Investigating implied asset correlation and capital requirements: empirical evidence from the italian banking systems

The Basel Committee’s reform to strengthen the global capital framework, known as Basel III, takes into account a series of measures to address procyclicality and, consequently, make banks’ capital requirements more stable during the different phases of the economic cycle. The range of possible approaches that Supervisory Authorities could follow to address this issue includes measures such as the use of through-the-cycle probability of default (PD) estimates and/or the calibration of the other risk parameters, i.e., the confidence level and the relation between PD and asset correlation, in an anti-cyclical way. Particularly, this paper aims at detecting further the relation between PD and asset correlation, based on Italian banking sys- tem empirical loss data. The authors test the regulatory asset value correlation assumptions through a measure of implied asset correlation that they get by equalling the empirically observed unexpected loss with the regulatory capital requirements. This research sheds more light on the inverse relation between PD and asset correlation, which is one of the main hy- potheses the internal ratings based approach is built on, and that has not been modified by the Basel III reform. The paper demonstrates that the sign of this relation depends on the combination of two opposite effects: the “PD effect”, which is consistent with the inverse relation hypothesis and the “PD volatility effect”, which has been neglected by prior literature. According to the provided 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.