00Thaler_FM i-xxvi.qxd

The WRSS profits under this model is:

(6)

where,

(7)

and, are the cross-sectional averages of β0,iand β1,i, respectively.
Eq. (6) indicates that the delayed reaction would generate positive mo-
mentum profits when δ>0. Intuitively, δis greater than zero if firms with
large contemporaneous betas also exhibit large lagged betas. Here, the con-
temporaneous betas are less dispersed than the sum of contemporaneous
and lagged betas. When δ>0, stock prices tend to move too closely to-
gether. In other words, if the market moves up, the prices of high beta
stocks will increase more than that of low beta stocks, but not by as much
as they would if the market fully responds to factor realizations contempo-
raneously. Hence, the higher beta stocks have higher returns in the subse-
quent period as well due to delayed reactions. Since momentum strategies
tend to buy high beta stocks following a market increase, they will profit
from the delayed response in the following period.
When lead-lag effects are generated in this way, large factor realizations
will be followed by large delayed reactions, and hence the profit in any pe-
riod will depend on the magnitude of factor realizations in the previous
period. Formally, JT show that the expected WRSS profits conditional on
the past factor portfolio return:

(8)

Eq. (8) implies that if the lead-lag effect contributes to momentum prof-
its, then the magnitude of the profits should be positively related to the
squared factor portfolio return in the previous period.
To investigate the importance of this source, JT estimate the following re-
gression using the value-weighted index as a proxy for the factor portfolio:

rpt,6=αp+θpr^2 mt,− 6 +uit,

where rpt,6is the WRSS profits and rmt,− 6 is the demeaned return on the
value-weighted index in months t−6 through t−1. Their estimates of θp
and the corresponding autocorrelation-consistent t-statistic over the 1965
to 1989 sample period are −1.77 and −3.56, respectively. The significantly

E,wriit t,1 f

i

N


f− t

=

∑ −

















=+

1

2

1

σδ^2

μ

ββ 01 and

δββββ≡−−

=

∑

1

0011

N 1

iiii

i

N

()(),,,,,

E,wriit,

i

N

f

=

∑

















=+

1

σδσ^22

μ

MOMENTUM 367