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The Distribution of the Sample Minimum-Variance Frontier

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  • 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.

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File URL: http://dx.doi.org/10.1287/mnsc.1070.0852
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Bibliographic Info

Article provided by INFORMS in its journal Management Science.

Volume (Year): 54 (2008)
Issue (Month): 7 (July)
Pages: 1364-1380

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Handle: RePEc:inm:ormnsc:v:54:y:2008:i:7:p:1364-1380

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Related research

Keywords: minimum-variance frontier; efficiency set constants; finite sample distribution;

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Cited by:
  1. Yen, Yu-Min & Yen, Tso-Jung, 2014. "Solving norm constrained portfolio optimization via coordinate-wise descent algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 737-759.
  2. Kourtis, Apostolos & Dotsis, George & Markellos, Raphael N., 2012. "Parameter uncertainty in portfolio selection: Shrinking the inverse covariance matrix," Journal of Banking & Finance, Elsevier, vol. 36(9), pages 2522-2531.

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