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Enhanced index tracking problem: a new optimization model and a sum-of-ratio based algorithm

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  • F. Hooshmand

    (Amirkabir University of Technology (Tehran Polytechnic))

  • Z. Rasouli

    (Amirkabir University of Technology (Tehran Polytechnic))

Abstract

Enhanced index tracking as one of the approaches of stock portfolio selection has received great attention from researchers. In this paper, a new optimization model with the objectives of maximizing the Omega-ratio and minimizing the deviation of the portfolio value from the scaled market-index value is presented. Since the objective function of the model is in the form of maximizing the subtraction of a linear fractional term and a convex quadratic term, it belongs to the category of sum-of-ratio problems which is difficult to solve. Thus, an efficient algorithm is adopted to solve it. Then, the model and algorithm are extended to incorporate the cardinality constraint. Computational experiments over real-world instances indicate that, on average, the portfolio obtained by our model outperforms the model that solely optimizes the Omega-ratio in terms of different metrics such as accumulated return and tracking error on out-of-sample data.

Suggested Citation

  • F. Hooshmand & Z. Rasouli, 2023. "Enhanced index tracking problem: a new optimization model and a sum-of-ratio based algorithm," OPSEARCH, Springer;Operational Research Society of India, vol. 60(3), pages 1286-1311, September.
    • Handle: RePEc:spr:opsear:v:60:y:2023:i:3:d:10.1007_s12597-023-00658-9
    DOI: 10.1007/s12597-023-00658-9
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    References listed on IDEAS

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    1. Zhihua Zhao & Hao Wang & Xiangyu Yang & Fengmin Xu, 2021. "CVaR-cardinality enhanced indexation optimization with tunable short-selling constraints," Applied Economics Letters, Taylor & Francis Journals, vol. 28(3), pages 201-207, February.
    2. O. Strub & S. Brandinu & D. Lerch & J. Schaller & N. Trautmann, 2019. "A Three-phase Approach to an Enhanced Index-tracking Problem with Real-life Constraints," The Engineering Economist, Taylor & Francis Journals, vol. 64(3), pages 227-253, July.
    3. Gnägi, M. & Strub, O., 2020. "Tracking and outperforming large stock-market indices," Omega, Elsevier, vol. 90(C).
    4. Patrizia Beraldi & Maria Elena Bruni, 2022. "Enhanced indexation via chance constraints," Operational Research, Springer, vol. 22(2), pages 1553-1573, April.
    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. Roman, Diana & Mitra, Gautam & Zverovich, Victor, 2013. "Enhanced indexation based on second-order stochastic dominance," European Journal of Operational Research, Elsevier, vol. 228(1), pages 273-281.
    8. YongJin Kim & YunChol Jong & JinWon Yu, 2021. "A parametric solution method for a generalized fractional programming problem," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(4), pages 971-989, December.
    9. P. Kumar & Jyotirmayee Behera & A. K. Bhurjee, 2022. "Solving mean-VaR portfolio selection model with interval-typed random parameter using interval analysis," OPSEARCH, Springer;Operational Research Society of India, vol. 59(1), pages 41-77, March.
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    11. Gianfranco Guastaroba & Renata Mansini & Wlodzimierz Ogryczak & M. Grazia Speranza, 2020. "Enhanced index tracking with CVaR-based ratio measures," Annals of Operations Research, Springer, vol. 292(2), pages 883-931, September.
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