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FRM Part II · FRM Exam Part II · Parametric Approaches (II): Extreme Value

An analyst plots the sample mean excess function of portfolio losses against the threshold. Above a loss of 3% the plot is approximately linear with a clearly positive, upward slope. What is the most appropriate conclusion for a POT analysis?

A GPD with a positive shape parameter is plausible. The GPD mean excess function is linear in the threshold with slope ξ/(1−ξ), so an upward linear slope indicates ξ above zero, a heavy tail, and supports using the GPD above that threshold.

  1. AA GPD with a positive shape parameter (heavy tail) is plausible above that thresholdCorrect
  2. BA GPD with a negative shape parameter (bounded tail) is plausible above that threshold
  3. CThe exceedances are exponentially distributed, which implies ξ = 0
  4. DThe linear pattern shows the losses are normally distributed

Explanation

For a GPD the mean excess function is linear in the threshold with slope ξ/(1 − ξ). A positive slope therefore indicates ξ > 0, a heavy tail, and linearity supports the GPD fit above that threshold. A flat plot would indicate ξ = 0, and a downward slope would indicate ξ < 0 with a bounded tail. The mean excess of a normal distribution declines with the threshold, so a rising linear plot does not support normality.

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