Measuring business sector concentration by an infection model

Results from portfolio models for credit risk tell us that loan concentration in certain industry sectors can substantially increase the value-at-risk (V aR). The purpose of this paper is to analyse if a very tractable “infection model” can provide a meaningful estimate of the impact of concentration risk on the V aR. This would be achieved with quite parsimonious data requirements, which are comparable to those for Moody’s Binomial Expansion Technique (BET ) and considerably lower than for a multi–factor model. The infection model extends the BET by introducing default infection into the hypothetical portfolio on which the real portfolio is mapped in order to retain a simple, closed–form solution for the V aR. The infection–probability is calibrated for a range of typical values of input parameters which capture the concentration of a portfolio in industry sectors, default dependencies between exposures and their credit quality. The accuracy of the new model is measured for test portfolios with a realistic industry–sector composition, obtained from the German central credit register. We find that a carefully calibrated infection model provides a reasonably close approximation to the V aR obtained from a multi–factor model. It out–performs by far the BET which we dismiss for its lack of accuracy. Pending further robustness checks we conclude that the calibrated infection model promises to provide a fit–for–purpose tool to measure concentration risk in business sectors that could be useful for internal risk controllers as well as banking supervisors.