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

A risk manager is deciding whether to model the tail of a P&L series with a normal distribution or a Student t distribution. She produces two QQ plots of the same data, one against a normal and one against a t with 5 degrees of freedom. The normal QQ plot curves sharply away from the line in both tails, while the t QQ plot is close to linear throughout. What is the most reasonable implication for VaR estimation at the 99.9% confidence level?

Normal VaR would likely understate the loss at the 99.9% level, so the t distribution is the better choice. The t fits the tails in the QQ plot, and heavy-tailed distributions have larger extreme quantiles than a normal with the same variance.

  1. ANormal VaR would likely understate the loss at that level, so the t distribution is the better parametric choiceCorrect
  2. BNormal VaR would likely overstate the loss at that level, so the normal is conservative
  3. CBoth distributions give the same VaR because they share the same mean and variance
  4. DThe QQ plots are irrelevant to VaR because only the center of the distribution matters at high confidence

Explanation

The normal QQ plot departing in the tails shows heavy tails that the normal does not capture, while the t fits well. At very high confidence levels, the t quantile exceeds the normal quantile for the same variance, so normal VaR understates risk. Equal variance does not imply equal extreme quantiles.

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