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

A risk manager builds a QQ plot of a loss sample against a normal distribution and sees the points forming an S-shaped curve that is flatter than the reference line at both ends, so the sample extremes are less extreme than the normal's. Which implication is most consistent with this pattern if the manager uses a normal-based VaR at the 99% confidence level?

Normal VaR is likely to overstate tail risk. The QQ plot shows the sample has thinner tails than the normal, so the true 99% loss quantile is smaller than the normal model implies, and a normal-based VaR would be too conservative at that level.

  1. ANormal VaR is likely to overstate the tail riskCorrect
  2. BNormal VaR is likely to understate the tail risk
  3. CNormal VaR is unbiased because the centre fits well
  4. DNormal VaR is invalid at 95% but fine at 99%

Explanation

Flatter ends mean thinner tails than the normal, so the actual 99% quantile is closer to the centre than the normal one. The normal-based VaR therefore overstates the loss. Good centre fit does not ensure a correct tail estimate.

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