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Quantile regression for index tracking and enhanced indexation

Author

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  • H Mezali

    (Brunel University, Uxbridge, UK)

  • J E Beasley

    (Brunel University, Uxbridge, UK)

Abstract

Quantile regression differs from traditional least-squares regression in that one constructs regression lines for the quantiles of the dependent variable in terms of the independent variable. In this paper we apply quantile regression to two problems in financial portfolio construction, index tracking and enhanced indexation. Index tracking is the problem of reproducing the performance of a stock market index, but without purchasing all of the stocks that make up the index. Enhanced indexation deals with the problem of out-performing the index. We present a mixed-integer linear programming formulation of these problems based on quantile regression. Our formulation includes transaction costs, a constraint limiting the number of stocks that can be in the portfolio and a limit on the total transaction cost that can be incurred. Numeric results are presented for eight test problems drawn from major world markets, where the largest of these test problems involves over 2000 stocks.

Suggested Citation

  • H Mezali & J E Beasley, 2013. "Quantile regression for index tracking and enhanced indexation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 64(11), pages 1676-1692, November.
  • Handle: RePEc:pal:jorsoc:v:64:y:2013:i:11:p:1676-1692
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    References listed on IDEAS

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    1. 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.
    2. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, March.
    3. 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.
    4. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    5. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    6. 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.
    7. N. Meade & J. E. Beasley, 2011. "Detection of momentum effects using an index out-performance strategy," Quantitative Finance, Taylor & Francis Journals, vol. 11(2), pages 313-326.
    8. Enrico Angelelli & Renata Mansini & M. Speranza, 2012. "Kernel Search: a new heuristic framework for portfolio selection," Computational Optimization and Applications, Springer, vol. 51(1), pages 345-361, January.
    9. 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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    Cited by:

    1. repec:spr:jglopt:v:70:y:2018:i:1:d:10.1007_s10898-017-0513-1 is not listed on IDEAS
    2. Valle, C.A. & Meade, N. & Beasley, J.E., 2014. "Absolute return portfolios," Omega, Elsevier, vol. 45(C), pages 20-41.
    3. 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.
    4. Filippi, C. & Guastaroba, G. & Speranza, M.G., 2016. "A heuristic framework for the bi-objective enhanced index tracking problem," Omega, Elsevier, vol. 65(C), pages 122-137.

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