A long-standing puzzle to financial economists is the difficulty of outperforming the benchmark random walk model in out-of-sample contests. Using data from the USA over the period of 1872–2007, this paper re-examines the out-of-sample predictability of real stock prices based on price–dividend (PD) ratios. The current research focuses on the significance of the time-varying mean and nonlinear dynamics of PD ratios in the empirical analysis. Empirical results support the proposed nonlinear model of the PD ratio and the stationarity of the trend-adjusted PD ratio. Furthermore, this paper rejects the non-predictability hypothesis of stock prices statistically based on in- and out-of-sample tests and economically based on the criteria of expected real return per unit of risk. Copyright © 2011 John Wiley & Sons, Ltd.