A Simple Multi-Factor “Factor Adjustment” for the Treatment of Credit Capital Diversification

We present a simple adjustment to the single-factor credit capital model, which recognizes the diversification from a multi-factor credit setting. The model can be applied to extend the Basel II regulatory framework to a general multi-factor setting, thus allowing for more accurate modeling of diversification for portfolios across various asset classes, sectors and regions, and in particular within mixed portfolios in developed and emerging economies. We introduce the concepts of a diversification factor at the portfolio level, as well as marginal diversification factors at the obligor or sub-portfolio level, which further capture diversification contributions to the portfolio. We estimate the diversification factor for a family of multi-factor models, and show that it can be expressed as a function of two parameters that broadly capture the size concentration and the average cross-sector correlation. This model supports an intuitive capital allocation methodology, where the diversification contribution of a given sector can be further attributed to three components: the overall portfolio diversification, the relative size of the sector to the overall portfolio, and its cross-sector correlation. The estimated diversification factor can be tabulated for the implementation of credit portfolio decision management support tools as well as potential regulatory applications. As a risk management tool, it can be used to understand concentration risk, capital allocation and sensitivities, as well as to compute “real-time” marginal risk contributions for new deals or portfolios. 4 The views expressed in this paper are solely those of the authors. The authors would like to thank Michael Pykhtin, Michael Gordy for valuable discussions and suggestions on the methodology and the paper. Further thanks to Helmut Mausser and the participants in the workshop “Concentration Risk in Credit Portfolios” (Eltville, November 2005) for their useful comments on earlier versions of the paper. Dan Rosen further acknowledges the kind support of the Fields Institute and Algorithmics Inc.