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FRM Part I · FRM Exam Part I · Hypothesis Testing

A bank's 99% one-day VaR model is backtested over 1,000 days, yielding 16 exceptions. Using the normal approximation to the binomial with p = 0.01, the analyst tests H0: p = 0.01 at the 1% significance level, two-sided (critical value 2.576). Which statement is correct?

Do not reject the model. Expected exceptions are 10 and the standard deviation is about 3.15, so z is roughly 1.9, below the 2.576 two-sided critical value at 1% significance. The 16 observed exceptions do not provide sufficient evidence that the model is inadequate.

  1. Az is about 1.90, so do not reject; the model is not shown to be inadequateCorrect
  2. Bz is about 6.00, so reject
  3. Cz is about 1.90, so reject because it exceeds 1.645
  4. Dz is about 1.60, so reject the model at 1% significance

Explanation

Expected exceptions = 1,000 x 0.01 = 10. Standard deviation = sqrt(1,000 x 0.01 x 0.99) = sqrt(9.9) = 3.146. z = (16 - 10)/3.146 = 1.91, about 1.90, below 2.576, so do not reject. Comparing with 1.645 uses the wrong critical value for a two-sided 1% test; z of 6 results from omitting the division by the standard deviation.

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