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Game Theoretical Approach for Reliable Enhanced Indexation

Author

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  • Miguel A. Lejeune

    (Decision Sciences Department, The George Washington University, Washington, DC 20052)

Abstract

Enhanced indexation is a structured investment approach that combines passive and active financial management techniques. We propose an enhanced indexation model whose goal is to maximize the excess return that can be attained with high reliability, while ensuring that the relative market risk does not exceed a specified limit. We measure the relative risk with the coherent semideviation risk functional and model the asset returns as random variables. We consider that the probability distributions of the index fund and excess returns are imperfectly known and belong to a class of distributions characterized by an ellipsoidal distributional set. We provide a game theoretical formulation for the enhanced indexation problem in which we maximize the minimum excess return over all allowable probability distributions. The variance of the excess return is calculated with a computationally efficient method that avoids model specification issues. Finally, we show that the game theoretical model can be recast as a convex programming problem and discuss the results of numerical experiments.

Suggested Citation

  • Miguel A. Lejeune, 2012. "Game Theoretical Approach for Reliable Enhanced Indexation," Decision Analysis, INFORMS, vol. 9(2), pages 146-155, June.
    • Handle: RePEc:inm:ordeca:v:9:y:2012:i:2:p:146-155
    DOI: 10.1287/deca.1120.0239
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    References listed on IDEAS

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    Cited by:

    1. Fengmin Xu & Meihua Wang & Yu-Hong Dai & Dachuan Xu, 2018. "A sparse enhanced indexation model with chance and cardinality constraints," Journal of Global Optimization, Springer, vol. 70(1), pages 5-25, January.
    2. Li, Xuepeng & Xu, Fengmin & Jing, Kui, 2022. "Robust enhanced indexation with ESG: An empirical study in the Chinese Stock Market," Economic Modelling, Elsevier, vol. 107(C).
    3. Ali Yekkehkhany & Timothy Murray & Rakesh Nagi, 2021. "Stochastic Superiority Equilibrium in Game Theory," Decision Analysis, INFORMS, vol. 18(2), pages 153-168, June.
    4. Tingting Yang & Xiaoxia Huang, 2022. "A New Portfolio Optimization Model Under Tracking-Error Constraint with Linear Uncertainty Distributions," Journal of Optimization Theory and Applications, Springer, vol. 195(2), pages 723-747, November.
    5. Guastaroba, G. & Mansini, R. & Ogryczak, W. & Speranza, M.G., 2016. "Linear programming models based on Omega ratio for the Enhanced Index Tracking Problem," European Journal of Operational Research, Elsevier, vol. 251(3), pages 938-956.
    6. Filippi, C. & Guastaroba, G. & Speranza, M.G., 2016. "A heuristic framework for the bi-objective enhanced index tracking problem," Omega, Elsevier, vol. 65(C), pages 122-137.
    7. Spiridon Penev & Pavel Shevchenko & Wei Wu, 2019. "Myopic robust index tracking with Bregman divergence," Papers 1908.07659, arXiv.org, revised Jul 2021.
    8. Jason R. W. Merrick & Fabrizio Ruggeri & Refik Soyer & L. Robin Keller, 2012. "From the Editors---Games and Decisions in Reliability and Risk," Decision Analysis, INFORMS, vol. 9(2), pages 81-85, June.
    9. Andrea C. Hupman & Jay Simon, 2023. "The Legacy of Peter Fishburn: Foundational Work and Lasting Impact," Decision Analysis, INFORMS, vol. 20(1), pages 1-15, March.
    10. Patrizia Beraldi & Maria Elena Bruni, 2022. "Enhanced indexation via chance constraints," Operational Research, Springer, vol. 22(2), pages 1553-1573, April.
    11. Zhiping Chen & Shen Peng & Abdel Lisser, 2020. "A sparse chance constrained portfolio selection model with multiple constraints," Journal of Global Optimization, Springer, vol. 77(4), pages 825-852, August.
    12. H Mezali & J E Beasley, 2013. "Quantile regression for index tracking and enhanced indexation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 64(11), pages 1676-1692, November.
    13. Zhiping Chen & Xinkai Zhuang & Jia Liu, 2019. "A Sustainability-Oriented Enhanced Indexation Model with Regime Switching and Cardinality Constraint," Sustainability, MDPI, vol. 11(15), pages 1-14, July.

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