Avaliação de carteiras de ações: desempenho comparativo entre o índice Bovespa e carteiras propostas com base no modelo de Markowitz

Abstract

Due to the growth of the Brazilian stock exchange in 2016 and 2017 the number of new unprepared investors has grown. So, in this work, a model is presented for the choice of investments in the Brazilian stock market. The main objectives are to reduce non-systemic risks through efficient diversification and the construction of investment portfolios that show higher returns than the Bovespa index. For this, we apply Operational Research methods, which perform optimizations, to reduce risk and obtain returns according to objectives and constraints. For this, the method proposed by Markowitz (1952) is applied, which consists in reducing the risk of the choice of investment through diversification. A spreadsheet software was used and the algorithm used is called the non-linear GRG solution. The results consist of comparing the returns of the proposed portfolios with the Ibovespa index. The modeled portfolios were defined according to the basic Markowitz thesis. Then this basic model and two systems with 50% risk definition and 150% more of the minimum variance of the basic Markowitz model were constructed. We used an approach that analyzed one to four years of past data and simulations of portfolio permanence of one to three years. The portfolios that use one year of data and have remained for a year since their purchase obtained the best results, obtaining positive and relevant gains when compared to the Ibovespa. The portfolios that used two years of data obtained an oscillating performance, sometimes with high returns and in others with results below the standard index.