Beating the market with small portfolios: Evidence from Brazil

Optimal portfolios with a restriction on the number of assets, also referred to as cardinality-constrained portfolios, have been receiving attention in the literature due to its popularity among market practitioners and retail investors. In most cases, however, the interest is in proposing efficient optimization methods to solve the problem, with little or no attention to the characteristics of the resulting portfolio such as risk-adjusted performance and turnover. We address this question by implementing a tractable reformulation of the cardinality-constrained version of the minimum variance portfolio. We analyze the out-of-sample performance of cardinality-constrained portfolios according to alternative criteria and check the robustness of the results for portfolios with alternative number of assets and under alternative re-balancing frequencies. Our empirical application for the Brazilian equities market shows that cardinality-constrained minimum variance portfolios with very few assets, e.g. 3 stocks, can deliver statistically lower portfolio risk and higher Sharpe ratios in comparison to the market index. Similar results are obtained for constrained portfolios with 5 and 10 assets and under daily, weekly, and monthly re-balancing frequencies. Our evidence indicates that it is possible to obtain better risk-adjusted performance with fewer securities in the portfolio by using an improved allocation scheme..