Higher moments Portfolio Optimization based on Generalized CAPM with asymmetric power distribution and fat tail

Every investor wants to select the optimal combination of return and risk in order to maximize their utility. In this study, an attempt was made to explain the optimal model for estimating returns and risk in cases where there is a financial crisis and the distribution of return on assets does not follow the normal distribution.For this purpose, we use CAPM with independent and identically asymmetric power distribution (CAPM-IIAPD) and CAPM with independent identically saymmetric exponential power distribution with two tail parameters (CAPM-IAEPD) instead of traditional CAPM. When the assumption of normality is violated, higher moments are used to optimize the model. In the next step, using Polynomial Goal Programming, we calculate optimal portfolios with third and fourth moments.The time horizon of the research from 2011 to 2018 and the statistical population has been all the companies of Tehran Stock Exchange, among which 30 companies have been selected.The results show that CAPM-IIAPD Model is the best model among three models and the adjusted return on risk in optimized models with thirs and fourth moemnts in generalized CAPM models is significantly different from the traditional model and has a better performance.