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Myopic robust index tracking with Bregman divergence

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  • Spiridon Penev
  • Pavel Shevchenko
  • Wei Wu

Abstract

Index tracking is a popular form of asset management. Typically, a quadratic function is used to define the tracking error of a portfolio and the look back approach is applied to solve the index tracking problem. We argue that a forward looking approach is more suitable, whereby the tracking error is expressed as expectation of a function of the difference between the returns of the index and of the portfolio. We also assume that there is an uncertainty in the distribution of the assets, hence a robust version of the optimization problem needs to be adopted. We use Bregman divergence in describing the deviation between the nominal and actual distribution of the components of the index. In this scenario, we derive the optimal robust index tracking strategy in a semi-analytical form as a solution of a system of nonlinear equations. Several numerical results are presented that allow us to compare the performance of this robust strategy with the optimal non-robust strategy. We show that, especially during market downturns, the robust strategy can be very advantageous.

Suggested Citation

  • Spiridon Penev & Pavel Shevchenko & Wei Wu, 2019. "Myopic robust index tracking with Bregman divergence," Papers 1908.07659, arXiv.org, revised Jul 2021.
    • Handle: RePEc:arx:papers:1908.07659
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    References listed on IDEAS

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    1. Goh, Gyuhyeong & Dey, Dipak K., 2014. "Bayesian model diagnostics using functional Bregman divergence," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 371-383.
    2. Penev, Spiridon & Naito, Kanta, 2018. "Locally robust methods and near-parametric asymptotics," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 395-417.
    3. Yuhong Xu, 2014. "Robust valuation and risk measurement under model uncertainty," Papers 1407.8024, arXiv.org.
    4. 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.
    5. de Paulo, Wanderlei Lima & de Oliveira, Estela Mara & do Valle Costa, Oswaldo Luiz, 2016. "Enhanced index tracking optimal portfolio selection," Finance Research Letters, Elsevier, vol. 16(C), pages 93-102.
    6. Andriosopoulos, Kostas & Nomikos, Nikos, 2014. "Performance replication of the Spot Energy Index with optimal equity portfolio selection: Evidence from the UK, US and Brazilian markets," European Journal of Operational Research, Elsevier, vol. 234(2), pages 571-582.
    7. Guastaroba, G. & Mansini, R. & Ogryczak, W. & Speranza, M.G., 2016. "Linear programming models based on Omega ratio for the Enhanced Index Tracking Problem," European Journal of Operational Research, Elsevier, vol. 251(3), pages 938-956.
    8. Miguel A. Lejeune, 2012. "Game Theoretical Approach for Reliable Enhanced Indexation," Decision Analysis, INFORMS, vol. 9(2), pages 146-155, June.
    9. Dose, Christian & Cincotti, Silvano, 2005. "Clustering of financial time series with application to index and enhanced index tracking portfolio," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(1), pages 145-151.
    10. 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.
    11. Paul Glasserman & Xingbo Xu, 2014. "Robust risk measurement and model risk," Quantitative Finance, Taylor & Francis Journals, vol. 14(1), pages 29-58, January.
    12. 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.
    13. 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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    1. 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.

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