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

A validator computes the Accuracy Ratio (AR) for a corporate rating model. The area between the model's CAP curve and the random-model diagonal is 0.30. The area between the perfect-model CAP curve and the diagonal is 0.45. What is the AR, and what is the corresponding AUC of the ROC curve, using the relationship AR = 2 x AUC - 1?

The Accuracy Ratio is the model's area over the diagonal divided by the perfect model's area, 0.30/0.45, or about 0.67. Since AR = 2 x AUC - 1, AUC = (1 + 0.67)/2, or about 0.83.

  1. AAR = 0.67; AUC = 0.83Correct
  2. BAR = 0.67; AUC = 0.67
  3. CAR = 0.30; AUC = 0.65
  4. DAR = 0.45; AUC = 0.73

Explanation

AR = 0.30 / 0.45 = 0.667. Rearranging AR = 2 x AUC - 1 gives AUC = (1 + 0.667)/2 = 0.833. Setting AUC equal to AR ignores the transformation, and using the raw area 0.30 ignores the scaling by the perfect model.

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