00Thaler_FM i-xxvi.qxd

causes the impulse response function to reach higher peak values. Also, the
unconditional volatility of monthly returns rises monotonically.^16 It turns
out, however, that the effect of risk tolerance on the pricing error (Pt−P*t) is
U-shaped: the pricing error first falls, and then rises, as risk tolerance is in-
creased. On the one hand, more momentum trading accelerates the reaction
of prices to information, which reduces underreaction and thereby decreases
pricing errors. On the other hand, more momentum trading also exacerbates
overreaction, which increases pricing errors. Evidently, the two effects inter-
act so as to produce a nonmonotonic pattern.^17
Finally, in figure 14.3, we allow the information-diffusion parameter zto
vary. Increasing zhas a monotonic effect on the intensity φof momentum
trade: the slower the newswatchers are to figure things out, the greater the
profit opportunities are for momentum traders. In the range of the parameter
space where j≥z−1, the induced increase in φin turn has a monotonic effect
on the peak impulse response—more aggressive momentum trade leads to
more pronounced overshooting, and correspondingly, to negative autocorre-
lations that are generally larger in absolute value during the reversal phase.^18

2 .Extensions of the Basic Model: More Rational Arbitrage

We now consider a few extensions of the basic model. The overall spirit
here is to ask: What happens as we allow for progressively more rational
behavior by arbitrageurs?

A. Contrarian Strategies

A. 1 .contrarians and momentum traders are two separate groups

We have emphasized repeatedly that our results are attributable to the as-
sumption that momentum traders make “simple” forecasts—that is, they can
only run univariate regressions. But even if one accepts this restriction at face
value, it begs the following question: Why do alltraders have to use the same
single forecasting variable? Why not allow for some heterogeneity in trading
styles, with different groups focusing on different predictive variables?

516 HONG AND STEIN

(^16) Although volatility rises with momentum trading, it is not necessarily (though it may be)
“excessive” relative to a rational expectations benchmark. This is because we are starting
from a point where there is underreaction, which leads to lowervolatility than under a ran-
dom walk.
(^17) The fact that momentum trading can increase both volatility and pricing errors serves as
another counterexample to Friedman’s (1953) famous claim that profitable speculation must
stabilize prices. See also Hart and Kreps (1986), Stein (1987), and DeLong et al. (1990).
(^18) When j<z−1, there is no longer a monotonic link between φand the degree of over-
shooting. This is because the biggest momentum trades are already being unwound before
newswatchers have fully incorporated a news shock into their forecasts.