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

## TL;DR

This paper critiques Solvency II's use of V@R for capital requirements, showing how firms can exploit corporate networks to hide risks, and advocates for more comprehensive risk measures like AVaR.

## Contribution

It demonstrates how distortion risk measures like V@R can be manipulated through network structures and proposes alternative risk measures to improve regulation effectiveness.

## Key findings

- V@R-based capital requirements can be circumvented via corporate networks.
- Explicit constructions of network portfolios reveal risk hiding strategies.
- Convex risk measures like AVaR are less susceptible to manipulation.

## Abstract

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.