Eq. (A.13) then gives the following set of equations that determine

the β’s in equilibrium:

(A.14)

and

(A.15)

Using equations (A.14) and (A.15), it is not hard to show that in a

covariance stationary equilibrium: (1) the returns still exhibit posi-

tive serial correlation for finite levels of smart money risk tolerance,

γs<∞; and (2) when smart money investors are risk neutral, prices

follow a random walk.

Since returns are serially correlated when the risk tolerance of

smart money is finite, φ=0 cannot be an equilibrium when we add

momentum traders to the model. Since smart money investors have

access to the entire history of past price changes, it follows from the

logic of Eq. (A.11) that the conjectured price function with momen-

tum traders is now

(A.16)

Assuming that a covariance stationary equilibrium exists, the hold-

ing of the smart money is

(A.17)

while the holding of the momentum investors is given by Eq. (A.7).

At the conjectured equilibrium price in Eq. (A.16), we have

(A.18)

for the smart money and Eq. (A.8) for the momentum investors.

ζβεκtS ii

it

tz

iti

i

=+P

=+

+−

−

=

∞

∑∑

1

1

1

∆

ζ

γεε

t εε

S

S

tttt tztt

tttt tztt

EP PD P P P

Var P P D P P P

=

−

−

+++−−− −∞

+++−−− −∞

[,,..., , , ,..., ]

[,,..., , , ,..., ]

(^11112).
11112




∆∆ ∆
∆∆ ∆
PD
z
zz
PP
tt t tz iti
i
z
iti
i
ti
i
j
=+
−
+⋅⋅⋅
++
++−+

−
−

∞
−

++∑

∑∑

()

.

11

11

1

1

11

εβε

κφ

ε

∆∆

βγ

ββ

βσ

1

1

1

2

2

1

1

= 21

+−

+













=−

−

−

S ii

z

z

z

iz

()

,,...,.

βγ

β

βσ

1

1

1

2

2

1

1

=

−

+











−

S

z

z

z

536 HONG AND STEIN