Habit Formation, the Cross Section of Stock Returns and the Cash-Flow Risk Puzzle∗

Non-linear external habit persistence models, which feature prominently in the recent “equity premium” asset pricing and macroeconomics literature, generate counterfactual predictions in the cross-section of stock returns. In particular, we show that in the absence of crosssectional heterogeneity in firms’ cash-flow risk, these models produce a “growth premium,” that is, stocks with high price-to-fundamental ratios command a higher premium than stocks with low price-to-fundamental ratios. This implication is at odds with the well-established empirical observation of a “value premium” in the cross-section of stock returns. Substantial heterogeneity in firms’ cash-flow risk yields both a value premium as well as most of the stylized facts about the cross-section of stock returns, but it generates a “cash-flow risk puzzle”: Quantitatively, value stocks have to have “too much” cash-flow risk compared to the data to generate empirically plausible value premiums. ∗We thank seminar participants at Carnegie Mellon, UCLA, Princeton University, The Federal Reserve Bank of New York, Columbia Business School, London Business School, London School of Economics, and the Graduate School of Business of the University of Chicago for their comments and Gene Fama, Lars Hansen, John Heaton, and Wei Jiang for valuable suggestions. Errors, of course, remain our own. This paper has circulated previously under the title “Cash-flow Risk, Discount Risk and the Value Premium”