The Distribution of the Sample Minimum-Variance Frontier
Management Science · 2008 · Volume 54 · Issue 7
Abstract
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.
Keywords
minimum-variance frontier, efficiency set constants, finite sample distribution
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