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An extension of Sharpe's single-index model: portfolio selection with expert betas

Author:
Bilbao Terol, Amelia MaríaUniovi authority; Arenas Parra, María del MarUniovi authority; Pérez Gladish, Blanca MaríaUniovi authority; Jiménez López, Mariano; Rodríguez Uría, María VictoriaUniovi authority
Subject:

Portfolio Selection, Sharpe'S Single-Index Model, Expert Betas, Fuzzy Number, Fuzzy Goal Programming

Publication date:
2006
Editorial:

Palgrave Macmillan

Publisher version:
http://dx.doi.org/10.1057/palgrave.jors.2602133
Citación:
Journal of the Operational Research Society, 57, p. 1442–1451 (2006); doi:10.1057/palgrave.jors.2602133
Descripción física:
p. 1442-1451
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.

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.

URI:
http://www.palgrave-journals.com/jors/journal/v57/n12/abs/2602133a.html
http://hdl.handle.net/10651/9661
ISSN:
0160-5682; 1476-9360
DOI:
10.1057/palgrave.jors.2602133
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