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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 model is backtested over 250 days. The expected number of exceedances is 2.5. A validator notes that the test has low power at this confidence level and sample size. What is the most accurate implication?

Low power means the backtest often fails to reject a misspecified model. With only about 2.5 expected exceedances in 250 days, sampling noise is large, so a model with true coverage worse than 99% can still pass, producing Type II errors.

  1. AThe test will rarely reject a model whose true coverage is somewhat worse than 99%, so an incorrect model may be acceptedCorrect
  2. BThe test will frequently reject correct models, causing excessive Type I errors by design
  3. CThe test is unbiased and so power is irrelevant to model validation
  4. DThe test cannot detect any model that has fewer than 2.5 exceedances

Explanation

With so few expected exceedances, sampling noise is large relative to the signal. A model with a true exceedance probability of, say, 2% may still produce counts within the acceptance region. Low power means Type II errors, i.e. accepting bad models, are common.

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