IDEAS home Printed from https://ideas.repec.org/a/pal/assmgt/v21y2020i6d10.1057_s41260-020-00175-0.html
   My bibliography  Save this article

The Shapley value of regression portfolios

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1057/s41260-020-00175-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1057/s41260-020-00175-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Shalit, Haim, 2012. "Using OLS to test for normality," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 2050-2058.
    2. Stan Lipovetsky & Michael Conklin, 2001. "Analysis of regression in game theory approach," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 17(4), pages 319-330, October.
    3. 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.
    4. 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.
    5. Riccardo Colini-Baldeschi & Marco Scarsini & Stefano Vaccari, 2018. "Variance Allocation and Shapley Value," Methodology and Computing in Applied Probability, Springer, vol. 20(3), pages 919-933, September.
    6. Jobson, J. D. & Korkie, Bob, 1982. "Potential performance and tests of portfolio efficiency," Journal of Financial Economics, Elsevier, vol. 10(4), pages 433-466, December.
    7. 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.
    8. 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.
    9. Jobson, J. D. & Korkie, Bob, 1983. "Statistical Inference in Two-Parameter Portfolio Theory with Multiple Regression Software," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 18(2), pages 189-197, June.
    10. Haim Shalit, 2021. "The Shapley value decomposition of optimal portfolios," Annals of Finance, Springer, vol. 17(1), pages 1-25, March.
    11. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Haim Shalit, 2021. "The Shapley value decomposition of optimal portfolios," Annals of Finance, Springer, vol. 17(1), pages 1-25, March.
    2. Patrick S. Hagan & Andrew Lesniewski & Georgios E. Skoufis & Diana E. Woodward, 2021. "Portfolio risk allocation through Shapley value," Papers 2103.05453, arXiv.org.
    3. 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.
    4. Pera, Rebecca & Viglia, Giampaolo & Furlan, Roberto, 2016. "Who Am I? How Compelling Self-storytelling Builds Digital Personal Reputation," Journal of Interactive Marketing, Elsevier, vol. 35(C), pages 44-55.
    5. Viglia, Giampaolo & Abrate, Graziano, 2017. "When distinction does not pay off - Investigating the determinants of European agritourism prices," Journal of Business Research, Elsevier, vol. 80(C), pages 45-52.
    6. Haim Shalit, 2024. "The Nonsense of Bitcoin 1n Portfolio Analysis," Working Papers 2401, Ben-Gurion University of the Negev, Department of Economics.
    7. Penaranda, Francisco, 2007. "Portfolio choice beyond the traditional approach," LSE Research Online Documents on Economics 24481, London School of Economics and Political Science, LSE Library.
    8. Haim Shalit, 1995. "Mean-Gini analysis of stochastic externalities: The case of groundwater contamination," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 6(1), pages 37-52, July.
    9. Trajtenberg, Manuel & Yitzhaki, Shlomo, 1989. "The Diffusion of Innovations: A Methodological Reappraisal," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(1), pages 35-47, January.
    10. Miguel A. Lejeune & John Turner, 2019. "Planning Online Advertising Using Gini Indices," Operations Research, INFORMS, vol. 67(5), pages 1222-1245, September.
    11. Marie Brière & Bastien Drut & Valérie Mignon & Kim Oosterlinck & Ariane Szafarz, 2013. "Is the Market Portfolio Efficient? A New Test of Mean-Variance Efficiency when all Assets are Risky," Finance, Presses universitaires de Grenoble, vol. 34(1), pages 7-41.
    12. Shalit, Haim & Yitzhaki, Shlomo, 1985. "Evaluating the Mean-Gini Approach to Portfolio Selection," Working Papers 232632, Hebrew University of Jerusalem, Center for Agricultural Economic Research.
    13. Blavatskyy, Pavlo, 2016. "Probability weighting and L-moments," European Journal of Operational Research, Elsevier, vol. 255(1), pages 103-109.
    14. Zhenlong Jiang & Ran Ji & Kuo-Chu Chang, 2020. "A Machine Learning Integrated Portfolio Rebalance Framework with Risk-Aversion Adjustment," JRFM, MDPI, vol. 13(7), pages 1-20, July.
    15. 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.
    16. Maria-Teresa Bosch-Badia & Joan Montllor-Serrats & Maria-Antonia Tarrazon-Rodon, 2017. "Analysing assets’ performance inside a portfolio: From crossed beta to the net risk premium ratio," Cogent Economics & Finance, Taylor & Francis Journals, vol. 5(1), pages 1270251-127, January.
    17. Turtle, H.J. & Zhang, Chengping, 2012. "Time-varying performance of international mutual funds," Journal of Empirical Finance, Elsevier, vol. 19(3), pages 334-348.
    18. repec:dau:papers:123456789/9297 is not listed on IDEAS
    19. Shlomo Yitzhaki, 2003. "Gini’s Mean difference: a superior measure of variability for non-normal distributions," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 285-316.
    20. Sadefo Kamdem, Jules, 2012. "A nice estimation of Gini index and power Pen's parade," Economic Modelling, Elsevier, vol. 29(4), pages 1299-1304.
    21. Ran Ji & Miguel A. Lejeune & Srinivas Y. Prasad, 2017. "Properties, formulations, and algorithms for portfolio optimization using Mean-Gini criteria," Annals of Operations Research, Springer, vol. 248(1), pages 305-343, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pal:assmgt:v:21:y:2020:i:6:d:10.1057_s41260-020-00175-0. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.palgrave-journals.com/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.