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

A retail bank validates a new application scorecard using the Kolmogorov-Smirnov (KS) statistic. Which description of the KS statistic is correct?

The KS statistic is the maximum vertical distance between the cumulative score distributions of good and bad accounts. A higher value indicates the scorecard separates defaulters from non-defaulters better. It measures discrimination, not calibration of predicted default probabilities.

  1. AThe maximum vertical distance between the cumulative score distributions of good and bad accountsCorrect
  2. BThe area under the ROC curve minus 0.5, multiplied by two
  3. CThe difference between the mean scores of good and bad accounts divided by the pooled standard deviation
  4. DThe proportion of accounts whose predicted default probability differs from the observed default rate

Explanation

KS measures the maximum separation between the cumulative distributions of scores for goods and bads. A larger value means better discrimination. The Gini-style expression in option B is a different metric, and options C and D describe a standardized mean difference and a calibration gap, respectively.

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