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The Shapley value decomposition of optimal portfolios

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  • Haim Shalit

    (Ben-Gurion University of the Negev)

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.

Suggested Citation

  • Haim Shalit, 2021. "The Shapley value decomposition of optimal portfolios," Annals of Finance, Springer, vol. 17(1), pages 1-25, March.
    • Handle: RePEc:kap:annfin:v:17:y:2021:i:1:d:10.1007_s10436-020-00380-2
    DOI: 10.1007/s10436-020-00380-2
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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.
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    2. Bastien Lextrait, 2022. "Optimizing portfolios in the illiquid, unlisted market of SME crowdlending," EconomiX Working Papers 2022-23, University of Paris Nanterre, EconomiX.
    3. Pankaj Kumar & Xiaojin Liu & Akbar Zaheer, 2022. "How much does the firm's alliance network matter?," Strategic Management Journal, Wiley Blackwell, vol. 43(8), pages 1433-1468, August.
    4. Haim Shalit, 2024. "The Nonsense of Bitcoin 1n Portfolio Analysis," Working Papers 2401, Ben-Gurion University of the Negev, Department of Economics.
    5. Patrick S. Hagan & Andrew Lesniewski & Georgios E. Skoufis & Diana E. Woodward, 2021. "Portfolio risk allocation through Shapley value," Papers 2103.05453, arXiv.org.
    6. 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.
    7. Haim Shalit, 2020. "The Shapley value of regression portfolios," Journal of Asset Management, Palgrave Macmillan, vol. 21(6), pages 506-512, October.

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    More about this item

    Keywords

    Mean-variance portfolios; Mean-Gini portfolios; Efficient frontier; Systematic risk; Asset allocation;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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