Estimating the impact of combined correlated credit scorecards

Błażej Kochański and Saul Fine

Abstract

The validity of combined risk models can be difficult to estimate without primary data. In this study, we introduce a novel algorithm designed specifically for this purpose. The algorithm requires just four parameters: the separation powers of two scorecards; the correlation between the two scorecards; and the default rate of the target population. By assuming an underlying multivariate normal structure, the algorithm returns either the estimated Gini coefficient or the area under the receiver operating characteristic curve of the combined scorecard. We examine the efficacy of this model through a series of Monte Carlo simulations, and test it using empirical data from four independent samples of consumer loans from financial institutions using a psychometric scorecard together with a traditional credit bureau scorecard. Overall, our model offers a practical tool for researchers and practitioners, and it illustrates the trade-offs in validity between the collinearity and discriminatory power of combined predictive models.