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FRM Part II · FRM Exam Part II · Validating Bank Holding Companies' Value-at-Risk Models for Market Risk

A risk analyst applies Kupiec's proportion-of-failures (unconditional coverage) test to a 99% one-day VaR model. Which statement correctly describes the test?

Kupiec's test is a likelihood-ratio test of whether the observed exception frequency equals the model's expected rate, here 1%. Under the null it follows a chi-square distribution with one degree of freedom. It tests frequency only, not clustering, and can reject for too many or too few exceptions.

  1. AIt is a likelihood-ratio test comparing the observed exception rate with 1%, with a chi-square distribution with 1 degree of freedom under the nullCorrect
  2. BIt tests whether exceptions cluster over time, using a chi-square with 2 degrees of freedom
  3. CIt measures the average size of losses beyond VaR and compares it with expected shortfall
  4. DIt rejects the model only if too few exceptions occur

Explanation

Kupiec's POF test is a likelihood ratio comparing the observed failure rate to the expected rate (1% here), distributed chi-square with 1 degree of freedom under the null. It checks frequency only, not clustering, so B is wrong. It can reject for too many or too few exceptions, so D is wrong.

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