How Robust Is the Value-at-Risk of Credit Risk Portfolios?

Abstract

In this paper, we assess the magnitude of model uncertainty of credit risk portfolio models, i.e., what is the maximum and minimum Value-at-Risk (VaR) of a portfolio of risky loans that can be justied given a certain amount of available information. Puccetti and Ruschendorf (2012a) and Embrechts et al. (2013) propose the rearrangement algorithm (RA) as a general method to approximate VaR bounds when the loss distributions of the dierent loans are known but not their interdependence (unconstrained bounds). Their numerical results show that the gap between worst-case and best-case VaR is typically very high, a feature that can only be explained by lack of using dependence information. We propose a modication of the RA that makes it possible to approximate sharp VaR bounds when besides the marginal distributions also higher order moments of the aggregate portfolio such as variance and skewness are available as sources of dependence information. A numerical study shows that the use of moment information makes it possible to signicantly improve the (unconstrained) VaR bounds. However, VaR assessments of credit portfolios that are performed at high condence levels (as it is the case in Solvency II and Basel III) remain subject to signicant model uncertainty and are not robust.

Keywords: Rearrangement algorithm, Moment bounds, Value-at-Risk, Credit risk portfolio. Minimum variance

JEL Classification: c10