Utilização da teoria moderna do portifólio e simulação de Monte carlo para seleção de carteira de investimento no mercado de ações brasileiro

Abstract

This study aims to apply Markowitz's Modern Portfolio Theory and Monte Carlo simulation in constructing efficient portfolios in the Brazilian stock market. Five assets are analyzed: Embraer S.A. (EMBR3), Companhia Energética de Minas Gerais (CMIG4), Petróleo Brasileiro S.A. (PETR3), Porto Seguro S.A. (PSSA3), and Suzano S.A. (SUZB3). The research has a quantitative nature, with an explanatory objective and a survey method, utilizing modeling and simulation. The study explores price evolution and asset behavior over the analyzed period, in addition to calculating average returns and the covariance matrix. Subsequently, a simulation was conducted to determine the efficient frontier by maximizing the Sharpe Ratio and minimizing volatility. A total of 100,000 random portfolios were generated to identify the optimal risk-return combinations. The study also discussed the weight distribution of the optimal portfolios, observing that the performance of the optimized portfolios exceeded the Bovespa index (IBOV), with particular emphasis on the portfolio that maximizes the Sharpe Ratio. This work contributes to understanding efficient portfolio construction in the Brazilian context by applying Markowitz's theory and simulating scenarios that aim to maximize the risk-return ratio, providing a robust analysis for investors.