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

An analyst plots the ordered sample of 200 returns against a reference distribution. The sample mean is 0% and standard deviation is 2%. A QQ plot against a standard normal shows a straight line through the origin with slope 2%, except that the lowest five points lie well below the line while the highest points lie on it. A normal 99% VaR using the sample sigma is 2.326 × 2% = 4.65%. Which interpretation is best?

Returns are roughly normal in the body but have a fatter left tail, so the normal 99% VaR of 4.65% may understate potential losses. The slope matches the 2% volatility, the right tail fits, and only the lowest points fall below the line.

  1. AReturns are roughly normal but with a fatter left tail, so the 99% VaR of 4.65% may be too low for lossesCorrect
  2. BReturns are symmetric and fat tailed, so VaR should be raised for both gains and losses
  3. CReturns have lighter left tail, so 4.65% is too high
  4. DThe slope shows the data are not normal at all, so VaR cannot be computed

Explanation

The slope of 2% matches the sample sigma, so the body is normal. Only the lower tail departs below the line, which indicates a heavier left tail (negative skew in the tail). Losses at extreme quantiles exceed the normal prediction, so 4.65% likely understates loss VaR. The right tail fits, so symmetry is not indicated.

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