A Simple Theory of Asset Pricing under Model Uncertainty

The focus of our paper is on the implications of model uncertainty for the crosssectional properties of returns. We perform our analysis in the context of a tractable single-period mean-variance framework. We show that there is an uncertainty premium in equilibrium expected returns on financial assets and study how the premium varies across the assets. In particular, the cross-sectional distribution of expected returns can be formally described by a two-factor model, where expected returns are derived as compensation for the asset’s contribution to the equilibrium risk and uncertainty of the market portfolio. In light of the large empirical literature on the cross-sectional characteristics of asset returns, understanding the implications of model uncertainty even in such a simple setting would be of significant value. By characterizing the crosssection of returns we are also able to address some of the observational equivalence issues raised in the literature. That is, whether model uncertainty in financial markets can be distinguished from risk, and whether uncertainty aversion at an individual level can be distinguished from risk aversion. ∗Leonid Kogan is with the Sloan School of Management of the Massachusetts Institute of Technology, Cambridge, MA 02142, USA. [email protected]; Tan Wang is with the Faculty of Commerce and Business Administration, University of British Columbia, Vancouver, British Columbia, Canada, V6T 1Z2. [email protected]. The authors are grateful to Lorenzo Garlappi, Burton Hollifield, Raman Uppal, Stan Zin, and seminar participants at Carnegie Mellon University and MIT for helpful comments. The paper was presented at the 2002 Western Finance Association Meetings. Tan Wang thanks the Social Sciences and Humanities Research Council of Canada for financial support.