A generalized mean-variance model for portfolio optimization problem in the simultaneous presence of random and uncertain returns

Abstract

In this paper, a composite mean-variance model for portfolio optimization problems in the simultaneous presence of random and uncertain returns has been revisited and generalized. The expressions for the mean and variance of the total uncertain random return have been obtained using chance distribution. The model is flexible, as it is capable of dealing with both types of stocks: those with sufficient past records and those that are newly introduced. A generalized uncertainty distribution is defined to represent the returns of newly introduced stocks. And, the return vector of the stocks with sufficient past records is assumed to follow a multivariate normal distribution. By varying the parameter(s) involved in the generalized uncertain return distribution, different representative problems can be obtained. Thus, the model provides the scope for incorporating subjective preferences. A comparative analysis of the solutions obtained for different problems has been conducted. The most suitable one may be selected by the analysis. The method of solution of the proposed model has been illustrated by constructing a numerical example involving 30 stocks randomly selected from Bombay Stock Exchange (BSE) India, out of which 20 stocks give a random return and the remaining 10 stocks give an uncertain return. The problem has been solved using the function “fmincon” in Matlab R2018a.