FRM Part II · FRM Exam Part II · Credit Scoring and Rating
A bank's rating grade B was assigned a PD of 2.0% at calibration. Over the year, 400 obligors were in grade B and 12 defaulted. Assuming independent defaults and using a normal approximation, what is the approximate z-statistic for testing whether the realized default rate exceeds the predicted PD?
The z-statistic is about 1.43. Expected defaults are 8, the binomial standard deviation is 2.8, and the excess of 4 defaults divided by 2.8 gives 1.43. This is below the 1.645 one-sided critical value, so calibration is not rejected at 5%.
- A0.71
- B1.43Correct
- C2.14
- D3.00
Explanation
Expected defaults = 400 × 0.02 = 8. Standard deviation = sqrt(400 × 0.02 × 0.98) = sqrt(7.84) = 2.8. z = (12 − 8)/2.8 = 1.43. Using the variance without the (1−PD) factor or other errors gives different values; 1.43 is below 1.645, so the one-sided 5% test does not reject.
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