Comparison of Optimization Methods and Estimation of the Expected Return on the Optimal Portfolio Shares

Modern Portfolio Theory is based on Harry Markowitz''s 1952 work on mean-variance portfolios. He stated that a rational investor should either maximize his expected return for a given level of risk، or minimize his risk for a given expected return. In this study the Markowitz model with cardinality constraints was studied. We extend the standard model to include cardinality constraints that limit a portfolio to have a specified number of assets، and to impose limits on the proportion of the portfolio held in a given asset (if any of the assets is held). Since considering the Markowitz model with cardinality constraints leads to NP-hard optimization problem، we introduce a Genetic Algorithm. In the usual manner، mean of the historical returns are used as inputs in the Markowitz model as rate of stock returns estimation. With studying the security prices، are shows that the rate of stock returns is difference with mean of historical returns، so with the aim of artificial neural networks، they were estimated. The proposed method was experienced on Tehran stock Exchange and the method was showed good results.