Do Basel II correlation assumptions for credit portfolios match with banks’ risk profile? Empirical evidence from the Italian system

Following the methodology underlying the Basel II Internal-Ratings Based (IRB) approach, which can be traced back to Gordy (2003), banks’ minimum capital requirements are function, among the other things, of the borrowers’ joint default probability, measured by the asset correlation. This paper aims at providing an empirical study of the Basel II asset value correlation assumptions by statistically analyzing Italian banking system empirical loss data within the context of the IRB modelling framework. By equalling the empirically observed unexpected loss with the regulatory capital requirement, based on the IRB supervisory formula, we derive a measure of implied asset correlation. Our findings support the conservatism of the regulatory coefficients and confirm that asset correlation vary geographically and across different industries, entailing that Basel II assumptions might not appropriately differentiate the relative risk profile of bank assets. Furthermore, we shed more light on the inverse relation between probability of default and asset correlation, which is one of the main hypothesis the IRB regulatory model is built on. We demonstrate that the sign of this relation depends on the combination of two opposite effects: the “PD effect”, which is consistent with the inverse relation and the “PD volatility effect”, which has been neglected by prior literature. According to our evidence, if a certain change in the PD comes along with a change in the volatility of the default rate distribution, the inverse relation doesn’t hold.