publication . Article . 2008

The Distribution of the Sample Minimum-Variance Frontier

Raymond Kan; Daniel R. Smith;
Open Access
  • Published: 01 Jan 2008 Journal: Management Science, volume 54, pages 1,364-1,380 (issn: 0025-1909, eissn: 1526-5501, Copyright policy)
  • Publisher: Institute for Operations Research and the Management Sciences (INFORMS)
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.
free text keywords: minimum-variance frontier, efficiency set constants, finite sample distribution, Management Science and Operations Research, Strategy and Management, Population, education.field_of_study, education, Multivariate statistics, Econometrics, Minimum-variance unbiased estimator, Estimator, Mathematical optimization, Statistics, Mathematics, Frontier, Sample size determination, Exact distribution, Bias of an estimator
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