In credit risk modelling, the correlation of unobservable asset returns is a crucial component for the measurement of portfolio risk. In this paper, we estimate asset correlations from monthly time series of Moody's KMV asset values for around 2,000 European firms from 1996 to 2004. We compare correlation and value-atrisk (VaR) estimates in a one-factor or market model and a multi-factor or sector model. Our main finding is a complex interaction of credit risk correlations and default probabilities affecting total credit portfolio risk. Differentiation between industry sectors when using the sector model instead of the market model has only a secondary effect on credit portfolio risk, at least for the underlying credit portfolio. Averaging firm-dependent asset correlations on a sector level can, however, cause a substantial underestimation of the VaR in a portfolio with heterogeneous borrower size. This result holds for the market as well as the sector model. Furthermore, the VaR of the IRB model is more stable over time than the VaR of the market model and the sector model, while its distance from the other two models fluctuates over time.
Keywords: Asset correlations, sector concentration, credit portfolio risk
JEL Classification: G 21, C 15
Non-Technical SummaryThe correlations between two firms' asset-value returns, commonly referred to as asset correlation, are a key factor in measuring the credit risk of loan portfolios.Since asset values are not directly observable, we employ time series of asset values of European firms which are based on the Moody's KMV model. A descriptive analysis of these asset correlations and correlations with industry sector indices is a first contribution of this paper. We observe a considerable fluctuation of asset correlations which suggests further research on their stability over time. The second contribution is a comprehensive analysis how asset correlations as input parameters into a credit risk model affect the value-at-risk which is a measure of credit risk for a portfolio. We observe that borrower-dependent asset correlations produces a substantially higher value-at-risk than median asset correlations computed on a sector level. We attribute this finding mainly to the empirical fact that asset correlations tend to increase with borrower size, which means that sector averages understate the correlation effect. We conclude that the way asset correlations are used in the credit risk model also has a substantial impact on the risk assessment of a portfolio. This methodological challenge adds to the empirical challenge of estimating asset correlations reliably. Furthermore, our results suggest that the regulatory capital charge of the internal ratings-based approach of Basel II is less volatile over time than value-at-risk in the other credit risk models in our study.
Nichttechnische Zusammenfassung