We find that the Campbell–Cochrane external-habit model can generate a value premium if the persistence of the consumption surplus is sufficiently low. Such low persistence is supported by micro evidence on consumption. If the mean and conditional volatility of consumption growth are highly persistent, as in the Bansal–Yaron long-run risk model, then fast-moving habit can also generate, without eroding the value premium: i) empirically sensible long horizon return predictability; and ii) a price–dividend ratio for market equity that exhibits the high autocorrelation found in the data. Fast-moving habit also delivers several empirical properties of market-dividend strips.