Regressão linear integrada ao modelo de Markowitz: quantificando a incerteza na fronteira eficiente de portfólios e sua relação com fatores macroeconômicos

Abstract

This study investigates how linear regression analysis can complement the Markowitz model in the selection and optimization of investment portfolios. Regression models were adjusted to predict the returns of two assets based on macroeconomic variables, and the results were integrated into Markowitz's theory to construct a new efficient frontier. The assets chosen from the Brazilian Stock Exchange (IBOVESPA) database were BBAS3 and IVVB11, on a monthly scale from 2017 to 2024, with the 2024 data being used only to evaluate the portfolio return predictions. Among the macroeconomic indicators, the IBOVESPA index and the dollar exchange rate were considered. The comparison between historical, predicted and actual returns demonstrated that the use of statistical modeling improves the accuracy of forecasts, reducing the mean error (RMSE) and bringing estimated returns closer to actually observed values. The results indicate that the inclusion of regression models can offer more accurate estimates than the simple use of historical averages (RMSE= 0.009 versus RMSE=0.014), reinforcing the importance of economic forecasting in decision making. However, it should be noted that effective forecasts require reliable estimates of future macroeconomic indicators.