Relaxing the assumption of conditional independence in an asymptotic single risk factor model

Frederic Menninger

Abstract

We demonstrate the impact of conditional correlation on an asymptotic single risk factor model within the framework of dynamic credit provisioning and stress testing. Specifically, we show the effect on the extraction of historic systematic risk factors, the calibration of the factor loading and the expected distribution of defaults. For unbiased models, the findings indicate that ignoring conditional correlation results in unjustified volatility in credit provisions through two channels: the extracted systematic risk factors during model development become less stable, and the sensitivity parameter of the systematic risk factor increases. These effects result in insufficient credit provisions during most of the business cycle and excessive credit provisions in the trough of the business cycle. In addition, disregarding conditional correlation leads to inappropriately strict bounds for model performance monitoring. Our results show that, in conservative applications, ignoring conditional correlation leads to an underestimation of portfolio loss quantiles.