On constructing expert Betas for single-index model

The aim of this paper is to design flexible decision making models for portfolio selection including expert’s knowledge and imprecise preferences provided by financial analysts and investors, respectively.Sharpe’s single-index model involves the estimation of Beta for each potential asset; these estimations are obtained based on past data and using statistical methods in order to obtain future Betas. The main contribution of our paper is the methodological proposal of an extension of Sharpe’s single-index model, called “Sharpe’s model with expert Betas”. This extension has been carried out through the construction of Betas obtained from both, statistical and imprecise expert estimations taking, also, into account several views of the market. Defined Betas, called “Expert Betas”, must have suitable features with respect to the quality and handling of information such that they can be incorporated in useful mathematical programming models. In this sense, the inclusion of these Expert Betas in a Goal Programming (GP) decision making model for portfolio selection is proposed.