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We investigate whether sophisticated volatility estimation improves the out-ofsample performance of mean-variance portfolio strategies relative to the naïve 1/N strategy. The portfolio strategies rely solely upon second moments. Using a diverse group of econometric and portfolio models across multiple datasets, we show that a majority of models achieve significantly higher Sharpe ratios and lower portfolio volatility relative to the naïve rule, even after controlling for turnover costs. Our results suggest that there are benefits to employing more sophisticated econometric models than the sample covariance matrix, and that mean-variance strategies often outperform the naïve portfolio across multiple datasets and assessment criteria.