The Expected Value Premium

Long Chen∗

Eli Broad College of BusinessMichigan State University

Ralitsa Petkova†

Weatherhead School of ManagementCase Western Reserve University

Lu Zhang‡

Simon School of BusinessUniversity of Rochester and NBER

November 2005

Abstract

We estimate the expected value premium using expected rates of dividend growth andexpected dividend-price ratios for value and growth portfolios. We find that duringthe 1941—2002 period, the expected value premium is positive in every year, significantin various subsamples, and countercyclical. Unlike the equity premium, there is nonoticeable trend in the expected value premium. Potential driving sources of ourresults are suggested.

∗East Lansing, MI 48821; tel: (517)353-2955, fax: (517)432-1080, email: chen@bus.msu.edu.†10900 Euclid Avenue, Cleveland OH 44106. Tel: (216)368-8553, email: Ralitsa.Petkova@case.edu.‡Carol Simon Hall 3-160B, University of Rochester, Rochester, NY 14627. Tel: (585)275-3491, fax:

(585)273-1140, and email: zhanglu@simon.rochester.edu.

Contents

2

1 Introduction

It is well known that value stocks outperform growth stocks in terms of realized average

returns. However, there still exists a heated controversy around the issue of whether this

value premium is due to rational compensations for risk or irrational behavior on the side

of investors. Furthermore, some recent studies (e.g., Schwert (2002)) suggest that the value

premium has declined over time, implying that academic research might have influenced the

efficiency of capital markets. In this paper we offer a fresh look at the controversy about the

value premium. We use fundamentals (dividends) to estimate the expected value premium

rather than the average realized historical return. The main advantage of this approach is

that the average realized return is at best a noisy proxy for the expected return (e.g., Elton

(1999)). The expected value premium estimates based on fundamentals will help us shed

more light on the debate about the source of the value premium and its magnitude.

In this study, we focus on three main economic questions. First, is there an ex ante

expected value premium? In the current literature, the majority of papers documenting

the existence of the value premium implicitly assume that the average realized return is an

unbiased proxy for the expected return (e.g., Fama and French (1993); Lakonishok, Shleifer,

and Vishny (1994); and Davis, Fama, and French (2000)). However, recent studies have

cast doubt on this practice. In particular, the average realized return might not converge

to the expected return in finite samples. For example, Elton (1999) observes that there are

periods longer than ten years during which the stock market return is on average lower than

the risk free rate (1973—1984), and periods longer than 50 years during which risky bonds

underperform on average the risk free rate (1927—1981).1

1See also Brav, Lehavy, and Michaely (2003) and Campello, Chen, and Zhang (2003).

3

In light of these issues, we construct an ex ante measure of the expected value premium.

The logic behind our measure can be explained through a simple rearrangement of Gordon’s

growth formula:

R =D

P+ g,

where R is the equity return, DPis the dividend-price ratio, and g is the dividend growth

rate. If we take expectation on both sides, the formula implies that the expected equity

return can be decomposed into an expected dividend-price ratio component and an expected

dividend growth component. Blanchard (1993) regresses the dividend-price ratio and the

future dividend growth rate on a set of conditional macroeconomic variables to analyze the

path of the expected market risk premium. The fitted values from the regressions are then

used to construct the time series of the expected equity premium. We follow the same

method in analyzing the expected value premium.

More precisely, we use the dividend growth rates of value and growth stocks to estimate

their corresponding expected rates of dividend growth, which can then be combined with the

expected dividend-price ratios to obtain expected returns. The conditional expected return

is the sum of the fitted values from time-series regressions of the realized dividend-price ratio

and a weighted average future dividend growth rate on a set of predetermined variables. This

method avoids the use of the average realized return as a proxy for the expected return. Our

work is thus in the spirit of a growing literature that uses valuation models to estimate

expected returns (e.g., Claus and Thomas (2000), Gebhardt, Lee, and Swaminathan (2000),

Fama and French (2002)).

Note that the method we use to construct the value premium lets us compute the path

of the conditional expected return spread between value and growth portfolios rather than

4

the unconditional expected return spread (e.g., Fama and French (2002)). The advantage of

analyzing the conditional expected value premium is that we can answer the second research

question on our agenda: is the expected value premium countercyclical? The cyclicality of

the expected value premium might be the key to distinguishing alternative theories about

the value premium. Recent rational theories (e.g., Zhang (2003)) predict that the expected

value premium should be countercyclical. Specifically, in bad times firms usually invest at

a lower rate than the long run average. In bad times, value firms, having lower profitability

than growth firms, will start to disinvest. Since cutting capital is more costly than expanding

capital, value firms do not have enough flexibility to scale down. Therefore, value firms are

affected more by economic downturns, and are hence riskier than growth firms in bad times.

The countercyclical risk dispersion between value and growth, combined with a constant or a

countercyclical price of risk, implies a countercyclical expected value premium. In contrast,

the overreaction theory on the value premium focuses on the predictability of the abnormal

return of the value strategy, as opposed to its time-varying expected return (e.g., DeBondt

and Thaler (1985); Lakonishok, Shleifer, and Vishny (1994); and Daniel, Hirshleifer, and

Subrahmanyam (1998)).

The third question we address is: is there a long-run trend in the expected value premium?

Recent studies (e.g., Schwert (2002)) have argued that the value premium has decreased over

the past ten years, suggesting that academic research has made capital markets more efficient.

We investigate this hypothesis using an ex ante measure of the expected value premium.

Our main findings can be summarized as follows. First, there exists a significantly positive

expected value premium. Its sample average (measured by the expected HML return) is 5.1%

per year in the period from 1941 to 2002. Similar results are obtained in the subsample from

5

1963 to 2002. This evidence reinforces the view that the value premium is real and is not

due to sample selection or data-snooping biases.

Second, the expected value premium exhibits countercyclical movements. For example, in

the sample from 1941 to 2002, the correlation between the expected value premium (measured

by the expected HML return) and the default spread (a countercyclical variable) is 0.39 (p-

value 0.00). The correlation between the expected HML return and the growth rate of real

investment (a procyclical variable) is -0.28 (p-value 0.03). The results are similar over the

period from 1963 to 2002. This evidence provides support for the theoretical prediction in

Zhang (2003) that the expected value premium is countercyclical.

Third, we find that the expected value premium responds to macroeconomic shocks

significantly and in the direction predicted by rational asset pricing theory. A positive shock

to real consumption growth or real investment growth leads to lower expected value premia.

Therefore, the evidence suggests that the ex ante value premium goes up with negative

macro shocks, and it goes down with positive macro shocks. The covariance of the expected

value premium with macroeconomic factors whose risks cannot be diversified away provides

support for the view that the expected value premium is a compensation for systematic risk.

Finally, we document an increase in the expected value premium from 1950 to the early

1980s and a decrease thereafter. A combination of technological innovation and investor

learning may be responsible for this finding. In summary, we contribute to the current

literature on the value premium by providing new evidence on the magnitude and cyclical

movements in the expected value premium.

The rest of the paper is organized as follows. Section 2 describes in detail the methods we

use to construct the expected value premium. In Section 3 we document various descriptive

6

statistics for the ex ante value premium and its components—the expected dividend-price ratio

and the expected dividend growth rate. Section 4 studies the trend and cyclical movements

in the expected value premium. It also examines the relation between the premium and

various macroeconomic variables. Section 5 provides a variety of robustness checks and

Section 6 offers a summary and interpretation of our results.

2 Research Design

This section describes the empirical methods we use to construct the expected value

premium. Section ?? discusses the basic idea and Section ?? presents implementation details

including the construction of our sample.

2.1 The Basic Idea

The method we use to construct expected returns follows closely that of Blanchard (1993),

who studies movements in the expected equity premium. The basic idea is to use dividend

growth rates to estimate expected rates of dividend growth, which can then be combined

with expected dividend-price ratios to obtain expected returns.

To be precise, let Rt+1 be the realized stock return from time t to t+1, i.e., 1+Rt+1=

(Dt+1+Pt+1)/Pt, where Pt is the stock price known at time t, and Dt+1 is the real dividend

paid over the period from t to t+1; Dt+1 is unknown until the beginning of time t+1.

If we assume that the dividend-price ratio is stationary, we can solve for Pt as the present

value of future dividends discounted by the sequence of realized rates of return. We next

divide both sides by Dt, take conditional expectations at time t, and linearize to obtain the

7

expected return at time t, denoted as Et[Rt+1]

Et[Rt+1] = Et

∙Dt+1

Pt

¸+Et[Agt+1], (1)

where Agt+1 is the long-run growth rate of dividends defined as the annuity value of the

growth rate of future dividends

Agt+1 ≡∙r − g

1 + r

¸ ∞Xi=0

∙1 + g

1 + r

¸igt+i+1, (2)

with g and r being the average growth rate of real dividends and the average real stock

return, respectively. Finally, gt+1 denotes the growth rate of real dividends from time t to

t+1.

The interpretation of equation (??) is straightforward—the expected return conditional

on time t is the sum of the expected dividend-price ratio and the expected long-run growth

rate of dividends, both conditional on time t. Accordingly, the expected value premium

equals the sum of the dispersion in the expected dividend-price ratio and the dispersion in

the expected long-run growth rate of dividends between value and growth.

2.2 Implementation

We now discuss the details of estimating expected returns based on equations (??) and (??)

for value and growth portfolios.

Data

We obtain relevant data from three main sources. The first source is the Center for Research

in Securities Prices (CRSP) monthly stock file that contains information on stock prices,

shares outstanding, dividends, and returns for NYSE, AMEX, and Nasdaq stocks. The

8

second source is the COMPUSTAT annual research file that provides accounting information

for publicly traded U.S. firms. To alleviate the potential survivorship bias due to backfilling

data, we require that firms be on COMPUSTAT for two years before using the data. The

third source is Moody’s book equity information used in Davis, Fama, and French (2000),

available from Kenneth French’s web site.2

Our sample period begins in 1941 and ends in 2002. In earlier periods, only a few firms

have data on dividends once we classify them into value and growth portfolios. Potential

problems with disclosure regulations also affect our choice of the starting date of the sample

period.

We construct value and growth portfolios by sorting on book-to-market ratios. We

implement both a one-way sort on book-to-market to obtain five quintile portfolios and

a two-way, two-by-three sort on size and book-to-market to obtain six portfolios (e.g., Fama

and French (1993)). Our timing in portfolio construction differs slightly from that commonly

used in the literature. Instead of in June, we form portfolios in December of each year t. We

use book equity from the fiscal year ending in calendar year t−1 divided by market equity

at the end of December of year t. This method avoids any look-ahead bias that might arise

as accounting information from the current fiscal year is often not available at the end of the

calendar year. Portfolio ranking is effective from January of year t+1 to December of year

t+1. This portfolio timing is lined up with the timing of dividend growth which occurs from

the beginning to the end of the calendar year. The different timing convention that we use

is not a source of concern, however. In fact, using slightly more lagged information on book

value makes it harder to find an ex ante value premium. We repeat the analysis using the

original book-to-market and size portfolios constructed by Fama and French, and we find

2http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data-library.html

9

similar results.

Our definition of book equity follows that of Cohen, Polk, and Vuolteenaho (2003). In

particular, book equity is defined as stockholders’ equity plus balance sheet deferred taxes

(item 74) and investment tax credit (item 208 if available) plus post-retirement benefit

liabilities (item 330 if available) minus the book value of preferred stock. Depending on data

availability, we use redemption (item 56), liquidation (item10), or par value (item 130), in

this order, to represent the book value of preferred stock. Stockholders’ equity is equal to

Moody’s book equity (whenever available) or the book value of common equity (item 60)

plus the par value of preferred stock. If neither is available, stockholders’ equity is calculated

as the book value of assets (item 6) minus total liability (item 181).

Estimating Expected Returns

To estimate the expected returns for value and growth portfolios, we have to construct the

time series of their dividend-price ratios and dividend growth rates.

For each portfolio, we construct the real dividend-price ratio from the time series

of value-weighted realized stock returns with and without dividends and the time series

of the consumer price index from the U.S. Bureau of Labor Statistics. In particular,

Dt+1/Pt =¡Rt+1 −RX

t+1

¢(CPIt/CPIt+1), where Rt+1 is the nominal return with dividends

from time t to t+1, RXt+1 is the nominal return without dividends over the same period,

and CPIt is the level of the consumer price index. The real dividend growth is calculated as

gt+1=Dt+1/PtDt/Pt−1

¡RXt + 1

¢(CPIt−1/CPIt)−1. The resulting real dividend growth rates are quite

volatile even at the portfolio level. To trim the outliers, we replace any annual observations

of dividend growth higher than 50% with 50% and those lower than −50% with −50%.

Next, we construct the long-run dividend growth rate, Agt+1, given by equation (??), for

10

each portfolio. We estimate r as the sample average of the realized real equity returns, and

g as the sample average of the real dividend growth rates. Agt+1 is an infinite sum of future

real dividend growth rates. In practice we use a finite sum of 100 years of future growth. We

assume that the future real dividend growth rates beyond 2002 equal the average dividend

growth rate during the 1980—2002 period. We also use the full-sample average and find the

results to be quite stable. The focus on the 1980—2002 period intends to pick up the recent

trend of dividend growth.

Finally, we regress Agt+1 and Dt+1/Pt on a set of conditioning variables. The fitted values

from these regressions provide the two components of the expected returns. Their sum gives

us the time series of expected portfolio returns.

The set of conditioning variables includes four aggregate variables and one portfolio-

specific variable. Our choice of the four aggregate conditioning variables is standard from

the time series predictability literature. These variables include: the aggregate dividend

yield, computed as the sum of dividend payments accruing to the CRSP value-weighted

portfolio over the previous 12 months, divided by the contemporaneous level of the index

(e.g., Fama and French (1988)); the default premium, defined as the yield spread between

Moody’s Baa and Aaa corporate bonds from the monthly database of the Federal Reserve

Bank of Saint Louis (e.g., Keim and Stambaugh (1986) and Fama and French (1989)); the

term premium, defined as the yield spread between a long-term and a one-year Treasury

bond from Ibbotson Associates (e.g., Campbell (1987) and Fama and French (1989)); and

the one-month Treasury bill rate from CRSP (e.g., Fama and Schwert (1977) and Fama

(1981)).

Previous studies find that the log book-to-market spread, defined as the log book-to-

11

market of portfolio ten minus the log book-to-market of portfolio one from ten deciles sorted

on book-to-market, can predict future value-minus-growth returns (e.g., Asness, Friedman,

Krail, and Liew (2000); Cohen, Polk, and Vuolteenaho (2003)). Theoretical explanation

of this predictability is provided in Gomes, Kogan, and Zhang (2003) and Zhang (2003).

Therefore, we also use the log book-to-market spread to predict the long-run dividend growth

rate and the dividend-price ratio of value strategies. We obtain data on the returns and the

year-end book-to-market ratios of all book-to-market deciles from Kenneth French’s web

site. From January to December of year t, the book-to-market of a portfolio is calculated by

dividing its book-to-market ratio at the end of December of year t−1, where book value and

market value are both measured at the end of December, by its compounded gross return

from the end of December of year t−1 to the current month of year t.

3 Preliminary Analysis

This section presents some preliminary analysis on estimating the expected value premium.

Table ?? reports descriptive statistics for returns, growth rates, dividend yields, both

realized and expected, for value and growth portfolios. We report the results for the full

sample from 1941 to 2002 and the subsample from 1963 to 2002. When we use the one-way

sort on book-to-market, we denote the resulting five portfolios as Low, 2, 3, 4, and High.

Portfolios Low and High represent the extremes in terms of book-to-market. The difference

between the returns of High and Low is denoted as p5-1 and it represent the value-minus-

growth strategy for the one-way sort of the assets.

When we use the two-way sort on size and book-to-market, we denote the resulting

six portfolios by two letters—LS, LB, MS, MB, HS, and HB. For example, portfolio LS

12

contains stocks with the bottom 30% book-to-market ratios and the bottom 50% market

capitalizations. The value-minus-growth strategy for the two-way sort of the assets is defined

as 1/2*(HS+HB)-1/2*(LS+LB) and it is denoted as HML. Note that this is not the HML

factor used by Fama and French (1993) due to our different timing convention in forming

portfolios. Later in the paper we repeat the analysis using their original factor and find

similar results.

3.1 Average Returns

The first two rows of all panels in Table ?? show that value-minus-growth strategies are

profitable in our samples. For example, the average realized return of portfolio p5-1 is 5.8%

per year (t-statistic 2.88) in the full sample, and 4.6% per year (t-statistic 2.10) in the

subsample. Similarly, the average realized annual return of HML is 6% in the full sample

and 5.9% in the subsample; both are highly significant.

3.2 Growth Rates

Rows three and four in all panels of Table ?? show that the realized real dividend growth rate

of value portfolios is on average higher than that of growth portfolios, albeit the difference

is not significant. The real dividend growth rate, gt+1, of portfolio High-minus-Low is on

average 4.5% per year in the full sample. Controlling for size increases the number further to

5.6% for HML. Moreover, the middle two rows of all panels show that the expected long-run

real dividend growth, Et[Agt+1], follows largely the same pattern. Except for p5-1 in the

subsample, the value portfolio has significantly higher expected long-run growth than the

growth portfolio. The average expected long-run dividend growth of HML is 3.5% per year

(t-statistic 19.90) in the full sample, and 2.8% (t-statistic 21.00) in the subsample.

13

Importantly, our evidence does not contradict the conventional wisdom that growth

stocks have higher proportions of growth opportunities and grow faster than value stocks.

The reason is that our evidence is obtained from portfolios rebalanced annually, while the

conventional wisdom is based on portfolios with fixed sets of firms without rebalancing.

To illustrate this point, we study the event-time evolution of profitability (defined as the

earnings-lagged book equity), the rate of dividend payment (defined as the dividend-lagged

book equity), and the real dividend growth rate for value and growth stocks during 21 years

around the portfolio formation year. Our test design follows closely that of Fama and French

(1995). We define value and growth portfolios both from book-to-market quintiles and from

six size and book-to-market portfolios. The sets of stocks in the value and growth portfolios

are fixed throughout the event years.

The sample we use is from 1941 to 2002. We back out data on dividends from value-

weighted portfolio returns with and without dividends. Since data on earnings is not available

for the pre-COMPUSTAT years we follow Cohen, Polk, and Vuolteenaho (2003) and use the

clean-surplus relation to compute earnings from data on book equity and dividends, i.e.,

earnings(t) =book value(t)−book value(t−1)+dividends(t). To be consistent, we use this

method to compute earnings in later years even when earnings data from COMPUSTAT is

available.

Figure ?? reports the results. First, Panels A and D confirm the main result in Fama

and French (1995, Figure 1) that growth firms are persistently more profitable than value

firms. Panels B and E show that growth firms also have higher rates of dividends than value

firms. The dispersion in dividend rates appears even more persistent than the dispersion in

profitability, especially for the two-way sort. More importantly, Panels C and F show that

14

the real dividend growth rates of growth stocks are higher than the real dividend growth rates

of value stocks. This dispersion is large at the portfolio formation year. It remains positive

for almost ten years for the one-way sort. However, for the two-way sort the dispersion is

much more short-lived and converges in about three years.

However, when the portfolios are rebalanced annually, the firms in the growth portfolio

next year are not the same as the firms in the growth portfolio this year. There is no

particular reason to expect the dividend growth of growth portfolios to be higher than the

dividend growth of value portfolios, given that growth rates are measured using different

sets of firms. Consistent with this observation, Figure ?? plots the time series of the annual

realized real dividend growth rates for portfolios five and one in the book-to-market quintiles

(Panel A), portfolio five-minus-one (Panel B), portfolios High and Low from the six portfolios

sorted on size and book-to-market (Panel C), and HML (Panel D). Panels B and D show that

the real dividend growth rates for the value-minus-growth strategies are frequently negative.

3.3 Expected Returns

Not surprisingly, Table ?? reports that the average expected dividend-price ratio,

Et[Dt+1/Pt], is higher for value firms than for growth firms. Given that the expected long-run

dividend growth and the expected dividend-price ratio are both higher for value firms, their

expected returns are even higher than the expected returns of growth firms. The last two

rows of Panels A and B show that the expected return of p5-1 is 3.7% per year (t-statistic

14.91) in the full sample, and 2.8% (t-statistic 12.05) in the subsample. Similarly, the last

two rows of Panels C and D show that the expected return on HML is 5.1% (t-statistic 40.89)

in the full sample, and 5.1% (t-statistic 31.73) in the subsample. To sum up, the expected

value premium is significantly positive on average.

15

An interesting result that emerges from Table 1 is that the expected return for each

portfolio in the one-way and two-way sorts is substantially lower than the average realized

return of the portfolio. Such a result has been documented before for the excess return on the

market portfolio. For example, Fama and French (2002) report that for the sample period

1951-2002 the expected equity premium is 4.32% per year, while the average realized equity

premium is 7.43% per year. Our evidence suggests that this result holds in the cross-section

of portfolios sorted by size and book-to-market. However, the expected value premium within

each sorting procedure is not far away from the average realized return. This indicates that

the difference between the expected return and the average realized return cancels out at

the cross-sectional level.

We next study the time series of the expected p5-1 return, the expected HML return,

their respective expected long-run dividend growth rates, and their expected dividend-price

ratios. Figure ?? plots the sample paths. Panels A and C show that the expected p5-

1 and HML returns are positive throughout the sample. Both series of expected returns

display positive spikes during most of the recessions in the sample. They also seem to covary

positively with the default premium, a well-known countercyclical variable commonly used to

predict the business cycle and the excess return of the market (e.g., Jagannathan and Wang

(1996)). Therefore, this informal analysis suggests that the expected value premium is also

countercyclical. Panels A and C also suggest that the expected value premium increased in

the period 1950-1980 and decreased after that.

Panels B and D of Figure ?? show that the expected dividend growth rates and the

expected dividend-price ratios of p5-1 and HML covary negatively with each other. There

has been a noticeable decline in the expected long-run dividend growth from the early 1940s

16

to the early 1980s, but an increase thereafter. The expected dividend-price ratios display the

opposite long-term movements. As a result, these graphs do not show an obvious trend in

the expected value premium, although the expected p5-1 return appears to decline slightly

over time.

Finally, Table ?? reports the results of autocorrelations and MacKinnon (1994) unit

root tests for the expected p5-1 return, the expected HML return, and their respective

components—the expected dividend-growth rate and the expected dividend-price ratio. The

table shows that the two separate components are more persistent than the expected value

premium itself. The unit root tests fail to reject the unit-root null for the expected dividend-

price ratios of both p5-1 and HML, but the null is rejected for the expected dividend growth

rates and the expected value premium.

3.4 The Equity Premium

The method we use to derive the expected value premium is the dynamic extension of the

method used in Fama and French (2002) to compute the equity premium. It is therefore

interesting to compare the properties of the equity premium constructed our way to those

documented in Fama and French. First, our estimates are close to those obtained by Fama

and French (2002). During the 1951—2000 period studied by Fama and French, our estimates

of the expected long-run real dividend growth rate, the expected real dividend yield, the

expected real equity return, and the average realized real market return are 0.84%, 4.07%,

4.91%, and 10.21%, respectively. These numbers are reasonably close to their counterparts

in Fama and French—1.05%, 3.70%, 4.75%, and 9.62%, respectively. The differences are likely

due to the way we use to construct our sample.

Second, consistent with Fama and French (2002), the equity premium that we estimate

17

is much lower than the average realized real equity return. The expected equity premium

from 1941 to 2002 is 4.25% per year, compared to the realized real equity premium of 7.76%

per year for the same period.

More importantly, our estimates also show that the equity premium has declined over

time. The time series plot in Figure ?? shows that the equity premium reaches its peak of

about 10% in the early 1950s, declines over the next two decades to about 2.5% in the mid

1970s, climbs up to about 5% in the mid 1980s, then declines over the next one and half

decades to about 1% in the early 2000s. Using the equity premium in a trend regression

yields a negative slope of -0.077% (t-statistic -8.46) in the 1941—2002 sample. Although the

slope is only an insignificant -0.021% (t-statistic -1.65) in the post-1963 sample, it increases

in magnitude to -0.142% (t-statistic -7.73) in the sample after 1980.

4 The Expected Value Premium

We now study the dynamics, including both trend and cyclical movements, of the expected

value premium in more details.

4.1 Trend Dynamics

We use two methods to isolate the cyclical component of the expected value premium from

the low-frequency, trend component. The first method is to regress the expected value

premium on a time trend

ValuePremiumt = a+ b t+ εt, (3)

where the fitted component including the intercept is defined as the trend component and

the residual is defined as the cyclical component. The second method is to pass the expected

18

value premium through the Hodrick-Prescott (1997) (HP) filter that separates the trend and

the cyclical components of the premium.

The results from regression (??) indicate that the expected p5-1 return exhibits a

downward trend in the 1941—2002 and the 1963—2002 samples, but the expected HML return

does not. The expected HML return exhibits a downward trend in the 1980—2002 sample,

but the expected p5-1 return does not. Specifically, the slope coefficient, b, is -0.078% for the

expected p5-1 return (t-statistic -8.01) in the 1941—2002 sample, -0.052% (t-statistic -2.83)

in the post-1963 sample, and -0.091% (t-statistic -1.86) in the 1980—2002 sample. The slope

is -0.010% (t-statistic -1.47) for the expected HML return in 1941—2002, -0.011% (t-statistic

-0.76) in 1963—2002, and -0.097% (t-statistic -3.12) in the 1980—2002 sample.

Using the HP filter yields somewhat different results. Figure ?? plots the trend and

cyclical components of the expected p5-1 return and the expected HML return. Panel B

shows a downward movement in the HP-filtered, low frequency component of the expected

p5-1 and HML returns. Panel A shows the patterns for the low frequency movements of

p5-1 and HML in the case of the time-trend regression (estimated using the full sample). As

pointed out before, there is a downward trend for p5-1 and no clear trend for HML. Overall,

the evidence based on the time-trend regression and the HP filter indicates a downward

trend in the low-frequency movements of the expected value premium.

4.2 Cyclical Dynamics

Panels C and D of Figure ?? trace the cyclical components of the expected p5-1 and HML

return. Panel C is based on the residuals from the time-trend regression, while Panel D is

based on the HP filter. Both panels plot the NBER recession dummy which takes the value

of one in recessions and zero otherwise. The graphs show that the expected value premium

19

is countercyclical—the expected value premium rises in recessions and drops in expansions.

We use two additional methods to study the cyclical properties of the expected value

premium. As an informal test, we first report the lead-lag cross-correlation structure of

the expected value premium with a list of cyclical indicators. We then supplement the

cross-correlations with a more formal VAR analysis.

Cross Correlations

Table ?? reports the cross-correlations. The list of cyclical indicators includes the default

premium, the NBER recession dummy, the real investment growth rate, and the real

consumption growth rate. Among the four variables, the default premium and the recession

dummy are countercyclical, while the real investment and consumption growth rates are

procyclical.

The middle column in Panel A of Table ?? shows that the contemporaneous correlation

between the expected p5-1 return and the default premium is 0.49 and that between the

expected p5-1 return and the recession dummy is 0.50. Both correlations are significant.

Further, the contemporaneous correlation between the expected p5-1 return and real

investment growth is -0.36 and that between the expected p5-1 return and real consumption

growth is -0.32 (both are significant). The middle column in Panel B shows that using the

expected HML return yields similar results. To sum up, the evidence suggests that the

expected value premium is countercyclical.

The middle columns of the two panels also show that the countercyclical property of the

expected value premium derives mostly from a similar property of the expected dividend-

price ratio. The dividend price ratios of p5-1 and HML have significantly positive correlations

with the default premium. Their correlations with the other cyclical variables are not

20

significant. In contrast, the expected dividend growth rates of p5-1 and HML exhibit only

weak comovements with the business cycle, relative to the expected dividend-price ratio.

VAR Analysis

We next supplement the lead-lag correlations with a more formal VAR analysis. The VAR

contains one measure of the expected value premium (either the expected p5-1 or the HML

return) and one cyclical indicator. We use two cyclical variables separately in the VAR—the

investment growth and the real consumption growth. Using other cyclical variables yields

similar results (not reported). The lag in the VAR is one, which is chosen according to the

Akaike information criterion. In some specifications, we also include the one-month T-bill

rate in the VAR in an effort to isolate the business cycle shock from the monetary policy

shocks.

Table ?? reports the results. Panel A shows that the coefficients of real investment growth

in the VAR are negative and significant (in the full sample period for portfolio p5-1 they are

marginally significant). The result holds with and without controlling for the T-bill. Panel

B shows that the coefficients of real consumption growth rate are all negative; they are all

significant for both the long and the short sample periods. These results suggest that the

expected value premium responds negatively to aggregate shocks. A positive shock to real

consumption growth or real investment leads to lower expected value premia.

To interpret the magnitudes of the VAR coefficients and to quantify the business cycle

sensitivity of the expected value premium, we study the impulse response functions implied

by the estimated VARs. Figure 6 plots these impulse response functions of the expected

value premium in the presence of a one standard deviation shock to the explanatory variable.

Panels A—C report the response of the expected value premium to a one-standard deviation

21

positive shock to real investment growth, while Panels E—H report the results relative to

real consumption growth. In all cases, the premium responds negatively to good news about

investment and consumption.

4.3 Predictive Regressions

Previous studies (e.g., Asness et al. (2000) and Cohen, Polk, and Vuolteenaho (2003))

document that the realized value premium is predictable using the log book-to-market spread,

suggesting that the expected value premium is time-varying. We investigate this issue further

within our empirical framework. Specifically, we regress the value premium defined as the

sum of the long-run dividend growth, Agt+1, and the dividend-price ratio, Dt+1/Pt, on a set

of conditioning variables including the aggregate dividend yield, the default premium, the

term premium, the log book-to-market spread, and the one-month T-bill rate. To study the

predictability of the two separate components of the value premium, we also regress Agt+1

and Dt+1/Pt on the same set of conditioning variables. These regressions have been used to

construct the expected dividend growth and the expected dividend-price ratio. To adjust

for the small-sample bias in the slopes and their standard errors (e.g., Stambaugh (1999)),

we use the simulation method of Nelson and Kim (1993).

Table ?? reports the results. The first three rows of all panels show that the value

premium is indeed predictable. The adjusted R2 clusters around 30% except for the HML

return in the 1941—2002 sample that has an adjusted R2 of 15.60%. Although not reported

in the table, the null hypothesis that all the slopes are jointly zero is strongly rejected

in all cases. The results suggest that the aggregate dividend yield has reliable predictive

power with positive slopes, except for the HML return in the period from 1941 to 2002.

Further, the term premium has significant predictive ability for the expected value premium

22

with negative slopes in all cases and across both sample periods. Consistent with previous

studies, we find that the log book-to-market spread is largely a positive predictor of the value

premium, except for predicting the p5-1 return in the post-1963 sample (Panel B). However,

our results also show that its predictive power is weak, given that all corresponding p-values

are close to 0.20. The default premium and the short-term rate do not have significant

predictive ability for the expected value premium in the presence of the other conditioning

variables.

The rest of Table ?? reports the results of predicting the two separate components of

the value premium including the dividend growth and dividend-price ratio. The set of

conditioning variables does an overall better job in predicting the separate components than

the value premium itself. This is reflected in much higher adjusted R2s; in some cases the

goodness-of-fit coefficients are more than doubled. Moreover, in some cases, the conditioning

variables have different signs when predicting the two components, consistent with the results

in Figure ?? that the expected dividend growth and the expected dividend-price ratio are

negatively correlated. Specifically, the short rate is a significantly positive predictor of the

long-run dividend growth, and a significantly negative predictor of the dividend-price ratio.

A similar result holds for the term premium variable.

5 Robustness

This section reports a set of robustness checks such as incorporating stock repurchases into

the computation of the payout, using an alternative set of instruments to model expectations,

and using a different set of portfolios to measure the value premium.

23

5.1 Stock Repurchases

Fama and French (2001) document that the proportion of firms paying dividends has fallen

dramatically over the years regardless of their levels of earnings. Grullon and Michaely

(2002) show that dividends have been the dominant form of payout in earlier periods, but

repurchases have become more important in recent years.

In light of this evidence, we add net stock repurchases as part of the dividends. We

replicate the results on gt+1, Et[Agt+1], Et[Dt+1/Pt], and Et[Rt+1] in Table ??, the time series

plots in Figure ??, and the VAR analysis in Table ?? and Figure 6.

Table 6 reports the descriptive statistics for returns, dividend growth rates, and dividend

yields, both realized and expected, for value and growth portfolios. Including stock

repurchases in the payout makes all numbers in the table larger than their counterparts

in Table ??. The value-minus-growth strategies are even more profitable in the case of

repurchases—for example, the average realized return of p5-1 is 6.4% per year in the full

sample and 5.7% per year in the subsample. Both values are significant. A similar result

holds for the average realized return of HML. The expected value premium remains positive

and significant—for example, the average expected return of p5-1 is 4.5% per year in the full

sample and 4.2% per year in the subsample. The average expected return of HML is higher—

it is 5.5% per year for 1941—2002 and 5.7% for 1963—2002. The table also shows that value

portfolios have significantly higher expected long-run dividend growth rates and expected

dividend-price ratios than growth portfolios.

Figure 7 plots the trend and cyclical components of the expected p5-1 and HML returns,

taking into account stock repurchases. Panel B shows that there is no obvious downward

or upward movement in the HP-filtered, low-frequency component of both HML and p5-

24

1. Panel A, however, shows a downward trend for the p5-1 portfolio using the time trend

regression method. There is a slight upward trend for HML in Panel A.

Table 7 reports the results from the VAR analysis of the expected value premium in the

case of stock repurchases. In Panel A, the coefficients of real investment growth in the VAR

are negative and significant. The result holds with and without controlling for monetary

policy. Panel B shows that the coefficients of real consumption growth rate are all negative;

they are all significant for both the long and the short sample periods. These results suggest

that the expected value premium responds negatively to aggregate shocks.

Finally, Figure 8 presents the impulse response functions implied by the estimated VAR in

Table 7. Panels A—C report the response of the expected value premium to a one-standard

deviation positive shock to real investment growth, while Panels E—H report the results

relative to real consumption growth. In all cases, the expected value premium responds

negatively to good news about investment and consumption.

In summary, when stock repurchases are included in the computation of the expected

value premium, the results are qualitatively very similar to the ones reported for our base

case. The expected value premium is still significantly positive and countercyclical. The

new result that emerges is that there does not exist a clear trend pattern in the movement

of the expected value premium.

5.2 Alternative Instruments

We also study the robustness of our benchmark results with respect to alternative sets of

instruments. We first exclude the log book-to-market spread from the list of conditioning

variables. The results look qualitatively very similar to the ones reported for our base case

(they are not reported for the sake of brevity, but are readily available upon request).

25

Alternatively, we include Lettau and Ludvigson’s (2001, 2004) cay and cdy variables in

the set of conditioning variables used to predict the dividend growth and the dividend-price

ratio of value and growth. The new results indicate that there is a significant downward

trend in the expected HML return once we use the HP filter. This is consistent with our

previous findings based on the benchmark case. The impulse response functions from the

VAR analysis indicate that, once we control for monetary policy, the value premium responds

negative to good news about investment and consumption in the first year, but the response

is positive in the second year.

5.3 Alternative Portfolios

Finally, we use the portfolios already constructed by Fama and French to measure the

expected value premium and its components. These portfolios include the group of 6

constructed by a 2x3 sort on size and book-to-market, as well as the 25 portfolios constructed

by a 5x5 sort on size and book-to-market. The results reported before are robust to the choice

of these portfolio. They are not reported for the sake of brevity, but are readily available

upon request.

6 Summary and Interpretation

In this paper we use fundamentals (dividends) to estimate the expected value premium. We

show that over the period from 1941 to 2002, the expected value premium is positive and

significant. Its magnitude is 5.1% per year based on the expected HML return. In addition,

we document that the expected value premium is countercyclical—it rises in recessions and

decreases in expansions. Furthermore, the expected value premium tends to be positively

correlated with countercyclical variables like the default spread and negatively correlated

26

with procyclical variables like the growth in real consumption. We also report that the

expected value premium increases with negative macroeconomic shocks and decreases as a

result of positive macroeconomic shocks. There is some evidence that the expected value

premium has decreased over time.

What might explain the time variation in the expected value premium? Why is the

expected value premium be countercyclical? Why do the dividend growth rates of value

firms respond more to shocks to aggregate economic conditions? The rational asset pricing

model of Zhang (2003) provides a unified explanation for the cyclical properties of the value

premium and the spread in dividend growth between value and growth.

Using a neoclassical framework, Zhang (2003) argues that the expected value premium is

countercyclical. There are two key features in Zhang’s model. First, costly reversibility

implies that it is more costly for firms to cut their productive assets than to expand

them (e.g., Abel and Eberly (1994)). Second, a countercyclical price of risk implies that

shareholders’ discount rates are higher in bad times than in good times (e.g., Fama and

French (1989) and Campbell and Cochrane (2000)).

Specifically, firms usually invest at a lower rate than the long run average rate in

recessions. Value firms, having lower profitabilities than growth firms, will start to disinvest.

Without costly reversibility, value firms will have enough flexibility to scale down. With

costly reversibility, disinvestment implies higher adjustment costs which prevents value firms

from scaling down as much as they would have otherwise.

A countercyclical price of risk further complements and propagates the effects of costly

reversibility. When the price of risk is countercyclical, firms’ discount rates are higher in

recessions. Higher discount rates lead to lower conditional expectation of the firm value as

27

the net present value of its future dividends. As future prospects become gloomier, value

firms would scrap even more capital than in the case with a constant price of risk. Because

costly reversibility prevents value firms from disinvesting, these firms are burdened with

more unproductive assets in bad times.

Growth firms, on the other hand, are relatively immune to the effects of costly reversibility

and a countercyclical price of risk in recessions. Growth firms have more productive assets,

and hence have fewer incentives to scale down in recessions. The net effect is a countercyclical

value premium. In summary, we test the following refutable hypothesis formulated by Zhang

(2003): The expected value premium is countercyclical; in particular, the expected returns

of value firms are more sensitive to negative shocks to aggregate economic conditions than

those of growth firms.

28

References

Abel, Andrew B., and Jannice C. Eberly, 1994, A unified model of investment underuncertainty, American Economic Review 84, 1369—1384.

Asness, Clifford, Jacques Friedman, Robert Krail, and John Liew, 2000, Style timing: valueversus growth, Journal of Portfolio Management 26, 50—60.

Blanchard, Olivier J., 1993, Movements in the equity premium, Brookings Papers onEconomic Activity 2, 75—138.

Campbell, J. Y., 1987, Stock Returns and the term structure, Journal of FinancialEconomics 18, 373—399.

Campbell, John Y., and John H. Cochrane, 2000, Explaining the poor performance ofconsumption-based asset pricing models, Journal of Finance 55, 2863—2878.

Cohen, Randolph B., Christopher Polk, and Tuomo Vuolteenaho, 2003, The value spread,Journal of Finance 58, 609—641.

Daniel, Kent D., David Hirshleifer, and Avanidhar Subrahmanyam, 2001, Overconfidence,arbitrage, and equilibrium asset pricing, Journal of Finance 56, 921—965.

Davis, James L., Eugene F. Fama, and Kenneth R. French, 2000, Characteristics,covariances, and average returns: 1929 to 1997, Journal of Finance 55, 389—406.

DeBondt, Werner F. M., and Richard Thaler, 1985, Does the stock market overreact?Journal of Finance 40, 793—805.

Elton, E. J., 1999, Expected return, realized return, and asset pricing tests, Journal ofFinance 54, 1199-1220.

Fama, Eugene F., 1981, Stock returns, real activity, inflation, and money, AmericanEconomic Review 71, 545—565.

Fama, Eugene F., and Kenneth R. French, 1988, Dividend yields and expected stock returns,Journal of Financial Economics 22, 3—25.

Fama, Eugene F., and Kenneth R. French, 1989, Business conditions and expected returnson stocks and bonds, Journal of Financial Economics 25, 23—49.

Fama, Eugene F., and Kenneth R. French, 1993, Common risk factors in the returns onstocks and bonds, Journal of Financial Economics 33, 3—56.

Fama, Eugene F., and Kenneth R. French, 1995, Size and book-to-market factors in earningsand returns, Journal of Finance 50, 131—155.

Fama, Eugene F., and Kenneth R. French, 2001, Disappearing dividends: changing firmcharacteristics or lower propensity to pay? Journal of Financial Economics 60, 3—43.

29

Fama, Eugene F., and Kenneth R. French, 2002, The equity premium, Journal of Finance57, 637—659.

Fama, Eugene F., and G. William Schwert, 1977, Asset returns and inflation, Journal ofFinancial Economics 5, 115—146.

Gomes, Joao F., Leonid Kogan, and Lu Zhang, 2003, Equilibrium cross-section of returns,Journal of Political Economy 111, 693—732.

Grullon, G., and R. Michaely, 2002, Dividends, share repurchases, and the substitutionhypothesis, Journal of Finance 57, 1649—1684.

Hodrick, Robert J., and Edward C. Prescott, 1997, Postwar U.S. business cycles: Anempirical investigation, Journal of Money, Credit, and Banking 29, 1—16.

Jagannathan, Ravi, and Zhenyu Wang, 1996, The conditional CAPM and the cross-sectionof expected returns, Journal of Finance 51, 3—54.

Keim, D. B., and R. F. Stambaugh, 1986, Predicting returns in the stock and bond markets,Journal of Financial Economics 17, 357—390.

Lakonishok, Josef, Andrei Shleifer, and Robert W. Vishny, 1994, Contrarian investment,extrapolation, and risk, Journal of Finance 49, 1541—1578.

Lettau, Martin, and Sydney C. Ludvigson, 2001, Consumption, aggregate wealth, andexpected stock returns, Journal of Finance 56, 815—849.

Lettau, Martin, and Sydney C. Ludvigson, 2005, Expected returns and expected dividendgrowth, Journal of Financial Economics 76, 583—626.

MacKinnon, James G., 1994, Approximate asymptotic distribution functions for unit-rootand cointegration tests, Journal of Business and Economic Statistics 12, 167—176.

Nelson, Charles R., and Myung J. Kim, 1993, Predictable stock returns: the role of smallsample bias, Journal of Finance 48, 641—661.

Schwert, G. W., 2002, Anomalies and market efficiency, in George Constantinides, MiltonHarris, and Rene Stulz, eds.: Handbook of the Economics of Finance (North-Holland,Amsterdam).

Stambaugh, Robert F., 1999, Predictive regressions, Journal of Financial Economics, 54,375—421.

Zhang, Lu, 2005, The value premium, Journal of Finance 60, 67—103.

30

Tab

le1

:D

escr

ipti

veSta

tist

ics

for

The

Rea

lize

dR

eturn

s,R

ealize

dD

ivid

end

Gro

wth

,Expec

ted

Lon

g-ru

nD

ivid

end

Gro

wth

,Expec

ted

Div

iden

dY

ield

,an

dExpec

ted

Ret

urn

sof

Val

ue

and

Gro

wth

Por

tfol

ios

Thi

sta

ble

repo

rts

the

sam

ple

aver

ages

ofth

ere

aliz

edre

turn

,R

t+1,

the

real

ized

divi

dend

grow

th,

g t+

1,

the

expe

cted

long

-run

divi

dend

grow

th,

Et[A

g t+

1],

the

expe

cted

divi

dend

yiel

d,E

t[D

t+1/P

t],a

ndth

eex

pect

edre

turn

,E

t[R

t+1]f

orva

riou

sva

lue

and

grow

thpo

rtfo

lios.

The

corr

espo

ndin

gt-

stat

isti

csar

ere

port

edin

the

row

sbe

low

the

sam

ple

aver

ages

.T

here

sult

sfo

rbo

thth

efu

llsa

mpl

efr

om19

41to

2002

and

for

the

subs

ampl

efr

om19

63to

2002

are

repo

rted

.Pan

els

Aan

dB

cont

ain

the

resu

lts

for

five

quin

tile

sso

rted

onbo

ok-t

o-m

arke

t,w

hile

Pan

els

Can

dD

cont

ain

the

resu

lts

for

six

port

folio

sba

sed

ona

two-

by-t

hree

sort

onsi

zean

dbo

ok-t

o-m

arke

t.In

Pan

els

Aan

dB

,p5

-1de

note

sth

edi

ffere

nce

betw

een

port

folio

Hig

han

dpo

rtfo

lioLow

inth

efiv

ebo

ok-t

o-m

arke

tqu

inti

les.

InPan

els

Can

dD

,por

tfol

ios

are

deno

ted

bytw

ole

tter

s,fo

rex

ampl

e,po

rtfo

lioLS

cont

ains

stoc

ksw

ith

the

bott

om30

%bo

ok-t

o-m

arke

tra

tios

and

the

bott

om50

%m

arke

tca

pita

lizat

ion.

Sign

ifica

ntav

erag

ere

aliz

edan

dex

pect

edre

turn

sfo

rp5

-1an

dH

ML

and

thei

rt-

stat

isti

csar

ehi

ghlig

hted

.

Pan

elA

:19

41–2

002,

one-

way

sort

Pan

elB

:19

63–2

002,

one-

way

sort

Low

23

4H

igh

p5-1

Low

23

4H

igh

p5-1

Rt+

10.

071

0.07

50.

090

0.10

50.

129

0.05

80.

058

0.05

80.

077

0.10

30.

104

0.04

63.

123.

604.

594.

584.

602.

882.

012.

333.

584.

414.

032.

10g t

+1

0.01

30.

016

0.02

60.

036

0.05

80.

045

0.01

60.

013

0.02

30.

039

0.03

60.

020

0.59

0.60

1.22

1.53

2.12

1.42

0.53

0.34

0.79

1.30

1.04

0.48

Et[A

g t+

1]

0.01

70.

017

0.01

90.

028

0.03

10.

014

0.01

90.

016

0.01

40.

025

0.01

90.

000

14.8

517

.70

16.1

532

.58

12.1

44.

6511

.06

11.6

911

.59

24.6

413

.18

0.12

Et[D

t+1/P

t]0.

031

0.04

10.

048

0.05

40.

054

0.02

30.

023

0.03

30.

042

0.05

00.

050

0.02

817

.55

22.2

228

.63

28.0

130

.08

15.1

029

.97

30.3

627

.47

21.1

723

.14

14.6

0E

t[R

t+1]

0.04

80.

058

0.06

70.

082

0.08

50.

037

0.04

10.

049

0.05

60.

075

0.06

90.

028

23.6

324

.36

27.5

435

.67

21.6

914

.91

20.6

423

.19

31.9

429

.53

23.2

112

.05

Pan

elC

:194

1–20

02,t

wo-

way

sort

Pan

elD

:196

3–20

02,t

wo-

way

sort

LS

LB

MS

MB

HS

HB

HM

LLS

LB

MS

MB

HS

HB

HM

L

Rt+

10.

085

0.07

30.

123

0.08

00.

157

0.12

00.

060

0.06

60.

059

0.11

30.

066

0.14

30.

101

0.05

92.

893.

294.

473.

965.

124.

564.

241.

832.

123.

573.

004.

434.

113.

81g t

+1

0.00

90.

014

0.05

00.

015

0.08

70.

048

0.05

60.

005

0.01

50.

053

0.01

10.

077

0.03

30.

045

0.33

0.69

2.07

0.72

3.45

1.99

2.07

0.14

0.51

1.52

0.41

2.49

1.13

1.22

Et[A

g t+

1]

0.00

30.

018

0.04

10.

008

0.06

20.

030

0.03

50.

001

0.02

00.

039

0.00

10.

054

0.02

30.

028

3.54

15.1

944

.34

5.47

33.7

519

.64

19.9

01.

156

11.5

130

.08

1.12

40.3

325

.60

21.0

0E

t[D

t+1/P

t]0.

032

0.03

30.

042

0.04

80.

040

0.05

70.

016

0.01

70.

025

0.03

10.

042

0.03

40.

054

0.02

310

.66

18.9

716

.87

28.2

325

.51

29.8

69.

9013

.77

31.0

621

.42

25.3

321

.82

22.5

114

.74

Et[R

t+1]

0.03

50.

051

0.08

30.

056

0.10

20.

087

0.05

10.

018

0.04

50.

070

0.04

40.

088

0.07

70.

051

10.3

625

.22

28.4

519

.86

32.6

727

.13

40.8

98.

7820

.81

29.9

920

.00

39.6

024

.49

31.7

3

30

Table 2 : Autocorrelations and Unit Root Tests for the Expected Value Premiumand Its Two Components (1941—2002)

This table reports autocorrelations of orders 1, 2, 3, 4, 5, and 10, MacKinnon unit root test statistics, and

their corresponding p-values for the expected return of portfolio 5-1 (Panel A), the expected return of HML

(Panel B), and their respective two components—the expected long-run dividend growth rate, Et[Agt+1] and

the expected dividend-price ratio, Et[Dt+1/Pt].

Panel A: p5-1

Autocorrelations (order) Unit-Root Test

1 2 3 4 5 10 Statistic p-value

Et[Agt+1] 0.811 0.731 0.675 0.615 0.599 0.496 -2.889 0.047Et[Dt+1/Pt] 0.873 0.720 0.608 0.583 0.574 0.235 -1.992 0.290Premium 0.638 0.473 0.368 0.295 0.323 0.275 -5.180 0.000

Panel B: HML

Autocorrelations (order) Unit-Root Test

1 2 3 4 5 10 Statistic p-value

Et[Agt+1] 0.740 0.576 0.513 0.468 0.459 0.440 -3.740 0.004Et[Dt+1/Pt] 0.916 0.808 0.728 0.705 0.688 0.423 -1.705 0.428Premium 0.534 0.188 0.028 -0.066 0.010 0.070 -6.058 0.002

31

Tab

le3

:Lea

d-L

agC

orre

lati

ons

bet

wee

nth

eExpec

ted

Val

ue

Pre

miu

m,Expec

ted

Div

iden

dG

row

th,an

dExpec

ted

Div

iden

d-P

rice

Rat

ioan

dC

ycl

ical

Indic

ator

s(1

941–

2002

)

Thi

sta

ble

repo

rts

the

lead

-lag

corr

elat

ions

betw

een

the

expe

cted

valu

epr

emiu

m,e

xpec

ted

divi

dend

grow

th,an

dex

pect

eddi

vide

nd-p

rice

rati

oof

port

folio

sp5

-1an

dH

ML

and

alis

tof

cycl

ical

indi

cato

rsin

clud

ing

the

defa

ult

prem

ium

,DE

F,t

heN

BE

Rre

cess

ion

dum

my,

Cyc

le,r

ealin

vest

men

tgr

owth

,gIN

V,a

ndre

alco

nsum

ptio

ngr

owth

,gC

ON.

Pan

elA

repo

rts

the

resu

lts

for

port

folio

5-1,

and

Pan

elB

does

the

sam

efo

rH

ML.p

-val

ues

are

repo

rted

inth

ero

ws

belo

wth

eco

rrel

atio

ns.

Pan

elA

:p5

-1Pan

elB

:HM

L

-5-4

-3-2

-10

12

34

5-5

-4-3

-2-1

01

23

45

Exp

ecte

dV

alue

Pre

miu

m,E

t[A

g t+

1]+

Et[D

t+1/P

t]

Exp

ecte

dV

alue

Pre

miu

m,E

t[A

g t+

1]+

Et[D

t+1/P

t]

DE

F0.

090.

05-0

.03

0.13

0.42

0.49

0.28

-0.2

2-0

.29

-0.1

3-0

.05

0.13

0.10

0.02

0.08

0.28

0.39

0.36

-0.2

2-0

.31

-0.2

1-0

.08

0.50

0.71

0.83

0.32

0.00

0.00

0.03

0.10

0.02

0.33

0.69

0.33

0.47

0.88

0.53

0.03

0.00

0.00

0.10

0.02

0.11

0.55

Cyc

le-0

.13

-0.0

1-0

.03

0.03

0.28

0.50

0.12

-0.3

4-0

.24

-0.0

30.

06-0

.07

0.08

0.09

0.05

0.16

0.41

0.18

-0.2

8-0

.25

-0.1

50.

070.

320.

940.

820.

830.

030.

000.

370.

010.

060.

830.

680.

620.

560.

510.

680.

210.

000.

160.

030.

060.

260.

61R

ealg

INV

-0.0

10.

220.

130.

18-0

.14

-0.3

6-0

.35

-0.1

50.

150.

180.

140.

040.

190.

110.

14-0

.16

-0.2

8-0

.34

-0.2

40.

070.

210.

210.

920.

100.

340.

180.

270.

000.

010.

260.

250.

190.

320.

770.

150.

430.

280.

230.

030.

010.

060.

630.

120.

11R

ealg

CO

N-0

.07

0.22

0.20

0.17

0.07

-0.3

2-0

.54

-0.2

60.

130.

210.

12-0

.05

0.16

0.11

0.08

0.04

-0.2

4-0

.49

-0.3

10.

040.

240.

220.

610.

100.

130.

190.

620.

010.

000.

040.

320.

110.

390.

720.

240.

430.

560.

770.

060.

000.

020.

740.

080.

10

Exp

ecte

dD

ivid

end

Gro

wth

,Et[A

g t+

1]

Exp

ecte

dD

ivid

end

Gro

wth

,Et[A

g t+

1]

DE

F-0

.32

-0.3

6-0

.39

-0.3

4-0

.27

-0.2

7-0

.38

-0.5

8-0

.54

-0.4

6-0

.42

-0.3

4-0

.38

-0.3

8-0

.27

-0.1

7-0

.19

-0.4

2-0

.57

-0.4

8-0

.33

-0.3

40.

020.

010.

000.

010.

030.

040.

000.

000.

000.

000.

000.

010.

000.

000.

040.

200.

140.

000.

000.

000.

010.

01C

ycle

0.06

0.19

0.20

0.15

0.14

0.13

-0.

03-0

.15

-0.0

8-0

.02

0.03

-0.0

10.

170.

180.

140.

150.

13-0

.11

-0.2

2-0

.08

0.05

0.02

0.64

0.15

0.13

0.27

0.28

0.30

0.80

0.26

0.54

0.86

0.82

0.96

0.20

0.17

0.29

0.24

0.30

0.41

0.09

0.54

0.72

0.89

Rea

lgIN

V0.

010.

260.

250.

24-0

.02

-0.1

6-0

.11

-0.0

40.

040.

050.

040.

000.

340.

310.

26-0

.07

-0.2

6-0

.14

0.00

0.08

0.01

-0.0

00.

920.

050.

060.

070.

910.

210.

400.

740.

760.

700.

770.

990.

010.

020.

040.

620.

040.

280.

990.

570.

920.

98R

ealg

CO

N0.

030.

230.

230.

150.

09-0

.10

-0.1

20.

030.

140.

140.

12-0

.01

0.30

0.29

0.15

0.05

-0.2

1-0

.20

0.05

0.18

0.07

0.02

0.85

0.08

0.08

0.26

0.48

0.42

0.38

0.81

0.28

0.31

0.40

0.96

0.02

0.03

0.25

0.70

0.10

0.13

0.71

0.18

0.61

0.86

Exp

ecte

dD

ivid

end-

Pri

ceR

atio

,Et[D

t+1/P

t]E

xpec

ted

Div

iden

d-P

rice

Rat

io,E

t[D

t+1/P

t]

DE

F0.

430.

470.

450.

460.

590.

770.

920.

690.

490.

410.

430.

490.

520.

490.

500.

600.

700.

770.

600.

440.

380.

420.

000.

000.

000.

000.

000.

000.

000.

000.

000.

000.

000.

000.

000.

000.

000.

000.

000.

000.

000.

000.

000.

00C

ycle

-0.0

8-0

.10

-0.1

4-0

.11

-0.0

30.

190.

270.

07-0

.05

-0.0

80.

01-0

.08

-0.1

6-0

.19

-0.1

20.

010.

160.

170.

02-0

.06

-0.0

60.

020.

560.

450.

290.

400.

840.

140.

040.

620.

690.

550.

930.

560.

230.

140.

360.

930.

210.

180.

890.

650.

670.

90R

ealg

INV

-0.0

1-0

.02

-0.0

50.

03-0

.00

-0.0

4-0

.20

-0.2

3-0

.09

0.03

0.07

-0.0

2-0

.14

-0.1

6-0

.07

-0.0

00.

00-0

.12

-0.1

4-0

.03

0.05

0.05

0.93

0.86

0.71

0.82

0.99

0.75

0.12

0.08

0.48

0.82

0.58

0.86

0.29

0.24

0.58

0.97

0.98

0.35

0.28

0.83

0.71

0.72

Rea

lgC

ON

-0.1

4-0

.12

-0.1

1-0

.02

0.01

-0.0

4-0

.26

-0.3

6-0

.22

-0.0

10.

04-0

.10

-0.1

8-0

.16

-0.0

4-0

.02

-0.0

3-0

.18

-0.2

6-0

.14

0.03

0.03

0.29

0.38

0.42

0.88

0.92

0.74

0.04

0.01

0.09

0.96

0.78

0.45

0.19

0.23

0.74

0.91

0.84

0.16

0.05

0.30

0.83

0.85

32

Tab

le4

:VA

RA

nal

ysi

s

Thi

sta

ble

repo

rts

the

resu

lts

from

afir

st-o

rder

VA

Rth

atin

clud

esth

eex

pect

edva

lue

prem

ium

and

one

oftw

ocy

clic

alin

dica

tors

–rea

lin

vest

men

tgr

owth

,gIN

V,a

ndre

alco

nsum

ptio

ngr

owth

,gC

ON.

The

tabl

ere

port

sth

eeq

uati

onfo

rth

eex

pect

edva

lue

prem

ium

forth

e19

41–2

002

and

1963

–200

2sa

mpl

es.

We

also

repo

rtth

ere

sult

sw

ith

and

wit

hout

cont

rolli

ngfo

rm

onet

ary

polic

yas

capt

ured

byth

eon

e-m

onth

T-b

illra

te.

The

lag

inth

eVA

Ris

one,

whi

chis

chos

enba

sed

onth

eA

kaik

ein

form

atio

ncr

iter

ion.

p-v

alue

sas

soci

ated

wit

hN

ewey

-Wes

tt-

stat

isti

csad

just

edfo

rhe

tero

sced

asti

city

and

auto

corr

elat

ion

ofup

tosi

xla

gsar

ere

port

edin

the

row

sbe

low

the

coeffi

cien

ts.

Pan

elA

:Rea

lg I

NV

Pan

elB

:R

ealg

CO

N

1941

–200

219

63–2

002

1941

–200

219

63–2

002

noT

-bill

wit

hT

-bill

noT

-bill

wit

hT

-bill

noT

-bill

wit

hT

-bill

noT

-bill

wit

hT

-bill

Exp

ecte

dp5

-1R

etur

n-0

.008

-0.0

07-0

.031

-0.0

24-0

.158

-0.1

22-0

.255

-0.1

430.

071

0.06

60.

015

0.00

60.

000

0.00

00.

000

0.00

5E

xpec

ted

HM

LR

etur

n-0

.016

-0.0

17-0

.042

-0.0

41-0

.239

-0.2

31-0

.342

-0.2

950.

021

0.02

00.

029

0.02

60.

000

0.00

00.

001

0.00

4

33

Tab

le5

:P

redic

tive

Reg

ress

ions

for

the

Val

ue

Pre

miu

man

dIt

sT

wo

Com

pon

ents

–the

Lon

g-R

un

Div

iden

dG

row

thR

ate

and

the

Div

iden

d-P

rice

Rat

io

Thi

sta

ble

repo

rts

pred

icti

vere

gres

sion

sfo

rth

eva

lue

prem

ium

,A

g t+

1+

Dt+

1/P

t,an

dit

stw

oco

mpo

nent

s–th

elo

ng-r

undi

vide

ndgr

owth

rate

,A

g t+

1,an

dth

edi

vide

nd-p

rice

rati

o,D

t+1/P

t.W

ere

port

resu

lts

for

both

port

folio

5-1

from

the

one-

way

sort

onbo

ok-t

o-m

arke

tan

dH

ML

from

the

two-

way

sort

onsi

zean

dbo

ok-t

o-m

arke

t.T

here

are

five

regr

esso

rs,

(i)

divi

dend

yiel

d,di

v,co

mpu

ted

asth

esu

mof

divi

dend

sac

crui

ngto

the

CR

SPva

lue-

wei

ghte

dpo

rtfo

lioov

erth

epr

evio

us12

mon

ths

divi

ded

byth

ecu

rren

tin

dex

leve

l;(i

i)de

faul

tpr

emiu

m,d

ef,w

hich

isth

eyi

eld

spre

adbe

twee

nB

aaan

dA

aaco

rpor

ate

bond

s;(i

ii)te

rmpr

emiu

m,t

erm

,com

pute

das

the

yiel

dsp

read

betw

een

ten-

year

and

one-

year

gove

rnm

ent

bond

s;(i

v)lo

gbo

ok-t

o-m

arke

tsp

read

,ls,

defin

edas

the

log

book

-to-

mar

ket

ofde

cile

ten

min

usth

atof

deci

leon

efr

omte

nbo

ok-t

o-m

arke

tpo

rtfo

lios;

and

(v)

one-

mon

thTre

asur

ybi

ll,rf

.A

llre

gres

sors

are

stan

dard

ized

toha

veze

rom

ean

and

unit

vari

ance

.W

ere

port

inte

rcep

ts,

slop

es,bi

asin

slop

es,

adju

sted

R2s,

and

p-v

alue

sad

just

edfo

rsm

all-sa

mpl

epr

oble

ms

usin

gN

elso

nan

dK

im(1

993)

met

hods

.

Pan

elA

:19

41–2

002,

p5-1

Pan

elB

:19

63–2

002,

p5-1

inte

rcep

tdi

vde

fte

rmls

rfad

j.R

2in

terc

ept

div

def

term

lsrf

adj.

R2

Pre

miu

m0.

045

0.00

70.

015

-0.0

160.

012

-0.0

130.

301

0.03

90.

018

0.00

5-0

.016

-0.0

11-0

.015

0.31

5bi

as-0

.002

0.00

00.

001

0.00

10.

001

-0.0

05-0

.002

0.00

10.

003

0.00

0p

0.03

40.

015

0.00

20.

213

0.02

50.

010

0.20

60.

012

0.24

90.

103

Ag t

+1

0.01

70.

007

0.00

3-0

.017

0.00

6-0

.020

0.54

00.

028

0.02

4-0

.002

-0.0

200.

002

-0.0

300.

485

bias

-0.0

010.

000

0.00

1-0

.001

0.00

0-0

.003

-0.0

010.

001

0.00

2-0

.002

p0.

071

0.38

50.

002

0.31

00.

006

0.00

10.

425

0.00

10.

490

0.00

7

Dt+

1/P

t0.

028

0.00

10.

013

0.00

10.

006

0.00

70.

581

0.01

1-0

.006

0.00

80.

004

-0.0

130.

015

0.57

5bi

as-0

.001

-0.0

01-0

.001

0.00

20.

000

-0.0

02-0

.001

0.00

00.

001

0.00

1p

0.34

60.

000

0.25

20.

290

0.04

40.

226

0.02

10.

099

0.10

10.

010

Pan

elC

:194

1–20

02,H

ML

Pan

elD

:19

63–2

002,

HM

L

inte

rcep

tdi

vde

fte

rmls

rfad

j.R

2in

terc

ept

div

def

term

lsrf

adj.

R2

Pre

miu

m0.

055

0.00

30.

004

-0.0

060.

011

0.00

30.

156

0.06

60.

017

0.00

2-0

.009

0.01

2-0

.006

0.30

9bi

as-0

.001

-0.0

010.

000

0.00

3-0

.001

-0.0

03-0

.002

0.00

00.

003

-0.0

01p

0.12

80.

099

0.04

90.

180

0.21

20.

002

0.25

50.

035

0.26

00.

294

Ag t

+1

0.03

80.

005

-0.0

04-0

.008

0.01

4-0

.006

0.79

40.

058

0.02

3-0

.005

-0.0

130.

023

-0.0

190.

721

bias

-0.0

010.

000

0.00

00.

000

-0.0

01-0

.001

-0.0

010.

000

0.00

1-0

.002

p0.

036

0.18

30.

008

0.07

60.

112

0.00

00.

207

0.00

10.

042

0.00

8

Dt+

1/P

t0.

016

-0.0

020.

008

0.00

2-0

.003

0.00

90.

395

0.00

8-0

.006

0.00

70.

004

-0.0

110.

013

0.45

2bi

as0.

000

-0.0

01-0

.001

0.00

20.

000

-0.0

01-0

.001

-0.0

010.

002

0.00

0p

0.22

10.

004

0.15

00.

263

0.00

70.

118

0.00

90.

063

0.05

70.

005

34

Tab

le6

:In

cludin

gR

epurc

has

es:

Des

crip

tive

Sta

tist

ics

for

The

Rea

lize

dR

eturn

s,R

ealize

dD

ivid

end

Gro

wth

,Expec

ted

Lon

g-ru

nD

ivid

end

Gro

wth

,Expec

ted

Div

iden

dY

ield

,an

dExpec

ted

Ret

urn

sof

Val

ue

and

Gro

wth

Por

tfol

ios

Thi

sta

ble

repo

rts

the

sam

ple

aver

ages

ofth

ere

aliz

edre

turn

,R

t+1,

the

real

ized

divi

dend

grow

th,

g t+

1,

the

expe

cted

long

-run

divi

dend

grow

th,

Et[A

g t+

1],

the

expe

cted

divi

dend

yiel

d,E

t[D

t+1/P

t],an

dth

eex

pect

edre

turn

,E

t[R

t+1]f

orva

riou

sva

lue

and

grow

thpo

rtfo

lios.

The

com

puta

tion

ofdi

vide

nds

incl

udes

net

stoc

kre

purc

hase

s.T

heco

rres

pond

ing

t-st

atis

tics

are

repo

rted

inth

ero

ws

belo

wth

esa

mpl

eav

erag

es.

The

resu

lts

for

both

the

full

sam

ple

from

1941

to20

02an

dfo

rth

esu

bsam

ple

from

1963

to20

02ar

ere

port

ed.

Pan

els

Aan

dB

cont

ain

the

resu

lts

for

five

quin

tile

sso

rted

onbo

ok-t

o-m

arke

t,w

hile

Pan

els

Can

dD

cont

ain

the

resu

lts

for

six

port

folio

sba

sed

ona

two-

by-t

hree

sort

onsi

zean

dbo

ok-t

o-m

arke

t.In

Pan

els

Aan

dB

,p5

-1de

note

sth

edi

ffere

nce

betw

een

port

folio

Hig

han

dpo

rtfo

lioLow

inth

efiv

ebo

ok-t

o-m

arke

tqu

inti

les.

InPan

els

Can

dD

,po

rtfo

lios

are

deno

ted

bytw

ole

tter

s,fo

rex

ampl

e,po

rtfo

lioLS

cont

ains

stoc

ksw

ith

the

bott

om30

%bo

ok-t

o-m

arke

tra

tios

and

the

bott

om50

%m

arke

tca

pita

lizat

ion.

Sign

ifica

ntav

erag

ere

aliz

edan

dex

pect

edre

turn

sfo

rp5

-1an

dH

ML

and

thei

rt-

stat

isti

csar

ehi

ghlig

hted

.

Pan

elA

:194

1–20

02,o

ne-w

ayso

rtPan

elB

:19

63–2

002,

one-

way

sort

Low

23

4H

igh

p5-1

Low

23

4H

igh

p5-1

Rt+

10.

073

0.08

00.

097

0.11

10.

137

0.06

40.

060

0.06

50.

086

0.11

00.

117

0.05

73.

223.

834.

924.

844.

903.

192.

102.

593.

994.

724.

562.

59g t

+1

0.03

20.

029

0.04

80.

050

0.08

00.

048

0.04

40.

034

0.05

40.

062

0.06

80.

024

1.31

1.03

2.09

1.92

2.77

1.47

1.30

0.83

1.76

1.71

1.89

0.61

Et[A

g t+

1]

0.03

60.

024

0.04

10.

039

0.05

40.

017

0.04

30.

026

0.04

30.

042

0.05

10.

008

21.7

524

.72

81.9

761

.09

46.7

08.

0823

.90

18.7

490

.52

72.7

359

.91

5.23

Et[D

t+1/P

t]0.

036

0.04

70.

055

0.06

10.

064

0.02

80.

030

0.04

20.

053

0.06

00.

064

0.03

424

.68

34.7

140

.58

38.8

243

.64

18.1

829

.62

34.8

231

.95

28.8

034

.11

22.3

6E

t[R

t+1]

0.07

20.

071

0.09

60.

100

0.11

70.

045

0.07

30.

068

0.09

50.

102

0.11

50.

042

44.9

040

.28

91.6

471

.03

50.4

527

.09

32.0

430

.94

68.9

151

.73

48.0

836

.72

Pan

elC

:194

1–20

02,t

wo-

way

sort

Pan

elD

:196

3–20

02,t

wo-

way

sort

LS

LB

MS

MB

HS

HB

HM

LLS

LB

MS

MB

HS

HB

HM

L

Rt+

10.

090

0.07

60.

131

0.08

60.

166

0.12

70.

063

0.07

40.

063

0.12

30.

074

0.15

50.

111

0.06

43.

103.

414.

764.

265.

404.

824.

432.

052.

253.

903.

364.

804.

564.

07g t

+1

0.03

50.

029

0.07

40.

033

0.10

90.

064

0.05

40.

039

0.03

80.

086

0.03

90.

112

0.05

80.

047

1.19

1.27

2.79

1.37

4.06

2.59

2.22

1.02

1.15

2.25

1.17

3.30

1.90

1.47

Et[A

g t+

1]

0.02

90.

031

0.06

40.

024

0.08

80.

044

0.03

60.

036

0.03

70.

069

0.02

30.

088

0.04

40.

030

19.6

719

.71

62.5

660

.71

139.

3347

.01

24.5

826

.64

19.7

998

.13

42.7

114

8.01

51.1

723

.57

Et[D

t+1/P

t]0.

038

0.03

80.

051

0.05

50.

050

0.06

60.

020

0.02

60.

032

0.04

30.

053

0.04

90.

065

0.02

715

.58

26.4

826

.94

40.1

950

.42

42.0

311

.69

22.5

129

.51

33.2

430

.58

39.4

832

.46

19.2

7E

t[R

t+1]

0.06

70.

069

0.11

50.

079

0.13

80.

110

0.05

50.

062

0.06

90.

111

0.07

60.

137

0.10

90.

057

43.6

439

.04

98.7

058

.78

118.

8047

.63

52.5

548

.34

27.8

088

.47

46.9

211

6.08

41.2

057

.38

35

Tab

le7

:In

cludin

gR

epurc

has

es:

VA

RA

nal

ysi

s

Thi

sta

ble

repo

rts

the

resu

lts

from

afir

st-o

rder

VA

Rth

atin

clud

esth

eex

pect

edva

lue

prem

ium

and

one

oftw

ocy

clic

alin

dica

tors

–rea

lin

vest

men

tgr

owth

,g I

NV,an

dre

alco

nsum

ptio

ngr

owth

,g C

ON.

The

com

puta

tion

ofdi

vide

nds

incl

udes

net

stoc

kre

purc

hase

s.T

heta

ble

repo

rts

the

equa

tion

for

the

expe

cted

valu

epr

emiu

mfo

rth

e19

41–2

002

and

1963

–200

2sa

mpl

es.

We

also

repo

rtth

ere

sult

sw

ith

and

wit

hout

cont

rolli

ngfo

rm

onet

ary

polic

yas

capt

ured

byth

eon

e-m

onth

T-b

illra

te.

The

lag

inth

eVA

Ris

one,

whi

chis

chos

enba

sed

onth

eA

kaik

ein

form

atio

ncr

iter

ion.

p-v

alue

sas

soci

ated

wit

hN

ewey

-Wes

tt-

stat

isti

csad

just

edfo

rhe

tero

sced

asti

city

and

auto

corr

elat

ion

ofup

tosi

xla

gsar

ere

port

edin

the

row

sbe

low

the

coeffi

cien

ts.

Pan

elA

:Rea

lgC

ON

Pan

elB

:R

ealg

CO

N

1941

–200

219

63–2

002

1941

–200

219

63–2

002

noT

-bill

wit

hT

-bill

noT

-bill

wit

hT

-bill

noT

-bill

wit

hT

-bill

noT

-bill

wit

hT

-bill

Exp

ecte

dp5

-1R

etur

n-0

.009

-0.0

09-0

.034

-0.0

30-0

.149

-0.1

42-0

.203

-0.1

590.

012

0.01

30.

000

0.00

00.

000

0.00

00.

000

0.00

0E

xpec

ted

HM

LR

etur

n-0

.014

-0.0

14-0

.035

-0.0

34-0

.177

-0.1

78-0

.210

-0.1

950.

006

0.00

90.

000

0.00

00.

000

0.00

00.

000

0.00

0

36

Fig

ure

1:

Eve

nt-

Tim

eEvo

luti

onof

Pro

fita

bility,

Rea

lD

ivid

end/L

agge

dB

ook

Equity,

and

Rea

lD

ivid

end

Gro

wth

for

Val

ue

and

Gro

wth

Por

tfol

ios

(194

1–20

03)

Thi

sfig

ure

plot

sth

eev

ent

tim

eev

olut

ion

ofdi

vide

ndgr

owth

rate

san

dth

era

tios

ofdi

vide

ndan

dla

gged

book

equi

tyfo

rva

lue

and

grow

thpo

rtfo

lios.

We

cons

truc

tva

lue

and

grow

thpo

rtfo

lios

usin

ga

one-

way

sort

onbo

ok-t

o-m

arke

tin

tofiv

equ

inti

les

and

usin

ga

two-

by-t

hree

sort

onsi

zean

dbo

ok-t

o-m

arke

tin

tosi

xpo

rtfo

liosas

Fam

aan

dFr

ench

(199

3).

Pan

elA

plot

spr

ofita

bilit

yde

fined

asea

rnin

gsdi

vide

dby

lagg

edbo

okva

lue,

Et+

1/B

t,fo

rpo

rtfo

lios

five

(val

ue)

and

one

(gro

wth

)fr

omth

equ

inti

les,

and

Pan

elD

does

the

sam

efo

rfo

urpo

rtfo

lios

incl

udin

gsm

all-hi

gh(S

/H),

big-

high

(B/H

),sm

all-lo

w(S

/L),

and

big-

low

(B/L

)fr

omth

esi

xpo

rtfo

lios

sort

edon

size

and

book

-to-

mar

ket.

Pan

elpl

ots

the

divi

dend

-lag

ged

book

equi

ty,

Dt+

1/B

t,fo

rpo

rtfo

lios

five

and

one

from

the

quin

tile

s,an

dPan

elE

does

the

sam

efo

rS/

H,B

/H,S/

L,an

dB

/L.Pan

elC

plot

sth

ere

aldi

vide

ndgr

owth

rate

s,g t

+1,fo

rpo

rtfo

lios

five

and

one

from

the

quin

tile

s,an

dPan

elF

does

the

sam

efo

rS/

H,B

/H,S/

L,a

ndB

/L.

Pan

elA

:Et+

1/B

t,on

e-w

ayso

rtPan

elB

:D

t+1/B

t,o

ne-w

ayso

rtPan

elC

:gt+

1,o

ne-w

ayso

rt

−10

−8

−6

−4

−2

02

46

810

0.06

0.080.

1

0.12

0.14

0.16

0.180.

2

0.22

0.24

Val

ue S

tock

sG

row

th S

tock

s

−10

−8

−6

−4

−2

02

46

810

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.090.

1V

alue

Sto

cks

Gro

wth

Sto

cks

−10

−8

−6

−4

−2

02

46

810

0.9

0.951

1.051.

1

1.15

Val

ue S

tock

sG

row

th S

tock

s

Pan

elD

:Et+

1/B

t,tw

o-w

ayso

rtPan

elE

:Dt+

1/B

t,t

wo-

way

sort

Pan

elF:g t

+1,tw

o-w

ayso

rt

−10

−8

−6

−4

−2

02

46

810

0.04

0.06

0.080.

1

0.12

0.14

0.16

0.180.

2

0.22

S/H

B/H

S/L

B/L

−10

−8

−6

−4

−2

02

46

810

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

S/H

B/H

S/L

B/L

−10

−8

−6

−4

−2

02

46

810

0.9

0.951

1.051.

1

1.15

S/H

B/H

S/L

B/L

37

Figure 2 : Times Series of the Annual Realized Real Dividend Growth Rates ofValue and Growth Portfolios (1941—2002)

This figure plots the sample paths of the annual realized real dividend growth rates of value and growth

portfolios. We construct value and growth portfolios using a one-way sort on book-to-market (into five

quintiles) and using a two-by-three sort on size and book-to-market (into six portfolios). Panel A plots the

annual real dividend growth rates for portfolios five and one from the quintiles, and Panel B plots that for

portfolio five-minus-one, p5-1. Panel C plots the annual real dividend growth rates for portfolios High and

Low defined from the six portfolios after controlling for size as in Fama and French (1993). Panel D does the

same for HML. In Panels A and C, the solid lines represent the value portfolios, and the broken lines represent

the growth portfolios. The real dividend growth is measured as gt+1=Dt+1/PtDt/Pt−1

(RXt + 1)(CPIt−1/CPIt)− 1,

where RXt is the nominal value-weighted portfolio return without dividend from year t−1 to t, and CPIt is the

consumer price index at year t. The dividend yield is constructed as Dt+1/Pt=(Rt+1−RXt+1)(CPIt/CPIt+1),

where Rt+1 is the nominal value-weighted portfolio return with dividend from year t to t+1.

Panel A: Portfolios 5 and 1 Panel B: p5-1

1950 1960 1970 1980 1990 2000−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5Value StocksGrowth Stocks

1950 1960 1970 1980 1990 2000

−0.6

−0.4

−0.2

0

0.2

0.4

0.6Dividend Growth Diff. between Value and Growth Stocks

Panel A: Portfolios High and Low Panel B: HML

1950 1960 1970 1980 1990 2000−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5Value StocksGrowth Stocks

1950 1960 1970 1980 1990 2000

−0.6

−0.4

−0.2

0

0.2

0.4

Dividend Growth Diff. between Value and Growth Stocks

38

Figure 3 : Times Series of the Expected Value Premium and Its TwoComponents—the Expected Long-Run Dividend Growth and the Expected

Dividend-Price Ratio (1941—2002)

This figure plots the times series of the expected value premium, Et[Rt+1], and its two components—the

expected long-run dividend growth, Et[Agt+1], and the expected dividend-price ratio, Et[Dt+1/Pt]. Panel

A plots the expected return of portfolio five-minus-one, p5-1, and Panel B plots its two components—the

expected long-run dividend growth and the expected dividend-price ratio. Panel C plots the expected HML

return, and Panel D plots its two components—the expected long-run dividend growth and the expected

dividend-price ratio. In Panels A and C, we also plot the scaled default spread defined as the Baa yield over

the Aaa yield scaled by two. In all panels, the shadowed rectangles represent the NBER recession dummy,

which takes the value of one in recessions and zero otherwise.

Panel A: p5-1: Expected Return Panel B: p5-1: Et[Agt+1] and Et[Dt+1/Pt]

1950 1960 1970 1980 1990 20000

0.02

0.04

0.06

0.08

0.1

0.12The Expected Value PremiumScaled Default Spread

1950 1960 1970 1980 1990 2000

−0.04

−0.02

0

0.02

0.04

0.06

Expected Dividend GrowthExpected Dividend Price Ratio

Panel C: HML: Expected Return Panel D: HML: Et[Agt+1] and Et[Dt+1/Pt]

1950 1960 1970 1980 1990 20000.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

The Expected Value PremiumScaled Default Spread

1950 1960 1970 1980 1990 2000−0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08Expected Dividend GrowthExpected Dividend Price Ratio

39

Figure 4 : Time Series of the Expected Equity Premium (1941—2002)

This figure plots the time series of the constructed expected equity premium.

1950 1960 1970 1980 1990 20000

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

The Expected Market Equity Premium

40

Figure 5 : Trend and Cyclical Components of the Expected Value Premium(1941—2002)

This figure reports trend and cyclical components of the expected value premium including both that from

a one-way sort on book-to-market (broken line) and that from a two-way sort on size and book-to-market

(solid line). Panel A reports the time trend and Panel B reports the trend components from a Hodrock

and Prescott (HP) filter. Panel C reports the cyclical component after the time trend is removed from the

expected value premium, and Panel D reports the cyclical component from the HP-filter. In all panels, the

shadowed rectangles represent the NBER recession dummy, which takes the value of one in recessions and

zero otherwise.

Panel A: Time Trend Panel B: HP-filtered Trend

1950 1960 1970 1980 1990 20000.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0.055

0.06

Two−way sortOne−way sort

1950 1960 1970 1980 1990 20000.04

0.05

0.06

0.07

0.08

0.09

0.1Two−way sortOne−way sort

Panel C: Cyclical Component with Time Trend Panel D: HP-filtered Cyclical Component

1950 1960 1970 1980 1990 2000−0.03

−0.02

−0.01

0

0.01

0.02

0.03

0.04

0.05Two−way sortOne−way sort

1950 1960 1970 1980 1990 2000−0.03

−0.02

−0.01

0

0.01

0.02

0.03

0.04Two−way sortOne−way sort

41

Fig

ure

6:

Impuls

eR

espon

seFunct

ions

for

the

Expec

ted

Val

ue

Pre

miu

mA

fter

AO

ne-

Sta

ndar

d-D

evia

tion

Pos

itiv

eShoc

kto

Rea

lIn

vest

men

tG

row

thor

the

Rea

lC

onsu

mpti

onG

row

th

Thi

sfig

ure

plot

sth

eim

puls

ere

spon

sefu

ncti

ons

for

the

expe

cted

retu

rnof

p5-1

and

the

expe

cted

HM

Lre

turn

inth

epr

esen

ceof

aon

e-st

anda

rd-

devi

atio

npo

siti

vesh

ock

tore

alin

vest

men

tgr

owth

,gIN

V(P

anel

sA

–D),

and

tore

alco

nsum

ptio

ngr

owth

,gC

ON

(Pan

els

E–H

).W

ere

port

the

resu

lts

wit

han

dw

itho

utco

ntro

lling

for

the

one-

mon

thT

-bill

rate

inth

eVA

R.In

allp

anel

s,a

two-

stan

dard

-err

orba

ndis

also

plot

ted.

Pan

elA

:p5-

1:g I

NV,n

oT

-bill

Pan

elB

:p5

-1:

g IN

V,w

ith

T-b

illPan

elC

:H

ML:g

INV,n

oT

-bill

Pan

elD

:HM

L:g

INV,w

ith

T-b

ill

01

23

45

67

89

10−

3

−2.

5

−2

−1.

5

−1

−0.

50

0.51

x 10

−3

01

23

45

67

89

10−

2.5

−2

−1.

5

−1

−0.

50

0.5

x 10

−3

01

23

45

67

89

10−

5

−4

−3

−2

−101

x 10

−3

01

23

45

67

89

10−

4

−3.

5

−3

−2.

5

−2

−1.

5

−1

−0.

50

0.51

x 10

−3

Pan

elE

:p5

-1:

g CO

N,n

oT

-bill

Pan

elF:p

5-1:

g CO

N,w

ith

T-b

illPan

elG

:HM

L:g

CO

N,n

oT

-bill

Pan

elH

:HM

L:g C

ON,w

ith

T-b

ill

01

23

45

67

89

10−

5

−4

−3

−2

−101

x 10

−3

01

23

45

67

89

10−

4

−3.

5

−3

−2.

5

−2

−1.

5

−1

−0.

50

0.51

x 10

−3

01

23

45

67

89

10−

7

−6

−5

−4

−3

−2

−101

x 10

−3

01

23

45

67

89

10−

6

−5

−4

−3

−2

−101

x 10

−3

42

Figure 7 : Including Repurchases: Trend and Cyclical Components of the ExpectedValue Premium (1941—2002)

This figure reports trend and cyclical components of the expected value premium including both that from

a one-way sort on book-to-market (broken line) and that from a two-way sort on size and book-to-market

(solid line). The computation of dividends includes net stock repurchases. Panel A reports the time trend

and Panel B reports the trend components from a Hodrock and Prescott (HP) filter. Panel C reports the

cyclical component after the time trend is removed from the expected value premium, and Panel D reports

the cyclical component from the HP-filter. In all panels, the shadowed rectangles represent the NBER

recession dummy, which takes the value of one in recessions and zero otherwise.

Panel A: Time Trend Panel B: HP-filtered Trend

1950 1960 1970 1980 1990 20000.03

0.035

0.04

0.045

0.05

0.055

0.06

0.065Two−way sortOne−way sort

1950 1960 1970 1980 1990 20000.03

0.035

0.04

0.045

0.05

0.055

0.06

0.065

0.07

0.075

0.08Two−way sortOne−way sort

Panel C: Cyclical Component with Time Trend Panel D: HP-filtered Cyclical Component

1950 1960 1970 1980 1990 2000−0.02

−0.01

0

0.01

0.02

0.03

0.04

0.05Two−way sortOne−way sort

1950 1960 1970 1980 1990 2000−0.03

−0.02

−0.01

0

0.01

0.02

0.03

0.04Two−way sortOne−way sort

43

Fig

ure

8:

Incl

udin

gR

epurc

has

es:

Impuls

eR

espon

seFunct

ions

for

the

Expec

ted

Val

ue

Pre

miu

mA

fter

AO

ne-

Sta

ndar

d-D

evia

tion

Pos

itiv

eShoc

kto

Rea

lIn

vest

men

tG

row

than

dR

ealC

onsu

mpti

onG

row

th

Thi

sfig

ure

plot

sth

eim

puls

ere

spon

sefu

ncti

ons

for

the

expe

cted

retu

rnof

p5-1

and

the

expe

cted

HM

Lre

turn

inth

epr

esen

ceof

aon

e-st

anda

rd-

devi

atio

npo

siti

vesh

ock

tore

alin

vest

men

tgr

owth

,g I

NV

(Pan

els

A–D

),an

dto

real

cons

umpt

ion

grow

th,

g CO

N(P

anel

sE

–H).

The

com

puta

tion

ofdi

vide

nds

incl

udes

net

stoc

kre

purc

hase

s.W

ere

port

the

resu

lts

wit

han

dw

itho

utco

ntro

lling

for

the

one-

mon

thT

-bill

rate

inth

eVA

R.In

all

pane

ls,a

two-

stan

dard

-err

orba

ndis

also

plot

ted.

Pan

elA

:p5-

1:g I

NV,n

oT

-bill

Pan

elB

:p5

-1:

g IN

V,w

ith

T-b

illPan

elC

:H

ML:g

INV,n

oT

-bill

Pan

elD

:HM

L:g

INV,w

ith

T-b

ill

01

23

45

67

89

10−

3

−2.

5

−2

−1.

5

−1

−0.

50

0.51

x 10

−3

01

23

45

67

89

10−

2.5

−2

−1.

5

−1

−0.

50

0.5

x 10

−3

01

23

45

67

89

10−

4

−3.

5

−3

−2.

5

−2

−1.

5

−1

−0.

50

0.51

x 10

−3

01

23

45

67

89

10−

4

−3.

5

−3

−2.

5

−2

−1.

5

−1

−0.

50

0.51

x 10

−3

Pan

elE

:p5

-1:

g CO

N,n

oT

-bill

Pan

elF:p5

-:g C

ON,w

ith

T-b

illPan

elG

:HM

L:g

CO

N,n

oT

-bill

Pan

elH

:HM

L:g C

ON,w

ith

T-b

ill

01

23

45

67

89

10−

4

−3.

5

−3

−2.

5

−2

−1.

5

−1

−0.

50

0.51

x 10

−3

01

23

45

67

89

10−

4

−3.

5

−3

−2.

5

−2

−1.

5

−1

−0.

50

0.51

x 10

−3

01

23

45

67

89

10−

5

−4

−3

−2

−101

x 10

−3

01

23

45

67

89

10−

5

−4

−3

−2

−101

x 10

−3

44