Before revision:  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  .
After revision:  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 . 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 .