The Shapley value decomposition of optimal portfolios

Abstract

Investors want the ability to evaluate the true and complete risk of the financial assets held in a portfolio. Yet, the current analytic methods provide only partial risk measures. I suggest that, by viewing a portfolio of securities as a cooperative game played by the assets that minimize portfolio risk, investors can calculate the exact value, each security contributes to the common payoff of the game, which is known as the Shapley value. It is determined by computing the contribution of each asset to the portfolio risk by looking at all the possible coalitions in which the asset would participate. I develop this concept in order to decompose the risk of mean-variance and mean-Gini efficient portfolios. This decomposition gives us a better rank of assets by their comprehensive contribution to the risk of optimal portfolios. Such a procedure allows investors to make unbiased decisions when they analyze the inherent risk of their holdings. The Shapley value is calculated for index classes and the empirical results based on asset allocation data are contrary to some of the findings of conventional wisdom and beta analysis.