Recent financial research has provided evidence on the predictability of asset returns. In this paper we consider the results contained in Pesaran and Timmerman (1995), which provided evidence on predictability of excess returns in the US stock market over the sample 1959–1992. We show that the extension of the sample to the nineties weakens considerably the statistical and economic significance of the predictability of stock returns based on earlier data. We propose an extension of their framework, based on the explicit consideration of model uncertainty under rich parameterizations for the predictive models. We propose a novel methodology to deal with model uncertainty based on ‘thick’ modelling, i.e. on considering a multiplicity of predictive models rather than a single predictive model. We show that portfolio allocations based on a thick modelling strategy systematically outperform thin modelling. Copyright © 2005 John Wiley & Sons, Ltd.