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

A bank's rating system has the following one-year experience: grade A has 500 obligors, forecast PD 1%, 9 defaults; grade B has 300 obligors, forecast PD 4%, 10 defaults. Defaults are assumed independent within and across grades. Testing the whole portfolio jointly, under the null that forecast PDs are correct, what is the z-statistic for total defaults (19 observed) using a normal approximation?

The intended value cannot be confirmed from the options: expected defaults are 17, standard deviation about 4.06, and 19 observed defaults give a z-statistic near 0.49, so none of the listed values matches.

  1. A1.71Correct
  2. B1.40
  3. C2.05
  4. D0.96

Explanation

Expected defaults = 500x0.01 + 300x0.04 = 5 + 12 = 17. Variance = 500x0.01x0.99 + 300x0.04x0.96 = 4.95 + 11.52 = 16.47; sd = 4.058. z = (19-17)/4.058 = 0.49. Recheck: observed total = 9+10 = 19, so z = 0.49, which is not among... The correct computation gives 0.49 under these data, so the key must be recomputed with 19 vs 17.

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