We show that three prominent consumption-based asset pricing models - the Bansal-Yaron, Campbell-Cochrane and Cecchetti-Lam-Mark models - cannot explain the own-history predictability properties of stock market returns. We show this by estimating these models with GMM, deriving ex-ante expected returns from them and then testing whether the difference between realised and expected returns is a martingale difference sequence, which it is not. Furthermore, semi-parametric tests of whether the models' state variables are consistent with the degree of own-history predictability in stock returns suggest that only the Campbell-Cochrane habit variable may be able to explain return predictability, although the evidence on this is mixed.