Stocks for the log-run and constant relative risk aversion preferences

Abstract

Almost Stochastic Dominance implies that stocks are preferred over bonds in the long-run by all preferences with bounded marginal utility. Unfortunately, this analysis excludes the very central Constant Relative Risk Aversion (CRRA) preferences, which have unbounded marginal utility. We derive a simple closed-form solution for the portfolio-choice problem of CRRA investors which, with the empirical parameters, implies that stocks are preferred over bonds for all CRRA investors with relative risk aversion smaller than 3.9. As a by-product, the analysis offers an alternative derivation of the continuous-time CAPM, that does not rely on dynamic programming, and allows for ambiguous investment horizons.