Otimização do risco retorno de um portfolio de ações utilizando a programação binária

Abstract

Building an investment portfolio is a complex task where countless variables not exclusively linked to the assets themselves must be taken into account. The objective, however, is always to obtain the maximum return by exposing yourself to the lowest possible risk. The literature points out several methodologies for obtaining an optimal portfolio, involving programming logic and mathematical modeling, however, many fails to verify the real effectiveness of methodologies in the real world, in addition to too much complexity, remaining only in the theoretical-academic part. In this work it was proposed the composition of a portfolio in a similar way to the backpack problem using binary programming and the composition of the efficient frontier by means of non-linear programming to verify its effectiveness in comparison to a portfolio of 10 (ten) shares of a website investment. The programming variables were based on Markowitz's Theory of Portfolio Selection and the following contributors to their studies. From the portfolio chosen via binary programming, the efficient frontier was elaborated by means of non-linear programming to analyze the performance of the investment site portfolio during 30 days. Due to the complexity of the calculations, the Solver tool of the Microsoft Excel program was used to carry out the programming both to obtain the portfolio of 10 (ten) shares in the portfolio and to obtain the optimal portfolios that made up the efficient frontier. The portfolio obtained exceeded the percentage performance obtained from the investment website in the same period when considering the maximum possible return, the minimum global variance and also in the naive distribution.