On the optimal combination of naive and mean-variance portfolio strategies

Vanderveken, Rodolphe [UCL] Lassance, Nathan [UCL] Vrins, Frédéric [UCL]

Tu and Zhou (2011) reaffirm the value of mean-variance portfolio theory by proposing a methodology to combine the sample mean-variance portfolio with the naive equally weighted portfolio. We show that the seemingly natural convexity constraint they impose---the two combination coefficients must sum to one---is unnecessary and yields several undesirable consequences relative to the unconstrained portfolio combination. In particular, it leads to an overinvestment in the sample mean-variance portfolio, and a worse performance than the risk-free asset for sufficiently risk-averse investors. 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. Empirically, the constrained combination outperforms the unconstrained one for investors with small risk aversion, but severely deteriorates as risk aversion increases. In contrast, the shrinkage unconstrained combination enjoys the best of both strategies and performs consistently well for all levels of risk aversion.