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FRM Part I · FRM Exam Part I · Hypothesis Testing

Using the setting of a 99% VaR backtest over 250 days (expected exceptions 2.5, standard deviation 1.57 under the null), a risk manager observes 6 exceptions and applies a normal approximation with a one-sided test at 5% significance (critical z = 1.645). What is the conclusion?

Reject the model. The z-statistic is (6 minus 2.5) divided by 1.57, about 2.23, which exceeds the one-sided 5% critical value of 1.645. Too many exceptions indicate the 99% VaR model likely understates risk.

  1. AReject the model since z is about 2.23, above 1.645Correct
  2. BFail to reject since z is about 1.43, below 1.645
  3. CFail to reject since z is about 3.50, indicating no evidence
  4. DReject the model since z is about 1.43, above the critical value

Explanation

z = (6 - 2.5)/1.57 = 3.5/1.57 ≈ 2.23. This exceeds 1.645, so the null of a correctly calibrated model is rejected, suggesting VaR understates risk. 1.43 would come from dividing by 2.45 (wrong spread).

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