We propose the so-called ρ-dependent strategy and test its performances against the extremely simple yet effective 1/N naïve rule and two Markowitz-related policies. Our out-of-sample results show that the ρ-dependent strategy tends to present significant higher portfolio Sharpe ratios and lower portfolio variance relative to these well-known benchmarks. Additionally, this enhanced performance is not explained by large exposures to traditional risk factors as indicated by the reported positive and statistically significant Carhart's alphas. More importantly, our results are robust to several portfolio configurations, time periods and markets even after accounting for transaction costs.