A Tractable Model to Measure Sector Concentration Risk in Credit Portfolios

We explore a simplified version of the value-at-risk approximation developed by Pykhtin (Risk Magazine, March, 85–90, 2004), which only requires risk parameters on a sector level. We measure the impact of credit concentrations in business sectors on the economic capital of credit portfolios. We base our portfolios’ sector composition on credit information from the German central credit register. Our results show that the approximation formula performs well for fine-grained portfolios that are homogeneous on a sector level in terms of probability of default (PD) and exposure size. We explore the robustness of our results for portfolios which are heterogeneous in terms of these two characteristics. We find that low granularity ceteris paribus causes the approximation formula to underestimate economic capital, whereas heterogeneity in individual PDs causes overestimation. Indicative results imply that in typical credit portfolios of banks, PD heterogeneity will at least compensate for the granularity effect. This result suggests that the approximation estimates economic capital reasonably well and/or errs on the conservative side.