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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 is accurate in the center of the P&L distribution but understates the likelihood of extreme losses. The validation team wants a distribution test that is more powerful than the Kolmogorov-Smirnov test at detecting this flaw. Which is the most appropriate choice?

The Anderson-Darling test is most appropriate because it places greater weight on differences between the empirical and theoretical CDFs in the tails. KS is most sensitive near the middle of the distribution, and exceedance-count tests like Kupiec examine only a single quantile.

  1. AAnderson-Darling test, because it weights discrepancies in the tails more heavilyCorrect
  2. BA second KS test using a smaller sample, because less data increases tail sensitivity
  3. CThe Basel traffic light approach, because it measures magnitude of exceedances
  4. DThe Kupiec proportion-of-failures test, because it tests the full distribution

Explanation

Anderson-Darling uses a weighting that emphasizes the tails, so it detects tail misspecification better than KS, which is most sensitive in the center. Kupiec and the traffic light approach rely only on exceedance counts at one confidence level.

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