A Consumption-Based Explanation of Expected Stock Returns

When utility is nonseparable in nondurable and durable consumption and the elasticity of substitution between the two consumption goods is sufficiently high, marginal utility rises when durable consumption falls. The model explains both the crosssectional variation in expected stock returns and the time variation in the equity premium. Small stocks and value stocks deliver relatively low returns during recessions, when durable consumption falls, which explains their high average returns relative to big stocks and growth stocks. Stock returns are unexpectedly low at business cycle troughs, when durable consumption falls sharply, which explains the countercyclical variation in the equity premium. EXPLAINING THE VARIATION IN EXPECTED RETURNS across stocks and the variation in the equity premium over time as trade-offs between risk and return is a challenge for financial economists. In his review article on market efficiency, Fama (1991, p. 1610) concludes In the end, I think we can hope for a coherent story that (1) relates the cross-section properties of expected returns to the variation of expected returns through time, and (2) relates the behavior of expected returns to the real economy in a rather detailed way. Or we can hope to convince ourselves that no such story is possible. This paper proposes a “coherent story” that satisfies both criteria. A well-known empirical fact in finance is the high average returns of small stocks relative to big stocks (i.e., low relative to high market equity stocks) and of value stocks relative to growth stocks (i.e., high relative to low bookto-market equity stocks). The evidence suggests that there are size and value premia in the cross-section of expected stock returns. In an equilibrium asset ∗Motohiro Yogo is with the Wharton School of the University of Pennsylvania. This paper is a substantially revised version of Chapter 1 of my PhD thesis at Harvard University. An earlier draft was circulated as “A Consumption-Based Explanation of the Cross Section of Expected Stock Returns.” I am grateful for advice and encouragement from my thesis committee: John Campbell (chair), James Stock, and Tuomo Vuolteenaho. I have also benefited from comments by John Cochrane, Domenico Cuoco, Borja Larrain, Jonathan Parker, Monika Piazzesi, Amir Yaron, the referees and an associate editor, and seminar participants at Carnegie Mellon, the Federal Reserve Board, Harvard (Economics Department, Business School, and Kennedy School of Government), Michigan, NYU, Northwestern, Princeton, Stanford, UCLA, Wharton, and Yale. This paper is based upon work supported under a National Science Foundation Graduate Research Fellowship.