Aplica\c{c}\~ao do Movimento Browniano Geom\'etrico para Simula\c{c}\~ao de Pre\c{c}os de A\c{c}\~oes do \'Indice Brasileiro de Small Caps

TL;DR

This paper applies geometric Brownian motion to simulate stock prices of Brazilian Small Caps, comparing simulated data with actual prices from 2019, and evaluates portfolio performance based on risk and return metrics.

Contribution

The study demonstrates the effectiveness of geometric Brownian motion in simulating Small Cap stock prices and portfolio optimization in the Brazilian market.

Findings

Simulated prices closely match actual 2019 data.

Portfolios with higher returns and lower risks perform better.

Higher Sharpe Index portfolios show improved performance.

Abstract

This work addressed the use of the geometric Brownian motion to simulate the prices of shares listed in the Small Caps index of the Brazilian stock exchange B3 (Brazil, Bolsa, Balc\~ao). The data used refer to the price history from January 2016 to December 2018. The price history of 2019 was used to be compared with the simulated prices. The data was imported from the Yahoo Finance database using the Python programming language, and the simulations were performed for each stock individually, and for portfolios formed based on expected returns, risk and the Sharpe Index. The results were better for portfolios with higher returns, lower risks and higher Sharpe Indexes.