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FRM Part II · FRM Exam Part II · Backtesting VaR

A bank's 99% one-day VaR model is backtested over 250 days. Using the Kupiec test's non-rejection region at the 95% confidence level, which approach correctly identifies the range of exceptions for which the model is not rejected, and what is the main concern with the test at this confidence level?

The non-rejection region has both lower and upper bounds, so the test is two-sided and can reject overly conservative models as well as lax ones. At 99% with 250 days the expected exceptions are only 2.5, so power in the lower tail is weak.

  1. AThe region is symmetric around 2.5 exceptions, and the concern is only Type I error
  2. BThe region has both a lower and an upper bound, and the test can reject a model that is too conservative as well as one too lax, but has low power to detect too-low rates at 99%Correct
  3. CThe region has only an upper bound, because too few exceptions can never indicate a problem
  4. DThe region is fixed at 0 to 4 exceptions regardless of sample size

Explanation

The Kupiec test is two-sided: too many exceptions signal understated risk and too few signal overstated, inefficient capital. At 99% with 250 observations the expected count is only 2.5, so the lower tail is hard to distinguish from zero and power to detect overly conservative models is poor. The region depends on sample size and confidence level, so a fixed range is wrong.

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