# Discriminatory Power

## Contents

## Definition

**Discriminatory Power** (also *Predictive Power*, *Scorecard Strength*) in the context of Credit Risk analysis is the ability to discriminate *ex ante* between defaulting and non-defaulting borrowers. The discriminatory power of any classification procedure (e.g. a Credit Scorecard) can be assessed using a number of statistical measures of discrimination.

## Statistical Measures of Discriminatory Power

The following measures have been suggested in the literature or are popular in the financial industry^{[1]}

- Cumulative Accuracy Profile (CAP) and its summary index, the Accuracy Ratio (AR),
- Receiver Operating Characteristic (ROC) and its summary indices, the ROC measure and the Pietra coefficient,
- Bayesian Error Rate,
- Conditional Entropy, Kullback-Leibler Distance, and Conditional Information Entropy Ratio (CIER),
- Information Value (Divergence Statistic, Portfolio Stability Index),
- Kendall’s tau and Somers’ D (for shadow ratings), and
- Brier Score
- Gains Chart
- Lift Curve

## Role in Basel II regulation

Tests of the discriminatory power of a credit rating system are one of the two major quantitative tests required for assessing the suitability of such a system for calculating Risk Capital requirements for regulated financial institutions (the other broad area being the assessment of calibration quality).

## References

- ↑ BIS Working Paper No. 14 Studies on the Validation of Internal Rating Systems