Minimum Variance Portfolios in the Brazilian Equity Market

Abstract

We investigate minimum variance portfolios in the Brazilian equity market using different methods to estimate the covariance matrix, from the simple model of using the sample covariance to multivariate GARCH models. We compare the performance of the minimum variance portfolios to those of the following benchmarks: (i) the IBOVESPA equity index, (ii) an equally-weighted portfolio, (iii) the maximum Sharpe ratio portfolio and (iv) the maximum growth portfolio. Our results show that the minimum variance portfolio has higher returns with lower risk compared to the benchmarks. We also consider long-short 130/30 minimum variance portfolios and obtain similar results. The minimum variance portfolio invests in relatively few stocks with low βs measured with respect to the IBOVESPA index, being easily replicable by individual and institutional investors alike.

Keywords

• portfolio optimization
• minimum variance portfolios
• asset allocation
• quantitative asset management
• shrinkage