The distribution of the sample minimum-variance frontier

• 成果类型: Article
• 署名作者: Kan, Raymond; Smith, Daniel R.
• 署名单位: University of Toronto; Simon Fraser University
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.1070.0852
• 发表日期: 2008
• 页码: 1364-1380
• 关键词: minimum-variance frontier; efficiency set constants; finite sample distribution

摘要

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.