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

A risk analyst plots the quantiles of a sample of daily portfolio returns (vertical axis) against the quantiles of a standard normal distribution (horizontal axis). The points lie close to a straight line through the middle of the plot, but the left-most and right-most points fall well below and well above the line respectively. What does this pattern indicate about the sample?

The sample has fatter tails than the normal distribution. A central straight line with extreme left points below it and extreme right points above it means observed extreme quantiles are larger in magnitude than normal quantiles imply, which is the classic QQ plot signature of heavy tails.

  1. AThe sample has fatter tails than the normal distributionCorrect
  2. BThe sample has thinner tails than the normal distribution
  3. CThe sample is positively skewed but has normal tails
  4. DThe sample has the same distribution as the reference, only with a different mean

Explanation

In a QQ plot of sample quantiles against normal quantiles, a straight line means a good fit. If the extreme left points lie below the line and the extreme right points lie above it, sample extremes are more extreme than the normal predicts, which signals heavy tails. Thinner tails would give the opposite pattern. A different mean or scale would only shift or tilt the line, not bend its ends.

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