Fuzzy portfolio optimization based on higher moments and entropy

Portfolio selection problem has been an important issue of finance and investment in every period. The essence of the problem is to find the best portfolio with certain criteria and constraints. Criteria and constraints may vary according to investors. However, the main element of the portfolio is the return and risk items. In Modern Portfolio Theory defined by Markowitz, these items are associated with portfolio mean and variance, respectively. According to the Modern Portfolio Theory, the decision-maker can reduce the portfolio risk by not including the stocks that have positive correlation among themselves in the portfolio. One of the most important assumptions of Modern Portfolio Theory is the normal distribution of the series. The cases where the return series of stocks are not normally distributed are common in the literature. In cases where the normal distribution is not observed and the utility functions of investors are different from the quadratic structure, higher order moments such as skewness and kurtosis can be added to the portfolio optimization process. One of the biggest problems faced by portfolio models based on moments is the corner solutions which are frequently produced by the models and where there is an accumulation of certain stocks. In addition, portfolios consist of stocks that may be affected by different events such as future returns, political crisis, financial fluctuations and technological developments. When portfolio models are created using only historical data, structural risk is ignored. In order to solve these problems, the portfolio model includes entropy functions that provide natural diversity, independent of the historical data. However, entropy functions can produce results that are far from the decision maker's point of view and dominate other objective functions. In this study, the performance of portfolio models consisting of higher order moments and entropy functions are investigated. For this purpose, four different programming approaches, four different data sets and four different entropy functions were established with portfolio models. As a contribution to the literature, the use of higher order moments and entropy in portfolio selection was examined in detail for the first time and two new suggestions and a new fuzzy entropy function were defined in portfolio programming approaches. It is observed that combined use of higher order moments and entropy functions yielded better results. With the suggestions presented in the study, the accumulation of certain stocks in the portfolio, the imbalance between the functions in the sample, the misinterpretation of the investor preferences to the portfolio models which are the problems of the classical models have been eliminated, and at the same time, non-sampling performance reflecting real financial performance has been achieved better than the models in the literature.