Suitability of Capital Allocations for Performance Measurement

TL;DR

This paper investigates how capital allocation methods can be effectively used for performance measurement, identifying conditions for their suitability and extending existing theories to reward-risk frameworks.

Contribution

It introduces the concept of suitability for performance measurement, proves the existence of suitable allocations under various assumptions, and extends characterization results to reward-risk settings.

Findings

Suitable allocation methods exist under strict risk measure assumptions.

A known suitable allocation principle does not require properties of the risk measure.

The theory is extendable to game theoretic frameworks.

Abstract

Capital allocation principles are used in various contexts in which a risk capital or a cost of an aggregate position has to be allocated among its constituent parts. We study capital allocation principles in a performance measurement framework. We introduce the notation of suitability of allocations for performance measurement and show under different assumptions on the involved reward and risk measures that there exist suitable allocation methods. The existence of certain suitable allocation principles generally is given under rather strict assumptions on the underlying risk measure. Therefore we show, with a reformulated definition of suitability and in a slightly modified setting, that there is a known suitable allocation principle that does not require any properties of the underlying risk measure. Additionally we extend a previous characterization result from the literature from a mean-risk to a reward-risk setting. Formulations of this theory are also possible in a game theoretic setting.