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### Transcript of Menzly, Santos and Veronesi, Understanding svnieuwe/pdfs/PhDPres2007/pres5_2.pdf Menzly, Santos and

• Menzly, Santos and Veronesi, Understanding Predictability

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 week Why the dividend growth is almost non-predictable

General equilibrium model

Habit persistence Time-varying dividend growth through cash flow modeling

Main intuition of the model

Time-varying risk preference induces the standard positive relationship between dividend yield and future return Time-varying dividend growth induces a negative relationship between 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 = 1 St

= 11−(Xt/Ct) follows

dYt = k(Y − Yt)dt − α(Yt − λ)(dct − Et [dct ])

Log consumption ct = log(Ct) follows

dct = µcdt + σcdB 1 t

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 = Σ n i=0D

i t

Share of consumption for each asset s it = D it Ct

ds it = φ i (s i − s it)dt + s itσi(st)dB′t

Covariance between share and consumption growth

Covt( ds it s it , dCt Ct

) = θiCF − Σnj=0θ j CF s

j t

Then dividend growth is

dδit = µ i D(st)dt + σ

i D(st)dB

′ t

µiD(st) = µc + φ i (

s i

s it − 1)− 1

2 σi(st)σ

i(st) ′

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

• Prices - Total Wealth Portfolio

Price of asset g paying Dgτ = s g τ Cτ at time τ

Pgt = Et [

∫ ∞ t

e−ρ(τ−t)[ uc(Cτ − Xτ ) uc(Ct − Xt)

]Dgτ dτ ]

= Ct Yt

Et [

∫ ∞ 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)]σTWR (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) = σ

2 c .

Then dividend yield is P it D it

= ai0 + a i 1St + a

i 2

s i

s it + ai3

s i

s it St

When dividend share s i

s it high,

P it D it

is high.

Expected return

Et [dR i t ] = [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 i t ] = b

i 0(St) + b

i 1(St)

D it P it

+ bi2(St) C it P it

Dependence on the speed of mean aversion φi . When φi is low, bi1 is greater than b

i 2. 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 [dδ i ] = mi0(St , st) + m

i 1(St)

P it D it

mi1(St) = φi

ai2+a i 3St

St in m i 1(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 using

dividend/share repurchases.

Choice of parameters

Match basic moments of the market portfolio Share 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 growth is forced to be predictable

Statistical issue

Overlapping samples (Finite sample property is not very good) Persistent regressor (Boudoukh, Richardson and Whitelaw 2006)

overlapping samples

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