The Shapley decomposition for portfolio risk

Abstract

The aim of this article is to provide an application of the Shapley value to decompose financial portfolio risk. Decomposing the sample covariance risk measure, gives us relative measures, which can be, classified securities of a portfolio according to risk scales.

Notes

¹See Mussard and Terraza (2005) for the definition of within- and between-security risk measures of the Gini index.

²The Shapley value could have been applied directly to the between-security risk. But in this case, the result is trivial: each security contributes with the same proportion to the between-security risk. This result can be obtained upon the request of the author.

³Consider Shapley's elimination principle. Starting from F(r_i , r_j ), we have one chance out of two to obtain F(r_i ), one chance out of two to have F(r_j ), etc.