Modeling portfolio risk by risk discriminatory trees and random forests

Abstract

Common tree-splitting strategies involve minimizing a criterion function for minimum impurity (ie, difference) within child nodes. In this paper, we propose an approach based on maximizing a discriminatory criterion for maximum risk difference between child nodes. Maximum discriminatory separation based on risk is expected in credit risk scoring and rating. The search algorithm for an optimal split, proposed in this paper, is efficient and simple, just a scan through the data set. Choices of different trees, with options either more or less aggressive in variable splitting, are made possible. Two special cases are shown to relate to the Kolmogorov-Smirnov and the intracluster correlation statistics. As a validation of the proposed approaches, we estimate the exposure at default for a commercial portfolio. Results show that the risk discriminatory trees, constructed and selected using the bagging and random forest techniques, are robust. It is expected that the tools presented in this paper will add value to general portfolio risk modeling.