Coherent allocation of risk capital

Michel Denault

Abstract

ABSTRACT

The allocation problem stems from the diversification effect observed in risk measurements of financial portfolios: the sum of the risks of many portfolios is larger than the risk of the sum of the portfolios. The allocation problem is to apportion this diversification advantage to the portfolios in a fair manner, yielding, for each portfolio, a risk appraisal that takes diversification into account. Our approach is axiomatic, in the sense that we first argue for the necessary properties of an allocation principle and then consider principles that fulfill the properties. Important results from the area of game theory find a direct application. Our main result is to provide conceptual justification for a risk allocation principle that is based on the gradient of the risk measure. A numerical example based on the rules of the Securities Exchange Commission for margin computations is provided.