we consider the limiting case where tgoes to infinity. This simplifies matters
by allowing us to focus on steady-state trading strategies—that is, strategies
that do not depend on how close we are to the terminal date.^5
In order to capture the idea that information moves gradually across
the newswatcher population, we divide this population into zequal-sized
groups. We also assume that every dividend innovation εjcan be decom-
posed into zindependent subinnovations, each with the same variance σ^2 /z:
εj=ε^1 j+...+εzj. The timing of information release is then as follows. At time
t, news about εt+z− 1 begins to spread. Specifically, at time t, newswatcher
group 1 observes ε^1 t+z− 1 , group 2 observes ε^2 t+z− 1 , and so forth, through
group z, which observes εzt+z− 1. Thus at time t, each subinnovation of εt+z− 1
has been seen by a fraction 1/zof the total population.
Next, at time t+1, the groups “rotate,” so that group 1 now observes
ε^2 t+z− 1 , group 2 observes ε^3 t+z− 1 , and so forth, through group z, which now
observes ε^1 t+z− 1. Thus at time t+1 the information has spread further, and
each subinnovation of εt+z− 1 has been seen by a fraction 2/zof the total
population. This rotation process continues until time t+z−1, at which
point every one of the zgroups has directly observed each of the subinno-
vations that comprise εt+z− 1. So εt+z− 1 has become totally public by time
t+z−1. Although this formulation may seem unnecessarily awkward, the
rotation feature is useful, because it implies that even as information moves
slowly across the population, everybody is on average equally well-
informed.^6 This symmetry makes it transparently simple to solve for prices,
as is seen momentarily.
In this context, the parameter zcan be thought of as a proxy for the
(linear) rate of information flow—higher values of zimply slower infor-
mation diffusion. Of course, the notion that information spreads slowly is
more appropriate for some purposes than others. In particular, this con-
struct is fine if our goal is to capture the sort of underreaction that shows
up empirically as unconditional positive correlation in returns at short
horizons. However, if we are also interested in capturing phenomena like
postearnings-announcement drift—where there is apparently underreac-
tion even to data that is made available to everyone simultaneously—we
need to embellish the model. We discuss this embellishment later on; for
now it is easiest to think of the model as only speaking to the uncondi-
tional evidence on underreaction.
506 HONG AND STEIN
(^5) A somewhat more natural way to generate an infinite-horizon formulation might be to
allow the asset to pay dividends every period. The only reason we push all the dividends out
into the infinite future is for notational simplicity. In particular, when we consider the strategies
of short-lived momentum traders below, our approach allows us to have these strategies depend
only on momentum traders’ forecasts of price changes, and we can ignore their forecasts of
interim dividend payments.
(^6) Contrast this with a simpler setting where group 1 always sees all of εt+z− 1 first, then
group 2 sees it second, etc. In this case, group 1 newswatchers are better-informed than their
peers.