Portfolio optimization

As the main achievement of the modern portfolio theory, portfolio diversifica-tion based on risk and return has attracted the attention of many researchers. The Markowitz mean-variance problem is a convex quadratic problem turned into a mixed-integer quadratic programming problem when incorporating car-dinality constraints. Due to the high number of stocks in a market, this problem becomes an NP-hard problem. In this paper, a metaheuristic approach is pro-posed to solve the portfolio optimization problem with cardinality constraints using the differential evolution algorithm, while it is also intended to improve the solutions generated by the algorithm developed. In addition, variance, val-ue-at-risk, and conditional value-at-risk are assessed as risk measures. Candi-date models are solved for 50 top stocks introduced by the Tehran Stock Ex-change by considering the cardinality constraints of not more than five stocks within the portfolio and 24 trading periods. Finally, the obtained results are compared with the results of genetic algorithm. The results show that the pro-posed method has reached the optimal solution in a shorter time.

The existence of bubbles in the market, especially the capital market, can be a factor in preventing the participation of investors in the capital market process and the correct allocation of financial resources for the economic development of the country. On the other hand, due to the goal of investors in achieving a portfolio of high returns with the least amount of risk, the need to pay attention to these markets increases. In this research, with the aim of maximizing return and minimizing investment risk, an attempt has been made to form an optimal portfolio in conditions where the capital market has a price bubble. According to the purpose, the research is of applied type, and in terms of data, quantitative and post-event, and in terms of type of analysis, it is of descriptive-correlation type. In order to identify the months with bubbles in the period from 2015 to 2021 in the Tehran Stock Exchange market, sequence tests and skewness and kurtosis tests were used. After identifying periods with bubbles, the meta-heuristic algorithms were used to optimize the portfolio. The results indicate the identification of 14 periods with price bubbles in the period under study. Also, in portfolio optimization, selected stock portfolios with maximum returns and minimum risk are formed. This research will be a guide for investors in identifying bubble courses and how to form an optimal portfolio in these conditions.

An investment portfolio is a collection of financial assets consisting of investment tools such as stocks, bonds, and bank deposits, among others, which are held by a person or a group of persons. In this research, we use the Markowitz model to optimize the stock portfolio and identify the minimum spanning tree (MST) structure in the portfolio consisting of 50 stocks traded in the TSE. The observable which is used to detect the minimum spanning tree (MST) of the stocks of a given portfolio is the synchronous correlation coefficient of the daily difference of logarithm of closure price of stocks. The correlation coefficient is calculated between all the possible pairs of stocks present in the portfolio in a given time course. The goal of the present study is to obtain the taxonomy of a portfolio of stocks traded in the TSE by using the information of time series of stock prices only. In this research, report results obtained by investigating the portfolio of the stocks used to compute 50 stocks of the Iran Stock Exchange in the time period from January 2012 to October 2022.