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

A bank's 99% one-day VaR backtest over 500 days produces 10 exceptions. Using the Kupiec proportion-of-failures test with a 5% significance level (critical value 3.84), the log-likelihood ratio is computed as 3.9. Which conclusion is correct?

Reject the model. The Kupiec likelihood ratio of 3.9 exceeds the 5% chi-square critical value of 3.84 with one degree of freedom, so the observed exception rate is statistically inconsistent with the 1% expected rate. Clustering is not assessed by this test.

  1. AReject the model because 3.9 exceeds 3.84Correct
  2. BAccept the model because 10 exceptions is above the expected 5
  3. CAccept the model because the LR statistic is below 5
  4. DReject the model because exceptions are clustered

Explanation

The Kupiec LR is compared with a chi-square with one degree of freedom; 3.9 > 3.84, so the null of a 1% exception rate is rejected. The test says nothing about clustering, which needs an independence test.

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