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FRM Part I · FRM Exam Part I · Common Univariate Random Variables

A risk manager replaces a normal model with a fat-tailed model having the same mean and variance. Which outcome is most likely at very high confidence levels such as 99.9%?

At very high confidence levels the fat-tailed model usually gives a larger VaR than the normal model. Although the variances match, the heavier tails put more probability beyond extreme thresholds, pushing the extreme quantile outward. Equal variance does not mean equal tail quantiles.

  1. AThe fat-tailed VaR is typically larger than the normal VaRCorrect
  2. BThe fat-tailed VaR is typically smaller than the normal VaR
  3. CBoth models give identical VaR because the variances match
  4. DVaR becomes undefined for fat-tailed models

Explanation

With matched variance, fat-tailed distributions place more mass far in the tails, so quantiles at extreme confidence levels lie further out than the normal's. At moderate levels such as 95% the fat-tailed VaR can be smaller because of the more peaked center. Matching variance does not equalize quantiles.

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