(Proposition 1). However, even though the event is unrelated to the prior
mispricing, the more underpriced the security, the more positive on average
will be the stock price reaction to further news. Thus, a favorable event-date
stock price change is associated with a positive future average trend. Clearly,
then, even though the event itself does not predict future returns, the market
is inefficient.
Part 2 of Proposition 4 predicts larger postevent average returns the more
the nonselective event (perhaps a cash flow surprise) and the preevent stock
price runup are in opposition (e.g., positive preevent runup and negative
event).^9 Intuitively, holding constant the private signal (as reflected in P 1 ), the
higher is the public signal, the more likely that the fundamental θis high, and
therefore the bigger the average shortfall of the private signal relative to the
fundamental. Thus, a higher public signal is associated with a larger (more
positive) postevent return.
Both parts 1 and 2 of Proposition 4 can be tested using data on specific
nonselective events. These are presumably events that are not initiated by
an informed party such as a manager with an incentive to take into account
mispricing. Such events might include news about product demand that
emanates from outside of the company (e.g., news about competitors’ ac-
tions), or regulatory and legislative outcomes (e.g., FDA decisions on drugs
proposed by a pharmaceutical company).
We now show that selective public events, that is, events that are corre-
lated with preevent stock mispricing, will forecast future price changes.
Consider a manager who observes P 1 (and therefore infers the private sig-
nal s 1 ) and receives his own signal s 2 at date 2. The manager can undertake
a debt/equity exchange offering, and the attractiveness of a larger exchange
depends on how high the market price is relative to fundamental value. He
can condition the size of the offering on the mispricing at date 2, which he
knows precisely, since he knows both s 1 and s 2. It can easily be shown that
in this setting the date 2 pricing error is proportional to the expected error
in the private signal, ≡E[P 1 , s 2 ], where the expectation is again taken
with respect to rational beliefs. For tractability, we consider selective events
that are linear functions of the date 2 mispricing.
When <0, the manager believes the market has undervalued the firm,
so the firm can “profit” by exchanging debt for equity; the more underval-
ued the firm, the greater the size of the offering. If *>0, an equity-for-debt
swap would be preferred instead. It is easy to show that
E[P 3 −P 2 *>0]< 0 <E[P 3 −P 2 *<0]; (8)that is, events taken in response to market undervaluation (e.g., repurchase)
are associated with high postevent returns, and events taken in response to
overvaluation (e.g., new issue) with low postevent returns.
472 DANIEL, HIRSHLEIFER, SUBRAHMANYAM
(^9) We thank an anonymous referee for suggesting we explore this issue.