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

A risk analyst plots the ordered daily returns of a portfolio against the corresponding quantiles of a standard normal distribution. The points lie close to a straight line in the centre of the plot but curve sharply away from the line at both ends, with the lowest points far below the line and the highest points far above it. What is the most appropriate conclusion?

The data have heavier tails than the normal distribution. Sample extreme quantiles lie beyond those implied by the normal at both ends, bending the QQ plot away from the line. Differences in mean or variance would only change the intercept or slope of a straight line.

  1. AThe data have heavier tails than the normal distributionCorrect
  2. BThe data have lighter tails than the normal distribution
  3. CThe data are normal but have a different mean
  4. DThe data are normal but have a larger variance

Explanation

In a QQ plot, points that fall below the line at the lower end and above it at the upper end show that sample extremes are more extreme than the normal's quantiles, which means fat tails. A different mean or variance only shifts or rotates the line (intercept or slope) and does not curve the ends.

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