  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
networks, unless a consolidated solvency balance sheet is required for each
economic scenario. In this case, they can largely reduce their total capital
requirements via appropriate transfer agreements within a network 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
network portfolio, and finally demonstrate how these findings can be extended
beyond distortion risk measures. We also discuss why consolidation requirements
cannot completely eliminate this problem. Capital regulation should thus be
based on coherent or convex risk measures like average value at risk or
expectiles.
