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—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.

本研究旨在探索如何最优地将样本均值-方差投资组合（sample mean-variance portfolio）与朴素等权重投资组合相结合，以优化投资的样本外表现。我们发现，看似合理的凸性约束——要求两个组合系数之和恒为1——实则并不适宜，因为相较于无约束组合配置方案，该约束会大幅限制无风险资产的配置比例。与此同时，我们证实，放松凸性约束会放大组合系数的估计误差，对此可通过针对无约束组合配置方案的收缩估计量（shrinkage estimator）加以缓解。实证结果显示，约束组合配置在多数小幅风险厌恶水平下表现优于无约束组合配置，但在其余场景下其性能会出现显著下滑。与之形成对比的是，引入收缩估计的无约束组合配置兼收两者之长，在所有风险厌恶水平下均能保持稳定优异的表现。