MOACO Algorithm

This study examines the criterion of value at risk from another perspective and presents a new type of mean-value at Risk model. To solve the portfolio optimization problem in Tehran Stock Exchange, we use NSGA II, MOACO, and MOABC algorithms and then compare the mean-pVaR model with the mean-SV model. Given that, finding the best answer is very important in meta-heuristic methods, we use the concept of dominance in the discussion of multi-objective optimization to find the best answers and show that, at low iterations, the performance of the NSGA II algorithm is better than the MOABC and MOACO algorithms in solving the portfolio optimization problem. As the iteration increases, the performance of the algorithms improves, but the rate of improvement is not the same, in a way, the performance of the MOABC algorithm is better than that of the NSGA II and MOACO algorithms. Then, to compare the performance of the “mean-percentage of Value at Risk” model and the “mean-semi variance” model, we examine both models in the standard mean-variance model and show that the mean-pVaR model, compared to the mean-SV model, Has better performance in stock portfolio optimization.

Price return and P/E are two interesting factors for a lot of investors; The Bohmian quantum mechanics used referring to the time correlation of return and P/E of the stock market under consideration. In this study, we extend the quantum potential concept to determine the behaviour of P/E and also price return in two different industry of Tehran stock market during a time interval of April. 2008 to march 2019. The obtained results show that the quantum potential behaves in the same manner for P/E and price return, also confines the variations of the P/E and price return into a specific domain. Furthermore, a joint quantum potential as a function of return and P/E is derived by the probability distribution function (PDF) constructed by the real data of a given market. It serves as a suitable instrument to investigate the relationship between these variables. The resultant PDF and the corresponding joint quantum potential illustrate that where we have light points in joint quantum potential chart, the probability of those amount of P/E and price return are more than other points. In addition, because of the rectangular shape of the joint quantum potential chart we can say that these two variables behave as two independent variables in the Market.