does so by creating a further price increase that the next generation partially
misinterprets as more good news. This causes the next generation to buy, and
so on. At some point, the buying has gone too far, and the price overshoots
the level warranted by the original news. Given the inability of momentum
traders to condition directly on the ε’s, everybody in the chain is behaving as
rationally as possible, but the externality creates an apparently irrational
outcome in the market as a whole.
D. Winners and LosersA natural question is whether the bounded rationality of either the news-
watchers or the momentum traders causes them to systematically lose
money. In general, both groups can earn positive expected returns as long
as the net supply Qof the asset is positive. Consider first the case where
Q=0. In this case, it can be shown that the momentum traders earn posi-
tive returns, as long as their risk tolerance is finite. Because with Q=0, this
is a zero-sum game, it must therefore be that the newswatchers lose money.
The one exception is when momentum traders are risk-neutral, and both
groups break even.^13
When Q>0, the game becomes positive-sum, as there is a return to risk-
sharing that can be divided between the two groups. Thus even though the
newswatchers may effectively lose some money on a trading basis to the
momentum traders, this can be more than offset by their returns from risk-
sharing, and they can make a net profit. Again, in the limit where the mo-
mentum traders become risk-neutral, both groups break even. The logic is
similar to that with Q=0, because risk-neutrality on the part of momen-
tum traders dissipates all the risk-sharing profits, restoring the zero-sum na-
ture of the game.
E. Numerical Comparative StaticsIn order to develop a better feeling for the properties of the model, we per-
form a variety of numerical comparative statics exercises.^14 For each set of
parameter values, we calculate the following five numbers (1) the equilib-
rium value of φ; (2) the unconditional standard deviation of monthly re-
turns ∆P; (3) the standard deviation of the pricing errorrelative to a rational
expectations benchmark, (Pt−P*t); (4) the cumulative impulse response
of prices to a one-unit εshock; and (5) the autocorrelations of returns. The
A UNIFIED THEORY OF UNDERREACTION 513(^13) This result is related to the fact that newswatchers have time-inconsistent strategies, so
that in formulating their demands they ignore the fact that they will be transacting with mo-
mentum traders who will be trying to take advantage of them. Thus in some sense, the
newswatchers are more irrational than the momentum traders in this model.
(^14) The appendix briefly discusses our computational methods.