in a covariance stationary equilibrium. In general, we have not had much
problem finding fixed points for wide parameter regions around those ex-
hibited in the text.

D. Remaining Proofs

Proof of Proposition 3

The equilibrium condition to determine wis for the utilities from the

two strategies to be equal. Given our assumptions on the preferences

of the momentum and contrarian investors and the distributions of

the εs, it follows from Grossman and Stiglitz (1980) that this is equiv-

alent to the conditional variance of the j-period returns being equal

across the two strategies. Given that both momentum and contrarian

investors have the same j-period horizon, it follows that this is equiv-

alent to the conditional covariance of the j-period returns being equal

across the two strategies. QED

Proof of Proposition 4

Suppose initially that there are only newswatchers and smart money

investors (i.e., there are no momentum investors). Smart money

investors have finite risk tolerance given by γsand maximize one-

period returns. We conjecture the following equilibrium price

function:

(A.11)

Note that we are once again suppressing all calculations related

to the constant. The holdings of the smart money investors are

given by

(A.12)

At the conjectured equilibrium price given in equation (A.11), we

have that

ζβεt (A.13)

S

ii

it

tz

=

=+

+−

∑

1

1

.

ζ

γεε

t εε

S

S

tttt tz

tttt tz

EP PD

Var P P D

=

−

−

+++−

+++−

[,,..., ]

[,,..., ]

(^111).
111




PD
z
ttzzt tzi iti
z
=+
−
++−++⋅⋅⋅+ +

−

∑

()

.

11

11

1

1

εεβε

A UNIFIED THEORY OF UNDERREACTION 535