The Quantitative Diversity Index in Multi-Objective Portfolio Model

Document Type : Original Article


1 Associate Prof., Faculty of Industrial Engineering, K.N. Toosi University of Technology, Tehran, Iran. Pardis St. Molasadra Ave., Vanak Sq, Tehran 19395-1999, Iran

2 Ph.D. Candidate, Department of Financial Engineering, Faculty of Industrial Engineering, K.N. Toosi University of Technology, Tehran, Iran. Pardis St. Molasadra Ave., Vanak Sq, Tehran 19395-1999, Iran

3 Assistant Prof., Faculty of Industrial Engineering, K.N. Toosi University of Technology, Tehran, Iran.


The primary purpose of investors is maximizing the utility that is characterized by two essential criteria include risk and return. Regarding investors' uncertainty about the future, one of the main ways to reduce risk is to diversify the investment portfolio. In this research, we proposed an index conducted by Euclidean distance for assessing portfolio diversity. Besides, we designed a multi-objective model to select optimal stock portfolios with considering value at risk (VaR), which is one of the critical indicators of unacceptable risk, portfolio Beta as systematic risk, and portfolio variance as unsystematic risk simultaneously. The model presented in this paper aims to maximize diversification while minimizing value at risk and stock risks. Furthermore, maximizing returns are considered as a limitation of this model. Since the proposed model is nonlinear and concerning computational complexity, it is NP-hard; therefore, we utilized the PSO and the GE metaheuristic algorithms that are improved for solving multi-objective problems to solve the model. The results of the model implementation in multiple iterations showed that the average yield of selected portfolios by the model is higher than the desirable condition. The evaluation of stock performance indicators also shows the satisfactory performance of the multi-objective model.


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