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Bad Beta, Good Beta
John Campbell and Tuomo VuolteenahoHarvard University and NBER
Presentation atOxford Finance Summer Symposium
11/6/2004
RESEARCH AGENDA
High P/B – growth or glamour? 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
Low stock returns…
…caused by risk or mispricing? Risk…
Valuation level caused by mispricing
…is risk caused by fundamentals
or mispricing?
Risks caused by covariances in
mispricing
Risk is caused by covariances in fundamentals
BBGB
BAD BETA, GOOD BETA
The CAPM 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 i.e., low or even negative market beta
If an asset performs poorly when the market performs poorly, then it is risky
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? 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?
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
MM
tMtM gk
DP
1,
,
Intuition from Gordon model
Merton's ICAPM idea
We break the market return in two components:
We also break up the CAPM beta of a stock into two components:
cash-flow beta, βCF
discount-rate beta, βDR
1,,1,,1,1, )( tDRMtCFMtMttM NNrEr
tCAPMitMt
tMtittDRitCFi
tMt
tDRMtittDRi
tMt
tCFMtittCFi
r
rr
r
Nr
r
Nr
MM
MM
,,1,
1,1,,,,,
1,
1,,1,,,
1,
1,,1,,,
)(var
),(cov
)(var
),(cov
)(var
),(cov
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
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
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 discount-rate 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
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-and-BE/ME-sorted portfolios
's are beta-sorted portfolios
Some previous research
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, 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
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
1,1,
111
01111
tDRtCF
jjt
jtt
iit
ittttt
NN
rEEdEErEr
VAR implementation
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
1,1,
1
1,111
)11(,)1(
]0,,0,1[1,)(
1,
tCFMtDRM
etMtttt
ueeNueN
eI
rzeuzaz
VAR state variables
Excess market return log return on CRSP VW minus log return on three-month T-
bills TERM yield spread (in percentage points)
Yield on ten-year taxable T-bonds minus yield on short-term taxable T-notes
Smoothed P/E Log S&P 500 price index minus log 10-year trailing moving
average of S&P 500's aggregate earnings Small-stock value spread
Log(BE/ME) of small-value Fama-French 2-by-3 portfolio minus log(BE/ME) of small-growth portoflio
Logic behind state variables
TERM yield spread High TERM yield spread forecasts high returns on long-
term bonds Since stocks are long-term assets, expected stock returns
should also be high Predicted coefficient positive
Smoothed P/E Ten-year trailing moving average controls for cash-flow-
generating 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
Small-stock value spread 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
PEVS TY
Monthly VAR, 1928:12-2001:12
Properties of the news terms
Moving-average news
Summary of the market's news
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:
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
DRMCFM
tDRMti
DRMCFM
tDRMtiDRi
DRMCFM
tCFMti
DRMCFM
tCFMtiCFi
NN
Nr
NN
Nr
NN
Nr
NN
Nr
M
M
,,
1,,,
,,
,,,,
,,
1,,,
,,
,,,,
ˆˆrav
ˆ,vocˆˆrav
ˆ,vocˆ
ˆˆrav
ˆ,vocˆˆrav
ˆ,vocˆ
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
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
market return, change in term-yield spread, and change in the small-stock value spread
Data ranges: 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
Small minus bigValue minus growth
βDR
βCF
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
)1/()1(
)]([)1(
)](,[
1
111
1
1
1
ttt
ttt
UEC
UECU
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
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:
),(cov)1(
),(cov
2
1,1,
11,2,
1,1,
tptit
ttittitrftit
rr
crrrE
)(var2
log 1,11,1 tptttpttt rcrEcE
Substituting out consumption
),(cov)1(
),(cov2
),(cov)1(
),(cov
2
11,11,
1,1,1,
2,
1,1,
n consumptioZin -Epstein optimal in the ngsubstituti and,constraintbudget theofion approximatlinear a using
ticity,homoskedas assumingn consumptioout Substitute
1,1,
11,2,
1,1,
jjtp
jttit
tpttptitti
trftit
tptit
ttittitrftit
rEr
rErrrrE
rr
crrrE
Discount-rate news NDR
Asset pricing model
Recognizing that unexpected return equals cash-flow news minus discount-rate news allows us to rewrite the first-order condition:
tDRitptCFitp
tDRptit
tCFptitti
trftit
pp
Nr
NrrrE
,,2
,,,2
,
1,,1,
1,,1,
2,
1,1,
),(cov
),(cov2
Premium on cash-flow beta Premium on
discount-rate beta
Implementation
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
MM DRiMCFiMrfi RRE ,2
,2 ˆˆˆˆ)(
One free parameter
Plug in the market's historical variance
Test assets
25 Fama-French ME-and-BE/ME-sorted portfolios Value vs. growth Small caps vs. large caps
20 risk-sorted portfolios formed on betas w/r market return, change in term-yield spread, and change in the small-stock value spread
Data ranges: 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: Inclusion of the small-stock value-spread variable
in the VAR state vector Inclusion of at least one lagged month at the beta-
estimation stage ρ = δ value between .941/12 and .961/12 Exclusion of momentum portfolios from the asset-
pricing test
CONCLUSIONS
Conclusions
Merton's ICAPM predicts that, if investors are conservative, "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: 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 (zero-beta rate constrained to T-bill rate and discount-rate-beta premium to market's variance.)
Open questions
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 -NDR,
ICAPM predicts 1
Premium on covariance with NCF,
ICAPM predicts γ
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