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A methodology for index tracking based on time-series clustering

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  • Sergio Focardi
  • Frank Fabozzi

Abstract

With the increased acceptance of capital market efficiency, there has been a significant increase in the money managed on an indexed basis. Several methodologies are available to replicate the target index. In this paper, we discuss the problems of (1) defining suitable performance objectives and tracking error that scale properly over the entire management period and (2) implementing an optimal investment strategy when full replication of an index is not deemed suitable. We then argue that clustering might be a viable methodology for building parsimonious tracking portfolios. With suitably defined distances between the time series of asset prices, clustering 'discovers' the correlation and cointegration structure of an index. Sampling the clusters with appropriate heuristics and optimization techniques, an optimal tracking portfolio can be constructed. One advantage of this approach is that it eschews the difficulties and computational burden of density forecasts and full optimization.

Suggested Citation

  • Sergio Focardi & Frank Fabozzi, 2004. "A methodology for index tracking based on time-series clustering," Quantitative Finance, Taylor & Francis Journals, vol. 4(4), pages 417-425.
    • Handle: RePEc:taf:quantf:v:4:y:2004:i:4:p:417-425
    DOI: 10.1080/14697680400008668
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    References listed on IDEAS

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    1. R. Mantegna, 1999. "Hierarchical structure in financial markets," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 11(1), pages 193-197, September.
    2. 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.
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    4. Stanley Pliska & Kiyoshi Suzuki, 2004. "Optimal tracking for asset allocation with fixed and proportional transaction costs," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 233-243.
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    Citations

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    Cited by:

    1. Cesarone, Francesco & Lampariello, Lorenzo & Sagratella, Simone, 2019. "A risk-gain dominance maximization approach to enhanced index tracking," Finance Research Letters, Elsevier, vol. 29(C), pages 231-238.
    2. Paskalis Glabadanidis, 2020. "Portfolio Strategies to Track and Outperform a Benchmark," JRFM, MDPI, vol. 13(8), pages 1-26, August.
    3. Li, Qian & Bao, Liang, 2014. "Enhanced index tracking with multiple time-scale analysis," Economic Modelling, Elsevier, vol. 39(C), pages 282-292.
    4. 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.
    5. 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.
    6. Paskalis Glabadanidis & Leon Zolotoy, 2013. "Benchmark replication portfolio strategies," Journal of Asset Management, Palgrave Macmillan, vol. 14(2), pages 95-110, April.
    7. Jun Nakayama & Daisuke Yokouchi, 2018. "Applying Time Series Decomposition to Construct Index-Tracking Portfolio," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 25(4), pages 341-352, December.
    8. Gidea, Marian & Goldsmith, Daniel & Katz, Yuri & Roldan, Pablo & Shmalo, Yonah, 2020. "Topological recognition of critical transitions in time series of cryptocurrencies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 548(C).
    9. Reza Bradrania & Davood Pirayesh Neghab & Mojtaba Shafizadeh, 2022. "State-dependent stock selection in index tracking: a machine learning approach," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 36(1), pages 1-28, March.
    10. Sant’Anna, Leonardo R. & Filomena, Tiago P. & Caldeira, João F., 2017. "Index tracking and enhanced indexing using cointegration and correlation with endogenous portfolio selection," The Quarterly Review of Economics and Finance, Elsevier, vol. 65(C), pages 146-157.
    11. Pier Francesco Procacci & Tomaso Aste, 2018. "Forecasting market states," Papers 1807.05836, arXiv.org, revised May 2019.
    12. Gautier Marti & Frank Nielsen & Miko{l}aj Bi'nkowski & Philippe Donnat, 2017. "A review of two decades of correlations, hierarchies, networks and clustering in financial markets," Papers 1703.00485, arXiv.org, revised Nov 2020.
    13. Yoontae Hwang & Stefan Zohren & Yongjae Lee, 2024. "Temporal Representation Learning for Stock Similarities and Its Applications in Investment Management," Papers 2407.13751, arXiv.org.
    14. Jiang, Pan & Perez, M. Fabricio, 2021. "Follow the leader: Index tracking with factor models," Journal of Empirical Finance, Elsevier, vol. 64(C), pages 337-350.
    15. Donatien Tafin Djoko & Yves Till�, 2015. "Selection of balanced portfolios to track the main properties of a large market," Quantitative Finance, Taylor & Francis Journals, vol. 15(2), pages 359-370, February.
    16. 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.
    17. 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.

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