14.127 Behavioral Economics. Lecture 12
Xavier Gabaix
April 29, 2004
0.1
Twin stocks
• Shell and Royal Dutch – claims on the same company
• There is a difference between prices
• The difference is driven by the difference in aggrogate movements in London vs Dutch stock markets
• Sharpe ratio (expected return/standard deviation) of this aribtrage is not
great
0.2
Are noise traders eliminated from the market?
• DSSW setup E (RNT − RA) =
E
h³
λNT
t
− λA
t
´
i
(r + pt+1 − pt (1 + r)) =
ρ∗
−
(1+r)2(ρ∗2+σ∗2)
2γµσρ2
• Might be both positive and negative
• If γ is large enough, then E (RNT − RA) > 0 and noise traders prevail
• This is because noise traders are more optimistic and take more risk
• But by construction EU A > EU NT
• Stock returns look like a random walk [see slides]
• Evidence from stock splits – supports efficient market hypothesis [see
slides]
• Event study methodology [see slides]
• Jensen: “The Efficient Market Hypothesis is the best established fact in all
of social sciences”
• de Bondt and Thaler JoF 1985 [see slides]
• Value vs growth [see slides]: a recent attempt at explanation by consumption covariance – growth stocks have low covariance with consumption
because most of risk is idiosyncratic; conversely GM has high covariance
(Parker, Julliard, Barsal)
• Initial Public Offerings [see slides]
0.3
Campbell-Cochrane “By force of habit” JPE 1999
• Explains low equity premium in booms and high in recessions
P t (Ct−Xt)1−γ
• U= δ
where Xt is your habit
1−γ
−Xt
• Denote St = CtC
surplus/consumption ratio, st = ln St < 0.
t
•
Uct
= (Ct − Xt
)−γ
and
t
−CUcc
Uct
γ
t
= γC C
=
St > γ.
t −Xt
• “Catching up with the Joneses economy” – what makes me happy is not
my consumption compared to my past consumption (internal habit) but
my consumption compared to past consumption in the economy (external
habit).
• This is too simplify the problem: noone’s current consumption impacts his
or her future habit
• Representative consumer economy. Aggregate sa = ln S a < 0, Sta =
Cta−Xta
Cta
• Postulates
sat+1
=
(1 − φ) s̄ + φsat
+ λ (sat)
³
a
ln Ct+1
− ln Cta
−g
´
where g is mean growth rate and φ ∈ (0, 1) determines mean reversion.
a =g+v
• Lucas economy ∆ ln Ct+1
t+1
• Euler equation
µ
Mt+1
1=E
Rt+1
1+r
¶
with
Mt+1 = δ
³
a , Xa
Uc Ct+1
t+!
¡
Uc Cta, Xta
¢
´
=δ
³
a − Xa
Ct+1
t+1
´−γ
¡ a
¢−γ
a
Ct − Xt
à a !−γ à a !−γ
St+1
Ct+1
−γ ((1−φ)(s̄−st)+g (1+λ(sat))vt+1)
=δ
=
δe
Sta
Cta
• They postulate 1 + r = E [Mt+1] is constant
³
´
2
−γ (1−φ)(s̄−st)+g 2(1+λ(sat)) σv2
1 + r = δe
• Hence
1q
λ (st) =
1 + 2 (s̄ − st) − 1
S̄
• To price stocks, use
Rt+1 =
Pt+1 + Dt+1
Pt
to write the Euler equation as
1=
• Thus
"
P
+ Dt+1
1
E Mt+1 t+1
1+r
Pt
"
Ã
#
Pt
D
1
P
=
E Mt+1 t+1 1 + t+1 st+1
Dt
1+r
Dt
Pt
D
!#
Pt
• Postulate, D
= f (st), ln Dt+1 = gD + wt+1 and solve for f (st).
t
t