IDEAS home Printed from https://ideas.repec.org/p/hhs/oruesi/2018_002.html
   My bibliography  Save this paper

Bayesian inference for the tangent portfolio

Author

Listed:

Abstract

In this paper we consider the estimation of the weights of tangent portfolios from the Bayesian point of view assuming normal conditional distributions of the logarithmic returns. For di↵use and conjugate priors for the mean vector and the covariance matrix, we derive stochastic representations for the posterior distributions of the weights of tangent portfolio and their linear combinations. Separately we provide the mean and variance of the posterior distributions, which are of key importance for portfolio selection. The analytic results are evaluated within a simulation study, where the precision of coverage intervals is assessed.

Suggested Citation

  • Bauder, David & Bodnar, Taras & Mazur, Stepan & Okhrin, Yarema, 2018. "Bayesian inference for the tangent portfolio," Working Papers 2018:2, Örebro University, School of Business.
    • Handle: RePEc:hhs:oruesi:2018_002
    as

    Download full text from publisher

    File URL: https://www.oru.se/globalassets/oru-sv/institutioner/hh/workingpapers/workingpapers2018/wp-2-2018.pdf
    File Function: Full text
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Zhenyu Wang, 2005. "A Shrinkage Approach to Model Uncertainty and Asset Allocation," The Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 673-705.
    2. Victor DeMiguel & Lorenzo Garlappi & Raman Uppal, 2009. "Optimal Versus Naive Diversification: How Inefficient is the 1-N Portfolio Strategy?," The Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 1915-1953, May.
    3. Winkler, Robert L., 1973. "Bayesian Models for Forecasting Future Security Prices," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 8(3), pages 387-405, June.
    4. Klein, Roger W. & Bawa, Vijay S., 1976. "The effect of estimation risk on optimal portfolio choice," Journal of Financial Economics, Elsevier, vol. 3(3), pages 215-231, June.
    5. 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.
    6. Barry, Christopher B, 1974. "Portfolio Analysis under Uncertain Means, Variances, and Covariances," Journal of Finance, American Finance Association, vol. 29(2), pages 515-522, May.
    7. 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.
    8. Bodnar, Taras & Parolya, Nestor & Schmid, Wolfgang, 2018. "Estimation of the global minimum variance portfolio in high dimensions," European Journal of Operational Research, Elsevier, vol. 266(1), pages 371-390.
    9. 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.
    10. Jorion, Philippe, 1986. "Bayes-Stein Estimation for Portfolio Analysis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(3), pages 279-292, September.
    11. Doron Avramov & Guofu Zhou, 2010. "Bayesian Portfolio Analysis," Annual Review of Financial Economics, Annual Reviews, vol. 2(1), pages 25-47, December.
    12. Golosnoy, Vasyl & Okhrin, Yarema, 2008. "General uncertainty in portfolio selection: A case-based decision approach," Journal of Economic Behavior & Organization, Elsevier, vol. 67(3-4), pages 718-734, September.
    13. Vasyl Golosnoy & Yarema Okhrin, 2007. "Multivariate Shrinkage for Optimal Portfolio Weights," The European Journal of Finance, Taylor & Francis Journals, vol. 13(5), pages 441-458.
    14. Ľuboš Pástor, 2000. "Portfolio Selection and Asset Pricing Models," Journal of Finance, American Finance Association, vol. 55(1), pages 179-223, February.
    15. Frost, Peter A. & Savarino, James E., 1986. "An Empirical Bayes Approach to Efficient Portfolio Selection," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(3), pages 293-305, September.
    16. Taras Bodnar & Yarema Okhrin, 2011. "On the Product of Inverse Wishart and Normal Distributions with Applications to Discriminant Analysis and Portfolio Theory," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(2), pages 311-331, June.
    17. 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.
    18. Winkler, Robert L & Barry, Christopher B, 1975. "A Bayesian Model for Portfolio Selection and Revision," Journal of Finance, American Finance Association, vol. 30(1), pages 179-192, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Bodnar, Olha & Bodnar, Taras & Niklasson, Vilhelm, 2024. "Constructing Bayesian tangency portfolios under short-selling restrictions," Finance Research Letters, Elsevier, vol. 62(PA).
    2. Mårten Gulliksson & Anna Oleynik & Stepan Mazur, 2024. "Portfolio Selection with a Rank-Deficient Covariance Matrix," Computational Economics, Springer;Society for Computational Economics, vol. 63(6), pages 2247-2269, June.
    3. Farrukh Javed & Stepan Mazur & Erik Thorsén, 2024. "Tangency portfolio weights under a skew-normal model in small and large dimensions," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 75(7), pages 1395-1406, July.
    4. Bodnar, Taras & Mazur, Stepan & Nguyen, Hoang, 2022. "Estimation of optimal portfolio compositions for small sampleand singular covariance matrix," Working Papers 2022:15, Örebro University, School of Business.
    5. Drin, Svitlana & Mazur, Stepan & Muhinyuza, Stanislas, 2023. "A test on the location of tangency portfolio for small sample size and singular covariance matrix," Working Papers 2023:11, Örebro University, School of Business.
    6. 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.
    7. Alfelt, Gustav & Mazur, Stepan, 2020. "On the mean and variance of the estimated tangency portfolio weights for small samples," Working Papers 2020:8, Örebro University, School of Business.
    8. Wang, Chou-Wen & Liu, Kai & Li, Bin & Tan, Ken Seng, 2022. "Portfolio optimization under multivariate affine generalized hyperbolic distributions," International Review of Economics & Finance, Elsevier, vol. 80(C), pages 49-66.
    9. Andrew Grant & Oh Kang Kwon & Steve Satchell, 2024. "Properties of risk aversion estimated from portfolio weights," Journal of Asset Management, Palgrave Macmillan, vol. 25(5), pages 427-444, September.
    10. Karlsson, Sune & Mazur, Stepan & Muhinyuza, Stanislas, 2020. "Statistical Inference for the Tangency Portfolio in High Dimension," Working Papers 2020:10, Örebro University, School of Business.

    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 & 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.
    2. Chiaki Hara & Toshiki Honda, 2014. "Asset Demand and Ambiguity Aversion," KIER Working Papers 911, Kyoto University, Institute of Economic Research.
    3. Doron Avramov & Guofu Zhou, 2010. "Bayesian Portfolio Analysis," Annual Review of Financial Economics, Annual Reviews, vol. 2(1), pages 25-47, December.
    4. Bodnar, Taras & Mazur, Stepan & Nguyen, Hoang, 2022. "Estimation of optimal portfolio compositions for small sampleand singular covariance matrix," Working Papers 2022:15, Örebro University, School of Business.
    5. Bauder, David & Bodnar, Taras & Parolya, Nestor & Schmid, Wolfgang, 2020. "Bayesian inference of the multi-period optimal portfolio for an exponential utility," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    6. Taras Bodnar & Mathias Lindholm & Vilhelm Niklasson & Erik Thors'en, 2020. "Bayesian Quantile-Based Portfolio Selection," Papers 2012.01819, arXiv.org.
    7. Evan Anderson & Ai-ru (Meg) Cheng, 2022. "Portfolio Choices with Many Big Models," Management Science, INFORMS, vol. 68(1), pages 690-715, January.
    8. Detlef Seese & Christof Weinhardt & Frank Schlottmann (ed.), 2008. "Handbook on Information Technology in Finance," International Handbooks on Information Systems, Springer, number 978-3-540-49487-4, November.
    9. Tu, Jun & Zhou, Guofu, 2011. "Markowitz meets Talmud: A combination of sophisticated and naive diversification strategies," Journal of Financial Economics, Elsevier, vol. 99(1), pages 204-215, January.
    10. 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.
    11. 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.
    12. 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.
    13. DeMiguel, Victor & Martin-Utrera, Alberto & Nogales, Francisco J., 2013. "Size matters: Optimal calibration of shrinkage estimators for portfolio selection," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 3018-3034.
    14. Andrew Paskaramoorthy & Tim Gebbie & Terence van Zyl, 2021. "The efficient frontiers of mean-variance portfolio rules under distribution misspecification," Papers 2106.10491, arXiv.org, revised Jul 2021.
    15. David Stefanovits & Urs Schubiger & Mario V. Wüthrich, 2014. "Model Risk in Portfolio Optimization," Risks, MDPI, vol. 2(3), pages 1-34, August.
    16. Fletcher, Jonathan, 2011. "Do optimal diversification strategies outperform the 1/N strategy in U.K. stock returns?," International Review of Financial Analysis, Elsevier, vol. 20(5), pages 375-385.
    17. Sangwon Suh, 2016. "A Combination Rule for Portfolio Selection with Transaction Costs," International Review of Finance, International Review of Finance Ltd., vol. 16(3), pages 393-420, September.
    18. Yuanyuan Zhang & Xiang Li & Sini Guo, 2018. "Portfolio selection problems with Markowitz’s mean–variance framework: a review of literature," Fuzzy Optimization and Decision Making, Springer, vol. 17(2), pages 125-158, June.
    19. Davide Pettenuzzo & Francesco Ravazzolo, 2016. "Optimal Portfolio Choice Under Decision‐Based Model Combinations," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(7), pages 1312-1332, November.
    20. Carmine De Franco & Johann Nicolle & Huyên Pham, 2019. "Dealing with Drift Uncertainty: A Bayesian Learning Approach," Risks, MDPI, vol. 7(1), pages 1-18, January.

    More about this item

    Keywords

    asset allocation; tangent portfolio; Bayesian analysis;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:hhs:oruesi:2018_002. 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: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/ieoruse.html .

    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.