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FRM Part II · FRM Exam Part II · Credit Scoring and Rating

A bank's rating grade 4 has a predicted one-year PD of 2.0%. Over the past year, 400 obligors were in grade 4 and 12 defaulted. Assuming defaults are independent, which conclusion best describes a binomial test of calibration at roughly a 95% one-sided level?

Expected defaults are 8 with a standard deviation of about 2.8, so 12 defaults is a z-score of roughly 1.43. That is below the 1.645 one-sided critical value, so the calibration of the 2.0% PD is not rejected at the 95% level.

  1. AThe observed default rate of 3.0% is about 1.43 standard deviations above the expected 2.0%, so the PD is not rejected as too lowCorrect
  2. BThe observed default rate of 3.0% is more than 3 standard deviations above 2.0%, so the PD is clearly too low
  3. CThe observed default rate is below the predicted PD, so the PD is too conservative
  4. DThe test cannot be applied because the number of defaults is below 30

Explanation

Expected defaults = 400 x 0.02 = 8. Standard deviation = sqrt(400 x 0.02 x 0.98) = 2.80. Z = (12 - 8)/2.80 = 1.43, below the 1.645 critical value. Treating the standard deviation as much smaller gives the exaggerated rejection.

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