Measures: An Introduction and Overview

A risk manager reports normal VaR for a portfolio with significantly fat-tailed returns. Compared with the true loss at the 99% confidence level, what is the most likely consequence of relying on the normal assumption, and what does it imply for the expected shortfall estimate?

Normal VaR assumes thin tails, so for fat-tailed returns it tends to understate losses at high confidence levels such as 99%, and the shortfall is even larger for expected shortfall because ES depends on the entire tail beyond VaR.

  1. AVaR at 99% and especially expected shortfall may be understated because the normal has thinner tailsCorrect
  2. BVaR at 99% is overstated because fat tails raise the mean
  3. CExpected shortfall equals VaR under the normal, so no error arises
  4. DVaR is unaffected because VaR depends only on the mean

Explanation

Fat-tailed distributions place more probability far out in the tail, so the normal tends to understate extreme losses at high confidence, and the understatement is larger for expected shortfall, which depends on the tail shape. Fat tails do not raise the mean. ES exceeds VaR under the normal. VaR depends on both mean and volatility.

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