Relative risk aversion must be close to 1

Any utility function that is unbounded either from below or from above implies paradoxical behavior. However, these paradoxes may be regarded as irrelevant if they involve wealth levels that are realistically meaningless. Employing real-world constraints on wealth reveals that CRRA utility with relative risk aversion outside of the range 0.75–1.15 yields paradoxical choices that very few individuals, if any, would ever make. Thus, relative risk aversion must be close to 1, the value corresponding to log preferences. These results shed new light on the longstanding debate about the geometric-mean criterion and the argument of stocks for the long-run.