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

A bank's 99% one-day VaR backtest over 500 days shows 5 exceptions, exactly the expected number. However, 4 of the 5 exceptions occurred in a single week. Which statement best describes what the standard unconditional coverage (Kupiec) test concludes and why this matters?

The unconditional coverage test sees 5 exceptions against 5 expected and passes the model. Because it uses only the total count and ignores timing, it cannot detect clustering, so an independence or conditional coverage test is needed.

  1. AIt would reject the model because clustering raises the exception count above 5
  2. BIt would be unable to detect the clustering because it only uses the total number of exceptions, so a conditional or independence test is neededCorrect
  3. CIt would detect the clustering because it tests the time spacing of exceptions
  4. DIt would reject the model because 4 of 5 exceptions is more than 1% of the days

Explanation

Expected exceptions are 1% x 500 = 5, matching the observed 5, so the unconditional coverage statistic is essentially zero and the model passes. The test uses only the count, not timing, so clustering (a violation of independence) goes unnoticed. Independence or conditional coverage tests are required to catch this.

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