On the Combination of Naive and Mean-Variance Portfolio Strategies

We study how to best combine the sample mean-variance portfolio with the naive equally weighted portfolio to optimize out-of-sample performance. We show that the seemingly natural convexity constraint that Tu and Zhou (2011) impose—the two combination coefficients must sum to one—is undesirable because it severely constrains the allocation to the risk-free asset relative to the unconstrained portfolio combination. However, we demonstrate that relaxing the convexity constraint inflates estimation errors in combination coefficients, which we alleviate using a shrinkage estimator of the unconstrained combination scheme. Empirically, the constrained combination outperforms the unconstrained one in a range of generally small degrees of risk aversion, but severely deteriorates otherwise. In contrast, the shrinkage unconstrained combination enjoys the best of both strategies and performs consistently well for all levels of risk aversion.