Group cohesion under individual regulatory constraints

TL;DR

This paper introduces cohesive risk measures to analyze how groups of business units with individual regulatory constraints can optimize capital requirements by leveraging diversification effects without altering liabilities.

Contribution

It defines and studies cohesive risk measures that enable groups to minimize capital requirements despite individual constraints, a novel approach in risk management.

Findings

Groups can achieve capital reduction through diversification.

Cohesive risk measures align group capital needs with single-unit levels.

The framework accounts for convex regulatory constraints.

Abstract

We consider a group consisting of N business units. We suppose there are regulatory constraints for each unit, more precisely, the net worth of each business unit is required to belong to a set of acceptable risks, assumed to be a convex cone. Because of these requirements, there are less incentives to operate under a group structure, as creating one single business unit, or altering the liability repartition among units, may allow to reduce the required capital. We analyse the possibilities for the group to benefit from a diversification effect and economise on the cost of capital. We define and study the risk measures that allow for any group to achieve the minimal capital, as if it were a single unit, without altering the liability of business units, and despite the individual admissibility constraints. We call these risk measures cohesive risk measures.