00Thaler_FM i-xxvi.qxd

When s 2 confirms s 2 (either s 1 =H, s 2 =Uor s 1 =L, s 2 =D), the player be-
comes overconfident and acts as if his precision were pCinstead of p, so

(A15)

When s 2 is informative (q > 1/2), this probability exceeds pC. When s 2 does
not confirm s 1 , the player does not become overconfident, so

(A16)

When evaluated with an informative signal s 2 (q>1/2), this probability is
less than p. With a risk neutral player, the price of the asset with value θ
can be calculated linearly using the above probabilities. The price at time
0 (P 0 ) is, by definition, equal to 0. As θcan take on a value of +1 or −1,
the price is (ρ)(+1)+(1−ρ)(−1) or, 2ρ−1, where ρis the probability that
θis +1.

(A17)

(A18)

(A19)

The price changes are ∆P 1 =P 1 −P 0 =P 1 and ∆P 2 =P 2 −P 1. E[P 1 ]=0, so
cov(∆P 1 , ∆P 2 )=E[∆P 1 ∆P 2 ]. The probabilities of the eight possible outcomes
are:

Pr(θ=+1, s 1 =H, s 2 =U)=Pr(θ=−1, s 1 =L, s 2 =D)=pq/2 (A20)

Pr(θ=−1, s 1 =H, s 2 =U)=Pr(θ=+1, s 1 =L, s 2 =D)

=(1−p)(1−q)/2 (A21)

Pr(θ=+1, s 1 =H, s 2 =D)=Pr(θ=−1, s 1 =L, s 2 =U)=p(1−q)/2 (A22)

Pr(θ=−1, s 1 =H, s 2 =D)=Pr(θ=+1, s 1 =L, s 2 =U)=(1−p)q/2. (A23)

PP sHsD

pq

pq pq

22 Hs D 22 Hs U^21121

2

ss 11 ,,Pr(,)

.

===− === =+ = = −

=

−

+−

θ

PP sHsU

pq

pq q

Hs U Hs D

C

C

222221121

1

211

ss 11 ,,Pr(,)

()()

===− === =+ = = −

=

+−

−+−

θ

PP 11 ss 11 ==HL=− =21 121Pr()θ=+sHp 1 = − = −

Pr

Pr Pr

Pr

(,)

(, )()

(, )

()

()()

.

θ

θθ

=+ = = =

===+=+

==

=

−

−+ −

1

11

1

11

12

12

12





sHsD

sHsD

sHsD

pq

pqqp

Pr

Pr Pr

Pr

(,)

(, )()

(,)

()()

.

θ

θθ

=+ = = =

===+=+

==

=

−+−

1

11

211

12

12

12





sHsU

sHsU

sHsU

pq

pq q

C

C

INVESTOR PSYCHOLOGY 493