Abstract
This paper presents an approach to the portfolio selection problem based on Sharpe's single-index model and on Fuzzy Sets Theory. In this sense, expert estimations about future Betas of each financial asset have been included in the portfolio selection model denoted as ‘Expert Betas’ and modelled as trapezoidal fuzzy numbers. Value, ambiguity and fuzziness are three basic concepts involved in the model which provide enough information about fuzzy numbers representing ‘Expert Betas’ and that are simple to handle. In order to select an optimal portfolio, a Goal Programming model has been proposed including imprecise investor's aspirations concerning asset's proportions of both, high-and low-risk assets. Semantics of these goals are based on the fuzzy membership of a goal satisfaction set. To illustrate the proposed model a real portfolio selection problem is presented.
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Acknowledgements
We are grateful and thank the referees and the editor for the helpful comments. This research has been supported by project MTM2004-07478 of the Spanish Education and Science Ministry. This work has been developed with the inestimable help of the PhD student Carlos Mallo.
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Bilbao, A., Arenas, M., Jiménez, M. et al. An extension of Sharpe's single-index model: portfolio selection with expert betas. J Oper Res Soc 57, 1442–1451 (2006). https://doi.org/10.1057/palgrave.jors.2602133
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DOI: https://doi.org/10.1057/palgrave.jors.2602133