IDEAS home Printed from https://ideas.repec.org/a/wly/mgtdec/v44y2023i7p4193-4200.html
   My bibliography  Save this article

Portfolio structures: Can they contribute to solving the low‐risk puzzle?

Author

Listed:
  • Tobias Hiller

Abstract

This article expands on previous studies of the so‐called low‐risk puzzle with concepts from cooperative game theory. To allocate portfolio risk to single assets, previous studies used concepts such as the Shapley value. In these concepts, the marginal contributions of assets to risks of subsets of the portfolio are used to allocate portfolio risk to assets. In this article, beyond the marginal contributions, a structure on a set of assets is considered in the allocation of portfolio risk. This structure can model the branch, firm size or the region of the assets. Specifically, the Myerson value and the Spectrum value of cooperative game theory are applied. We show the application by means of a simulation study. In this context, considering an additional structure could enhance the analysis of the so‐called low‐risk puzzle.

Suggested Citation

  • Tobias Hiller, 2023. "Portfolio structures: Can they contribute to solving the low‐risk puzzle?," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 44(7), pages 4193-4200, October.
    • Handle: RePEc:wly:mgtdec:v:44:y:2023:i:7:p:4193-4200
    DOI: 10.1002/mde.3928
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/mde.3928
    Download Restriction: no
    File URL: https://libkey.io/10.1002/mde.3928?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
    ---><---

    References listed on IDEAS

    as
    1. Álvarez-Mozos, Mikel & Hellman, Ziv & Winter, Eyal, 2013. "Spectrum value for coalitional games," Games and Economic Behavior, Elsevier, vol. 82(C), pages 132-142.
    2. van den Nouweland, Anne & Borm, Peter & Tijs, Stef, 1992. "Allocation Rules for Hypergraph Communication Situations," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(3), pages 255-268.
    3. Casajus, André, 2009. "Outside options, component efficiency, and stability," Games and Economic Behavior, Elsevier, vol. 65(1), pages 49-61, January.
    4. Tijs, S.H. & Driessen, T.S.H., 1986. "Game theory and cost allocation problems," Other publications TiSEM 376c24c5-c95d-4d29-96b6-4, Tilburg University, School of Economics and Management.
    5. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    6. Frazzini, Andrea & Pedersen, Lasse Heje, 2014. "Betting against beta," Journal of Financial Economics, Elsevier, vol. 111(1), pages 1-25.
    7. Harald Wiese, 2007. "Measuring The Power Of Parties Within Government Coalitions," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 9(02), pages 307-322.
    8. Robert P. Gilles, 2010. "The Cooperative Game Theory of Networks and Hierarchies," Theory and Decision Library C, Springer, number 978-3-642-05282-8, April.
    9. Malcolm Baker & Brendan Bradley & Jeffrey Wurgler, 2011. "Benchmarks as Limits to Arbitrage: Understanding the Low-Volatility Anomaly," Financial Analysts Journal, Taylor & Francis Journals, vol. 67(1), pages 40-54, January.
    10. AUMANN, Robert J. & DREZE, Jacques H., 1974. "Cooperative games with coalition structures," LIDAM Reprints CORE 217, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    11. René Brink, 2008. "Vertical wage differences in hierarchically structured firms," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(2), pages 225-243, February.
    12. Navarro, Florian, 2020. "The center value: A sharing rule for cooperative games on acyclic graphs," Mathematical Social Sciences, Elsevier, vol. 105(C), pages 1-13.
    13. John Lintner, 1965. "Security Prices, Risk, And Maximal Gains From Diversification," Journal of Finance, American Finance Association, vol. 20(4), pages 587-615, December.
    14. van den Brink, Rene & Gilles, Robert P., 1996. "Axiomatizations of the Conjunctive Permission Value for Games with Permission Structures," Games and Economic Behavior, Elsevier, vol. 12(1), pages 113-126, January.
    15. Dutt, Tanuj & Humphery-Jenner, Mark, 2013. "Stock return volatility, operating performance and stock returns: International evidence on drivers of the ‘low volatility’ anomaly," Journal of Banking & Finance, Elsevier, vol. 37(3), pages 999-1017.
    16. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    17. 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.
    18. Borm, P.E.M. & Owen, G. & Tijs, S.H., 1992. "On the position value for communication situations," Other publications TiSEM 5a8473e4-1df7-42df-ad53-f, Tilburg University, School of Economics and Management.
    19. Gilles, Robert P & Owen, Guillermo & van den Brink, Rene, 1992. "Games with Permission Structures: The Conjunctive Approach," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(3), pages 277-293.
    20. Homburg, Carsten & Scherpereel, Peter, 2008. "How should the cost of joint risk capital be allocated for performance measurement?," European Journal of Operational Research, Elsevier, vol. 187(1), pages 208-227, May.
    21. Stephane Mussard & Virginie Terraza, 2008. "The Shapley decomposition for portfolio risk," Applied Economics Letters, Taylor & Francis Journals, vol. 15(9), pages 713-715.
    22. Haim Shalit, 2020. "The Shapley value of regression portfolios," Journal of Asset Management, Palgrave Macmillan, vol. 21(6), pages 506-512, October.
    23. Balog, Dóra & Bátyi, Tamás László & Csóka, Péter & Pintér, Miklós, 2017. "Properties and comparison of risk capital allocation methods," European Journal of Operational Research, Elsevier, vol. 259(2), pages 614-625.
    24. Jorion, Philippe, 1985. "International Portfolio Diversification with Estimation Risk," The Journal of Business, University of Chicago Press, vol. 58(3), pages 259-278, July.
    25. Hellman, Ziv & Peretz, Ron, 2018. "Values for cooperative games over graphs and games with inadmissible coalitions," Games and Economic Behavior, Elsevier, vol. 108(C), pages 22-36.
    26. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    27. 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.
    28. Benjamin R. Auer & Tobias Hiller, 2019. "Can cooperative game theory solve the low‐risk puzzle?," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 24(2), pages 884-889, April.
    29. S. H. Tijs & T. S. H. Driessen, 1986. "Game Theory and Cost Allocation Problems," Management Science, INFORMS, vol. 32(8), pages 1015-1028, August.
    30. Calvo, Emilio & Lasaga, Javier & van den Nouweland, Anne, 1999. "Values of games with probabilistic graphs," Mathematical Social Sciences, Elsevier, vol. 37(1), pages 79-95, January.
    31. Blitz, D.C. & van Vliet, P., 2007. "The Volatility Effect: Lower Risk without Lower Return," ERIM Report Series Research in Management ERS-2007-044-F&A, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    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. Tobias Hiller, 2024. "Shapley-based risk rankings: some theoretical considerations," International Review of Economics, Springer;Happiness Economics and Interpersonal Relations (HEIRS), vol. 71(1), pages 67-74, March.

    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. 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.
    2. Tobias Hiller, 2024. "Shapley-based risk rankings: some theoretical considerations," International Review of Economics, Springer;Happiness Economics and Interpersonal Relations (HEIRS), vol. 71(1), pages 67-74, March.
    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. Tobias Hiller, 2021. "Hierarchy and the size of a firm," International Review of Economics, Springer;Happiness Economics and Interpersonal Relations (HEIRS), vol. 68(3), pages 389-404, September.
    5. Encarnacion Algaba & Rene van den Brink, 2021. "Networks, Communication and Hierarchy: Applications to Cooperative Games," Tinbergen Institute Discussion Papers 21-019/IV, Tinbergen Institute.
    6. C. Manuel & D. Martín, 2021. "A value for communication situations with players having different bargaining abilities," Annals of Operations Research, Springer, vol. 301(1), pages 161-182, June.
    7. Tobias Hiller, 2018. "The Effects of Excluding Coalitions," Games, MDPI, vol. 9(1), pages 1-7, January.
    8. René Brink, 2017. "Games with a permission structure - A survey on generalizations and applications," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 1-33, April.
    9. Michel Grabisch, 2013. "The core of games on ordered structures and graphs," Annals of Operations Research, Springer, vol. 204(1), pages 33-64, April.
    10. Tobias Hiller, 2015. "The $$\chi $$ χ value and team games," Theory and Decision, Springer, vol. 78(4), pages 539-548, April.
    11. Rene van den Brink & Ilya Katsev & Gerard van der Laan, 2023. "Properties of Solutions for Games on Union-Closed Systems," Mathematics, MDPI, vol. 11(4), pages 1-16, February.
    12. Encarnacion Algaba & Rene van den Brink, 2019. "The Shapley Value and Games with Hierarchies," Tinbergen Institute Discussion Papers 19-064/II, Tinbergen Institute.
    13. Abe, Takaaki & Nakada, Satoshi, 2023. "The in-group egalitarian Owen values," Games and Economic Behavior, Elsevier, vol. 142(C), pages 1-16.
    14. Daniel Li Li & Erfang Shan, 2021. "Cooperative games with partial information," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(1), pages 297-309, March.
    15. Malvika Saraf & Parthajit Kayal, 2022. "How Much Does Volatility Influence Stock Market Returns? – Empirical Evidence from India," Working Papers 2022-215, Madras School of Economics,Chennai,India.
    16. Antonio Magaña & Francesc Carreras, 2018. "Coalition Formation and Stability," Group Decision and Negotiation, Springer, vol. 27(3), pages 467-502, June.
    17. René van den Brink & Ilya Katsev & Gerard van der Laan, 2008. "An Algorithm for Computing the Nucleolus of Disjunctive Additive Games with An Acyclic Permission Structure," Tinbergen Institute Discussion Papers 08-104/1, Tinbergen Institute.
    18. Subhadip Chakrabarti & Amandine Ghintran & Rajnish Kumar, 2019. "Assignment of heterogeneous agents in trees under the permission value," Review of Economic Design, Springer;Society for Economic Design, vol. 23(3), pages 155-188, December.
    19. E. C. Gavilán & C. Manuel & R. Brink, 2023. "Directed communication in games with directed graphs," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 584-617, October.
    20. David Lowing, 2023. "Allocation rules for multi-choice games with a permission tree structure," Annals of Operations Research, Springer, vol. 320(1), pages 261-291, January.

    More about this item

    Statistics

    Access and download statistics

    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:wly:mgtdec:v:44:y:2023:i:7:p:4193-4200. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www3.interscience.wiley.com/cgi-bin/jhome/7976 .

    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.