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

An analyst compares the quantiles of a sample of loss data with those of a reference distribution in a QQ plot. The plotted points form an almost perfectly straight line with a slope of 2.0 and an intercept of 0.5 (sample quantile on the vertical axis). Which conclusion is most appropriate?

The sample is consistent with the reference distribution family up to a location and scale change. A straight QQ line means the shapes match; the slope of 2.0 shows scale about twice as large and the intercept of 0.5 shows a location shift.

  1. AThe sample is not from the reference family because the line does not have a slope of one
  2. BThe sample is consistent with the reference family up to a location and scale change, with a scale about twice and a location shift of about 0.5Correct
  3. CThe sample has tails twice as heavy as the reference distribution
  4. DThe sample has a mean of 2.0 and a standard deviation of 0.5 relative to the reference

Explanation

A linear QQ plot implies the sample is drawn from the same family as the reference, differing only by a linear transformation: sample = 0.5 + 2.0 × reference. Slope reflects relative scale and intercept reflects location. A slope different from one does not indicate a different shape. Heavy tails would appear as curvature, not a straight line.

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