The Distribution of the Sample Minimum-Variance Frontier
在收益率独立且服从多元正态分布的假设下，分析了样本最小方差前沿的有限样本性质，发现它是总体前沿的有偏估计，并提出了改进估计量，同时给出了样本最小方差组合的样本外均值和方差的精确分布。
In this paper, we present a finite sample analysis of the sample minimum-variance frontier under the assumption that the returns are independent and multivariate normally distributed. We show that the sample minimum-variance frontier is a highly biased estimator of the population frontier, and we propose an improved estimator of the population frontier. In addition, we provide the exact distribution of the out-of-sample mean and variance of sample minimum-variance portfolios. This allows us to understand the impact of estimation error on the performance of in-sample optimal portfolios.