The calibration of the IRB supervisory formula : a case study

The level of capital requirement generated by the IRB approach depends crucially on the asset correlation, a parameter that enters the regulatory risk weight formula and is determined by the Regulators. Several studies have estimated the asset correlations and found that the empirical values are materially lower than the regulatory calibration included in the Basel framework. However, the simple comparison between different estimates of this parameter does not easily translates into a clear economic interpretation. In this paper, we use detailed data from Italian banks to show how to extract from the regulatory risk measures easily interpretable figures i.e. the Worst-Case Default Rate (WCDR) and the Worst-Case Loss (WCL) and we show how the asset correlation influences these measures. We then provide a rationale for the regulatory calibration in terms of corrections to well-known limits of the underlying models like the assumption of perfect granularity. We claim that our approach can provide a better understating of the IRB risk measures fostering their transparency and reliability but also simplifying the comparison among different banks. We apply the proposed approach exploiting some data sources (publicly available and proprietary). As the data used is mainly referred to the Italian system and, in particular, to only two banks, the empirical results obtained are meant just to provide a practical example.