Stocks for the Log-Run and CRRA Preferences

Abstract

Almost Stochastic Dominance has been employed to support the case of stocks for the long-run. It implies that stocks are preferred over bonds in the long-run for all preferences with bounded marginal utility. Unfortunately, this analysis excludes the very central family of Constant Relative Risk Aversion (CRRA) preferences, which have unbounded marginal utility. In this paper, we derive a simple closed-form solution for the portfolio-choice problem of CRRA investors. This solution and the empirical return parameters imply that stocks are preferred over bonds for all CRRA investors with relative risk aversion smaller than 3.9. As most empirical and experimental estimates of relative risk aversion are much smaller than this value, the stocks-for-the-long-run argument turns out to also hold for most CRRA investors. 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.