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Polynomial goal programming and particle swarm optimization for enhanced indexation

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Abstract

Enhanced indexation is an investment strategy that aims to generate moderate and consistent excess returns with respect to a tracked benchmark index. In this work, we introduce an optimization approach where the risk of under-performing the benchmark is separated from the potential over-performance, and the Sharpe ratio measures the profitability of the active management. In addition, a cardinality constraint controls the number of active positions in the portfolio, while a turnover threshold limits the transaction costs. We adopt a polynomial goal programming approach to combine these objectives with the investor’s preferences. An improved version of the particle swarm optimization algorithm with a novel constraint-handling mechanism is proposed to solve the optimization problem. A numerical example, where the Euro Stoxx 50 Index is used as the benchmark, shows that our method consistently produces larger returns, with reduced costs and risk exposition, than the standard indexing strategies over a 10-year backtesting period.

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Notes

  1. For maximization problems, it suffices to replace > with < in (24) and (25).

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Acknowledgements

We thank two anonymous reviewers for their insightful suggestions to improve the manuscript.

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Authors and Affiliations

  1. Department of Economics, Business, Mathematics and Statistics, University of Trieste, Piazzale Europa 1, 34127, Trieste, Italy

    Massimiliano Kaucic & Federico Julian Camerota Verdù

  2. Chief Investment Officer Department, Generali Italia, Via Marocchesa 14, 31021, Mogliano Veneto, TV, Italy

    Fabrizio Barbini

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  1. Massimiliano Kaucic
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  2. Fabrizio Barbini
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  3. Federico Julian Camerota Verdù
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Correspondence to Massimiliano Kaucic.

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Kaucic, M., Barbini, F. & Camerota Verdù, F.J. Polynomial goal programming and particle swarm optimization for enhanced indexation. Soft Comput 24, 8535–8551 (2020). https://doi.org/10.1007/s00500-019-04378-5

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