FRM Part II · FRM Exam Part II · Credit Risk
A bank's retail risk team builds a scorecard and wants a single statistic that shows how well the score separates defaulters from non-defaulters across all possible cut-off scores. Which measure is most appropriate?
The area under the ROC curve is the best choice because it summarises how well a score ranks defaulters above non-defaulters across every possible cut-off. A value of 0.5 means random ranking and 1.0 means perfect separation. Average PD only describes portfolio risk level, not discrimination.
- AThe area under the ROC curveCorrect
- BThe average probability of default of the portfolio
- CThe loss given default of the worst decile
- DThe number of borrowers in the highest score band
Explanation
The ROC curve plots the hit rate against the false alarm rate over all cut-offs, and the area under it summarises discriminatory power. An AUC of 0.5 means no discrimination and 1.0 means perfect discrimination. The average PD describes the level of risk, not the ability to rank borrowers.
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