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Optimal construction and rebalancing of index-tracking portfolios

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  • Strub, O.
  • Baumann, P.

Abstract

Index funds aim to track the performance of a financial index, such as, e.g., the Standard & Poor’s 500 index. Index funds have become popular because they offer attractive risk-return profiles at low costs. The index-tracking problem considered in this paper consists of rebalancing the composition of the index fund’s tracking portfolio in response to new market information and cash deposits and withdrawals from investors such that the index fund’s tracking accuracy is maximized. In a frictionless market, maximum tracking accuracy is achieved by investing the index fund’s entire capital in a tracking portfolio that has the same normalized value development as the index. In the presence of transaction costs, which reduce the fund’s capital, one has to manage the trade-off between transaction costs and similarity in terms of normalized value developments. Existing mathematical programing formulations for the index-tracking problem do not optimize this trade-off explicitly, which may result in substantial transaction costs or tracking portfolios that differ considerably from the index in terms of normalized value development. In this paper, we present a mixed-integer linear programing formulation with a novel optimization criterion that directly considers the trade-off between transaction costs and similarity in terms of normalized value development. In an experiment based on a set of real-world problem instances, the proposed formulation achieves a considerably higher tracking accuracy than state-of-the-art formulations.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:264:y:2018:i:1:p:370-387
    DOI: 10.1016/j.ejor.2017.06.055
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    References listed on IDEAS

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    Cited by:

    1. Spiridon Penev & Pavel Shevchenko & Wei Wu, 2019. "Myopic robust index tracking with Bregman divergence," Papers 1908.07659, arXiv.org, revised Jul 2021.
    2. Gnägi, M. & Strub, O., 2020. "Tracking and outperforming large stock-market indices," Omega, Elsevier, vol. 90(C).
    3. 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).
    4. Dimitris Andriosopoulos & Michalis Doumpos & Panos M. Pardalos & Constantin Zopounidis, 2019. "Computational approaches and data analytics in financial services: A literature review," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 70(10), pages 1581-1599, October.
    5. Lijun Bo & Huafu Liao & Xiang Yu, 2020. "Optimal Tracking Portfolio with A Ratcheting Capital Benchmark," Papers 2006.13661, arXiv.org, revised Apr 2021.
    6. Ruchika Sehgal & Aparna Mehra, 2023. "Quantile Regression Based Enhanced Indexing with Portfolio Rebalancing," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 21(3), pages 721-742, September.
    7. Xianhua Peng & Chenyin Gong & Xue Dong He, 2023. "Reinforcement Learning for Financial Index Tracking," Papers 2308.02820, arXiv.org.
    8. 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.
    9. Yu Zheng & Bowei Chen & Timothy M. Hospedales & Yongxin Yang, 2019. "Index Tracking with Cardinality Constraints: A Stochastic Neural Networks Approach," Papers 1911.05052, arXiv.org, revised Nov 2019.
    10. Lijun Bo & Yijie Huang & Xiang Yu, 2023. "Stochastic control problems with state-reflections arising from relaxed benchmark tracking," Papers 2302.08302, arXiv.org, revised Apr 2024.
    11. Lijun Bo & Yijie Huang & Xiang Yu, 2023. "An extended Merton problem with relaxed benchmark tracking," Papers 2304.10802, arXiv.org, revised Jul 2024.
    12. 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.
    13. Lijun Bo & Yijie Huang & Xiang Yu, 2023. "On optimal tracking portfolio in incomplete markets: The reinforcement learning approach," Papers 2311.14318, arXiv.org, revised Oct 2024.
    14. Yuezhang Che & Shuyan Chen & Xin Liu, 2022. "Sparse Index Tracking Portfolio with Sector Neutrality," Mathematics, MDPI, vol. 10(15), pages 1-22, July.
    15. Yu Zheng & Timothy M. Hospedales & Yongxin Yang, 2018. "Diversity and Sparsity: A New Perspective on Index Tracking," Papers 1809.01989, arXiv.org, revised Feb 2020.
    16. 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).
    17. 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.
    18. 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.
    19. Stelios Arvanitis & Thierry Post & Nikolas Topaloglou, 2021. "Stochastic Bounds for Reference Sets in Portfolio Analysis," Management Science, INFORMS, vol. 67(12), pages 7737-7754, December.

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