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The link between the Shapley value and the beta factor

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  • Karl Michael Ortmann

    (Beuth University of Applied Sciences Berlin)

Abstract

In this article, we provide a link between the Shapley value in cooperative game theory and the capital asset pricing model (CAPM) in finance. In particular, the Shapley value of a suitably defined cooperative game is closely related to the beta factor in the CAPM. The beta factor for any given security may be interpreted as the asset’s fairly allocated share of the market risk or as the asset’s average marginal contribution to the market risk, respectively. Other fairness properties and axioms of the Shapley value may be reinterpreted in this context to attain a deeper understanding of the beta factor and the connotation of systematic risk. Our game theoretic approach further allows for a generalisation of the CAPM with respect to arbitrary risk measures other than variance. Last but not least, we discuss the volatility of an asset’s theoretical fair assessment of risk and of its systematic risk, respectively. This result lends itself to face the challenge of an empirical investigation on real stock markets.

Suggested Citation

  • Karl Michael Ortmann, 2016. "The link between the Shapley value and the beta factor," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 39(2), pages 311-325, November.
    • Handle: RePEc:spr:decfin:v:39:y:2016:i:2:d:10.1007_s10203-016-0178-0
    DOI: 10.1007/s10203-016-0178-0
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    References listed on IDEAS

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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. Haim Shalit, 2020. "The Shapley value of regression portfolios," Journal of Asset Management, Palgrave Macmillan, vol. 21(6), pages 506-512, October.
    3. Haim Shalit, 2021. "The Shapley value decomposition of optimal portfolios," Annals of Finance, Springer, vol. 17(1), pages 1-25, March.
    4. 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.
    5. Nicholas Moehle & Stephen Boyd & Andrew Ang, 2021. "Portfolio Performance Attribution via Shapley Value," Papers 2102.05799, arXiv.org.
    6. Patrick S. Hagan & Andrew Lesniewski & Georgios E. Skoufis & Diana E. Woodward, 2021. "Portfolio risk allocation through Shapley value," Papers 2103.05453, arXiv.org.

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    More about this item

    Keywords

    CAPM; Beta factor; Shapley value; Market risk; Systematic risk;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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