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

A risk team wants to assess a 99% VaR model using only 250 daily observations. The expected number of exceedances is 2.5. Which is the main statistical limitation of exceedance-based backtesting at this confidence level and sample size?

With only about 2.5 expected exceedances in 250 days at 99%, the test has low statistical power. A misspecified model can easily show an acceptable count, and a good model can breach by chance, so exceedance counts give weak evidence about model quality.

  1. AExceedances are too frequent to be informative
  2. BThe test has low power: with so few expected exceedances, an inaccurate model can easily pass and a sound one can fail by chanceCorrect
  3. CThe test overstates the number of expected exceedances because of fat tails
  4. DThe test cannot be applied unless returns are normal

Explanation

At 99% over 250 days only about 2.5 exceedances are expected, so one or two extra or fewer observations change the conclusion. This gives low power to distinguish good from bad models. Exceedances are rare, not frequent, and the binomial test does not need normal returns.

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