CORE Brown Bag Seminar

Author: Rodolphe Vanderveken

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

Abstract : In an influential paper, Tu and Zhou (2011, RFS) reaffirm the added 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 that the two combination coefficients must sum to one is unnecessary in theory and has 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, although wrong in theory, we demonstrate that the convexity constraint acts as a bound constraint on combination coefficients and thus can help improve performance when these are estimated. Empirically, we find that the constrained combination outperforms the optimal combination for investors with small risk aversion, but quickly deteriorates and delivers negative utilities as risk aversion increases. In contrast, the optimal combination performs consistently well for any degree of risk aversion. Therefore, we introduce a mixed strategy that succeeds in taking the best of the optimal and constrained combination.