Economic capital model validation: a comparative study

Abstract

Using a long history of public firm defaults, this study illustrates a validation approach for jointly testing the impact of probability of default and correlation upon economic capital model performance. We construct predicted default distributions using a variety of probability of default and correlation inputs and examine how the predicted distribution compares with the realized distribution. We conduct the comparison by looking at the percentile of realized defaults with respect to the predicted default distribution. We compare the performance of two typical portfolio parameterizations: a through-the-cycle style parameterization using agency-ratings-based long-term average default rates and Basel II correlations; and a point-in-time style parameterization using the public "expected default frequency" credit measure and the global correlation model (GCorr) of Moody's Analytics. We find that a through-the-cycle style parameterization results in a less conservative view of economic capital and substantial serial correlation in capital estimates; when point-in-time measures are used, the tested economic capital model produces consistent and conservative economic capital estimates over time.