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FRM Part II · FRM Exam Part II · Validating Bank Holding Companies' Value-at-Risk Models for Market Risk

Why do backtesting tests of 99% VaR models generally have low power, according to the validation literature?

Because a 99% VaR model produces only a few exceptions in a typical sample, such as about 2.5 in 250 days, a moderately wrong model can generate counts that look acceptable. This gives backtests low power and a high risk of failing to reject inaccurate models.

  1. AExceptions are too frequent at 99%, so the sample is dominated by noise
  2. BWith few expected exceptions, a moderately misspecified model often produces counts indistinguishable from a correct one over a typical sampleCorrect
  3. CStatistical tests cannot be applied to profit and loss data
  4. DThe chi-square distribution is not valid for likelihood ratios

Explanation

At 99% and 250 days only about 2.5 exceptions are expected, so a model whose true exception rate is, say, 2% can easily generate counts that look acceptable. This yields a high chance of Type II errors. Option A reverses the issue: exceptions are rare, not frequent.

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