Portfolio Selection with Robust Estimation
针对传统最小方差投资组合权重不稳定、受估计误差影响大的问题，提出一类使用稳健估计量的新组合，通过单步非线性规划同时完成估计与优化，在模拟和实证中表现更稳定且不牺牲样本外表现。
Mean-variance portfolios constructed using the sample mean and covariance matrix of asset returns perform poorly out of sample due to estimation error. Moreover, it is commonly accepted that estimation error in the sample mean is much larger than in the sample covariance matrix. For this reason, researchers have recently focused on the minimum-variance portfolio, which relies solely on estimates of the covariance matrix, and thus usually performs better out of sample. However, even the minimum-variance portfolios are quite sensitive to estimation error and have unstable weights that fluctuate substantially over time. In this paper, we propose a class of portfolios that have better stability properties than the traditional minimum-variance portfolios. The proposed portfolios are constructed using certain robust estimators and can be computed by solving a single nonlinear program, where robust estimation and portfolio optimization are performed in a single step. We show analytically that the resulting portfolio weights are less sensitive to changes in the asset-return distribution than those of the traditional portfolios. Moreover, our numerical results on simulated and empirical data confirm that the proposed portfolios are more stable than the traditional minimum-variance portfolios, while preserving (or slightly improving) their relatively good out-of-sample performance.