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Equally weighted cardinality constrained portfolio selection via factor models

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Abstract

In this work a proposal and discussion of two different 0-1 optimization models is carried out in order to solve the cardinality constrained portfolio problem by using factor models. Factor models are used to build portfolios based on tracking the market index, among other objectives, and require to estimate smaller number of parameters than the classical Markowitz model. The addition of the cardinality constraints limits the number of securities in the portfolio. Restricting the number of securities in the portfolio allows to obtain a concentrated portfolio while also limiting transaction costs. To solve this problem a new quadratic combinatorial problem is presented to obtain an equally weighted cardinality constrained portfolio. For a single factor model, some theoretical results are presented. Computational results from the 0-1 models are compared with those using a state-of-the-art Quadratic MIP solver.

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Notes

  1. Problem (2) can be linearized by considering variables \(u_{ij}=1\) if both \(x_i=1\) and \(x_j=1\), 0 otherwise, and the constraints \(u_{ij} \le x_i\), \(u_{ij} \le x_j\), \(u_{ij} \ge x_i + x_j - 1\).

  2. Monge matrices are named after the French mathematician Gaspard Monge [1746–1818].

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Acknowledgements

This work was partly supported by the Spanish Ministry for Economy and Competitiveness, the State Research Agency and the European Regional Development Fund under Grant MTM2016-79765-P (AEI/FEDER, UE). I am grateful to anonymous reviewers for numerous suggestions to improve this paper.

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  1. Department of Statistics, Mathematics and Computer Science, Center of Operations Research, Miguel Hernández University of Elche, Elche, Spain

    Juan F. Monge

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Correspondence to Juan F. Monge.

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Monge, J.F. Equally weighted cardinality constrained portfolio selection via factor models. Optim Lett 14, 2515–2538 (2020). https://doi.org/10.1007/s11590-020-01571-6

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