evolutionary algorithm

One of the most important issues for all investors, including individual and institutional investors in the stock market, is finding the optimal portfolio. Identifying the optimal portfolio in the stock market can be considered a two-objective optimization problem. This problem maximizes and minimizes the return and risk of the portfolio, respectively. Like other multi-objective optimization problems, the portfolio optimization problem can be solved by multi-objective evolutionary algorithms (MOEAs). Accordingly, the Non-dominated Sorting Genetic Algorithm ( ) and Strength Pareto Evolutionary Algorithm ( ), as the two advanced algorithms of multi-objective evolution algorithms, can be used to solve this problem. These algorithms identify the optimal solution by ranking and archiving solutions located on the Pareto frontier. The purpose of this research is to compare the performance of  and  in mean-variance and mean-semi-variance approaches to identify the optimal stock portfolio.

This research investigated 241 stocks enlisted on the Tehran Stock Exchange (TSE). It was conducted within 174 months from September 2006 to March 2019. The researchers first identified the optimal portfolio using NSGAII and SPEA2 algorithms through two approaches including mean-variance and mean-semi-variance. Then, by conducting a statistical hypothesis test on the average Sharp ratio of extracted portfolios, the performance of NSGAII and SPEA2 algorithms were compared. To confirm the research findings, a robustness test was done by comparing the performance of the SPEA2 algorithm with the traditional Markowitz model. Also, to ensure the stability of research findings, the performance of two algorithms in the mean-variance and mean-semi variance approaches were compared with quarterly data ending March 2022.

According to the obtained results, the SPEA2 algorithm has better performance than the NSGAII algorithm in both approaches. Backtesting the real data for the quarter ending inMarch 2022 confirmed the findings of the present study. Also by doing robustness tests, the researchers found the SPEA2 algorithm as the superior algorithm in this research with better performance than Markowitz's basic model.

The results indicated that the 2 algorithm has better performance in selecting the optimal portfolio than the  algorithm in both the mean-variance and mean-semi variance approaches. Regardless of how the stock returns are distributed, this study recommends that individual and institutional investors use the SPEA2 algorithm to determine the optimal portfolio arrangement.

Portfolio optimization is one of more important problems in financial area. The classic model consider that stocks is random variable with symmetric probability density function. But in real world, forecasting stock condition always faced with uncertainty and we need insert human factors in our forecasting. Fuzzy logic is one of methods that we can use this to model this condition. On other hand, experimental studies show that assets return isn’t normal and symmetric, so we should use down risk measure such as semi variance and semi absolute deviation.  In this research we consider two point in portfolio selection problem. Then we use two intelligent method based genetic and deferential evolutionary algorithm for solving the models. Making use of Tehran Stock Exchange data, it is concluded that considering semi absolute deviation has higher efficiency than semi variance model and intelligent method based deferential evolutionary algorithm has higher efficiency from intelligent method based genetic algorithm.