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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: [email protected].†10900 Euclid Avenue, Cleveland OH 44106. Tel: (216)368-8553, email: [email protected].‡Carol Simon Hall 3-160B, University of Rochester, Rochester, NY 14627. Tel: (585)275-3491, fax:
(585)273-1140, and email: [email protected].
Contents
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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).
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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
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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
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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
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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
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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
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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
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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
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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-
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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
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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.
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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
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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.
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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
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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
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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
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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
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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