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Under Solvency II the computation of capital requirements is based on valueat risk (V@R). V@R is a quantile-based risk measure and neglects extreme risksin the tail. V@R belongs to the family of distortion risk measures. A seriousdeficiency of V@R is that firms can hide their total downside risk in corporatenetworks, unless a consolidated solvency balance sheet is required for eacheconomic scenario. In this case, they can largely reduce their total capitalrequirements via appropriate transfer agreements within a network structureconsisting of sufficiently many entities and thereby circumvent capitalregulation. We prove several versions of such a result for general distortionrisk measures of V@R-type, explicitly construct suitable allocations of thenetwork portfolio, and finally demonstrate how these findings can be extendedbeyond distortion risk measures. We also discuss why consolidation requirementscannot completely eliminate this problem. Capital regulation should thus bebased on coherent or convex risk measures like average value at risk orexpectiles.

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