Stock Portfolio Optimization with MAD and CVaR Criteria by Comparing Classical and Metaheuristic Methods

Subject Areas : Financial engineering

Mohammad reza Haddadi ¹ , Younes Nademi ² , Fateme Tafi ³

1 - Department of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran
2 - Department of Economics, Ayatollah Boroujerdi University, Boroujerd, Iran
3 - Department of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran

Received: 2020-08-06 Accepted : 2020-10-31 Published : 2021-06-22

Keywords: Value at Risk, Conditional Value at Risk, Markowitz model, Nonlinear optimization,

Abstract :

Choosing the optimal stock portfolio is one of the main goals of capital management. There are several criteria for choosing the optimal portfolio. In this paper, using data of 10 stocks which randomly selected from the Tehran Stock Exchange including Vanovin, Vakharazm, Seghrab, Shepna, Vapetro, Dana, Khasapa, Shekarbon, Shadous and Khahen, first the returns of these stocks are calculated and their portfolio risk is calculated using the models of absolute deviation risk and risk value, and these two criteria are compared by the classical solution method. The portfolio optimization output with each of these risks represents a different weight per share. In the optimization with the risk criterion of absolute deviation, the Dana has the highest weight and in the optimization with the value at risk criterion, the stocks of Segharb, Shepna and Shekarbon have the most weight. In the following, the deviation-absolute risk model and value at risk model of metaheuristic method are compared. The results show that the NSGA2 model of metaheuristic method compared to the classical method in solving portfolio optimization problem showed more risk in both MAD and CVaR criteria and therefore it is a better method to solve such portfolio optimization problems.