Utility-implied term structures of equity risk premia

The fundamental asset pricing problem is extended to the frequency domain for commonly used utility functional forms. For each class of utility functions, closed-form solutions are presented for the term structure of the equity risk premium. The term structure is flat for time separable one-period utility and uncorrelated external habit formation utility, downward sloping for internal habit formation utility, upward sloping for time preference (recursive) utility, and can be upward sloping, downward sloping, or flat for production-based utility. These results suggest how observed risk premium term structures can be mapped to linear time series models consistent with utility preference classes.