Background: The present study compares different measures of risk using the stocks of Tehran Stock Exchange petrochemical companies and optimizing the portfolio of these companies.
Aim: The main purpose of this study is comparing the efficiency of new risk measures, namely Cumulative Entropy and Gini Mean Difference versus the traditional measure of Variance (Standard Deviation). other goals of this study are optimizing the portfolio of petrochemical companies and also comparing the amount of closing price risk in annual (long-term), seasonal (medium-term) and monthly (short-term) intervals.
Methodology: In the present study, the data of 15 petrochemical companies in Tehran Stock Exchange from 2013 to 2019 have been collected. In this research, the Markowitz portfolio optimization model is used and to solve the portfolio optimization problem, four patterns are designed by using Variance, Semi variance, Cumulative entropy and Gini mean difference measures. Finally, the most efficient risk measure and the best portfolio optimization pattern for optimizing petrochemical companies portfolio will be recognized.
Findings: The results show that Cumulative entropy and Gini mean difference measures have a strong linear relationship with the standard deviation and can be used as a risk measure. The risk of petrochemical companies closing price in the annual interval is less than the seasonal and monthly intervals. Also, by solving the portfolio optimization problem of petrochemical companies using 4 optimization patterns, the mean-cumulative entropy pattern has obtained better values for the objective functions of the optimization problem compared to other patterns.
Conclusions: Based on the findings of this study, Cumulative entropy is the most efficient measure of risk. Therefore, shareholders who intend to invest in Tehran Stock Exchange petrochemical companies can optimize portfolio according to the Mean-cumulative entropy pattern, and in order to have a lower risk portfo