abnormal price trends are of the same sign as the average initial event-date
reaction. We now slightly generalize the model to address this event-based re-
turn predictability.
Sophisticated managers or analysts who are not overconfident are likely
to undertake certain visible actions, such as repurchasing shares or making
buy recommendations, selectively when a firm’s shares are undervalued by
the market. We will show that the nature of the stock price reaction to an
event depends critically on whether or not the event is related to the date 2
mispricing by the market.
We assume that the date 2 signal is no longer public, but is instead re-
ceived privatelyby the firm’s manager (or other individual such as an ana-
lyst), and that this individual takes an action (the “event”) that is publicly
observed and fully reveals the signal. Let PC 2 (s 2 ) be the valuation that would
be placed on the security by an overconfident investor at date 2 were he to
observe the signal s 2 in addition to his signal s 1. (Since we examine events
that fully reveal s 2 , this is in equilibrium just the postevent stock price P 2 .)
Let PR 2 (s 2 ) be the comparable valuation that would be set by a fully rational
investor. The date 2 mispricingthen is defined as the difference PR 2 (s 2 )−
PC 2 (s 2 ) We define different kinds of events as follows.
Definition 1.An event is a random variable that depends only on the
information signals s 1 and s 2 .A nonselective eventis an event that is
independent of the date 2 mispricing PR 2 (s 2 )−PC 2 (s 2 ). A selective event
is an event whose occurrence and/or magnitude depends on the date
2 mispricing.A simple type of non-selective event is a random variable that is linearly re-
lated only to the second signal s 2.
Proposition 4.If overconfident investors observe a nonselective event:- The true expected postannouncement abnormal price change is
zero. - Conditional on the preevent return, the covariance between the
announcement date and the postannouncement price change is
positive: that is, cov(P 3 −P 2 , s 2 P 1 −P 0 )>0.
Since a non-selective event is an action that is unrelated to the pricing error
at date 2, it tells us nothing about mean future price movements. Although
the market underreacts to the event, it is equally likely to be underreacting
downward as upward. Part 1 therefore indicates that there will be no sys-
tematic postannouncement drift following events that are unrelated to the
prior market mispricing. Thus, Proposition 4 refutes the conventional inter-
pretation of drift as being equivalent to underreaction to new information.
The lack of event-based predictive power for future returns is surprising
given the positive autocorrelation of event-date and postevent price changes
INVESTOR PSYCHOLOGY 471