Validity of CARA function under expected utility

Abstract

This paper assumes that the agent will make the same decision regarding a risk game involving a little bit of money at different levels of wealth. Under this assumption, we prove that as long as the agent’s utility function is in the form of expected utility, then the agent’s utility function is the constant absolute risk aversion (CARA) utility function. This suggests that the CARA utility function is likely the form that most closely approximates the true utility function under classical conditions. As application, this paper presents an asset pricing model with heterogeneous consumers with CARA utility function. It is found that the equity premium, the logarithmic return of risk assets minus the logarithmic return of risk-free assets, is a linear expression of the per capita consumption. The required relative risk aversion coefficient is about 4 within a reasonable range of 2 to 10.