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FRM Part II · FRM Exam Part II · Estimating Default Probabilities

A bank validates a discriminant-analysis scoring model for corporate defaults. At the chosen cutoff, among 100 firms that later defaulted, the model flagged 80; among 900 firms that did not default, it flagged 180. What are the Type I error rate and Type II error rate, with a Type I error defined as classifying a defaulter as safe?

Both error rates are 20%. Twenty of the 100 defaulters were missed, giving a Type I error of 20%, and 180 of the 900 healthy firms were wrongly flagged, giving a Type II error of 20%. Each rate uses its own group as the denominator.

  1. AType I 20%, Type II 20%Correct
  2. BType I 20%, Type II 11%
  3. CType I 80%, Type II 20%
  4. DType I 25%, Type II 20%

Explanation

Type I error = defaulters classified as safe = 20/100 = 20%. Type II error = non-defaulters flagged as risky = 180/900 = 20%. Using 100 as the base for the Type II rate would give 180/1000 or similar wrong values, and 80% is the hit rate rather than the error rate.

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