00Thaler_FM i-xxvi.qxd

be positive in a setting where the extremum in the impulse response func-
tion is sufficiently smooth, because the negative autocovariance of price
changes surrounding a smooth extremum will be low in absolute terms. Such
a setting, based on biased self-attribution and outcome-dependent confi-
dence, is considered in section 3.
Since overconfidence causes wider swings at date 1 away from funda-
mentals, it causes excess price volatility around private signals (var(P 1 −P 0 ))
as in Odean (1998). Greater overconfidence also causes relative underweigh-
ing of the public signal, which tends to reduce date 2 variance. However,
the wide date 1 swings create a greater need for corrective price moves at
dates 2 and 3, so that greater overconfidence can either decrease or increase
the volatility around public signals (var(P 2 −P 1 )). (Explicit expressions for
the variances of this section are contained in appendix A.)
Consider again an econometrician who does not condition on the occur-
rence of private or public news arrival. He will calculate price change vari-
ances by placing equal weights on price changes P 1 −P 0 , P 2 −P 1 , and P 3 −P 2.
The unconditional volatility is therefore just the arithmetic mean of var
(P 3 −P 2 ), var(P 2 −P 1 ), and var(P 1 −P 0 ). Excess volatility is the difference
between the volatility with overconfidence and the volatility when σC^2 =σ^2
.
Let the subscript Rdenote the volatility if all individuals were rational.
We define the date tproportional excess volatility as

(7)

Proposition 3

1. Overconfidence increases volatility around private signals, can
   increase or decrease volatility around public signals, and in-
   creases unconditional volatility.


2. The proportional excess volatility is greater around the private
   signal than around the public signal.

Thus, consistent with the findings of Odean (1998), when there are only pri-
vate signals, there is a general tendency for overconfidence to create excess
volatility. Excess volatility is not an automatic implication of any model with
imperfect rationality. For example, if investors are underconfident, σC^2 >σ
^2 ,
then there will be insufficientvolatility relative to the rational level. Also, in
contrast with Odean, Proposition 3 implies that in samples broken down by
types of news event, either excess or deficient volatility may be possible.

B. 3 event study implications

Many recent studies have investigated abnormal average return performance
or “drift” following public news arrival. As mentioned in the introduction, a
striking regularity in virtually all these studies is that average postevent

V

PP PP

t PP

E tt Rtt

Rt t

≡

−− −

−

−−

−

var( ) var ( )

var ( )

(^11).
1
470 DANIEL, HIRSHLEIFER, SUBRAHMANYAM