Coherent allocation of risk capital

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 "risks" 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 accounts for diversification. 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 that the Aumann-Shapley value is both a coherent and practical approach to financial risk allocation.