Rational Momentum Effects

Momentum effects in stock returns need not imply investor irrationality, heterogeneous information, or market frictions. A simple, single-firm model with a standard pricing kernel can produce such effects when expected dividend growth rates vary over time. An enhanced model, under which persistent growth rate shocks occur episodically, can match many of the features documented by the empirical research. The same basic mechanism could potentially account for underreaction anomalies in general. THERE WOULD APPEAR TO BE FEW more f lagrant affronts to the idea of rational, efficient markets than the existence of large excess returns to simple momentum strategies in the stock market. So naturally do these profits suggest systematic underreaction by the market, and so unpromising seems the attempt to associate the rewards with risk factors, that asset pricing theorists have mostly seen the task as simply one of deciding which sort of investor irrationality is at work.1 This article suggests that the case for rational momentum effects is not hopeless, however. In fact, a simple, standard model of firm cash-f lows discounted by an ordinary pricing kernel can deliver a strong positive correlation between past realized returns and current expected returns. The framework is simplified and ignores many features crucial for valuing real firms. The point is just to call attention to a direct, plausible, and rational mechanism that may contribute to this puzzling phenomenon. The key to the model is stochastic expected growth rates. By their nature, such growth rates affect returns in a highly nonlinear way, and the dynamics they imply differ qualitatively from those of familiar linear factor models. Specifically, the curvature with respect to growth rates of equity prices is extreme: Their log is convex. This property means that growth rate risk rises with growth rates. Assuming that exposure to this risk carries a positive price, expected returns then rise with growth rates. Other things equal, firms that have recently had large positive price moves are more likely to have had positive growth rate shocks than other firms, with negative growth shocks more likely among poor performers. Hence, a momentum sort will * London Business School. I am indebted to the referee for several helpful comments. 1 The original momentum findings are in Jegadeesh ~1990! and Lehmann ~1990!. Behavioral explanations appear in Barberis, Shleifer, and Vishny ~1998!, Daniel, Hirshleifer, and Subrahmanyam ~1998!, and Hong and Stein ~1999!. THE JOURNAL OF FINANCE • VOL. LVII, NO. 2 • APRIL 2002