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

A bank backtests a 99% VaR model over 250 days with 6 exceptions. Using the approximation that the number of exceptions is normal with mean Np and standard deviation sqrt(Np(1-p)), what is the z-score of the observed exceptions (rounded to two decimals)?

The z-score is about 2.22. Expected exceptions are 2.5, the standard deviation is the square root of 2.475, or roughly 1.573, and (6 minus 2.5) divided by 1.573 gives 2.22, which is beyond the 1.96 two-sided 5% critical value.

  1. A1.00
  2. B2.22Correct
  3. C2.15
  4. D1.40

Explanation

Mean = 250 x 0.01 = 2.5. Standard deviation = sqrt(250 x 0.01 x 0.99) = sqrt(2.475) = 1.573. z = (6 - 2.5)/1.573 = 2.22. The 1.40 distractor wrongly uses the standard deviation sqrt(Np)=1.58 only partially, and 2.15 results from errors in the variance term; the 1.00 option is not supported by the data.

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