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Incorporating Economic Objectives into Bayesian Priors: Portfolio Choice under Parameter Uncertainty

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  • Tu, Jun
  • Zhou, Guofu

Abstract

This paper proposes a way to allow Bayesian priors to reflect the objectives of an economic problem. That is, we impose priors on the solution to the problem rather than on the primitive parameters whose implied priors can be backed out from the Euler equation. Using monthly returns on the Fama-French 25 size and book-to-market portfolios and their 3 factors from January 1965 to December 2004, we find that investment performances under the objective-based priors can be significantly different from those under alternative priors, with differences in terms of annual certainty-equivalent returns greater than 10% in many cases. In terms of an out-of-sample loss function measure, portfolio strategies based on the objective-based priors can substantially outperform both strategies under alternative priors and some of the best strategies developed in the classical framework.

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  • 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.
  • Handle: RePEc:cup:jfinqa:v:45:y:2010:i:04:p:959-986_00
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    3. Li, Yong & Yu, Jun, 2012. "Bayesian hypothesis testing in latent variable models," Journal of Econometrics, Elsevier, vol. 166(2), pages 237-246.
    4. Hautsch, Nikolaus & Voigt, Stefan, 2017. "Large-Scale Portfolio Allocation Under Transaction Costs and Model Uncertainty: Adaptive Mixing of High- and Low-Frequency Information," VfS Annual Conference 2017 (Vienna): Alternative Structures for Money and Banking 168222, Verein für Socialpolitik / German Economic Association.
    5. Lombardi, Marco J. & Ravazzolo, Francesco, 2016. "On the correlation between commodity and equity returns: Implications for portfolio allocation," Journal of Commodity Markets, Elsevier, vol. 2(1), pages 45-57.
    6. Taras Bodnar & Mathias Lindholm & Vilhelm Niklasson & Erik Thors'en, 2020. "Bayesian Quantile-Based Portfolio Selection," Papers 2012.01819, arXiv.org.
    7. Johannes Bock, 2018. "An updated review of (sub-)optimal diversification models," Papers 1811.08255, arXiv.org.
    8. Lubos Pastor & Pietro Veronesi, 2009. "Learning in Financial Markets," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 361-381, November.
    9. Yong Li & Zeng Tao & Jun Yu, "undated". "Robust Deviance Information Criterion for Latent Variable Models," Working Papers CoFie-04-2012, Singapore Management University, Sim Kee Boon Institute for Financial Economics.
    10. 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.
    11. 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.
    12. Kim, Dongwhan & Kang, Kyu Ho, 2021. "Conditional value-at-risk forecasts of an optimal foreign currency portfolio," International Journal of Forecasting, Elsevier, vol. 37(2), pages 838-861.
    13. 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.
    14. Carolina Fugazza & Massimo Guidolin & Giovanna Nicodano, 2015. "Equally Weighted vs. Long†Run Optimal Portfolios," European Financial Management, European Financial Management Association, vol. 21(4), pages 742-789, September.
    15. Dragon Yongjun Tang, 2014. "Potential losses from incorporating return predictability into portfolio allocation," Australian Journal of Management, Australian School of Business, vol. 39(1), pages 35-45, February.
    16. Gillen, Benjamin J., 2014. "An empirical Bayesian approach to stein-optimal covariance matrix estimation," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 402-420.
    17. 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.
    18. Thomas J. Brennan & Andrew W. Lo, 2010. "Impossible Frontiers," Management Science, INFORMS, vol. 56(6), pages 905-923, June.
    19. 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.
    20. Taras Bodnar & Vilhelm Niklasson & Erik Thors'en, 2022. "Volatility Sensitive Bayesian Estimation of Portfolio VaR and CVaR," Papers 2205.01444, arXiv.org.

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