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The Distribution of the Sample Minimum-Variance Frontier

  • 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)

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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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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  1. Andrew F. Siegel & Artemiza Woodgate, 2007. "Performance of Portfolios Optimized with Estimation Error," Management Science, INFORMS, vol. 53(6), pages 1005-1015, June.
  2. Miller, Robert E. & Gehr, Adam K., 1978. "Sample Size Bias and Sharpe's Performance Measure: A Note," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 13(05), pages 943-946, December.
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  7. Raman Uppal & Lorenzo Garlappi & Tan Wang, 2004. "Portfolio Selection with Parameter and Model Uncertainty: A Multi-Prior Approach," Money Macro and Finance (MMF) Research Group Conference 2004 54, Money Macro and Finance Research Group.
  8. Lars Peter Hansen & Ravi Jagannathan, 1994. "Assessing specification errors in stochastic discount factor models," Staff Report 167, Federal Reserve Bank of Minneapolis.
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  10. Dickinson, J. P., 1974. "The Reliability of Estimation Procedures in Portfolio Analysis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 9(03), pages 447-462, June.
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  13. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
  14. Kan, Raymond & Zhou, Guofu, 2007. "Optimal Portfolio Choice with Parameter Uncertainty," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 42(03), pages 621-656, September.
  15. Merton, Robert C., 1972. "An Analytic Derivation of the Efficient Portfolio Frontier," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 7(04), pages 1851-1872, September.
  16. Jorion, Philippe, 1985. "International Portfolio Diversification with Estimation Risk," The Journal of Business, University of Chicago Press, vol. 58(3), pages 259-78, July.
  17. Barry, Christopher B, 1974. "Portfolio Analysis under Uncertain Means, Variances, and Covariances," Journal of Finance, American Finance Association, vol. 29(2), pages 515-22, May.
  18. Okhrin, Yarema & Schmid, Wolfgang, 2006. "Distributional properties of portfolio weights," Journal of Econometrics, Elsevier, vol. 134(1), pages 235-256, September.
  19. Jorion, Philippe, 1986. "Bayes-Stein Estimation for Portfolio Analysis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(03), pages 279-292, September.
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