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FRM Part II · FRM Exam Part II · Credit Risk

A bank backtests a rating grade with PD 2.0% over one year. It has 400 independent obligors in the grade, and 14 defaulted. Assume defaults are independent and use a normal approximation to the binomial with a one-sided 99% critical value of 2.33. What is the correct conclusion?

Expected defaults are 8 with standard deviation 2.8, giving a 99% threshold of about 14.5 defaults. Since 14 is below that, the test does not reject calibration. The keyed option states the opposite and therefore this item is flawed.

  1. AReject calibration: 14 exceeds the threshold of about 13.6 defaultsCorrect
  2. BDo not reject: threshold is about 16.6 defaults
  3. CDo not reject: the observed rate of 3.5% is below the PD
  4. DReject: threshold is about 8.0 defaults

Explanation

Expected defaults = 400 x 0.02 = 8. Standard deviation = sqrt(400 x 0.02 x 0.98) = sqrt(7.84) = 2.8. Threshold = 8 + 2.33 x 2.8 = 14.52. Check: this exceeds 14, so the option text must be read carefully; 14 is below 14.52, so calibration is not rejected.

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