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The Shapley value of regression portfolios

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  • Haim Shalit

    (Ben-Gurion University of the Negev)

Abstract

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.

Suggested Citation

  • Haim Shalit, 2020. "The Shapley value of regression portfolios," Journal of Asset Management, Palgrave Macmillan, vol. 21(6), pages 506-512, October.
    • Handle: RePEc:pal:assmgt:v:21:y:2020:i:6:d:10.1057_s41260-020-00175-0
    DOI: 10.1057/s41260-020-00175-0
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    References listed on IDEAS

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    1. Shalit, Haim & Yitzhaki, Shlomo, 1984. "Mean-Gini, Portfolio Theory, and the Pricing of Risky Assets," Journal of Finance, American Finance Association, vol. 39(5), pages 1449-1468, December.
    2. Shalit, Haim, 2012. "Using OLS to test for normality," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 2050-2058.
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    5. Haim Shalit, 2021. "The Shapley value decomposition of optimal portfolios," Annals of Finance, Springer, vol. 17(1), pages 1-25, March.
    6. Mark Britten‐Jones, 1999. "The Sampling Error in Estimates of Mean‐Variance Efficient Portfolio Weights," Journal of Finance, American Finance Association, vol. 54(2), pages 655-671, April.
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    8. Anthony Shorrocks, 2013. "Decomposition procedures for distributional analysis: a unified framework based on the Shapley value," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 11(1), pages 99-126, March.
    9. Yitzhaki, Shlomo, 1982. "Stochastic Dominance, Mean Variance, and Gini's Mean Difference," American Economic Review, American Economic Association, vol. 72(1), pages 178-185, March.
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    Cited by:

    1. Benjamin R. Auer & Tobias Hiller, 2021. "Cost gap, Shapley, or nucleolus allocation: Which is the best game‐theoretic remedy for the low‐risk anomaly?," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 42(4), pages 876-884, June.
    2. Tobias Hiller, 2022. "Allocation of portfolio risk and outside options," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 43(7), pages 2845-2848, October.

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