An Axiomatic Approach to Capital Allocation

Capital allocation techniques are of central importance in portfolio management and risk-based performance measurement. In this paper we propose an axiom system for capital allocation and analyze its satisfiability and completeness: it is shown that for a given risk measure 03C1 there exists a capital allocation 039B03C1 that satisfies the main axioms if and only if 03C1 is subadditive and positively homogeneous. Furthermore, it is proved that the axiom system uniquely specifies 039B03C1. We apply the axiomatization to the most popular risk measures in the finance industry in order to derive explicit capital allocation formulae for these measures.