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

A risk manager notes that a model passes a Kupiec test on 99% VaR exceedances but its PIT histogram is clearly non-uniform in the middle of the distribution. What does this most directly illustrate about PIT-based backtesting?

PIT-based backtesting evaluates the entire forecast distribution, so it can reveal misspecification elsewhere in the distribution even when the model has the correct frequency of 99% VaR exceedances. An exceedance test examines only one quantile and may therefore miss such errors.

  1. APIT tests are less informative than exceedance counts because they ignore the tail
  2. BPIT-based tests assess the whole forecast distribution and can detect misspecification that an exceedance test at one quantile missesCorrect
  3. CThe Kupiec test is invalid whenever the PIT histogram is non-uniform
  4. DPIT tests can only be applied to models with normally distributed returns

Explanation

Exceedance tests use only a single quantile, so a model can match the 1% tail frequency while misforecasting the rest of the distribution. PIT tests use the entire forecast distribution and reveal such errors. They are not limited to normal models, and the Kupiec test remains valid for what it tests.

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