Modeling the Relationship between an Investment Portfolio and the Ibovespa Index

Abstract

This study addresses the modeling of the relationship between an investment portfolio composed of the five largest assets listed on the stock exchange. For B3 (Brazil, Stock Exchange, and Over-the-Counter Market), the largest companies in Brazil are those with the highest Market Cap (market capitalization): Petrobras (PETR4), Vale (VALE3), Itaú Unibanco (ITUB4), Ambev (ABEV3), Weg (WEGE3), and the Ibovespa index (IBOV), over a period of five years. Using historical data, the analysis focuses on the price perspective, investigating fluctuations during this same period. In this context, the research employs the least squares method to construct a linear regression that seeks to understand the influence of the Ibovespa index on the portfolio's performance. The article details the steps of the process, from data collection and pre-processing to the interpretation of results, highlighting the mathematical formulation of linear regression as the main method used. The results are presented through generated graphs that provide information about the relationship between the portfolio and the aforementioned index.