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The Distribution of the Sample Minimum-Variance Frontier

Author

Listed:
  • Raymond Kan

    (Joseph L. Rotman School of Management, University of Toronto, Toronto, Ontario M5S 3E6, Canada)

  • Daniel R. Smith

    (Faculty of Business Administration, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada)

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.

Suggested Citation

  • Raymond Kan & Daniel R. Smith, 2008. "The Distribution of the Sample Minimum-Variance Frontier," Management Science, INFORMS, vol. 54(7), pages 1364-1380, July.
    • Handle: RePEc:inm:ormnsc:v:54:y:2008:i:7:p:1364-1380
    DOI: 10.1287/mnsc.1070.0852
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    References listed on IDEAS

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