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FRM Part II · FRM Exam Part II · Backtesting VaR

A bank's 99% VaR model produces exactly 2.5 exceptions per 250 days on average, matching expectations, so it passes the unconditional coverage test. However, nearly all exceptions occur in consecutive days during stressed periods. A risk committee asks which conclusion is most appropriate under Christoffersen's framework and what it implies.

The model likely fails the independence test and so fails conditional coverage, even though its exception count is right. Exceptions bunched in consecutive days show that VaR is not adapting quickly to rising volatility, so the frequency test alone gives false comfort.

  1. AThe model passes conditional coverage because the frequency is correct, so no action is needed
  2. BThe model likely fails the independence component and therefore conditional coverage, suggesting VaR does not react quickly enough to changing volatilityCorrect
  3. CThe model fails only the unconditional test because exceptions are clustered
  4. DThe model should be accepted because clustering lowers expected shortfall

Explanation

Correct frequency satisfies unconditional coverage, but consecutive exceptions violate independence, so LR_ind and hence LR_cc will be large. Clustering typically indicates slow-adapting volatility estimates. Passing the frequency test does not imply passing conditional coverage.

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