Integrated Multi-Objective and Econometrics Model for Stock Portfolio Optimization

For the growth and development of countries, companies, and even individuals, investment on their part is necessary and vital, and these investments should be optimal for more benefit and effectiveness. Since the introduction of Markowitz's theory and even before that, the concept of optimal investment as a compromise between risk and return has been considered. During several decades after that, new definitions and dimensions of optimal criteria and especially risk have been proposed.In this article, an attempt has been made to present a model of liquidity risk using the concept of diversification in the form of Shannon's entropy and an econometric approach, an optimal portfolio of investments with the lowest risk and the highest return, in the form of a portfolio of 4 industrial groups of the Tehran Stock Exchange, including metal groups. Essentially, banks, oil products and metal ores, which have the highest market value of the Iranian stock market, should be provided.The statistical data of this research for selected industries include daily price index return and daily price gap return between 2015 and the end of 2019. To calculate the liquidity risk, using multivariate GARCH methods, the variance-covariance matrix of price index return and price gap, calculated and used in the presented model, and finally the optimal weight using coding in MATLAB software and using algorithm optimization method The genetics of non-excessive ranking of the second edition has been calculated for selected industries.The output results of the model show that the optimal weight of the groups with less variance in the optimal portfolio is higher. Besides, the effect of removing the concept of liquidity from the model leads to an increase in the weight of industries that have less liquidity, and along with the increase in risk, the return of the optimal portfolio also increases in this case. Also, by removing the limitation of Shannon's diversification index, the output results show that this limitation has almost no effect on the optimal weights (at least in this model).