Mathematical Modeling of Diversity in Portfolio Selection and Solving it with Genetic Algorithms

In the selection of a collection of investment assets, the expected utility of investor is determined via risk and return criteria. Regarding the uncertainty of the investor about the future, portfolio diversification is a common path towards risk reduction in investment problem. In this study, not only the Euclidean Distance Criterion (EDI) was introduced to be a measure of portfolio diversification, but also a multi-objective model was designed for portfolio selection. This model intended to maximize the return and diversification of portfolio, and also to minimize non-systematic risk of it. Since this is a non-linear model and in terms of complexity is among "NP-hard", regarding the computational efficiency of the Genetic Algorithms (GA) in optimization, it was used for solving the model. Results from the implementation of the dual-objective model (return and diversification) and triple-objective model (return, diversification, and non-systematic risk) with multiple-repetition showed that the average return of the portfolio selected by perposed model was higher than the favorable level. Investigation into portfolio performance indices indicates the efficiency of the dual-objective model (return and diversification).