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The Distribution of the Sample Minimum-Variance Frontier

Joseph L. Rotman School of Management, University of Toronto, Toronto, Ontario M5S 3E6, Canada
Faculty of Business Administration, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
kan{at}chass.utoronto.ca
drsmith{at}sfu.ca

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.

Key Words: minimum-variance frontier; efficiency set constants; finite sample distribution
History: Received: April 4, 2007;