Research Articles

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

Jun Tua1 and Guofu Zhoua2

a1 Lee Kong Chian School of Business, Singapore Management University, 50 Stamford Rd., Singapore 178899. [email protected]

a2 Olin School of Business, Washington University in St. Louis, 1 Brookings Dr., St. Louis, MO 63130. [email protected]


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.


We are grateful to Yacine Aït-Sahalia, Doron Avramov, Anil Bera, Henry Cao, Victor DeMiguel, Lorenzo Garlappi, Eric Ghysels, Bruce Hansen, Yongmiao Hong, Chih-Ying Hsiao, Ravi Jagannathan, Raymond Kan, Hong Liu, and Ľuboš Pástor; seminar participants at Fudan University, Tsinghua University, Washington University in St. Louis, the 2005 Finance Summer Camp of Singapore Management University, the 2006 International Symposium on Financial Engineering and Risk Management at Xiamen University, the 2006 China International Conference in Finance, the 18th Asian Finance Association Annual Meetings, and the 16th Annual Meetings of the Midwest Econometrics Group; and especially to Stephen Brown (the editor) and Martijn Cremers (the referee) for many insightful comments that substantially improved the paper. We also thank Lynnea Brumbaugh-Walter for many helpful editorial comments. Tu acknowledges financial support for this project from Singapore Management University Research Grant C207/MSS6B006.