On the other hand, if πLand πHare both at the low end, the investor be-
lieves that shocks are relatively likely to be reversed, regardless of the
regime: this leads to underreaction, but overreaction might not hold.
To confirm this intuition, we also show in figure 12.1 the ranges of (πL,
πH) pairs for which only underreaction or only overreaction holds. The
graph in the middle shows the parameter values for which only overreac-
tion obtains, while the graph to its right shows the values for which only
underreaction holds. The intersection of the two regions is the original
one shown in the graph at left. These figures confirm the intuition that if
πLand πHare on the high side, overreaction obtains, but underreaction
might not.
Figure 12.2 presents ranges of (πL, πH) pairs that generate both underre-
action and overreaction for a number of other values of λ 1 and λ 2. In all
cases, there are nontrivial ranges of (πL, πH) pairs for which the sufficient
conditions hold.
A MODEL OF INVESTOR SENTIMENT 443π π
π π
π π
π π
Figure 12.2. Shaded area shows the [πL, πH] pairs which satisfy the sufficient condi-
tions for both underreaction and overreaction for a variety of different values of λ 1
and λ 2. πL(πH) is the probability, in the mean-reverting (trending) regime, that next
period’s earnings shock will be of the same sign as last period’s earnings shock. λ 1
and λ 2 govern the transition probabilities between regimes.