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FRM Part I · FRM Exam Part I · External and Internal Credit Ratings

A bank's rating grade B was assigned a one-year PD of 4.0%. During the year 500 obligors in grade B were observed and 30 defaulted. Assuming independent defaults and using the normal approximation to the binomial, what is the z-statistic for testing whether the true PD equals 4.0%?

The z-statistic is about 2.27. The observed default rate is 6% versus the predicted 4%, and the standard error under the null is the square root of 0.04 times 0.96 divided by 500, about 0.88%. The 2-point gap divided by that is roughly 2.27.

  1. AApproximately 2.27Correct
  2. BApproximately 1.43
  3. CApproximately 3.21
  4. DApproximately 0.64

Explanation

Observed rate = 30/500 = 6.0%. Standard error = sqrt(0.04×0.96/500) = sqrt(0.0000768) = 0.008764. z = (0.06−0.04)/0.008764 = 2.28, about 2.27 as rounded. Using the observed rate in the variance gives 1.43-type errors; using the wrong base also gives different values.

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