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FRM Part I · FRM Exam Part I · Measuring Return, Volatility, and Correlation

Why do risk managers often find that a normal model understates 99.9% VaR for daily equity returns?

Daily equity returns show excess kurtosis, meaning fatter tails than the normal distribution. At extreme confidence levels such as 99.9%, actual loss quantiles lie further out than a normal model with the same variance suggests, so normal-based VaR is too low.

  1. ADaily returns have excess kurtosis, so extreme losses occur more frequently than the normal distribution predictsCorrect
  2. BDaily returns have negative kurtosis, so the normal overstates volatility
  3. CDaily returns are always perfectly symmetric, which makes the normal inaccurate
  4. DDaily returns have a lower variance than the normal distribution allows

Explanation

Empirical daily returns are leptokurtic, with fat tails. At extreme quantiles such as 99.9%, the true loss quantile lies further out than the normal quantile with the same variance. Hence the normal model understates VaR at those levels.

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