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FRM Part II · FRM Exam Part II · Credit Scoring and Retail Credit Risk Management

A bank validates a new behavioral scorecard on a holdout sample. The Kolmogorov-Smirnov (KS) statistic is 45%, but the Gini coefficient is computed as 0.52. A risk manager asked what the Gini coefficient (accuracy ratio) shows about the model. Which statement is most accurate?

The Gini coefficient equals twice the area under the ROC curve minus one, so a Gini of 0.52 corresponds to an AUC of 0.76. It measures rank-ordering power, not calibration, and differs from KS, which is the maximum gap between cumulative distributions.

  1. AIt equals 2 × AUC − 1, so an AUC of 0.76 corresponds to a Gini of 0.52Correct
  2. BIt equals AUC − 0.5, so an AUC of 1.02 is implied
  3. CIt equals the maximum separation between the cumulative good and bad score distributions
  4. DIt measures how well predicted default rates match observed default rates in each score band

Explanation

Gini = 2×AUC − 1, so AUC = (1+0.52)/2 = 0.76. The maximum cumulative separation describes KS, not Gini. Calibration of predicted versus observed rates is a separate test, as Gini measures only rank ordering. AUC − 0.5 is wrong and yields an impossible AUC.

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