overreaction, in the sense that the cumulative impulse response of
prices peaks at a value that is strictly greater than one.If the risk tolerance of the smart money traders is infinite, prices follow a
random walk, and there is no momentum trading: φ=0.
The proposition formalizes the intuitive point—common to many models
in this genre—that risk-averse fully rational arbitrageurs attenuate, but do
not eliminate, the effects induced by other less-than-rational traders. In our
particular setting, all the key qualitative results about the dynamics of
prices continue to apply.
3 .Empirical ImplicationsWe will not belabor the fact that our model delivers the right first-order pre-
dictions for asset returns: positive correlations at short horizons, and nega-
tive correlations at longer horizons. After all, it is designed to do just that.
More interesting are the auxiliary implications, which should allow it to be
tested against other candidate theories of underreaction and overreaction.
A. In What Stocks Do Momentum Strategies Work Best?In our model, short-term return continuation is a consequence of the gradual
diffusion of private information, combined with the failure of newswatchers
to extract this information from prices. This gradual-information-diffusion
story is logically distinct from the mechanism in other models, such as
BSV’s, that emphasizes a conservatism bias (Edwards 1968) with respect to
public information. Moreover, it has testable cross-sectional implications. If
momentum in stock returns does indeed come from gradual information
flow, then momentum strategies of the sort proposed by Jegadeesh and Tit-
man (1993) should be most profitable among those stocks for which infor-
mation moves most slowly across the investing public.
In research conducted subsequent to the development of the model here,
we attempt in Hong, Lim, and Stein (2000), to test this hypothesis. To do so,
we consider two different proxies for the rate of information diffusion. The
first is firm size. It seems plausible that information about small firms gets
out more slowly; this would happen if, for example, investors face fixed
costs of information acquisition, and choose to devote more effort to learn-
ing about those stocks in which they can take large positions. Of course, one
must be careful in drawing inferences because size may also capture a vari-
ety of other factors, such as cross-stock differences in arbitrage costs.^19 In
A UNIFIED THEORY OF UNDERREACTION 521(^19) Consequently, one might argue that virtually any behavioral model would be consistent
with there being more predictability in small stocks.