Weighted Risk Capital Allocations in the Presence of Systematic Risk

Abstract

Determining aggregate risk capital has become a fundamental problem in modern Enterprise Risk Management, and the determination process has been fairly well studied. The consequent exercise of allocating the aggregate risk capital to constituents has also been given high priority in, e.g., both life and general insurance in such contexts as pricing, performance management, and profitability testing. In fact, the allocation exercise has been often called the primary driver for calculating the aggregate risk capital.

Unfortunately, the allocation problem is, in general, noticeably more involved than the problem of the aggregate risk capital determination. In fact, allocating risk capital is not easy even when a specific risk measure that induces the allocation rule has been assumed, let alone when a class of risk measures is considered. In this paper we demonstrate that, quite often, the problems of determining and allocating the aggregate risk capital are of a similar complexity. Remarkably, this turns out to be the case for the entire class of weighted risk capital allocations, as well as for risk portfolios that are exposed to systematic and specific risk factors.

Keywords: Weighted risk measures, weighted risk capital allocations, systematic risk

JEL Classification: C02, G32