Positively Weighted Minimum-Variance Portfolios and the Structure of Asset Expected Returns
推导了最小方差投资组合所有权重为正的简单可计算条件，发现要么不存在这样的组合，要么前沿上只有一段连续区域满足。分析表明，即使均值与协方差支持某正权重组合有效，该区域占比也很小且随资产数量增加而缩小，均值微小扰动就可能导致无正权重组合。
In this paper, we derive simple, directly computable conditions for minimum-variance portfolios to have all positive weights. We show that either there is no minimum-variance portfolio with all positive weights or there is a single segment of the minimum-variance frontier for which all portfolios have positive weights. Then, we examine the likelihood of observing positively weighted minimum-variance portfolios. Analytical and computational results suggest that: i) even if the mean vector and covariance matrix are compatible with a given positively weighted portfolio being mean-variance efficient, the proportion of the minimum-variance frontier containing positively weighted portfolios is small and decreases as the number of assets in the universe increases, and ii) small perturbations in the means will likely lead to no positively weighted minimum-variance portfolios.