Menzly, Santos and Veronesi, UnderstandingPredictability
Presented by Jaewon Choi
October 9, 2007
Presented by Jaewon Choi Menzly, Santos and Veronesi, Understanding Predictability
Overview
Questions
Why the return predicting power of dividend yield is weekWhy the dividend growth is almost non-predictable
General equilibrium model
Habit persistenceTime-varying dividend growth through cash flow modeling
Main intuition of the model
Time-varying risk preference induces the standard positiverelationship between dividend yield and future returnTime-varying dividend growth induces a negative relationshipbetween dividend yield and future return
Presented by Jaewon Choi Menzly, Santos and Veronesi, Understanding Predictability
Model : Preferences
Representative consumer maximizing
E [
∫ ∞0
e−ρt log(Ct − Xt)dt]
Xt : External habit level.
Surplus/consumption ratio St
St =Ct − Xt
Ct
Inverse surplus Yt = 1St
= 11−(Xt/Ct)
follows
dYt = k(Y − Yt)dt − α(Yt − λ)(dct − Et [dct ])
Log consumption ct = log(Ct) follows
dct = µcdt + σcdB1t
Presented by Jaewon Choi Menzly, Santos and Veronesi, Understanding Predictability
Cash Flow Model
n risky financial assets paying a dividend rate {D it}ni=1.
D0t : Non-financial income flow.
In equilibrium, Ct = Σni=0D
it
Share of consumption for each asset s it = D i
tCt
ds it = φi (s i − s i
t)dt + s itσ
i(st)dB′t
Covariance between share and consumption growth
Covt(ds i
t
s it
,dCt
Ct) = θi
CF − Σnj=0θ
jCF s j
t
Then dividend growth is
dδit = µiD(st)dt + σi
D(st)dB′t
µiD(st) = µc + φi (
s i
s it
− 1)− 1
2σi(st)σ
i(st)′
Presented by Jaewon Choi Menzly, Santos and Veronesi, Understanding Predictability
Prices - Total Wealth Portfolio
Price of asset g paying Dgτ = sg
τ Cτ at time τ
Pgt = Et [
∫ ∞t
e−ρ(τ−t)[uc(Cτ − Xτ )
uc(Ct − Xt)]Dgτ dτ ]
=Ct
YtEt [
∫ ∞t
e−ρ(r−t)sgτ Yτdτ ]
Total wealth portfolio ( Dgτ = Cτ ) :
PTWt
Ct=
1
ρ(ρ+ kY St
ρ+ k)
Mean excess return and volatility
µTWR (St) = [1 + α(1− λSt)]σTW
R (St)σc
σTWR (St) = [1 +
kY St(1− λSt)α
kY St + ρ]σc
Presented by Jaewon Choi Menzly, Santos and Veronesi, Understanding Predictability
Prices - Individual Securities
Assume all assets have equal cash flow risk,Cov(dδit , dct) = σ2
c .
Then dividend yield isP i
t
D it
= ai0 + ai
1St + ai2
s i
s it
+ ai3
s i
s itSt
When dividend share s i
s it
high,P i
t
D it
is high.
Expected return
Et [dR it ] = [1 + α(1− λSt)](1 + kYStα(1−λSt)
kYSt+ρ[1+f (s i/s it )]
)σ2c
f (·) is a decreasing function. Positive relationship between
dividend share s i
s it
and expected excess return.
It weakens the predicting power of dividend yield.
Presented by Jaewon Choi Menzly, Santos and Veronesi, Understanding Predictability
Prices - Individual Securities
Rewriting expected return,
Et [dR it ] = bi
0(St) + bi1(St)
D it
P it
+ bi2(St)
C it
P it
Dependence on the speed of mean aversion φi .When φi is low, bi
1 is greater than bi2. This is because the
effect of dividend share s i
s it
is more pronounced when the
dividend share is persistent.
Expected log dividend growth
Et [dδi ] = mi0(St , st) + mi
1(St)P i
t
D it
mi1(St) = φi
ai2+ai
3St
St in mi1(St) and
P it
D it
go in the opposite direction
Presented by Jaewon Choi Menzly, Santos and Veronesi, Understanding Predictability
Data
Quarterly data from CRSP. Sample period 1947-2001.
20 value-weighted industry portfolios
Cash flow variable s it = D i
t/Ct constructed usingdividend/share repurchases.
Choice of parameters
Match basic moments of the market portfolioShare process parameters from time-series linear regressions
Presented by Jaewon Choi Menzly, Santos and Veronesi, Understanding Predictability
Model Parameters
Presented by Jaewon Choi Menzly, Santos and Veronesi, Understanding Predictability
Predictability of Dividend Growth
Presented by Jaewon Choi Menzly, Santos and Veronesi, Understanding Predictability
Predictability of Dividend Growth - Simulation
Presented by Jaewon Choi Menzly, Santos and Veronesi, Understanding Predictability
Predictability of Stock Returns
Presented by Jaewon Choi Menzly, Santos and Veronesi, Understanding Predictability
Predictability of Stock Returns - Simulation
Presented by Jaewon Choi Menzly, Santos and Veronesi, Understanding Predictability
Discussion
Key assumptions in the theory
Dividend share is stationary.Consumption growth is not predictable so the dividend growthis forced to be predictable
Statistical issue
Overlapping samples (Finite sample property is not very good)Persistent regressor (Boudoukh, Richardson and Whitelaw2006)
overlapping samples
Presented by Jaewon Choi Menzly, Santos and Veronesi, Understanding Predictability
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