1. ¹Universidad de Oviedo, Oviedo, Spain
2. ²Universidad del País Vasco, San Sebastián, País Vasco, Spain

Correspondence: B Perez Gladish, Departamento de Economía Cuantitativa, Facultad de Economicas, avda. del Cristo, s/n, Oviedo (Asturias), 33006, Spain. E-mail: bperez@uniovi.es

Received July 2004; Accepted October 2005; Published online 14 December 2005.

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.