By viewing portfolio optimization as a cooperative game played by the assets minimizing risk for a given return, investors can compute the exact value each security adds to the common payoff of the game. This is known the Shapley value that imputes the contribution of each asset, by looking at all the possible portfolios in which securities might participate. In this paper I use the Shapley value to decompose the risk and return of optimal portfolios that result from minimizing ordinary least squares. These regression portfolios are identical to tangency portfolios obtained by maximizing the Sharpe ratio of holdings on the mean-variance efficient frontiers. The Shapley value of individual assets is computed using the statistics resulting from the regressions. The value imputation prices assets by their comprehensive contribution to portfolio risk and return. This procedure allows investors to make unbiased decisions when analyzing the inherent risk of their holdings. By running OLS regressions, the Shapley value is calculated for asset allocation using Ibbotson’s aggregate financial data for the years 1926–2019.

中文翻译：

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回归投资组合的Shapley值

通过将投资组合优化视为资产所扮演的合作游戏，从而最大程度地降低了给定收益的风险，投资者可以计算出每种证券增加了游戏共同收益的确切价值。通过查看证券可能参与的所有可能的投资组合，这可以算出Shapley值，该值可以推算每种资产的贡献。在本文中，我使用Shapley值分解了因最小化普通最小二乘而产生的最优投资组合的风险和回报。这些回归组合与通过最大化均值方差有效边界上的夏普比率获得的相切组合相同。各个资产的Shapley值是使用回归得出的统计数据计算得出的。价值估算通过资产对投资组合风险和回报的综合贡献来定价。该程序使投资者在分析其持有的内在风险时可以做出公正的决定。通过运行OLS回归，使用Ibbotson的1926-2019年的总财务数据来计算Shapley值以进行资产分配。