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Minimal Cost Index Tracking Under Nonlinear Transaction Costs And Minimal Transaction Unit Constraints

Author

Listed:
  • HIROSHI KONNO

    (Center for Research in Advanced Financial Technology, Tokyo Institute of Technology, Japan;
    Department of Industrial Engineering and Management, Tokyo Institute of Technology, Japan)

  • ANNISTA WIJAYANAYAKE

    (Department of Industrial Engineering and Management, Tokyo Institute of Technology, Japan)

Abstract

Index tracking is a very common and popular approach in portfolio management. When there is neither (nonconvex) transaction costs nor minimal transaction unit constraints, the problem can be formulated as a convex least square problem, so that it can be solved by standard methods. However, when the transaction cost is nonconvex and not negligible, or if there is a minimal unit constraint on the amount of transaction, the problem becomes a nonconvex minimization problem with discrete variables. In this paper, we will propose a branch and bound algorithm for solving this class of problems and show that it can solve an index tracking problem of practical size in a reasonable amount of computation time.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijtafx:v:04:y:2001:i:06:n:s0219024901001292
    DOI: 10.1142/S0219024901001292
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    Citations

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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. Li, Helong & Huang, Qin & Wu, Baiyi, 2021. "Improving the naive diversification: An enhanced indexation approach," Finance Research Letters, Elsevier, vol. 39(C).
    4. 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.
    5. Strub, O. & Baumann, P., 2018. "Optimal construction and rebalancing of index-tracking portfolios," European Journal of Operational Research, Elsevier, vol. 264(1), pages 370-387.
    6. 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.
    7. Liu, Yiying & Zhou, Yongbin & Niu, Juanjuan, 2023. "Portfolio optimization: A multi-period model with dynamic risk preference and minimum lots of transaction," Finance Research Letters, Elsevier, vol. 55(PB).
    8. Björn Fastrich & Peter Winker, 2012. "Robust portfolio optimization with a hybrid heuristic algorithm," Computational Management Science, Springer, vol. 9(1), pages 63-88, February.
    9. Sant’Anna, Leonardo Riegel & Caldeira, João Frois & Filomena, Tiago Pascoal, 2020. "Lasso-based index tracking and statistical arbitrage long-short strategies," The North American Journal of Economics and Finance, Elsevier, vol. 51(C).
    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. 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.
    12. 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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