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