forcing each arbitrageur to choose whether to play a momentum strategy
(and condition on ∆Pt− 1 ) or a contrarian strategy (and condition on ∆Pt− 1 −c),
we now allow them all to play an optimal blended strategy.
The results of this experiment are also illustrated in figure 14.4. Relative
to the previous case of segregated momentum and contrarian trading, al-
lowing for bivariate regression-running arbitrageurs is more stabilizing. For
example, keeping all other parameters the same as before, the impulse re-
sponse function now reaches a peak of only 1.125, as compared to the
value of 1.146 with segregated momentum and contrarian trading. Never-
theless, its qualitative shape continues to remain similar. Thus while in-
creasing the computational power of arbitrageurs obviously attenuates the
results, it does not appear that we are in a knife-edge situation where every-
thing hangs on them being able to run only univariate regressions.
B. Fully Rational ArbitrageFinally, it is natural to ask whether our basic results are robust to the intro-
duction of a class of fully rational arbitrageurs. To address this question,
we extend the baseline model of section 1 as follows. In addition to the
newswatchers and the momentum traders, we add a third group of traders,
whom we label the “smart money.” To give these smart-money traders the
best shot at making the market efficient, we consider an extreme case where
they can observe and rationally condition on everythingin the model that is
observed by any other trader. Thus, at time t, the smart-money traders ob-
serve all the fundamental information that is available to any of the
newswatchers—that is, they see εt+z− 1 and all preceding news innovations
in their entirety. They also can use the complete past history of prices in
their forecasts. Like everyone else, the smart money have CARA utility. Fi-
nally, each generation has a one-period horizon.
Unlike in the cases with contrarian trading considered in sections 2.A.1
and 2.A.2 above, it is very difficult to solve explicitly for the equilibrium
with the smart-money traders, either analytically or via numerical methods.
This is because in the context of our infinite-horizon model, the optimal
forecasts of the smart money are a function of an unbounded set of vari-
ables, as they condition on the entire past history of prices. (They really
have to be very smart in this model to implement fully rational behavior.)
Nevertheless, as proven in the appendix, we are able to make the following
strong general statements about the properties of equilibrium:
Proposition 4:Assume that the risk tolerance of the smart-money
traders is finite. In any covariance-stationary equilibrium, given a
one-unit shock εt+z− 1 that begins to diffuse at time t: (1) there is al-
ways underreaction, in the sense that prices rise by less than one at
time t; (2) there is active momentum trading; (3) there is always520 HONG AND STEIN