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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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    References listed on IDEAS

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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.
    2. Thiemo Krink & Stefan Mittnik & Sandra Paterlini, 2009. "Differential evolution and combinatorial search for constrained index-tracking," Annals of Operations Research, Springer, vol. 172(1), pages 153-176, November.
    3. Walter Murray & Howard Shek, 2012. "A local relaxation method for the cardinality constrained portfolio optimization problem," Computational Optimization and Applications, Springer, vol. 53(3), pages 681-709, December.
    4. Leonardo Riegel Sant'Anna & Tiago Pascoal Filomena & Denis Borenstein, 2014. "Index Tracking with Control on the Number of Assets," Brazilian Review of Finance, Brazilian Society of Finance, vol. 12(1), pages 89-119.
    5. Tiago P. Filomena & Miguel A. Lejeune, 2014. "Warm-Start Heuristic for Stochastic Portfolio Optimization with Fixed and Proportional Transaction Costs," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 308-329, April.
    6. Diana Barro & Elio Canestrelli, 2009. "Tracking error: a multistage portfolio model," Annals of Operations Research, Springer, vol. 165(1), pages 47-66, January.
    7. Beasley, J. E. & Meade, N. & Chang, T. -J., 2003. "An evolutionary heuristic for the index tracking problem," European Journal of Operational Research, Elsevier, vol. 148(3), pages 621-643, August.
    8. Rubén Ruiz-Torrubiano & Alberto Suárez, 2009. "A hybrid optimization approach to index tracking," Annals of Operations Research, Springer, vol. 166(1), pages 57-71, February.
    9. Thiemo Krink & Stefan Mittnik & Sandra Paterlini, 2009. "Differential evolution and combinatorial search for constrained index-tracking," Annals of Operations Research, Springer, vol. 172(1), pages 153-176, November.
    10. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
    11. Enrico Angelelli & Renata Mansini & M. Speranza, 2012. "Kernel Search: a new heuristic framework for portfolio selection," Computational Optimization and Applications, Springer, vol. 51(1), pages 345-361, January.
    12. Manfred Gilli & Enrico Schumann, 2012. "Heuristic optimisation in financial modelling," Annals of Operations Research, Springer, vol. 193(1), pages 129-158, March.
    13. Christian L Dunis & Richard Ho, 2005. "Cointegration portfolios of European equities for index tracking and market neutral strategies," Journal of Asset Management, Palgrave Macmillan, vol. 6(1), pages 33-52, June.
    14. Hiroshi Konno & Annista Wijayanayake, 2001. "Minimal Cost Index Tracking Under Nonlinear Transaction Costs And Minimal Transaction Unit Constraints," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(06), pages 939-957.
    15. Gençay, Ramazan & Dacorogna, Michel & Muller, Ulrich A. & Pictet, Olivier & Olsen, Richard, 2001. "An Introduction to High-Frequency Finance," Elsevier Monographs, Elsevier, edition 1, number 9780122796715.
    16. Gaivoronski, Alexei A. & Krylov, Sergiy & van der Wijst, Nico, 2005. "Optimal portfolio selection and dynamic benchmark tracking," European Journal of Operational Research, Elsevier, vol. 163(1), pages 115-131, May.
    17. Eugene F. Fama & Kenneth R. French, 2010. "Luck versus Skill in the Cross‐Section of Mutual Fund Returns," Journal of Finance, American Finance Association, vol. 65(5), pages 1915-1947, October.
    18. Canakgoz, N.A. & Beasley, J.E., 2009. "Mixed-integer programming approaches for index tracking and enhanced indexation," European Journal of Operational Research, Elsevier, vol. 196(1), pages 384-399, July.
    19. Guastaroba, G. & Speranza, M.G., 2012. "Kernel Search: An application to the index tracking problem," European Journal of Operational Research, Elsevier, vol. 217(1), pages 54-68.
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    Cited by:

    1. Gnägi, M. & Strub, O., 2020. "Tracking and outperforming large stock-market indices," Omega, Elsevier, vol. 90(C).
    2. Chen, Qi-an & Hu, Qingyu & Yang, Hu & Qi, Kai, 2022. "A kind of new time-weighted nonnegative lasso index-tracking model and its application," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    3. 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.
    4. Patrizia Beraldi & Maria Elena Bruni, 2022. "Enhanced indexation via chance constraints," Operational Research, Springer, vol. 22(2), pages 1553-1573, April.
    5. 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.
    6. 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).
    7. 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.
    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.

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