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

A validator applies the Kolmogorov-Smirnov (KS) test to 250 PIT values from a bank's VaR model. Which statement best describes the KS test statistic?

The KS statistic is the maximum absolute vertical distance between the empirical CDF of the PIT values and the theoretical uniform CDF. It focuses on the single largest deviation, so it is most sensitive near the center of the distribution rather than the tails.

  1. AThe sum of squared differences between observed and expected exceedance counts
  2. BThe maximum absolute vertical distance between the empirical CDF of the PIT values and the uniform CDFCorrect
  3. CThe likelihood ratio between a model with autocorrelation and one without
  4. DThe weighted average squared difference between the empirical and theoretical CDFs, with extra weight on the tails

Explanation

The KS statistic is the largest absolute gap between the empirical and hypothesized CDFs. The tail-weighted squared-distance measure describes Anderson-Darling (or Cramér-von Mises without tail weights). The likelihood ratio describes Berkowitz-type tests.

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