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FRM Part II · FRM Exam Part II · Introduction to Credit Risk Modeling and Assessment

A risk team compares two scorecards on the same validation sample. Scorecard A has an AUC of 0.78 and Scorecard B has an AUC of 0.72. A manager concludes that A is better at every cutoff and that its accuracy ratio (Gini) is 0.78. Which statement is most accurate?

Scorecard A ranks risk better on average, with Gini of 0.56 from 2 times 0.78 minus 1. However, a higher AUC does not guarantee dominance at every cutoff because ROC curves can cross. Gini is not equal to AUC.

  1. AA has a higher overall rank-ordering power, but its ROC curve could still lie below B's at some cutoffs, and its Gini is 0.56Correct
  2. BA must dominate B at every cutoff, and its Gini is 0.56
  3. CA has a higher overall rank-ordering power, and its Gini equals its AUC of 0.78
  4. DA and B cannot be compared unless they use the same cutoff, and Gini is 0.28

Explanation

Gini (accuracy ratio) = 2*AUC - 1 = 2*0.78 - 1 = 0.56. A higher AUC measures better average rank-ordering but ROC curves can cross, so A need not be superior at every cutoff. Equating Gini with AUC is the key error in the other options.

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