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Estimation of optimal portfolio compositions for Gaussian returns

Author

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  • Bodnar Taras

    (European University Viadrina, Department of Statistics, Frankfurt (Oder), Deutschland)

  • Schmid Wolfgang

Abstract

We consider the expected return and the variance of the expected quadratic utility portfolio and the tangency portfolio. The expected returns on the individual assets and their covariance matrix are estimated by the sample mean and the sample covariance matrix. Replacing the unknown parameters by these estimators in the portfolio characteristics estimators of the expected portfolio return and the portfolio variance are obtained.In this paper we calculate the densities of these estimators assuming independent and multivariate normally distributed returns. Because the densities can be computed by using standard mathematical software packages these representations are very useful. These results can be applied to construct tests and confidence intervals for the parameters of the efficient frontier.

Suggested Citation

  • Bodnar Taras & Schmid Wolfgang, 2009. "Estimation of optimal portfolio compositions for Gaussian returns," Statistics & Risk Modeling, De Gruyter, vol. 26(3), pages 179-201, April.
    • Handle: RePEc:bpj:strimo:v:26:y:2009:i:3:p:179-201:n:1
    DOI: 10.1524/stnd.2008.0918
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    References listed on IDEAS

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    1. Taras Bodnar & Wolfgang Schmid, 2008. "A test for the weights of the global minimum variance portfolio in an elliptical model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 67(2), pages 127-143, March.
    2. MacKinlay, A Craig & Pastor, Lubos, 2000. "Asset Pricing Models: Implications for Expected Returns and Portfolio Selection," The Review of Financial Studies, Society for Financial Studies, vol. 13(4), pages 883-916.
    3. Tu, Jun & Zhou, Guofu, 2004. "Data-generating process uncertainty: What difference does it make in portfolio decisions?," Journal of Financial Economics, Elsevier, vol. 72(2), pages 385-421, May.
    4. Kan, Raymond & Zhou, Guofu, 2007. "Optimal Portfolio Choice with Parameter Uncertainty," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 42(3), pages 621-656, September.
    5. Jobson, J. D. & Korkie, Bob, 1989. "A Performance Interpretation of Multivariate Tests of Asset Set Intersection, Spanning, and Mean-Variance Efficiency," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(2), pages 185-204, June.
    6. Golosnoy, Vasyl & Ragulin, Sergiy & Schmid, Wolfgang, 2011. "CUSUM control charts for monitoring optimal portfolio weights," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 2991-3009, November.
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    Cited by:

    1. Andrew Kumiega & Thaddeus Neururer & Ben Van Vliet, 2014. "Trading system capability," Quantitative Finance, Taylor & Francis Journals, vol. 14(3), pages 383-392, March.

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