Footnote:
Nach Informationen von SSRN wurde die ursprüngliche Fassung des Dokuments July 25, 2022 erstellt
Description:
A disheartening fact in portfolio choice is that the naive equally weighted portfolio often outperforms the estimated optimal mean-variance portfolio out of sample. In an influential paper, Tu and Zhou (2011) reaffirm the value of portfolio theory by combining the two portfolios to optimize out-of-sample performance. They achieve this under a seemingly natural convexity constraint: the two combination coefficients must sum to one. We show that this constraint is unnecessary in theory and has several undesirable consequences relative to the unconstrained portfolio combination we derive. 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 they are estimated. Our empirical analysis shows that the Tu and Zhou 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 unconstrained portfolio 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