A Comparison of Portfolio Selection Models Based On the Random and the Fuzzy Random Security Returns in Tehran Stock Exchange

Introduction One of the basic problems of applied finance is the optimal selection of stocks by conflicting objective of maximizing future return and minimizing investment risk. The first systematic treatment of this dilemma is the mean variance approach proposed by Markowitz. Markowitz combined the optimization and probability theory to solve the dilemma. In Markowitz’s mean variance model, the security returns are assumed to be random variables, and the investors are postulated to establish equilibrium between the conflicted objectives, which the investment risk and return are respectively quantified by mean and variance of portfolio of security. A basic assumption behind Markowitz’s mean variance model is that the situation of the stock market in future can be correctly reflected by security data in the past, that is, mean and covariance of a portfolio of securities in the future are similar to the past ones. However, there are so many uncertain factors that this assumption cannot be guaranteed for the real ever changing stock markets. This uncertainty can be fuzzy variables, and consequently, a portfolio of securities can be selected on the assumption that security returns are considered to be fuzzy variables. A fuzzy variable is a measurable function from credibility space to a set of real numbers. Sometimes, fuzziness and randomness simultaneously appear in a system. A hybrid variable describes the quantities with