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Linear programming models based on Omega ratio for the Enhanced Index Tracking Problem

Author

Listed:
  • Guastaroba, G.
  • Mansini, R.
  • Ogryczak, W.
  • Speranza, M.G.

Abstract

Modern performance measures differ from the classical ones since they assess the performance against a benchmark and usually account for asymmetry in return distributions. The Omega ratio is one of these measures. Until recently, limited research has addressed the optimization of the Omega ratio since it has been thought to be computationally intractable. The Enhanced Index Tracking Problem (EITP) is the problem of selecting a portfolio of securities able to outperform a market index while bearing a limited additional risk. In this paper, we propose two novel mathematical formulations for the EITP based on the Omega ratio. The first formulation applies a standard definition of the Omega ratio where it is computed with respect to a given value, whereas the second formulation considers the Omega ratio with respect to a random target. We show how each formulation, nonlinear in nature, can be transformed into a Linear Programming model. We further extend the models to include real features, such as a cardinality constraint and buy-in thresholds on the investments, obtaining Mixed Integer Linear Programming problems. Computational results conducted on a large set of benchmark instances show that the portfolios selected by the model assuming a standard definition of the Omega ratio are consistently outperformed, in terms of out-of-sample performance, by those obtained solving the model that considers a random target. Furthermore, in most of the instances the portfolios optimized with the latter model mimic very closely the behavior of the benchmark over the out-of-sample period, while yielding, sometimes, significantly larger returns.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:251:y:2016:i:3:p:938-956
    DOI: 10.1016/j.ejor.2015.11.037
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    References listed on IDEAS

    as
    1. Manfred Gilli & Enrico Schumann, "undated". "Distributed Optimisation of a Portfolio's Omega," Swiss Finance Institute Research Paper Series 08-17, Swiss Finance Institute.
    2. 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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    1. repec:gam:jecomi:v:5:y:2017:i:4:p:38-:d:115667 is not listed on IDEAS
    2. repec:eee:dyncon:v:92:y:2018:i:c:p:103-128 is not listed on IDEAS
    3. repec:eee:ejores:v:264:y:2018:i:1:p:370-387 is not listed on IDEAS
    4. repec:spr:mathme:v:86:y:2017:i:3:d:10.1007_s00186-017-0613-1 is not listed on IDEAS
    5. Amita Sharma & Sebastian Utz & Aparna Mehra, 2017. "Omega-CVaR portfolio optimization and its worst case analysis," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(2), pages 505-539, March.

    More about this item

    Keywords

    Enhanced index tracking; Omega ratio; Portfolio optimization; Linear programming; Mixed integer linear programming;

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G1 - Financial Economics - - General Financial Markets
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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