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

A bank backtests a 99% daily VaR over 250 days with 2.5 expected exceedances. It observes 3 exceedances, but all 3 occurred in consecutive days during one week of market stress. Which statement best describes the weakness of a simple unconditional coverage test here?

An unconditional coverage test looks only at the total number of exceedances, so three clustered breaches against 2.5 expected still pass. It cannot detect that breaches are dependent, which indicates the model adapts slowly to volatility. An independence or conditional coverage test is needed to catch this.

  1. AIt will reject the model because 3 is above 2.5
  2. BIt focuses only on the total count, so it cannot detect that the exceedances are clustered, which signals the model reacts slowly to changing volatilityCorrect
  3. CIt automatically tests independence, so clustering would be detected
  4. DIt would fail to count exceedances that occur in consecutive days

Explanation

Unconditional coverage tests only compare the number of exceedances with the expected number. 3 versus 2.5 is well within acceptable range, so the test passes, yet clustering suggests the VaR does not adapt to volatility. Detecting this requires an independence test.

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