00Thaler_FM i-xxvi.qxd

(Note the distinction between qtand qt). Hence,

and

Substituting this into the original formula for price gives

Proposition 2.Suppose the underlying parametersπL, πH, λ 1 , and λ 2

satisfy

where

where q

• 
  

eand q–eare bounds on the unconditional mean of the ran-

dom variable qt. Then the conditions for both underreaction and

overreaction given in section 5.1. are satisfied. (Functions and vari-

ables not yet introduced will be defined in the proof.)

kq q

kq c cq

c

qq qq

qq

c

qq

qq

q

qc

qc

e

e

e

=+

=+ +

=

−

−

=

−

−

=

<

≥









1

2

1

2 12

1

2

2

2

0

0

∆

∆∆

∆∆

(),

(

*

),

() ()

,

() ()

,

*

if ,

if ,

kp p kp

p

21 2

2 0

<<

≥

,

,

pIQQ

pIQQ

10

1

1

20

1

2

0

1

2

1

11

1

11

1111

0010

10 10

=′+ +−

=− ′ + + −

′= − −

′=

′= −

−

−

δ

γδ δ γ

δ

γδ δ γ

γ

γ

γ

(( )[( ) ]),

(( )[( ) ]),

(, , , ),

(, ,, ),

(, , , ).

E( ) ( ) ( )( )

(,, ,).

ttjt t

j t

t

yyQqyQqj t

+ =′ +−′

′=

Φγ γ

γ 0101

Pr(yytj+ ==′t t
Φγ) Qqj t

452 BARBERIS, SHLEIFER, VISHNY