Aplicação do Modelo de Markowitz na Otimização de Carteiras: Um Estudo com Ações da B3

Abstract

This paper presents the application of mathematical optimization theory in the financial context, focusing on the construction of investment portfolios based on Harry Markowitz's model, known as Modern Portfolio Theory, to show how it is possible to maximize the expected return of a portfolio for a given level of risk, using statistical concepts. Initially, the main concepts of the financial market are presented and then the relationship between risk and return is presented, highlighting the importance of diversification as a strategy to reduce the non-systematic risk of a portfolio. Based on the principles of Markowitz's theory, an empirical analysis was carried out using historical return data from ten shares of Brazilian companies with the highest liquidity, listed on B3, in the period from April 2015 to April 2025. From this data, the average returns, standard deviations and correlation coefficients between the assets were calculated, enabling the construction of different portfolios and the identification of those that make up the efficient frontier — that is, the portfolios that offer the best balance between risk and return. The results confirm that mathematical modeling and statistical analysis are effective in investment management, showing that selecting assets based on their characteristics and correlations can provide superior performance to randomly constructed portfolios. The application of the Markowitz model thus proves to be an important contribution for investors seeking to make informed decisions aligned with their risk profile.