Higher moments

The main criterion in investment decisions is to maximize the investors utility. Traditional capital asset pricing models cannot be used when asset returns do not follow a normal distribution. For this reason, we use capital asset pricing model with independent and identically asymmetric power distributed (CAPM-IIAPD) and capital asset pricing model with asymmetric independent and identically asymmetric exponential power distributed with two tail parameters(CAPM-AIEPD) to estimate return and risk. When the assumption of normality is violated, the first and second moments lose their efficiency in optimization and we need to use the third and fourth moments. For the first time, we propose independent and identically asymmetric exponential power distributed with two tail parameters. Then, we use higher moments optimization with unequal weights to optimize portfolios. The results indicate that capital asset pricing model with independent and identically asymmetric power distributed (CAPM-IIAPD) is better than asymmetric independent and identically asymmetric exponential power distributed with two tail parameters(CAPM-AIEPD) to estimate return and risk. Adjusted Sharp ratio in portfolio optimization in second moments are higher than others. Adjusted returns to risk in third and fourth moments in the CAPM-IIAPD model significantly differ from the CAPM-AIEPD model and have a better performance.

The optimal portfolio selection is vital for investment. The risk of portfolio Selection and return is the most critical concern of investment companies and private investors. According to modern portfolio theory, diversification should cover the risk. This theory is based on the normality of assets return. Experimental findings indicate that the assets return non-normality. Higher moments are sed to upgrade traditional models with the primary presumption of a normal distribution in recent years. This study uses a higher moment and the entropy for diversification and selects a portfolio given a non-normality assumption. It is essential to use up-to-date information to increase the model's efficiency, and accordingly, we used the rolling window for new price information. For the financial information method, we use the total index return in the last five working days and weigh the shares of the banking, insurance, and leasing industries on the next working day and evaluate this for three years. Python, math, and NumPy libraries were used to analyze the data. The results show that a much higher moment model can provide better portfolio selection results in most cases.