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Index tracking with controlled number of assets using a hybrid heuristic combining genetic algorithm and non-linear programming

Author

Listed:
  • Leonardo Riegel Sant’Anna

    (Federal University of Rio Grande do Sul)

  • Tiago Pascoal Filomena

    (Federal University of Rio Grande do Sul)

  • Pablo Cristini Guedes

    (Federal University of Rio Grande do Sul)

  • Denis Borenstein

    (Federal University of Rio Grande do Sul
    Universidad de Cuenca)

Abstract

In this paper, we discuss the index tracking strategy using mathematical programming. First, we use a non-linear programming formulation for the index tracking problem, considering a limited number of assets. Since the problem is difficult to be solved in reasonable time by commercial mathematical packages, we apply a hybrid solution approach, combining mathematical programming and genetic algorithm. We show the efficiency of the proposed approach comparing the results with optimal solutions, with previous developed methods, and from real-world market indexes. The computational experiments focus on Ibovespa (the most important Brazilian market index), but we also present results for consolidated markets such as S&P 100 (USA), FTSE 100 (UK) and DAX (Germany). The proposed framework shows its ability to obtain very good results (gaps from the optimal solution smaller than 5 % in 8 min of CPU time) even for a highly volatile index from a developing country.

Suggested Citation

  • Leonardo Riegel Sant’Anna & Tiago Pascoal Filomena & Pablo Cristini Guedes & Denis Borenstein, 2017. "Index tracking with controlled number of assets using a hybrid heuristic combining genetic algorithm and non-linear programming," Annals of Operations Research, Springer, vol. 258(2), pages 849-867, November.
    • Handle: RePEc:spr:annopr:v:258:y:2017:i:2:d:10.1007_s10479-016-2111-x
    DOI: 10.1007/s10479-016-2111-x
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    1. Andrea Scozzari & Fabio Tardella & Sandra Paterlini & Thiemo Krink, 2013. "Exact and heuristic approaches for the index tracking problem with UCITS constraints," Annals of Operations Research, Springer, vol. 205(1), pages 235-250, May.
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    Cited by:

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    2. Mahdi Moeini, 2022. "Solving the index tracking problem: a continuous optimization approach," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 30(2), pages 807-835, June.
    3. Doering, Jana & Kizys, Renatas & Juan, Angel A. & Fitó, Àngels & Polat, Onur, 2019. "Metaheuristics for rich portfolio optimisation and risk management: Current state and future trends," Operations Research Perspectives, Elsevier, vol. 6(C).
    4. 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.
    5. Gnägi, M. & Strub, O., 2020. "Tracking and outperforming large stock-market indices," Omega, Elsevier, vol. 90(C).
    6. Frieder Meyer-Bullerdiek, 2022. "Selected Methods of optimized Sampling for Index Tracking – Evidence from German Stocks," Journal of Applied Finance & Banking, SCIENPRESS Ltd, vol. 12(6), pages 1-8.
    7. Patrizia Beraldi & Maria Elena Bruni, 2022. "Enhanced indexation via chance constraints," Operational Research, Springer, vol. 22(2), pages 1553-1573, April.
    8. Martin Boďa & Mária Kanderová, 2018. "What is the True Effect of Rebalancing - a Higher Return or a Lower Risk?," Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, Mendel University Press, vol. 66(6), pages 1417-1430.
    9. Chuting Sun & Qi Wu & Xing Yan, 2023. "Dynamic CVaR Portfolio Construction with Attention-Powered Generative Factor Learning," Papers 2301.07318, arXiv.org, revised Jan 2024.
    10. Julio Cezar Soares Silva & Adiel Teixeira de Almeida Filho, 2023. "A systematic literature review on solution approaches for the index tracking problem in the last decade," Papers 2306.01660, arXiv.org, revised Jun 2023.
    11. Sant’Anna, Leonardo Riegel & Righi, Marcelo Brutti & Müller, Fernanda Maria & Guedes, Pablo Cristini, 2022. "Risk measure index tracking model," International Review of Economics & Finance, Elsevier, vol. 80(C), pages 361-383.
    12. Sun, Chuting & Wu, Qi & Yan, Xing, 2024. "Dynamic CVaR portfolio construction with attention-powered generative factor learning," Journal of Economic Dynamics and Control, Elsevier, vol. 160(C).

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