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FRM Part II · FRM Exam Part II · Beyond Exceedance-Based Backtesting of Value-at-Risk Models

A bank's VaR model tends to misstate the extreme tail of losses while fitting the central part of the distribution well. The validation team wants a goodness-of-fit test that is more powerful than Kolmogorov-Smirnov for detecting this kind of deviation. Which test is most appropriate, and why?

The Anderson-Darling test is most appropriate because it weights deviations in the tails more heavily than the Kolmogorov-Smirnov test does. That makes it more powerful when a VaR model fits the center well but misrepresents extreme losses.

  1. AAnderson-Darling, because it places more weight on discrepancies in the tailsCorrect
  2. BAnderson-Darling, because it ignores the tails and focuses on the median
  3. CKolmogorov-Smirnov with a larger sample, because it is already tail-weighted
  4. DKupiec proportion-of-failures test, because it examines the whole distribution

Explanation

Anderson-Darling applies a weighting function that magnifies differences in the tails of the distribution, giving more power against tail misspecification. KS weights all points equally and is most sensitive near the center. Kupiec only tests the frequency of exceptions at one level.

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