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Bad Beta, Good Beta
John Campbell and Tuomo Vuolteenaho
Harvard University and NBER
Presentation at
Oxford Finance Summer Symposium
11/6/2004
RESEARCH AGENDA
High P/B – growth or glamour?

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High P/B must in the long run forecast either
high profitability (ROE) or low stock returns
(or both)
If high P/B forecasts stock returns, this may
be because high-P/B stocks are less risky or
because they are overvalued (or both)
If high-P/B stocks' returns are less risky than
low-P/B stocks', is this risk differential
caused by differential risk in fundamentals or
in mispricing (or both)?
Growth or glamour?
Does high P/B
forecast high ROE
or low returns?
High ROE…
…justifies high price
Risk is caused
by covariances
in fundamentals
Low stock
returns…
BBGB
…caused by risk
or mispricing?
Valuation level
caused by mispricing
Risk…
…is risk caused
by fundamentals
or mispricing?
Risks caused by
covariances in
mispricing
BAD BETA, GOOD BETA
The CAPM

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People have short investment horizons
The average investor holds the market
If an asset has a high return when the market
performs poorly, then the asset is insurance

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If an asset performs poorly when the market performs
poorly, then it is risky


i.e., low or even negative market beta
i.e., high market beta
The average investor requires a high return to hold
risky assets, and accepts a low return to hold
insurance
Why does the market fall?

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Bad news about future cash flows:
 wealth decreases and future investment opportunities
remain constant
The discount rate or cost of capital applied to the
market's cash flows increases
 wealth decreases but future investment opportunities
improve
To a long-horizon investor (with a constant relative risk
aversion higher than unity), the first case is much worse
news than the second

Suppose market portfolio of only corporate bonds: Would you
rather have bonds defaulting or interest rates going up?
Intuition from Gordon model
PM ,t 
DM ,t 1
kM  g M
D is dividend, P is price, k is discount rate, and g is dividend growth
k  (discount rate news) and/or
g  (cash-flow news)
P
Merton's ICAPM idea

We break the market return in two components:
rM ,t 1  Et (rM ,t 1 )  N M ,CF ,t 1  N M , DR,t 1

We also break up the CAPM beta of a stock into
two components:


cash-flow beta, βCF
discount-rate beta, βDR
 i ,CF
M
 i ,CF
M
,t
,t

cov t (ri ,t 1 , N M ,CF ,t 1 )
vart (rM ,t 1 )
  i , DRM ,t 
 i , DR
cov t (ri ,t 1 , rM ,t 1 )
vart (rM ,t 1 )
M
,t

cov t (ri ,t 1 , N M , DR,t 1 )
  i ,CAPM ,t
vart (rM ,t 1 )
Merton's ICAPM idea



Intuitively, covariance or beta with the really bad market
moves (market's cash-flow news) should have a higher risk
premium than covariance or beta with the less bad market
moves (market's discount-rate news)
Campbell's (1993) version of Merton's (1973) ICAPM
predicts:
 discount-rate-beta premium should equal the variance of
the market return, and
 cash-flow-beta premium should be γ times higher, where γ
is the coefficient of relative risk aversion of a
representative investor
This is because poor returns driven by increases in discount
rates are partially compensated by improved prospects for
future returns
Beta and cholesterol

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It used to be thought that heart attack risk could be measured
by the overall level of cholesterol. Routine blood tests
reported this level.
Now we know there are two types of cholesterol, HDL and
LDL. One (“bad cholesterol”) strongly increases the risk of a
heart attack, the other (“good cholesterol”) weakly reduces it.
Routine blood tests now report the two levels separately.
Similarly, beta has two types, but in this case “good beta” is
really “not so bad beta” as it does increase the risk premium.
We hope that routine risk analysis will in the future report
both types of beta separately.
An illustration
The Empire Strikes Back
Bad Beta
Not so
bad beta
Our paper's three steps



Estimate the market's cash-flow and
discount-rate news
Using the estimated series, measure the
cash-flow and discount-rate betas for
various assets
See how these betas explain average
returns, and compare the premia to those
predicted by the theory
Summary of results

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Value and small stocks have higher bad cash-flow
betas than growth and large stocks
 explains the value and size premia
Growth stocks have negative CAPM alphas because
their betas are predominantly of the good discountrate variety
 explains the negative CAPM alphas of growth stocks
Sorting on past CAPM betas induces little spread in
mean returns in the post-1963 sample, because the
sort creates a spread only in the good discount-rate
beta.
Risk vs. return 1963:7-2001:12

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E(Ri-Rrf) =
var(rM)βi,DR +var(rM)βi,DR +ei
Vertical axis is the average
realized return
Horizontal axis is the
predicted average return
's are selected ME-andBE/ME-sorted portfolios
's are beta-sorted portfolios
Some previous research

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The ICAPM theory: Merton (1973), Campbell (1993)
Decomposing the market's return: Campbell and Shiller (1988a,
1988b), Campbell (1991), Campbell and Ammer (1993)
Value spread predicts the market return: Eleswarapu and
Reinganum (2001), Brennan, Xia, and Wang (2001)
Value stocks are more sensitive than growth stocks to market's
cash-flow news: Liew and Vassalou (2000), Cohen, Polk, and
Vuolteenaho (2002)
Cross-sectional tests of the ICAPM: Campbell (1996), Li (1997),
Hodrick, Ng, and Sengmuller (1999), Lynch (1999), Chen (2000),
Brennan, Xia, and Wang (2001), Ng (2002), Guo (2000), etc.
ESTIMATING NEWS
Paper's three empirical steps



Estimate the market's cash-flow and
discount-rate news
Using the estimated series, measure the
cash-flow and discount-rate betas for
various assets
See how these betas explain average
returns, and compare the premia to those
predicted by the theory
Idea of news identification

If an asset’s return is unexpectedly high,
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its expected cash flows must have increased (i.e.,
cash-flow news must have been positive), and/or
future expected returns decreased (i.e., discount-rate
news must have been negative)
The objective is to empirically split the market
return into these two components
We use the Campbell-Shiller log-linear
present-value model and a VAR to do just
that
Defining news terms

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Cash-flow news: Change in discounted sum of
current and future expected dividend growth rates
Discount-rate news: Change in discounted sum of
future expected returns
Set the discount coefficient ρ to .95 annualized


i 0
j 1
rt 1  Et rt 1  Et 1  Et   i d t 1i  Et 1  Et   j rt 1 j
 N CF ,t 1  N DR,t 1
VAR implementation

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Assume that a VAR model generates returns
One can then compute unexpected returns and
discount-rate news
Cash-flow news can be taken as a residual
z t 1 a  zt  ut 1 ,
e

e1 zt 1  rM ,t 1
  ( I  ) 1 , e1  [1, 0, , 0]
N M , DR  (e1 )ut 1 , N M ,CF  (e1  e1 )ut 1
VAR state variables
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Excess market return
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TERM yield spread (in percentage points)
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Yield on ten-year taxable T-bonds minus yield on short-term
taxable T-notes
Smoothed P/E
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log return on CRSP VW minus log return on three-month Tbills
Log S&P 500 price index minus log 10-year trailing moving
average of S&P 500's aggregate earnings
Small-stock value spread
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Log(BE/ME) of small-value Fama-French 2-by-3 portfolio
minus log(BE/ME) of small-growth portoflio
Logic behind state variables
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TERM yield spread
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High TERM yield spread forecasts high returns on longterm bonds
Since stocks are long-term assets, expected stock returns
should also be high
Predicted coefficient positive
Smoothed P/E
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Ten-year trailing moving average controls for cash-flowgenerating ability of the stocks in S&P 500
Holding cash-flow-generating ability constant, higher price
must mean lower future stock returns
Predicted coefficient negative
Logic behind state variables
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Small-stock value spread
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If the ICAPM is to explain the value effect, value minus
growth stock returns must be correlated with changes in
discount rates, so a moving average of these returns
should be a proxy for the level of the discount rate
Growth stocks have a longer "duration," thus their values
should be especially dependent on discount rates
Imperfect-capital-markets story: High discount rates = SEO
market is closed. Maybe small growth stocks require
financing simply to survive?
Small growth stocks sensitive to "irrational exuberance?"
All these phenomena likely to be more extreme for small
stocks
Predicted coefficient negative
VAR state-variable data
VS
TY
PE
Monthly VAR, 1928:12-2001:12
Properties of the news terms
Moving-average news
Summary of the market's news
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At monthly frequency, market's discount-rate news
are about twice as volatile as cash-flow news (5%
per month vs. 2.5% per month)
Correlation between the news terms is low (.11)
An interpretation of the VAR:
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Negative cash-flow news corresponds to a profit recession
Positive discount-rate news corresponds to a valuation
recession
A drop in stock prices that is accompanied by a drop in the
P/E, higher TERM yield spread, and a shrinking value
spread are signs of a valuation recession
MEASURING BETAS
Paper's three empirical steps



Estimate the market's cash-flow and
discount-rate news
Using the estimated series, measure the
cash-flow and discount-rate betas for
various assets
See how these betas explain average
returns, and compare the premia to those
predicted by the theory
Defining betas
ˆ
ˆ



i ,CFM
i , DRM

côv ri ,t , Nˆ M ,CF ,t

vâr Nˆ
 Nˆ

M ,CF


M , DR
côv ri ,t , Nˆ M , DR,t

vâr Nˆ
 Nˆ

M ,CF

M , DR



côv ri ,t , Nˆ M ,CF ,t 1

vâr Nˆ
 Nˆ

côv ri ,t , Nˆ M , DR,t 1

vâr Nˆ
 Nˆ



M ,CF
M ,CF



M , DR
M , DR
We use fitted values of VAR news to estimate betas on
various portfolios
The denominator is equal to variance of unexpected market
return
We include a lag to alleviate infrequent-trading problems,
sluggish reaction of small stocks to new information, etc.
Test assets
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We measure the cash-flow and discount-rate betas
on Fama-French 25 ME-and-BE/ME-sorted
portfolios
We also create risk-sorted portfolios by sorting
stocks on pre-estimated regression loadings on

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market return,
change in term-yield spread, and
change in the small-stock value spread
Data ranges:
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Full period, 1929:1-2001:12
Early subsample, 1929:1-1963:6
Modern subsample, 1963:7-2001:12
Estimates for early period
Estimates for modern period
Beta evolution
βCF
Value minus growth
βDR
Small minus big
PRICING TESTS
Paper's three empirical steps



Estimate the market's cash-flow and
discount-rate news
Using the estimated series, measure the
cash-flow and discount-rate betas for
various assets
See how these betas explain average
returns, and compare the premia to those
predicted by the theory
Epstein-Zin objective function
U [Ct , Et (U t 1 )] 

1
1 1


1 

(1   )Ct   [ Et (U t 1 )] 


  (1   ) /(1  1 )


We assume that long-horizon investor has Epstein-Zin
(1989, 1991) preferences
If the elasticity of intertemporal substitution () approaches
1, the optimal consumption-wealth ratio approaches a
constant (=1-)
Epstein-Zin risk premia

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Suppose that the investor follows an optimal
portfolio strategy, denoted by p
Campbell (1993) shows that the approximate
optimality of portfolio strategy p requires that the
following first-order conditions are satisfied:

Et ct 1   log   Et rp ,t 1 
vart (ct 1 rp ,t 1 )
2
Et ri ,t 1  rrf ,t 1 
 i2,t
2

covt (ri ,t 1 , ct 1 )

 (1   ) covt (ri ,t 1 , rp ,t 1 )
Substituting out consumption
Et ri ,t 1  rrf ,t 1 
 i2,t
2

cov t (ri ,t 1 , ct 1 )

 (1   ) cov t (ri ,t 1 , rp ,t 1 )
Substituteout consumption assuming homoskedasticity,
using a linear approximat ion of the budget constraint,
and substituting in the optimal Epstein- Zin consumption
Et ri ,t 1  rrf ,t 1 
 i2,t
2
  cov t (ri ,t 1 , rp ,t 1  Et rp ,t 1 )

Discount-rate
news NDR
 (  1) cov t (ri ,t 1 , Et 1   j rp ,t 1 j )
j 1
Asset pricing model

Recognizing that unexpected return equals cashflow news minus discount-rate news allows us to
rewrite the first-order condition:
Et ri ,t 1  rrf ,t 1 

2
i ,t
2
  cov t (ri ,t 1 , N p ,CF ,t 1 )
 cov t (ri ,t 1 , N p , DR,t 1 )
  p2 ,t  i ,CF p ,t   p2 ,t  i , DRp ,t
Premium on
cash-flow beta
Premium on
discount-rate beta
Implementation
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Set the reference portfolio to the CRSP value-weight
index portfolio
Use an unconditional betas and mean returns
Use average simple returns on the left hand side
Include a lag in beta estimation
2 ˆ
ˆ
E ( Ri  Rrf )  ˆ i ,CFM  ˆ M i , DRM
2
M
One free
parameter
Plug in the market's
historical variance
Test assets
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25 Fama-French ME-and-BE/ME-sorted portfolios
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20 risk-sorted portfolios formed on betas w/r
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Value vs. growth
Small caps vs. large caps
market return,
change in term-yield spread, and
change in the small-stock value spread
Data ranges:
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Full period, 1929:1-2001:12
Early subsample, 1929:1-1963:6
Modern subsample, 1963:7-2001:12
Early-period pricing tests
Modern-period pricing test
?!?
Post-1963, ICAPM beats CAPM
R2 = 47.4%
R2 = - 61.6%
Critical issues

The following steps are critical for the
empirical success of our model:

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Inclusion of the small-stock value-spread variable
in the VAR state vector
Inclusion of at least one lagged month at the betaestimation stage
ρ = δ value between .941/12 and .961/12
Exclusion of momentum portfolios from the assetpricing test
CONCLUSIONS
Conclusions
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Merton's ICAPM predicts that, if investors are
conservative,
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"bad" cash-flow beta (covariance of a firm's stock
return with the market's cash-flow news) should
have a high premium
"good" discount-rate beta (covariance of a firm's
stock return with the market's discount-rate news)
should have a very small premium
Conclusions

We find that this prediction is supported by the
data:
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High returns of value and small stocks are explained by
their high bad cash-flow betas
Growth stocks have negative CAPM alphas because
their betas are predominantly of the good discount-rate
variety
The post-1963 sorts on CAPM beta only create a spread
in the good discount-rate beta  minimal premium
The model works with only one degree of freedom (zerobeta rate constrained to T-bill rate and discount-rate-beta
premium to market's variance.)
Open questions
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Where is this discount-rate variation coming from?
What are the exact economic fundamentals that
cause varying sensitivities to cash-flow and
discount-rate news?
Are high NDR betas of growth stocks due to
covariance of growth stocks' cash flows or expected
returns with the market's discount-rate news?
Market timing investor's first-order condition
Pricing of momentum portfolios
APPENDIX
Time-varying covariances
Premia on news covariances
Premium on
covariance with NCF,
ICAPM predicts γ
Premium on
covariance with -NDR,
ICAPM predicts 1