Solvency II, or How to Sweep the Downside Risk Under the Carpet

Under Solvency II the computation of capital requirements is based on value at risk (V@R). V@R is a quantile-based risk measure and neglects extreme risks in the tail. V@R belongs to the family of distortion risk measures. A serious deficiency of V@R is that firms can hide their total downside risk in corporate groups. They can largely reduce their total capital requirements via appropriate transfer agreements within a group structure consisting of sufficiently many entities and thereby circumvent capital regulation. We prove several versions of such a result for general distortion risk measures of V@R-type, explicitly construct suitable allocations of the group portfolio, and finally demonstrate how these findings can be extended beyond distortion risk measures.