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Fuzzy Portfolio Selection Models: A Numerical Study

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Financial Decision Making Using Computational Intelligence

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 70))

Abstract

In this chapter we analyze the numerical performance of some possibilistic models for selecting portfolios in the framework of risk-return trade-off. Portfolio optimization deals with the problem of how to allocate wealth among several assets, taking into account the uncertainty involved in the behavior of the financial markets. Different approaches for quantifying the uncertainty of the future return on the investment are considered: either assuming that the return on every individual asset is modeled as a fuzzy number or directly measuring the uncertainty associated with the return on a given portfolio. Conflicting goals representing the uncertain return on and risk of a fuzzy portfolio are analyzed by means of possibilistic moments: interval-valued mean, downside-risk, and coefficient of skewness. Thus, several nonlinear multi-objective optimization problems for determining the efficient frontier could appear. In order to incorporate possible trading requirements and investor’s wishes, some constraints are added to the optimization problems, and the effects of their fulfillment on the corresponding efficient frontiers are analyzed using a data set from the Spanish stock market.

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Acknowledgements

This research was partially supported by the Ministerio de Ciencia e Innovación of Spain under grant number MTM2008-03993. This manuscript was prepared during a research stay of E. Vercher at the Centre for Interdisciplinary Mathematics (CIM), Uppsala University (Sweden), supported by the Vicerectorat d’Investigació i Política Científica, University of València (Spain).

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  1. Department of Statistics and Operational Research, University of Valencia, C/ Dr. Moliner 50, 46100, Burjassot, Spain

    Enriqueta Vercher & José D. Bermúdez

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  1. Enriqueta Vercher
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  2. José D. Bermúdez
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Correspondence to Enriqueta Vercher .

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  1. Dept. Production Engineering, and Management, Technical University of Crete, University Campus, Chania, 731 00, Greece

    Michael Doumpos

  2. , Department of Production Engineering and, Technical University of Crete, University Campus, Chania, 73100, Greece

    Constantin Zopounidis

  3. , Department of Industrial and Systems Eng, University of Florida, Weil Hall 401, Gainesville, 32611, Florida, USA

    Panos M. Pardalos

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Vercher, E., Bermúdez, J.D. (2012). Fuzzy Portfolio Selection Models: A Numerical Study. In: Doumpos, M., Zopounidis, C., Pardalos, P. (eds) Financial Decision Making Using Computational Intelligence. Springer Optimization and Its Applications, vol 70. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-3773-4_10

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