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Solving the index tracking problem based on a convex reformulation for cointegration

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  • Sant'Anna, Leonardo Riegel
  • de Oliveira, Alan Delgado
  • Filomena, Tiago Pascoal
  • Caldeira, João Frois

Abstract

This paper derives a mixed-integer non-linear optimization (MINLP) problem from the cointegration methodology and checks its convexity. We apply this approach to solve the index tracking (IT) problem using datasets from two distinct stock markets. The MINLP reformulation encompasses stock selection procedure and is optimized through branch-and-cut algorithm. The quality of the generated portfolios demonstrated lower turnover, which implies lower transaction costs over time and better performance in most instances regarding their tracking error in-sample and out-of-sample when compared with the traditional cointegration based IT portfolios.

Suggested Citation

  • Sant'Anna, Leonardo Riegel & de Oliveira, Alan Delgado & Filomena, Tiago Pascoal & Caldeira, João Frois, 2020. "Solving the index tracking problem based on a convex reformulation for cointegration," Finance Research Letters, Elsevier, vol. 37(C).
    • Handle: RePEc:eee:finlet:v:37:y:2020:i:c:s1544612318306196
    DOI: 10.1016/j.frl.2019.101356
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    References listed on IDEAS

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    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. Kim, Jang Ho & Kim, Woo Chang & Fabozzi, Frank J., 2016. "Portfolio selection with conservative short-selling," Finance Research Letters, Elsevier, vol. 18(C), pages 363-369.
    5. 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.
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    8. João Frois Caldeira & Gulherme Valle Moura, 2013. "Selection of a Portfolio of Pairs Based on Cointegration: A Statistical Arbitrage Strategy," Brazilian Review of Finance, Brazilian Society of Finance, vol. 11(1), pages 49-80.
    9. 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.
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    Citations

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    Cited by:

    1. 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).
    2. Alireza Olama & Eduardo Camponogara & Paulo R. C. Mendes, 2023. "Distributed primal outer approximation algorithm for sparse convex programming with separable structures," Journal of Global Optimization, Springer, vol. 86(3), pages 637-670, July.
    3. Nakagawa, Kei & Suimon, Yoshiyuki, 2022. "Inflation rate tracking portfolio optimization method: Evidence from Japan," Finance Research Letters, Elsevier, vol. 49(C).

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    More about this item

    Keywords

    Mixed-integer non-linear optimization; Cointegration; Index tracking;
    All these keywords.

    JEL classification:

    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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