Menzly, Santos and Veronesi, Understanding...

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Menzly, Santos and Veronesi, Understanding Predictability Presented by Jaewon Choi October 9, 2007 Presented by Jaewon Choi Menzly, Santos and Veronesi, Understanding Predictability

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Menzly, Santos and Veronesi, UnderstandingPredictability

Presented by Jaewon Choi

October 9, 2007

Presented by Jaewon Choi Menzly, Santos and Veronesi, Understanding Predictability

Page 2: Menzly, Santos and Veronesi, Understanding Predictabilitypeople.stern.nyu.edu/svnieuwe/pdfs/PhDPres2007/pres5_2.pdf · Menzly, Santos and Veronesi, Understanding Predictability Presented

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

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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

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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

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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

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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

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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

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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

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Model Parameters

Presented by Jaewon Choi Menzly, Santos and Veronesi, Understanding Predictability

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Predictability of Dividend Growth

Presented by Jaewon Choi Menzly, Santos and Veronesi, Understanding Predictability

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Predictability of Dividend Growth - Simulation

Presented by Jaewon Choi Menzly, Santos and Veronesi, Understanding Predictability

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Predictability of Stock Returns

Presented by Jaewon Choi Menzly, Santos and Veronesi, Understanding Predictability

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Predictability of Stock Returns - Simulation

Presented by Jaewon Choi Menzly, Santos and Veronesi, Understanding Predictability

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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