IDEAS home Printed from https://ideas.repec.org/a/bpj/strimo/v28y2011i4p319-342n3.html
   My bibliography  Save this article

On the exact distribution of the estimated expected utility portfolio weights: Theory and applications

Author

Listed:
  • Bodnar Taras
  • Schmid Wolfgang

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

Abstract

In this paper we consider the portfolio weights obtained by maximizing the expected quadratic utility function. The unknown parameters of the return process, the mean vector and the covariance matrix, are estimated by their sample counterparts. Assuming independent and multivariate normally distributed returns we derive the conditional density of the estimated weights given the mean vector of the asset returns and the unconditional density of the estimated weights. Moreover, the characteristic function of the estimated weights is calculated and it is used to determine the moments of higher order. Furthermore a test for the mean-variance efficiency is presented.

Suggested Citation

  • Bodnar Taras & Schmid Wolfgang, 2011. "On the exact distribution of the estimated expected utility portfolio weights: Theory and applications," Statistics & Risk Modeling, De Gruyter, vol. 28(4), pages 319-342, December.
    • Handle: RePEc:bpj:strimo:v:28:y:2011:i:4:p:319-342:n:3
    DOI: 10.1524/strm.2011.1080
    as

    Download full text from publisher

    File URL: https://doi.org/10.1524/strm.2011.1080
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1524/strm.2011.1080?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    2. 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.
    3. Best, Michael J & Grauer, Robert R, 1991. "On the Sensitivity of Mean-Variance-Efficient Portfolios to Changes in Asset Means: Some Analytical and Computational Results," The Review of Financial Studies, Society for Financial Studies, vol. 4(2), pages 315-342.
    4. Stambaugh, Robert F., 1982. "On the exclusion of assets from tests of the two-parameter model : A sensitivity analysis," Journal of Financial Economics, Elsevier, vol. 10(3), pages 237-268, November.
    5. Okhrin, Yarema & Schmid, Wolfgang, 2006. "Distributional properties of portfolio weights," Journal of Econometrics, Elsevier, vol. 134(1), pages 235-256, September.
    6. Bob Korkie & Harry J. Turtle, 2002. "A Mean-Variance Analysis of Self-Financing Portfolios," Management Science, INFORMS, vol. 48(3), pages 427-443, March.
    7. 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.
    8. Gibbons, Michael R & Ross, Stephen A & Shanken, Jay, 1989. "A Test of the Efficiency of a Given Portfolio," Econometrica, Econometric Society, vol. 57(5), pages 1121-1152, September.
    9. Kandel, Shmuel & Stambaugh, Robert F, 1996. "On the Predictability of Stock Returns: An Asset-Allocation Perspective," Journal of Finance, American Finance Association, vol. 51(2), pages 385-424, June.
    10. Adler, Michael & Dumas, Bernard, 1983. "International Portfolio Choice and Corporation Finance: A Synthesis," Journal of Finance, American Finance Association, vol. 38(3), pages 925-984, June.
    11. Mark Britten‐Jones, 1999. "The Sampling Error in Estimates of Mean‐Variance Efficient Portfolio Weights," Journal of Finance, American Finance Association, vol. 54(2), pages 655-671, April.
    12. Ľuboš Pástor, 2000. "Portfolio Selection and Asset Pricing Models," Journal of Finance, American Finance Association, vol. 55(1), pages 179-223, February.
    13. Shanken, Jay, 1986. "Testing Portfolio Efficiency When the Zero-Beta Rate Is Unknown: A Note," Journal of Finance, American Finance Association, vol. 41(1), pages 269-276, March.
    14. 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.
    15. Merton, Robert C., 1972. "An Analytic Derivation of the Efficient Portfolio Frontier," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 7(4), pages 1851-1872, September.
    16. Bodnar, Taras & Okhrin, Yarema, 2008. "Properties of the singular, inverse and generalized inverse partitioned Wishart distributions," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2389-2405, November.
    17. Merton, Robert C., 1980. "On estimating the expected return on the market : An exploratory investigation," Journal of Financial Economics, Elsevier, vol. 8(4), pages 323-361, December.
    18. Taras Bodnar & Wolfgang Schmid, 2009. "Econometrical analysis of the sample efficient frontier," The European Journal of Finance, Taylor & Francis Journals, vol. 15(3), pages 317-335.
    19. Nicholas Barberis, 2000. "Investing for the Long Run when Returns Are Predictable," Journal of Finance, American Finance Association, vol. 55(1), pages 225-264, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bodnar, Taras & Parolya, Nestor & Schmid, Wolfgang, 2013. "On the equivalence of quadratic optimization problems commonly used in portfolio theory," European Journal of Operational Research, Elsevier, vol. 229(3), pages 637-644.
    2. Penaranda, Francisco, 2007. "Portfolio choice beyond the traditional approach," LSE Research Online Documents on Economics 24481, London School of Economics and Political Science, LSE Library.
    3. Muhinyuza, Stanislas & Bodnar, Taras & Lindholm, Mathias, 2020. "A test on the location of the tangency portfolio on the set of feasible portfolios," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    4. Bodnar, Taras & Mazur, Stepan & Okhrin, Yarema, 2017. "Bayesian estimation of the global minimum variance portfolio," European Journal of Operational Research, Elsevier, vol. 256(1), pages 292-307.
    5. Bodnar Taras & Schmid Wolfgang & Zabolotskyy Tara, 2012. "Minimum VaR and minimum CVaR optimal portfolios: Estimators, confidence regions, and tests," Statistics & Risk Modeling, De Gruyter, vol. 29(4), pages 281-314, November.
    6. Bodnar, Taras & Parolya, Nestor & Thorsén, Erik, 2023. "Is the empirical out-of-sample variance an informative risk measure for the high-dimensional portfolios?," Finance Research Letters, Elsevier, vol. 54(C).
    7. Taras Bodnar, 2009. "An exact test on structural changes in the weights of the global minimum variance portfolio," Quantitative Finance, Taylor & Francis Journals, vol. 9(3), pages 363-370.
    8. Tu, Jun & Zhou, Guofu, 2010. "Incorporating Economic Objectives into Bayesian Priors: Portfolio Choice under Parameter Uncertainty," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 45(4), pages 959-986, August.
    9. Mårten Gulliksson & Stepan Mazur, 2020. "An Iterative Approach to Ill-Conditioned Optimal Portfolio Selection," Computational Economics, Springer;Society for Computational Economics, vol. 56(4), pages 773-794, December.
    10. Taras Bodnar & Holger Dette & Nestor Parolya & Erik Thors'en, 2019. "Sampling Distributions of Optimal Portfolio Weights and Characteristics in Low and Large Dimensions," Papers 1908.04243, arXiv.org, revised Apr 2023.
    11. Okhrin, Yarema & Schmid, Wolfgang, 2006. "Distributional properties of portfolio weights," Journal of Econometrics, Elsevier, vol. 134(1), pages 235-256, September.
    12. Begoña Font, 2016. "Bootstrap estimation of the efficient frontier," Computational Management Science, Springer, vol. 13(4), pages 541-570, October.
    13. Bodnar, Taras & Mazur, Stepan & Podgórski, Krzysztof, 2016. "Singular inverse Wishart distribution and its application to portfolio theory," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 314-326.
    14. Bob Korkie & Harry J. Turtle, 2002. "A Mean-Variance Analysis of Self-Financing Portfolios," Management Science, INFORMS, vol. 48(3), pages 427-443, March.
    15. Chavez-Bedoya, Luis & Rosales, Francisco, 2022. "Orthogonal portfolios to assess estimation risk," International Review of Economics & Finance, Elsevier, vol. 80(C), pages 906-937.
    16. Taras Bodnar & Stepan Mazur & Krzysztof Podgórski, 2017. "A test for the global minimum variance portfolio for small sample and singular covariance," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(3), pages 253-265, July.
    17. Andrew F. Siegel & Artemiza Woodgate, 2007. "Performance of Portfolios Optimized with Estimation Error," Management Science, INFORMS, vol. 53(6), pages 1005-1015, June.
    18. Simaan, Majeed & Simaan, Yusif & Tang, Yi, 2018. "Estimation error in mean returns and the mean-variance efficient frontier," International Review of Economics & Finance, Elsevier, vol. 56(C), pages 109-124.
    19. David Bauder & Taras Bodnar & Nestor Parolya & Wolfgang Schmid, 2021. "Bayesian mean–variance analysis: optimal portfolio selection under parameter uncertainty," Quantitative Finance, Taylor & Francis Journals, vol. 21(2), pages 221-242, February.
    20. Bodnar, Olha & Bodnar, Taras & Parolya, Nestor, 2022. "Recent advances in shrinkage-based high-dimensional inference," Journal of Multivariate Analysis, Elsevier, vol. 188(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bpj:strimo:v:28:y:2011:i:4:p:319-342:n:3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.