Portfolio optimization using modified Markowitz model based on CO-GARCH modeling compared to the market

Abstract

Portfolio optimization and deciding which stocks deserve to be included in the investment portfolio and how to allocate capital are complex issues. Theoretically, the selection of the stock portfolio in the case of risk minimization can be solved Using mathematical formulas and through a quadratic equation, but in the real world, given that the behavior of the stock market does not follow a linear pattern, common linear methods also cannot be useful in describing this behavior. A natural way to consider time-based constraints of discrete processes is to use GARCH family models. The continuous-time GARCH (CO-GARCH) model is a direct analogue of the discrete-time GARCH that generalizes the basic features of the mentioned process in a natural way. Another advantage of the CO-GARCH model is that its second-order structure is known and defined. Therefore, in this research, portfolio optimization using the modified Markowitz model based on CO-GARCH modeling has been investigated in comparison with the market. The statistical population of the current research includes the information of the companies admitted to the Tehran Stock Exchange for the period of 2010 to 2019 and the statistical sample was selected using the systematic elimination method. First, the optimal investment model based on the Markowitz model based on the CO-GARCH model was presented and then compared with the market. The results of the research indicate that the efficiency of the optimal portfolio formed using the adjusted Markowitz model based on CO-GARCH fluctuations has a significant difference compared to the efficiency of the market.

Keywords

• portfolio optimization
• markowitz model
• co-garch modeling
• market