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

A bank backtests its internal rating grade with a PD of 1.0% over one year. The grade holds 2,500 independent obligors and 38 default. Assuming a binomial model approximated by the normal distribution and a one-sided 99% confidence level (critical value 2.33), what is the conclusion?

Expected defaults are 25 with a standard deviation of about 4.98. The 99% one-sided threshold is 25 + 2.33 × 4.98 ≈ 36.6 defaults. Since 38 defaults exceed this, the 1.0% PD is rejected as too low and underestimates default risk.

  1. AReject the PD as too low, because the observed 38 defaults exceed the threshold of about 36.6Correct
  2. BDo not reject, because the observed default rate of 1.52% is below 1.0%
  3. CDo not reject, because the threshold is about 44 defaults
  4. DReject the PD as too high, because fewer defaults than expected occurred

Explanation

Expected defaults = 2,500 × 0.01 = 25. Standard deviation = sqrt(2,500 × 0.01 × 0.99) = sqrt(24.75) ≈ 4.975. Threshold = 25 + 2.33 × 4.975 ≈ 36.6. Observed 38 exceeds it, so the PD is rejected as underestimating risk. Option B misstates that 1.52% is below 1.0%.

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