Consumption Based Asset Pricing in a General Model of Expected Utility Maximizing Investors

Abstract

This paper extends the generalized expected utility model of the 2009 Journal of Mathematical Economics paper, [1], to the case of a Markov investment returns process. Using this generalization of the additively separable model, we derive the equity premium in a Lucas asset pricing equilibrium with Markov consumption growth and extend the Mehra and Prescott, [2] calibration to the non-additively separable case. Riskfree rates and levered equity premia near the historical averages can be obtained by combining the assumption of a relatively high elasticity of substitution with the assumption that the relative risk aversion measure is also high. In particular we can, as is commonly done, assume an elasticity of substitution of one and combine this with the assumption of a high relative risk aversion measure. Surprisingly the calibration results for the generalized expected utility preferences are virtually the same as those obtained assuming Epstein-Zin, Weil (EZW) preferences with the same parameter values. The EZW generalization of the additively separable preferences does not assume expected utility maximization but is dynamically consistent while our generalization does retain the assumption of expected utility maximization but is not dynamically consistent. Throughout the paper we relate our approach to the standard development of the additively separable case and to the EZW approach. We also present a separate development of the case in which the elasticity of substitution is one, which in the additively separable case, is "the log case."