We introduce a variant of the Adaptive Beliefs System (ABS) of Brock and Hommes (1998) based on returns instead of prices. Agents form their demands according to the degree to which they are trend-following or contrarian. Empirically, the model requires that agents’ demands be coerced by leverage constraints. Using five samples of US stock returns, we show that the fit to realized returns is essentially driven by the total dispersion of the model’s returns. We also find that the latter are more realistic when forecasts are based on short-term estimates and when trend-followers and contrarians have the same ex-ante importance. We then provide evidence that the model is able to mimic most stylized facts observed on financial markets (tail decay, volatility clustering and autocorrelation patterns) quite closely. Finally, we find that portfolio policies designed according to the model’s predictions outperform the naive 1/N portfolio out-of-sample by 2% per annum