Sample evidence about the predictability of monthly stock returns is considered from the perspective of a risk-averse Bayesian investor who must allocate funds between stocks and cash. The investor uses the sample evidence to update prior beliefs about the parameters in a regression of stock returns on a set of predictive variables. The regression relation can seem weak when described by usual statistical measures, but the current values of the predictive variables can exert a substantial influence on the investor's portfolio decision, even when the investor's prior beliefs are weighted against predictability.