Stock Portfolio Optimization

The problem of optimal portfolio selection has attracted a great attention in the finance and optimization field. The future stock price should be predicted in an acceptable precision, and a suitable model and criterion for risk and the expected return of the stock portfolio should be proposed in order to solve the optimization problem. In this paper, two new criterions for the risk of stock price prediction has been presented, of which the first one is based on the interval predictions which vary with time and proportional to the uncertainty of stock price data, while the second one is a constant risk term that is proportional to the prediction error variances of the neural networks. A novel cost function has been presented to simultaneously consider the expected returns and risks. Genetic algorithm has been used to solve this optimization problem. Finally, 18 shares of the Tehran Stock Exchange have been considered to evaluate the performance of the proposed risk criterions. Two proposed risk criteria, by the conditional value at risk (CVaR) associated with the same stock. The problem of stock portfolio optimization has been solved for all three situations, and the PI-based risk criteria yielded a better return

stock market is considered as the most profitable and valuable areas of investment in any country. In this regard, high return depends on the correct choice of stock portfolio.That’s why today different methods of mathematical planning and decision-making have been proposed to solve such problems. Aiming to present a new method, the study designates 10 criteria for selecting the best stock portfolio options among the 21 most viewed options in the stock market. The method is a combination of fuzzy SAW and experimental design (2k factorial design). Analysis of variance results for the response variable is calculated . The value of R2 obtained from the response variable of 70% value, shows that this model has selected suitable options by removing ineffective criteria and analysing the results and discovering the relationships between criteria and ranking the criteria and presenting simpler solutions in addition to high accuracy. As a result, by considering and comparing the real values of the stock market in one-month and quarterly intervals, the model presents more capabilities for providing accurate ranking and higher portfolio returns than fuzzy TOPSIS in the capital and stock markets. The response surface method and the regression equation obtained in the proposed method are used to rank the options. In addition, Pareto method, which ranks the criteria based on the effectiveness of the criteria in the final result and regard to the surfaces of experiments and weights of capital market and stock market experts, is used for ranking the factors (criteria).

The purpose of this study is to make investment decisions with the approach of data envelopment analysis and making decision on selection of optimal stock portfolio employing meta heuristic algorithms for multi-objective functions subject to real-life constraints. The statistical population of this research in capital decision-making and selection of the optimal capital composition is 183 of the selected companies of Tehran Stock Exchange, which were finally 42 companies as justified investment options. After measuring the risk and return of efficient companies, the real limitations of the budget, requirements and expectations of the investor, determination and composition of the investment were formulated as a multi-objective model. For optimal decision, the modified genetic meta heuristic algorithm and MATLAB software with dual operators were used. Elimination of the risk minimization function in sensitivity analysis improved the level of decision return but also led to more risk. Eliminating the maximizing return function improved decision-making risk but also reduced investment return. Elimination of investment requirements and expectations improved returns and increased investment risk, but more companies became involved in optimal investment.