Optimal Versus Naive Diversification in Commodity Futures Markets

Motivated by the ongoing debate on whether optimal or naive diversification should be preferred when distributing wealth across investment alternatives, this article investigates how the choice of covariance estimator affects mean-variance portfolio selection. In an environment tailored to ideal tradability, we construct optimal commodity futures portfolios based on 12 promising covariance matrix estimators and compare their out-of-sample investment performance to a simple, equally weighted investment strategy by means of bootstrap testing. We find that neither the naive allocation approach nor the advanced covariance estimators can outperform the traditional sample covariance matrix. Because this empirical result is robust to modifications of the research design (including alternative investigation periods, data frequencies, estimation window sizes, holding period lengths, weight constraint specifications, and transaction cost levels), it opposes the recurrent suggestion of the equity-oriented literature that the sample covariance matrix should not be used for the purpose of portfolio optimization.