00Thaler_FM i-xxvi.qxd

price (virtually) does not move at date 2. However, if sign (θ+
)=sign (s 2 ),
then the new price is calculated using the new level of the assessed variance
of
. This price, denoted by P 2 C, is

(12)

A. 1 implications of the simple model

It can easily be shown that^16

cov(P 2 −P 1 , P 1 −P 0 )>0. (13)

Thus, the model shows that the overreaction phase, not just the correction
phase, can contribute positively to short-term momentum. As a result,

cov(P 3 −P 1 , P 1 −P 0 )<0; (14)

cov(P 3 −P 2 , P 2 −P 1 )<0, (15)

because the dates 1 and 2 overreactions must be reversed in the long-term.
Intuitively, further dates of noisy public information arrival should even-
tually cause the mispricing to be corrected (so long as confidence does not
explode infinitely). This process causes positive autocorrelation during the
correction phase, just as in the basic model of section 2. To examine this, let
us add a date 3′between dates 2 and 3, where a public signal θ+ηis re-
leased. For simplicity, we assume that overconfidence is not affected by the
release of the second public signal. As in section 2, ηis a zero mean, nor-
mally distributed variable with variance σ^2 p, and is independent of all other
random variables. The price at date 3′when overconfidence is not revised
at date 2 is given by equation (6). When overconfidence is revised at date 2,
the price at date 3′, denoted by P 3 ′Cis given by the same expression as
equation (6), except that σC^2 is replaced byσC^2 −k; that is,

(16)

where
With the extra date added to the model, it is easy to show that all of the
remaining single-period price change autocorrelations are negative except
for cov(P 3 −P 3 ′, P 3 ′−P 2 ), which is positive. This can be explained as fol-
lows. Date 2 is the extremum of the impulse response function (the “hump”
or “trough” date after which the average correction begins). The single-
period price-change single-lag autocorrelations that fall entirely within
either the overreaction phase or within the correction phase are positive,

Dk≡−++−σσθ^22 ()().CpCpσ^2 σ^2 kσ^2

P

k

DD

k

C D

Cp p C

′ =

−+

++

−

3

σσ^22 σ^22222

θ

σσ σσ

θθθ η

() ()


 ,

P

k

C

C

2

2

= (^22) +−+
σ
σσ
θ θ
θ
().

INVESTOR PSYCHOLOGY 479
(^16) Explicit calculations and expressions for covariances for this subsection are in presented
in Appendix D of Daniel, Hirshleifer, and Subrahmanyam (1998).