detailed calculations are not shown; rather we use plots of the impulse re-
sponses to convey the broad intuition.
We begin in figure 14.1 by investigating the effects of changing the mo-
mentum traders’ horizon j. We hold the information-diffusion parameter z
fixed at 12 months, and set the standard deviation of the fundamental ε
shocks equal to 0.5 per month. Finally, we assume that the aggregate risk
tolerance of the momentum traders, γ, equals 1/3.^15 We then experiment
with values of jranging from 6 to 18 months. As a baseline, focus first on
the case where j=12 months. Consistent with Proposition 1, the impulse
response function peaks 12 months after an εshock, reaching a value of
1.342. In other words, at the peak, prices overshoot the change in long-run
fundamentals by 34.2 percent. After the peak, prices eventually converge
back to 1.00, although not in a monotonic fashion—rather, there are a se-
ries of damped oscillations as the momentum-trading effects gradually
wring themselves out.
Now ask what happens as jis varied. As can be seen from the figure, the
effects on the impulse response function are nonmonotonic. For example,
514 HONG AND STEIN
Figure 14.1. Cumulative impulse response and momentum traders’ horizon. The
momentum traders’ horizon jtakes on values of 6, 12, and 18. Base is the cumula-
tive impulse response without momentum trading. The other parameter values are
set as follows: the information diffusion parameter zis 12, the volatility of news
shocks is 0.5 and the risk tolerance gamma is 1/3.
(^15) Campbell, Grossman, and Wang (1993) suggest that this value of risk tolerance is about
right for the market as a whole. Of course, for individual stocks, arbitrageurs may be more
risk-tolerant, since they may not have to bear systematic risk. As we demonstrate below, our
results on overreaction tend to become more pronounced when risk tolerance is increased.