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

An analyst builds a QQ plot of 200 daily returns against a normal distribution fitted by sample mean and standard deviation. The plot is a straight line except that the lowest point is far below the line, while the highest points follow it closely. Fitting the normal with the sample standard deviation, which statement is most accurate?

The sample appears to have a heavy left tail, and the single extreme loss may inflate the fitted standard deviation. Only the lowest point departs from the line, which indicates asymmetric tail behavior, and a lone outlier can distort the parameters used to build the reference line.

  1. AThe distribution is symmetric with heavy tails on both sides
  2. BThe sample appears to have a heavy left tail, and a single extreme loss may also have inflated the fitted standard deviationCorrect
  3. CThe sample has a thin left tail and a heavy right tail
  4. DThe sample is exactly normal because most points lie on the line

Explanation

Only the left end deviates downward, so the loss tail is heavier than normal, an asymmetric feature rather than symmetric heavy tails. One outlier can also inflate the sample standard deviation, affecting the fitted reference line. Most points on the line do not prove normality when tail behavior, which matters for VaR, deviates.

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