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

A risk manager fits a GEV to monthly block maxima of losses (block size n = 21 trading days). Which choice describes the main trade-off in choosing block size?

Larger blocks make the GEV approximation more accurate, lowering bias, but they leave fewer block maxima, which raises the variance of the parameter estimates. Smaller blocks give more data points but a poorer asymptotic fit. Block size therefore involves a bias-variance trade-off.

  1. ALarger blocks reduce bias from the asymptotic approximation but leave fewer maxima, raising parameter estimate varianceCorrect
  2. BLarger blocks increase both bias and the number of observations, so the trade-off is unambiguous
  3. CSmaller blocks always improve accuracy because they yield more data points
  4. DBlock size has no effect on the GEV fit because the distribution is stable under maxima

Explanation

Extreme value theory holds asymptotically, so larger blocks make the GEV approximation better (lower bias). But for a fixed sample, larger blocks mean fewer block maxima, so estimates have higher variance. Small blocks give more data but the maxima may not be well approximated by the GEV.

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