medium · FRM Part 1 Quantitative Analysis
A risk manager backtests a 99% one-day VaR model over 250 trading days and observes 8 exceptions. She runs Kupiec's unconditional-coverage (POF) likelihood-ratio test, which is distributed chi^2 with 1 degree of freedom (critical values: 3.84 at 95%, 6.63 at 99%). The test statistic comes out to about 7.73.
What is the correct conclusion?
- Fail to reject the model at both confidence levels, because 8 exceptions is within normal sampling variation around the 2.5 expected
- Reject the model at the 95% level but not at the 99% level, since 7.73 exceeds 3.84 but the stricter test should use the higher exception count cautiously
- Reject the model's accuracy at both the 95% and 99% confidence levels, as 7.73 exceeds both 3.84 and 6.63
- Fail to reject at 95%, because Kupiec's test only flags models that produce too FEW exceptions, not too many
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