Download Industry and Sector Equity Premium with Economic Dynamics: Keiichi Kubota

Industry and Sector Equity Premium with Economic Dynamics:
Evidence from Tokyo Stock Exchange Firms *), **)
Keiichi Kubota
Musashi University
Hitoshi Takehara
University of Tsukuba
November 27, 2004
JEL classifications: G12, G15, C52
* The authors’ affiliations are Musashi University and the University of Tsukuba, respectively. The address for
correspondence is Keiichi Kubota, Faculty of Economics, Musashi University, 1-26-1, Toyotama-kami, Nerima,
176-8534, Tokyo, Japan, tel. 81-3-5984-3727, fax 81-3-3991-1198. E-mail address: [email protected]
** This paper was presented at HEC School of Management and the authors thank Francesco Franzoni, Urlich
Hege, and Jacques Olivier for their helpful comments. They also thank Anton R. Braun, Nai-fu Chen, Bernard
Dumas, Ed Prescott, Susumu Saito, and Thomas Tallarini, Jr. for their helpful discussion. Both Keiichi Kubota
and Hitoshi Takehara acknowledge financial support from Grant-in-Aid for Scientific Research from Japan
Society for the Promotion of Science, and Keiichi Kubota also acknowledges financial support from Musashi
University. All remaining errors are our own.
Abstract
We estimate the cost of equity for all firms in the first section of Tokyo Stock Exchange with a
conditional version of Fama and French three-factor model. With considerations to the business cycles
we look into the lead and lag relationships between the equity premium of each industry and the sector
and the measures of the business cycles. The different relationships observed among sectors can be
rationally explained by application of two-sector growth model by Boldrin et al. where the equity
premiums of the investment goods sector and the consumption goods sector possess different business
cycle implications.
1
I. Introduction
The empirical identification of the equity premium has been a focal theme that has to be answered by
researchers in financial economics both at the aggregate market level (Mehra and Prescott, 1985) and
at the micro firm level (Fama and French, 1993). In this paper we fist estimate the return on equity at
the micro firm level with conditional asset pricing theory and then aggregate these estimates at the
industry and sector level. Next, we associate the equity premium for the industries with the
movements of economic output and investigate how the changes in equity premium anticipate the
future economic activities.
As for the estimates for return on equity, Fama and French (1997) estimated the return on equity
both at the individual level and at the industry level, using their three factor model and find that the
estimates at the individual levels are subject to severe estimation errors. They also present a very
simplified version of the conditional asset pricing model, which we will utilize in our estimation
processes. We use Japanese data from 1977 through 2003 and add new evidence on asset pricing using
the non-US data. For the US data Hodrick and Zhang (2000) cover and test various conceivable forms
of both the unconditional and the conditional asset pricing models and compare extensively the
empirical performance of these alternative models. Ferson and Siegel (2002) further extended the way
the instrument variables are utilized in forming the testing form of the Euler conditions.
The analyses of the equity premium at the industry level and sector level like ours can shed light on
differentiating the leading sector and the lagging sector of the economy with respect to the swing of
economic states. Campbell, Lo, and MacKinlay (1997) identify the lead and lags of auto-covariance
structure of the size sorted portfolio returns. Our study can identify the similar for the industry and
sector portfolios in relation to the changes in economic activities.
Section II presents a basic model of conditional asset pricing theory and the two-sector RBC model
to motivate our empirical study. Section III explains our data. Section IV reports the estimation results
of the equity premiums for industries both using the unconditional model and conditional model.
2
Section V briefly explains our filtering method of the production series and GDP series. Section VI
reports our empirical result on the relationship between the facets of the economic activities and the
industry and sector level risk premium changes. Section VII concludes.
II. Determining the Equity Risk Premium
a. Conditional Asset Pricing Theory
The fundamental valuation equation of the conditional asset pricing theory can be described as
follows, where we use the return form for asset prices. In an equation (1) Rt +1 is the N+1
dimensional vector of asset gross returns, including the risk free asset as a N+1th asset, Z t is the
conditioning information vector of instrumental variables in the publicly available information set at
time t, mt +1 is a stochastic pricing kernel, and 1 is a N+1 dimensional vector whose elements are all
ones. In this paper we adopt the definition of conditional asset pricing kernel by Hansen and Richard
(1987), which can be defined with respect to the publicly available information set at time t, Z t as
follows.
Et {mt +1 Rt +1 Z t } = 1
(1)
Although this Euler equation is oftentimes tested using GMM by taking the unconditional
expectations by applying Kronecker products with respect to the instruments vector Z t , Ferson and
Siegel (2002) generalize the way instrumental variables are used as follows, in which f(・) is a bounded
integrable function. Another interpretation of the equation (2) is that it reflects any asset allocation rule
employed based on the publicly available information set (Hodrick and Zhang, 2000).
Et {mt +1 ( Rt +1 f ( Z t ))} = E{1 f ( Z t )}
(2)
Among the asset pricing models that satisfies the above pricing kernel relationship, a standard
CAPM in an unconditional form, which we also estimate temporarily as a straw man, can be written as
follows. In the following equation (3) E ( Ri ) denotes the expected returns for each stock, E ( Rm )
3
the expected return for the market portfolio, R f the risk free rate, and β i the market beta.
E ( Ri ) = R f × (1 − β i ) + β i × E ( Rm )
(3)
Furthermore, the conditional version of CAPM can be generally written as follows (Hansen and
Richard, 1987, p.600), where Zt now is defined as the sigma algebra defining the information available
to economic agents at time t and we assume that the risk free return is constant for simplicity. Note
that the expected return of the market portfolio is unconditional with ergodic assumption which we use
throughout this paper. Specifically, we focus on the changes in factor loadings rather than the changes
in the expected return of the base portfolio.
Et ( Ri ,t +1 Z t ) = R f +
Covt ( Ri ,t , Rm,t Z t )
Vart ( Rm ,t Z t )
× ( Et ( Rm ,t ) − R f )
(4)
In this formulation the conditional expected returns are computed utilizing the time-varying betas
computed from publicly available information set. This is the basic approach we also use in expanding
the asset pricing model into multifactor forms.
It is well known that Fama and French three-factor model fits better to the empirical data both for
the USA (Fama and French, 1998) and for Japan (Jagannathan et al., 1998). Fama and French three
factor model is composed of the following three factors; the value-weight excess market returns, the
size factor spread portfolio (SMB), and the book-to-price ratio factor spread portfolio (HML).
The three factor model in an unconditional form can be denoted as the following equation (5),
where E ( RSMB ) is the expected return of the “small minus big” factor portfolio, and E ( RHML ) is
the expected return of the “high book-to-price ratio minus low book-to-price ratio” factor portfolio.
Each beta coefficient denotes the corresponding factor loading for the stock or the portfolio.
E ( Ri ) = R f + β i1 ( E ( Rm ) − R f ) + β i 2 E ( RSMB ) + β i 3 E ( RHML )
(5)
A simple form of the conditional version of Fama and French model can be expressed as follows
(Fama and French, 1997). This form of conditional asset pricing model is as defined in Cochrane
4
(1996) and is also discussed in detail in Hodrick and Zhang (2000). In this formulation the logs of MEi
and (BE/ME)i are measured net of their averages, respectively. It is to control for the aggregate effects
of si 2 and hi 2 to be zero for each time period and to keep the form of the unconditional form intact
at the aggregate level. This is the conditional version of Fama and French three factor model we use
for our further tests.
E ( Ri ,t ) = R f + bi1 ( E ( Rm ) − R f ) + ( si1 + si 2 ln(ME ) i ,t ) E ( RSMB )
+ (hi1 + hi 2 ln( BE / ME ) i ,t ) E ( RHML )
（６）
Note that as in conditional CAPM defined in equation (4) we also use the unconditional factor returns
for (6) and vary the factor loadings only on the size and the book-to-price ratio factors. We also used
36 month rolling-method of estimating these time-varying coefficients using the equation (5) based on
the framework as defined in equation (4) for single-factor model. Since these estimates are based only
on the available information set, it can be also considered as a form of conditional model. However,
our empirical pre-analysis showed that these rolling-method estimates were quite unstable over time
and may contain large sampling errors1.
Lewellen and Nagal (2004) use this form of conditional model to test for the consumption CAPM2.
Although this is a simple functional model restricted to a linear class using time-varying firms’
characteristics, given the fact that Fama and French three factor model is a good empirical asset
pricing model, we believe that this model can capture well both the aggregate economic risk
components contained in the expected returns of the factor portfolios and the changes in factor loading
emanating from firms’ individual characteristic changes over the business cycles facets.
We start from individual firm estimates and then aggregate these at the industry level and sector
1
The results are available upon request from the authors.
2
Lewllen et al. (2004) derive the functional relationship between the time changes in beta of CAPM and the conditional
equity risk premium and test for the mispricing components contained in the alpha coefficients.
5
level in our analysis below. We utilize this type of the model for the industry and sector analysis where
we seek to find the leading and lagged sectors in their output production activities along the phase of
peek and trough of business cycles. Menzly et al. (2004), for example, distinguish the high dividend
growth firms and low dividend growth firms among industries with a completely different framework
from ours. However, their insight and spirit of the industry analysis is similar to ours. In our analysis
we focus on the changes in factor loadings of the industry over time, keeping the factor returns
constant, while they disentangle the betas into the discounting factor and future dividend growth
components.
b. Two-Sector Economy and the Risk Premium
The theoretical relationship between production technology and asset returns has been analyzed in
Brock (1982) and Cox, Ingersoll, and Ross (1985) in a general equilibrium model. Euler equations
where both the investment returns and asset returns are included are also derived by Cochrane (1996).
In this paper we utilize the two-sector model developed by Boldrin, Christiano, and Fisher (1995,
2000) in which a steady-state equilibrium RBC model is derived and the resulting equity returns for
the sectors are derived. In this two-sector economy the consumption and the investment goods are
produced in different sectors, the households commit their employment contract prior to the realization
of the state of nature, and the firms issue risk-free debt as well as equity. The investors are assumed to
have habit persistent utility function. The investment goods, which we also call capital goods, are
resold at the end of every period and the consumption goods are perishable.
Formally, the model is as follows. The preference of households is described as follows. Ct is
consumption, β is a subjective discount factor ( 0 < β < 1 ), Xt is an evolution of habit stock whose
movements are as shown in equation (8), hs,t (s = i, c, f) are the labor hours spent at the investment
goods sector, the consumption goods sector, and the financial sector, respectively The labor work
hours are standardized to one. Finally, φ is the relative risk aversion coefficient and ν is the
6
aversion coefficient from labor work.
 ∞ t ((Ct − X t )(1 − hi ,t − hc ,t − h f ,t )ν )1−φ − 1
E 0 ∑ β

1−φ
 t =0

X t= sX t −1 + bCt −1
（ s ≥ 0, h ≥ 0 ）
(7)
(8)
This formulation can generally cover both the power utility case and habit formation case. However,
we use the habit formation case throughout our empirical analysis.
There are two goods in the economy; the perishable consumption goods and the investment goods
that depreciate over time. The consumption goods sector is denoted with the subscript c and the
investment goods sector with the subscript i.
K cα,t ( Z t hc ,t )1−α ≥ Ct .
(9)
hc ,t ≥ 0, hi ,t ≥ 0, h f ,t ≥ 0, hc ,t + hi ,t + h f ,t ≤ 1, ∀t ≥ 0
(10)
K cα,t ( Z t hc ,t )1−α + (1 − δ )( K c ,t + K i ,t ) ≥ K c ,t +1 + K i ,t +1
(11)
The RHS of the inequality (9) is the output produced by the consumption goods sector which binds the
consumption opportunities of the households. Z t t is a technology parameter embedded to human
capital satisfying the equation (12) and α is the marginal productivity of capital. K c ,t in equation
(11) denotes the stock of capital used at consumption goods industry and K i ,t in equation (11)
denotes the same used at investment goods sector and δ is the depreciation rate of the capital. The
investment goods produced and utilized, net of the depreciation, are as shown on the LHS of the
inequality (11) and the RHS is the capital stock used in two sectors.
The households maximize equation (7) subject to the constraints from (9) to (11). The technology
shock is i.i.d. as follows where this technology parameter Z t , is dependent on the realizations of
random drawing θ t and the previous technology state Z t −1 multiplicatively.
Z t = exp(θ t ) Z t −1 ,
θ is distributed as N (θ ,σ 2 ), ∀t ≥ 0
7
(12)
Thus, the production technology has autocorrelated structure of one.
On top of the original Boldrin, Christiano, and Fisher (1995) model we also add a financial sector.
This sector collects fee with consumption goods for the efforts of issuing bonds and stock. The
households allocate the labor time to this sector as well and work with the competitive wage rate for
this financial sector. The organizational form of this financial sector is assumed to be a cooperative so
that the sector does not issue stock and resolves with zero profit after servicing for the production
economy. We call this sector as f as we have already shown in households’ allocated labor time. This
co-operative does not employ any capital. Hence, it is a sort of derivative sector in the economy, which
affects the firms’ maximization problem only by reducing their profit by charging issuing cost for
bonds and stock which becomes a transfer from the firm to the households in labor wages3.
With this scenario of two production sectors and a financial co-operative, we can proceed with the
equilibrium analysis as follows. First of all, a constraint that proceeds of the firms are larger than the
expenses has to hold. This is shown in a following equation (13). We have two production sectors with
subscript x = c and i. π x ,t +1 is the profit for the firm x, Yx ,t +1 is the output sale, K x ,t +1 is the capital
used for each sector, Pk ,t +1 is the price of investment goods, Wx ,t +1 is the wage rate for each sector,
hx ,t +1 is the work hours spent, S x ,t is the market value of equity issued, rxe,t +1 is the net rate of
return on the stock, Bx ,t is the market value of bonds issued, rt f is the risk free bond rate, and C (・)
and Ｄ(・) are issuing costs of security
measured in the units of consumption goods for stock and
bonds. We assume that these issuing cost functions have positive first derivatives and negative second
derivatives.
3
What about modeling for a banking sector? Diaz-Gimenez et. al (1992) model the banking sector where banks pay
interest rates for deposits while lending money. This can be added to our model. However, for simplicity, we represent a
financial sector by this investment banking sector.
8
π x ,t +1 = Yx ,t +1 − (1 − δ ) K x ,t +1 Pk ,t +1 − Wx ,t +1hx ,t +1 − (1 + rxe,t +1 ) S x ,t
− (1 + rt f ) Bx ,t − C ( S x ,t ) − D ( Bx ,t ) ≥ 0
(13)
The producing firms maximize the following objective function subject to (13) where we assume that
the price of consumption goods to be used as a numeraire and given to be known exogenously.
max
S x ,t , K x ,T +1, B x ,t
Et max π x ,t +1 
 hx ,t +1

(14)
The financial co-operative on the other hand, maximizes the following profit function, where we
assume that the information for the production technology shown in equation (14) are the common
knowledge among households and firms.
max
S x ,t , Bx ,t , h f ,t +1
[
Et C ( S x ,t ) + D( Bx ,t ) − W f ,t +1h f ,t +1
]
(15)
Then, the equilibrium allocation in this economy can be attained by representative consumer’s
maximizing (7), subject to (9), (10) and (11), where we assume that K c , 0 > 0, K i , 0 > 0 are given. The
equilibrium attained is unique when only the investment goods sector and the consumption goods
sector are in the economy, because of the linear homogeneity of the technology as proven by Boldrin,
Christiano, and Fisher (1995). However, with the introduction of a new financial sector, in order to
guarantee that the equilibrium is unique, the C(・) and D(・) functions have to behave such that the
marginal productivity of the labor from underwriting the bonds and stock issue becomes equal to the
competitive wage rate prevalent in consumption and investment goods sector. This has to hold before
the households decide to commit their working hours among two sectors and a financial sector. We
assume that this is the case and the equilibrium is unique.
The equity rate of return formula for firms in two production sectors is as given in Boldrin,
Christiano, and Fisher (1995) except that in our paper the marginal cost of issuing bonds and stock
have to be now included in this first order condition. In equation (16) mpk is the marginal product of
capital and γ x,t is the leverage ratio for the firm x at time t measured at the market price in units of
9
consumption goods. Then, the equity rates of return for two sectors are the following for x = c and i.
1 + rxe,t +1 =
mpk x ,t +1 + (1 − δ ) Pk ,t +1 − C ′( S x ,t ) − D' ( Bx ,t )
Pk ,t
(1 + γ x ,t ) − (1 + rt f )γ x ,t
(16)
In this formula the excess return of both the investment goods sector and the consumption goods
sector are functions of capital stock and the leverage ratio of the corresponding sector. Note that the
consumption goods sector is influenced by the capital goods price changes and the depreciation rates
as well. The investment goods sector and the consumption goods sector are similarly influenced by the
same capital goods price changes, while the marginal productivity of the two sectors mpk will be in
general different among these two sectors. These differences cause different reactions of the equity
premium of these two sectors against the business cycle changes. Other parameters to cause changes in
equity premium between two sectors are the leverage ratios of the firms and the issuing cost of bonds
and stock of these firms. Thus, the productivity parameter mpk , leverage ratio, and the price of capital
(market value of equity ) will all affect the rates of return on equity. They are concurrently inter-twined.
What we estimate in our paper is how much the ex ante equity premium can predict the future output
fluctuations, especially their cyclical components. The ex ante equity premium as a predictor will be
able to predict the future equity rates of returns, which are functionally related to future mpl in
equation (16). Then, this predictor should be able to predict also the output fluctuations as an inverse
function of mpl. The movements of future equity premiums would be better and more accurately
predicted if the model is controlled for the changes in the factors that are related to the productivity
equation as shown in RHS of equation (16). Hence, the RHS variables are sort of control variables to
predict future output and some of these control variables are as contained in Fama and French three
factor model This indeed is the motivation for using Fama and French three factor model to computed
he ex ante equity premium to predict the future equity returns and hence the future output fluctuations.
In equation (16) the high leverage causes the risk premium to be higher, so does the increase in the
marginal productivity of labor and future capital prices. The faster economic depreciation caused the
10
premium to be lower and so does the financial friction cost. This way the expected return in the stock
market will be able to predict these changes given rational expectations assumptions.
From equation (16) our predicting equation at time t for the future output at time t+l (l > 0) is as
follows. In the equation f
−1
is the inverse of the production function and function g solves for mpk
from equation (16).
Yx ,t +l = f −1 (mpk x ,t +l ) = f −1 ( g (rxe,t +l ; Pi ,t +l +1 , Pk ,t +l ,δ , S x ,t +l , Bx ,t +l , γ x ,t +l , rt +f l ))
(17)
Instead of estimating this complicated function g, however, we use directly the expected equity
premium estimate from equation (6) as a surrogate variable to predict the future equity returns where
the control is done for the market value of the investment goods, the leverage ratios, and the risk free
rate, by using Fama and French asset pricing model.
Note as well that in this Fama and French model the market portfolio return is the weighted average
of these two sectors and it is expressed as (17). Note that in Fama and French model or other asset
pricing theories the ex ante expectations are usually used, while in RBC model this variable is a
random variable. The expected premium would be the rational forecasts of what is going to happen in
the future stock markets and in a real economy. This is why we predict future returns our ex ante
equity premium estimates estimated from the asset pricing theory.
Rm ,t +1 =
K c ,t +1
K t +1
rce,t +1 +
K i ,t +1
K t +1
rie,t +1
(18)
Finally, RBC model like the one by Boldrin, Christiano, and Fisher is a stationary equilibrium. The
production technology is, however, auto-correlated by assumption and also with the habit formation of
households there will be persistence in the output fluctuations in the economy when the model is
repeated over time. This justifies of our investigating the relationship between the ex ante risk
premium of the sectors and the industries and the future cyclical components of the output in the
economy and explores whether the equity premium can predict future business cycles and whether the
implications are different among industries and sectors. The result will reveal the speed of adjustments
11
of economic shocks among different sectors using the expected premium as a possible rational
predictor.
III. The Data
Our data are as follows. To measure the production level of the economy we choose two economic
indicators. For a monthly data we use industry production index among alternative production indices,
since this is most widely used in the empirical macroeconomic research.
The data on the production
indices are reported each month on the Industrial Statistics Monthly published by the Ministry of
International Trade and Industry, and we use the seasonally adjusted data. For quarterly data we use
real Gross Domestic Product reported in Japanese NPIA government statistics. The particular series
that we choose for our analysis is deflated and seasonally adjusted GDP numbers reported in the
Annual Account on National Accounts issued by the Ministry of Economy and Industry. We also use
per capita and seasonally adjusted real consumption series to compare the behavior between GDP and
consumption. It is well known that the consumption is a much more sticky process than GDP, which
has been circumventing the good fitting of the consumption based asset pricing theory to the actual
data for USA (Kocherlakota, 1996, Boldrin, Christiano, and Fisher, 2000) and in Japan (Kubota,
Tokunaga, and Wada, 2003). In the current paper we assume that the representative consumer is
equipped with utility function with habit persistence to cause the stickiness of the consumption series.
The above data and all return and accounting data used in our study are available at the University
of Tsukuba, Graduate School of Systems and Information Engineering. The primary source for
accounting variables to be used in computing the book-to-price ratios and the number of shares
outstanding as well as the data source for the return data is Nikkei Portfolio Master Database. The
value-weighted index is computed in-sample from our same data set. As for the risk free rate we use
the overnight “call rates without collateral,” equivalent of the federal funds rate in the USA, reported
by the Bank of Japan and available on Nikkei NEEDS data. We also use consumer price index, money
12
supply, and the term structure measured in yield spread, long term weighted Government bond yield
minus money market yield, to investigate the association between these macroeconomic variables and
our factor portfolio unconditional returns. The term structure data are taken from Ibbotson Associates
Inc., Japan. The testing period for our macroeconomic data is from First Quarter of 1980 through
Second Quarter of 2003 for quarterly observations and from January 1980 through December 2003 for
monthly observations.
The data covering period for our return data is from January 1977 to December 2003 and we
compute the factor loadings using this data. We use data of the firms listed in the first section of the
Tokyo Stock Exchange and impose the condition that at least 36 months of return data as well as the
financial reports preceding the computations of the book-to-price ratios and the total share outstanding
are available. As Table 1 shows, we have total observations of 1475 firms that satisfy these
requirements and we will use 33 industry classifications as officially defined by the Tokyo Stock
Exchange.
IV. Estimates of Equity Premium and the Loadings
Table I reports summary statistics of our initial estimates of the required rate of return using
unconditional asset pricing models as of end of December 2003: CAPM and Fama and French three
factor model. The last observation point is December 2003 and our sampling starts from the month of
September 1977. The industry classifications are based on the two-digit 33 classifications by the
Tokyo Stock Exchange. In the column furthest to the left, we report the number of firms included in
each industry. We caution that there are several industries with a very small number of sample firms:
e.g., Air Transportation and Mining. For most cases the cost of equity is higher for Fama and French
model than for CAPM. The numbers in the bottom row show the averages for all firms. By reading
from the median and mean values we find that the CAPM gives about 3 % lower estimate of the
expected return on equity than Fama and French three factor model. For example, when we compare
13
the median value the former is 3.83% and the latter is 6.84%. The result is in accordance with Fama
and French’s (1997) result for US data. It indicates that the CAPM underestimates the inherent risk of
individual firms, failing to pick up the relevant systematic risk components necessary to span the
mean-variance space. Also, the variation of the expected returns becomes much smaller for CAPM
estimates than Fama and French as we can find by comparing the 1st Quartile and 3rd Quartile numbers.
The extra factor risk is incorporated in case of Fama and French model, which CAPM fails to pick up.
These are why we choose to Fama and French model for our further tests in the paper. The industries
with high expected returns, using median values, are Securities, Construction, Marine Transportation,
and Mining, all above 10 per cent per annum, and the industries with low expected returns are
Services, Communication, and Pharmaceutical, all below 5 per cent per annum.
The next Table II shows the estimated factor loadings for unconditional CAPM, unconditional Fama
and French model, and conditional Fama and French model defined in the equation (6). These
estimates are aggregated by value weighting the initial individual estimates with the market value as of
end of December 2003 for each firm. By comparing the loadings on the market factor,
β , β M ,and γ M among these three methods, we find that the differences are only at the maximum
order of 0.26 for Air Transportation and 0.16 next for Oil and Coal Products. Between the
unconditional three-factor model and the conditional one the difference becomes even smaller for
market betas. This is because the estimation is conducted once for all for our same sampling period,
where in the conditional model there are extra two parameters to be estimated and the time-varying
explanatory variables, ln(ME) and ln(BE/ME) to estimate these parameters, as in equation (6), are
standardized over time for each firm. It is somewhat surprising that as far as loading is concerned, at
the industry level, the market beta from CAPM is doing quite well relative to our multivariate models.
When we compare the loading on the SMB factor and HML factor, β SMB , γ 0SMB and β HML , γ 0HML ,
the maximum difference for the former is 0.399 for Oil and Coal Products and for the latter it is 0.21
14
for Mining. For all sample the differences are 0.013 and 0.008, respectively. Although these
differences may look rather small, note that the loadings have the time varying components whose
sensitivities are measured in γ 1SBM , γ 1HML , which could amplify the effect of time varying effects of
firms’ characteristic changes in size and book-to-price ratios. So, by comparing these coefficients we
can infer where the time-varying components indeed come from in conditional model with our
specifications. This finding is nowhere available in the literature
using Japanese data.
Fama and French (1997) point out that there exist substantial estimation errors for individual firms’
estimates, especially when estimating unconditional Fama and French model. Similarly to this
observation we also find that the performance of aggregated conditional version of Fama and French
model from individual estimates is superior to the unconditional version for Japanese data. Our initial
estimation of the “36 month rolling” betas of Fama and French model using unconditional model were
quite unstable over time. We claim that both using the conditional model and aggregating the
individual estimates at the industry level can circumvent the sampling error problem pointed out by
Fama and French (1997). Specifically, we claim our method of value weighting the individual
estimates of conditional model (6) is robust with respect to the time changes of individual firm’s
characteristics because we can observe directly these characteristics without error. Furthermore, the
aggregation within the industry can collect for the individual sampling errors within the industry. Both
the industry specific systematic components and the industry specific sampling errors may still remain,
though. With these justifications we adopt the form of equation (6) to estimate loadings at the
individual firm’s level and then the aggregate these estimates using value-weighting both at the
industry level and the sector level to compute the equity premiums in the following.
V.
Filtering the Cyclical Components of Economic Activities
To extract the trends and the cyclical components of the macroeconomic variables, we use H-P filter
15
by Hodrick and Prescott (1997) among other methods4. In H-P filtering method the trend path ｛ lt
｝
is chosen in such a way that it minimizes the sum of the squared deviations from a given series｛ Yt ｝,
where the natural logarithms of the original variable are taken, subject to the constraint that the sum of
the squared second differences is not too large (Prescott (1986)). In equation (19) λ is a positively
valued smoothing parameter that is a priori specified by an econometrician and the λ value penalizes
the variability in growth components. Since Yt is measured in its logarithmic forms, the first difference
of the growth component lt can be also interpreted as the growth rates in logarithms.
T
T
t =1
t =2
2
2
min ∑ (Yt − lt ) + λ ∑ ((l t +1 − lt ) − (lt − lt −1 ))
{lt }Tt−1
（19）
As has been the case for the USA and other countries (Kydland, 1997), we use λ= 1600 to de-trend the
quarterly series and 6400 for the monthly series. The GDP series we use is quarterly observed and the
production index is monthly observed. In this paper we do not filter the stock returns because we use
particular forms of the asset pricing model that allows for time variations of the factor loadings every
month while keeping the factor returns constant over time.
The trends and the cyclical components of both the production series and GDP series are as shown
in Figure 1 and two figures on the left hand side highlight the smooth trend that was constructed from
the original GDP growth series and production series. The extracted cyclical components are as shown
in two figures on the right hand side. The choice of λ value 1600 is the coefficient value usually used
to describe the post war U.S. economy for quarterly data to fit to the US business cycles. According to
the definition by NBER the average length of one full cycle of the business cycles in the U.S. is about
5 years. For Japan, according to the official definition by the Economic Planning Agency, it is between
3 and 7 years for the post-war Japan. Thus, based also on the evidence applied to other countries by
Kydland (1997) as well, we use these a priori smoothing parameter values to de-trend our Japanese
4
An alternative method would be, for example, the one by Stock and Watson (1988).
16
macroeconomic data series and extract the cyclical components of production activities to be
associated with the changes in the equity premium for industries and sectors.
VI. Equity Premium and the Business Cycle: Empirical Evidence
a. Equity Premium Changes of Industries and Sectors
Table III shows the basic correlation structure of the Fama and French factor portfolios and the
major macroeconomic variables purportedly related to the asset prices. The production index, GDP,
and per capita consumption were all H-P filtered and these become cyclical components which are
standardized by subtracting the means and dividing those by the estimated standard deviations5. In
Panel (b) and Panel (d) the lower left hand side triangle elements show the estimated correlation
coefficients and the upper right hand triangle elements show corresponding p-values. Note that the
correlation between the cyclical components of the production (PLC) and the value weighted index
return (EVW) is negative. It means the aggregate stock returns are countercyclical as Boldrin,
Christiano, and Fisher (1995) claim. It is also the case with the cyclical components of GDP (GDPC)
as shown in Panel (d). The result is also similar with cyclical components of the per capita
consumption (CPC).
Counterintuitive is the observation that the short-term rate (CMR) and the business cycles are
positively related, and the term structure, ITS, and the business cycles are negatively related. It may be
due to the policy lags of Bank of Japan’s monetary policy. Inflation rate (QINF) is not strongly related
to the market returns, nor HML factor or SMB factor. Money supply (M2+CD) changes affect
positively the market return, but oppositely HML factor and SMB factor6.
5
Chen, Kubota, and Takehara (1997) reports the lead and lag relationship of the trends and cyclical components of GDP and
per capita consumption with the unconditional equity index premium changes in 1980s.
6
The similar evidence for the USA case is reported in Liew and Vassalou (2000).
17
In the following we try to associate the changes in expected equity premiums and the future
production. Based on the two-sector economy model presented in the previous section, the
consumption goods industry and investment goods industry possess different business cycle
implications in terms of marginal products of labor and also in the stock expected returns. We want to
investigate how stock market prices and expected equity premium can anticipate these future
production differences between the different sectors of the economy. Financial sector, though without
capital in our model in the previous section, should also possess different business cycle implications.
Figure 2 shows the over- the- time changes of the equity premiums aggregated into seven sectors as
defined below with value-weighting. Although there is some ambiguity among industries in which
both the investment goods and consumption goods are produced in the same industry, we use a priori
judgment to classify industries to the non-overlapping sectors. The similar classification is also
conducted by Boldrin, Christiano, and Fisher (1995), where they divide the stock
index into the
overlapping composite, capital goods, utility, finance, industrial, transportation. With our definition
the consumption goods sector includes fishery and agriculture, foods, textiles and apparels,
pharmaceutical, electric appliances, and other products. The investment goods sector includes mining,
construction, pulp and paper, chemicals, oil and coal product, rubber products, glass and ceramics
products, iron and steel, nonferrous metals, metal products, machinery, transportation equipment,
precision instrument. The commerce sector includes communication, wholesale trade, retail trade, and
services. Financial sector includes banks, securities, insurance, and other finance businesses.
Transportation sector includes land transportation, marine transportation, and air transportation. Utility
includes only the power and gas. Real estate sector includes real estate and warehousing. The
premiums for each sector is value weighted based on each firm’s market value as of December 2003.
From Figure 2 remarkably different patterns of the equity premium changes can be observable
between these seven sectors, especially between the consumption goods sector and the investment
goods sector. The consumption goods sector is relatively with lower risk with stable premium changes.
18
On the other hand, the investment goods sector is with higher risk along with slightly higher volatility
than the consumption goods sector, but their behavior is similar to other sectors. The real estate sector
and the finance sector are on the higher risk side and moving together, thus reflecting the bubble
phenomenon that are known to have arisen from these sectors in late 1980s in Japan. Thus, we can
find that there is a remarkable difference in the patterns of equity premium changes between sectors.
In the next tables, IV and V, we focus on the relationship between the industry equity premium and
the raw series of GDP and per capita consumption growth rates7. As we demonstrated in Section II.b
our
RBC model used in this paper is based on the habit persistent consumer and the immobility of
labor force. These assumptions influence differently the cycles of output fluctuations among different
sectors of the economy. Also, because Euler equations relate the asset returns to the consumption
growth, we also look at consumption growth rates for comparison purposes and investigate where
there is any qualitative difference between the production variable and the consumption variable in
terms of association with the changes in the equity premiums.
Table IV and V show the lead and lagged relationships between GDP and the per capita real
consumption and the equity premium, with regressing output growth and consumption on lagged
expected equity premium. These macroeconomic variables are measured as growth rates over the
previous quarter and the equity premium are the value weighted premium with the specification of the
equation (6). We find that the relationships are quite similar among GDP growth and consumption
growth. Overall, there are stronger relationships between the lead of the equity premium and the GDP
changes or the per capita consumption changes. The result indicate that, when the output expansion
(contraction) continues, the equity premium keeps going up (down) for another one year. From the
result from the lags one can find that the predicting power of the equity premium also exists, but with
slightly lower power than the persistence after the output changes. For almost all industry cases the
7
Chen (1991) also uses GDP and per capita consumption raw series to investigate the relationship between the
macroeconomic variables and the index returns in the USA.
19
signs of the regression coefficients are right ones. Also, at the aggregate index level, VW, the p-values
are largely significant, more so for GDP, although R-square values are quite small at the order of 0.1
for GDP and smaller for consumption. Because this is a simple exercise and pre-test, we did not use
Newey and West correction.
The purpose of conducting this rather simple and basic regression is to confirm that there is indeed a
positive relationship between the conditional equity premiums and the growth rates of output
production and the consumption with leads and lags. With this evidence next we investigate the
predictive ability of the equity premium for the future output fluctuations, particularly the cyclical
components of the output fluctuations.
b. Predictive Output Fluctuations with the Expected Equity Premium
In this final sub-section we investigate the predictive ability of the expected equity premium for the
cyclical components of production and GDP. The cyclical components may not be predictable as
much as the trend components in general and we want to investigate how much the industry-wise or
sector-wise equity premium can predict these unpredicted components of the economic output
activities.
The results for industries are as shown in Table VI. We find that the pulp and paper industry loads
negative to the equity premium change. Also, the pharmaceutical industry loads negative for GDP
cycle and so are the communications industry. On the other hand, the electric power and gas industry
loads negatively for production case, which is somewhat counterintuitive. Over all R-square values are
quite small, which was predicted from low R-square values in our previous regression, using even the
raw growth rates of GDP, as we discussed in Table IV.
The general tendencies and the comparisons between industries are rather difficult with these
industry aggregated level. However, the differences of the loadings become more conspicuous and
concrete once we aggregate the result shown in Table VI into the sectors as shown in Table VII and
20
Figure 3 and 4. Here, we aggregate the individual equity premium into seven sector indices by value
weighting the equity premium of each firm. The aggregated loadings for sectors are as shown in panel
(a) of Table VII and the regression results are shown in panel (b). From panel (a) we find that the
loading of the consumption goods sector is quite different from other sectors, except for the utility.
Also, from p-values in panel (b) we find that the coefficients for GDP case for third and fourth quarter
ahead is significant. This means that the equity premium of the consumption goods sector can
significantly predict the future cyclical components of GDP growth.
Figure 3 shows the changes in regression coefficients of running regressions of the lead of the
cyclical components of the production index on the conditional equity premium of previously defined
seven sectors. Figure 3 shows the similar coefficients of the case of running regressions of the lead of
cyclical components of GDP on the conditional equity premium. These two figures show that there are
remarkably different patterns between the consumption goods sector and the investment goods sector
as the two-sector model of Boldrin, Christiano, and Fisher (1995) rightly predicts. Financial sector
also shows somewhat different patterns from other industries.
Also, the remarkable is the fact that the R-square values increased to a small extent and the
sampling errors are reduced, compared to the less aggregated industry case. This observation is as
pointed out by Fama and French (1997) for the possible sampling errors at the individual estimation
level. So, our aggregation at sector level can reduce the sampling errors and at the same time can shed
more light into the sector dynamics of output fluctuations rather than at more disaggregated 33
industry level.
The loading of the consumption goods sector increases as the predicting period extends into the
future. In other words, the increase in the equity premium can predict strongly the future production
increase in this sector. On the other hand, we observe the stronger con-current relations of the response
of the investment goods sector. It suggests that the investment goods sector is a leading sector. This
relationship gets dampened over time, an opposite to the case for the consumption goods sector. Note
21
also that the time behavior of the consumption goods sector is parallel to the one of the utility industry,
although the latter response is lower. Finance industry is also strongly related with the expected equity
premium and the relationship decreases uniformly with a very slow declining pace. This pattern from
the financial industry is definitely different from the ones from the consumption goods sector and the
investment goods sector and worth separating the financial sector from other sectors both in the theory
and in the empirical pursuit.
Although our RBC model can only analyze the steady state equilibrium and does not explicitly
accommodate the lead and lag relationships found in our study, the patterns found in our study can be
possibly utilized to extend the stochastic processes of the production processes used in a theoretical
model. The resulting model will help explain the observed behavior between the changes in the equity
premium under the general conditional asset pricing model and the output fluctuations, in which the
sector differences are taken care of as in our study. This paper presented the first evidence that it could
be indeed the case with two production sector economy and with one financial sector, using
conditional version of Fama and French three factor model.
VII. Conclusion
We found that the business cycle relationship between the cyclical components of the production
and GDP and the expected equity premiums from industries are quire different among different sectors.
The basic model proposed by Boldrin, Christiano, and Fisher (1995, 2000) suggests these differences
which stem from whether the industry belongs to the consumption goods sector or to the investment
goods sector. As we added a financial sector into this two sector model and close the model with
equilibrium conditions, it is inferred that the financial sector will have also different business cycles
implications. Based on the model proposed by Dias-Gomez et al. (1992), we may be also able to
incorporate a banking sector, which also has different business cycle implications.
22
One can also extend implication from our study in that the possible unsystematic components may
exist in the industry or the sector characteristics which may not be diversifiable by the market portfolio
and other risk factor portfolios under the incomplete markets as Krebs (2004) has shown. In this case it
would affect both the stock returns and the corresponding business cycles of the industries, because
these unsystematic components may be large and persistent as Krebs claims. In this case the changes
in the conditional betas in Fama and French model may not be sufficient to explain the time variations
of the expected returns related to the cyclical components of the economic outputs. This possibility is
subject to our future research.
23
References:
Boldrin, M., L. J. Christiano, and J. D. M. Fisher, (1995), “Asset Pricing Lessons for Modeling
Business Cycles,” Working Paper, No. 560, Federal Reserve Bank of Minneapolis.
Boldrin, M., L. J. Christiano, and J. D. M. Fisher, (2000), “Habit Persistence, Asset Returns, and the
Business Cycles,” Staff Report, No. 280, Federal Reserve Bank of Minneapolis.
Brock, W. F., (1982), “Asset Prices in a Production Economy,” in J. J. McCall ed., The Economics of
Information and Uncertainty, University of Chicago Press, Chicago, Illinois.
Campbell, J.Y., A. W. Lo, and A. C. MacKinlay, (1997), The Econometrics of Financial Markets,
Princeton University Press, Princeton, New Jersey.
Chen, N., (1991), “Financial Investment Opportunities and Macroeconomy,” Journal of Finance, 41,
1739-1763.
Chen, N, K. Kubota, and H. Takehara, (1997), “Japanese Stock Returns and the Business Cycles,”
Musashi University Discussion Paper, No. 24.
Cochrane, J. H., (1996), “A Cross-Sectional Test of an Investment-Based Asset Pricing Model,”
Journal of Political Economy, 104, 572-621.
Cox, J.C, J. E. Ingersoll, Jr. and S. A. Ross, (1985), “An Intertemporal General Equilibrium Model of
Asset Prices,” Econometrica, 53, 385-407,
Diaz-Gimenez, E. Prescott, T. Fitzgerald, and F. Alvarez, (1992), “Banking in Computable General
Equilibrium Economies,” Journal of Economic Dynamics and Control, 16, 533-559.
Fama, E. F. and K. R. French, (1993), “Common Risk Factors in the Returns on Stock and Bonds,”
Journal of Finance, 48, pp. 427-65.
Fama, E. F. and K. R. French, (1997), “Industry Cost of Equity,” Journal of Financial Economics, 54,
1939-67.
Ferson, W. E., and A. F. Siegel, (2002), “Testing Portfolio Efficiency with Conditioning Information,”
Mimeo, Boston College and University of Washington.
Hansen, L. P., and S. F. Richard, (1987), “The Role of Conditioning Information in deducing Testable
Restrictions implied by Dynamic Asset Pricing Models,” Econometrica, 55, 3, 587-613.
Hodrick, R. J., and X. Zhang, (2000), “Evaluating the Specification Errors of Asset Pricing Models,”
NBER Working Paper, No. 7661.
Jagannathan, R., K. Kubota, and H. Takehara, (1998), “Relationship between Labor-Income Risk and
Average Return: Empirical Evidence from the Japanese Stock Market,” Journal of Business 71, pp.
319-47.
Jagannathan, R., and Z. Wang, (1996), “The Conditional CAPM and the Cross-section of Stock
Returns,” Journal of Finance, 51, 3-53.
Kocherlakota, N., (1996), “The Equity Premium: It’s still a Puzzle,” Journal of Economic Literature,
34, 42-71.
24
Krebs, T., (2004), “Testable Implications of Consumption-based Asset Pricing Models with
Incomplete Markets,” Journal of Mathematical Economics, 40, 191-206.
Kubota, K. and H. Takehara, (2003), “Financial Sector Risk and the Stock Returns: Evidence from
Tokyo Stock Exchange Firms,” Asia-Pacific Financial Markets, 10, 1-28.
Kubota, K., T. Tokunaga, and K. Wada, (2003), “Consumption Behavior, Asset Returns, and the Risk
Aversion: Evidence from Japanese Household Survey,” Paper presented at European Economic
Association Meeting in Stockholm.
Kydland, F., (1997), “Is the Business Cycles of Argentina “Different”?” Economic Review, Federal
Reserve Bank of Dallas (Fourth Quarter), 15-35.
Lettau, M., and S. Ludvigson, (2001), “Resurrecting the (C) CAPM: A Cross-Sectional Test When
Risk Premium are Time-Varying,” Journal of Political Economy, 109, 6, 1238-1287.
Lewllen, J., and S. Nagel, (2004), “The Conditional CAPM Does Not Explain Asset Pricing
Anomalies,” Paper presented at 2004 Western Finance Association Meeting.
Liew, J., and M. Vassalou, (2000), “Can Book-to-Market, Size and Momentum be Risk Factors that
Predict Economic Growth?” Journal of Financial Economics, 57, 221-245.
Menzly, L., T. Santos, and P. Veronesi, (2004), “Understanding Predictability,” Journal of Political
Economy, 112, 1, 1-47.
Mehra, R. and E. Prescott, (1985), “The Equity Premium: A Puzzle,” Journal of Monetary Economics,
15, 141-61.
Petkova, R., (2003), “Do the Fama-French Factors Proxy for Innovations in Predictive Variables?”
Paper presented at 2004 Western Finance Association Meeting.
Prescott, E. C., (1986), “Theory ahead of Business Cycle Measurement,” Quarterly Review, Federal
Reserve Bank of Minneapolis (Fall), 9-21.
Stock, J.H., and M. W. Watson, (1988), “Variable Trends in Economic Time Series,” Journal of
Economic Perspectives, 2 (Summer), 147-174.
25
Table I: Unconditional Expected Return on Equity for All Firms:
Estimated with CAPM and Fama and French Three Factor Model
Capital Asset Pricing Model
Fama and French 3 Factor Model
# of Firm 1st Qu. Median Mean 3rd Qu. 1st Qu. Median Mean
3rd Qu.
Fishery & Agriculture
8
3.42
3.61
3.66
3.85
6.91
9.34
7.74
9.82
Mining
6
3.55
4.00
3.94
4.13
7.78
10.49
9.94 12.17
Construction
103
3.37
3.72
3.76
4.10
7.83
10.73
10.70 12.55
Foods
73
2.77
3.22
3.17
3.55
4.55
6.39
6.19
7.88
Textiles & Apparels
44
3.56
3.86
3.87
4.19
7.19
8.39
8.86 10.73
Pulp & Paper
13
3.22
3.33
3.53
4.03
4.40
7.68
6.94
8.21
Chemicals
106
3.61
3.93
3.86
4.27
5.76
7.02
6.93
8.45
Pharmaceutical
34
3.04
3.40
3.33
3.70
2.97
4.53
4.50
6.58
Oil & Coal Products
7
3.26
3.64
3.99
4.26
8.46
9.12
10.63 12.01
Rubber Products
11
3.23
4.15
3.78
4.29
5.98
7.94
7.43
8.25
Glass & Ceramics Products
28
3.73
4.21
4.11
4.47
5.55
7.87
7.23
9.26
Iron & Steel
31
3.86
4.28
4.26
4.64
8.27
9.93
9.80 11.17
Nonferrous Metals
21
4.06
4.26
4.26
4.64
5.14
7.89
7.43
9.34
Metal Products
34
3.34
3.65
3.59
3.87
6.60
9.01
8.63 10.46
Machinery
109
3.75
4.12
4.16
4.54
5.57
7.96
7.80
9.93
Electric Appliances
139
3.66
4.18
4.11
4.46
3.09
5.12
5.03
7.09
Transportation Equipment
53
3.31
3.69
3.75
4.26
4.86
7.47
7.44 10.42
Precision Instruments
25
3.58
4.11
4.18
4.46
1.57
5.38
4.47
6.88
Other Products
51
3.38
3.78
3.87
4.19
4.65
6.55
6.96
9.94
Electric Power & Gas
14
2.81
2.89
2.96
3.15
6.17
6.45
6.17
7.04
Land Transportation
34
2.98
3.37
3.35
3.75
4.83
5.97
6.12
8.02
Marine Transportation
11
4.36
4.56
4.52
4.73
9.27
10.33
10.56 12.01
Air Transportation
4
3.55
4.02
4.20
4.67
6.06
6.64
6.64
7.21
Warehousing
11
3.57
3.70
3.82
4.06
8.85
9.14
9.48 10.06
Communication
10
4.14
4.59
5.23
5.55
1.01
1.92
2.59
4.91
Wholesale Trade
118
3.42
4.11
4.16
4.52
5.15
7.05
6.97
9.20
Retail Trade
109
2.85
3.48
3.42
3.89
3.63
6.28
6.33
8.14
Banks
80
2.28
2.63
2.89
3.05
4.23
5.53
6.05
6.33
Securities
16
4.80
5.13
5.16
5.91
9.39
11.77
10.49 12.90
Insurance
9
3.92
4.03
4.02
4.15
7.04
7.34
6.92
8.67
Other Financing Business
28
3.46
4.19
4.46
4.61
4.76
6.72
6.49
8.12
Real Estate
29
3.53
3.87
4.05
4.80
6.00
8.62
9.04 10.85
Services
106
3.61
4.34
4.50
5.09
-0.54
3.14
2.78
5.82
All Firms
1475
3.30
3.83
3.87
4.35
4.55
6.84
6.85
9.25
The samples are all listed firms in the First Section of the Tokyo Stock Exchange. The number of the firms is 1,475 and the
estimation period is from September 1977 through December 2003. We use both CAPM and Fama and French three-factor
model to estimate the expected excess return model with monthly data. The annual expected returns were computed by
multiplying these monthly numbers by 12 and adding the risk free rate of 1.32 per cent, the outstanding market rate as of end
of December 2003. All numbers are in per cent. The industry classification is based on Tokyo Stock Exchange 33 way
industry classifications.
26
Table II: Loadings of Unconditional CAPM and Unconditional and Conditional Fama
and French Three Factor Model
CAPM
β
Fishery & Agriculture
0.850
Mining
0.834
Construction
0.936
Foods
0.635
Textiles & Apparels
0.927
Pulp & Paper
0.772
Chemicals
0.949
Pharmaceutical
0.739
Oil & Coal Products
1.112
Rubber Products
0.841
Glass & Ceramics Products 0.908
Iron & Steel
1.244
Nonferrous Metals
1.077
Metal Products
0.864
Machinery
1.035
Electric Appliances
1.008
Transportation Equipment
0.839
Precision Instruments
0.875
Other Products
0.843
Electric Power & Gas
0.652
Land Transportation
0.575
Marine Transportation
1.145
Air Transportation
1.247
Warehousing
1.008
Communication
1.526
Wholesale Trade
1.257
Retail Trade
0.873
Banks
1.567
Securities
1.695
Insurance
1.231
Other Financing Business
1.165
Real Estate
1.112
Services
1.838
VW
1.105
Unconditional Fama-French
βM
β SMB
β HML
0.888
0.487
0.426
0.894
0.440
0.394
1.037
0.304
0.831
0.664
0.174
0.250
0.985
0.182
0.416
0.814 -0.016
0.387
0.969
0.308
0.146
0.730
0.018 -0.056
1.175
0.548
0.825
0.862
0.285
0.148
0.914
0.266
0.020
1.334
0.763
0.151
1.118
0.285
0.277
0.919
0.547
0.486
1.051
0.504
0.173
0.971
0.189 -0.234
0.852
0.047
0.143
0.832
0.062 -0.300
0.832
0.285
0.007
0.708 -0.580
0.480
0.612 -0.093
0.248
1.234
0.168
0.645
1.296
0.141
0.319
1.085
0.361
0.514
1.452 -0.251 -0.549
1.248
0.243 -0.003
0.863
0.323
0.094
1.577 -0.679
0.513
1.718 -0.354
0.300
1.252 -0.423
0.155
1.128
0.499 -0.093
1.173 -0.102
0.541
1.725
0.299 -0.734
1.100
0.041
0.039
Conditional Fama-French 3 Factor model
γ 0SMB
γ 1SMB
γ 0HML
γ 1HML
γM
0.870
0.505 -0.043
0.324 -0.407
0.845
0.424
0.159
0.182 -1.370
1.016
0.345 -0.198
0.711 -0.625
0.666
0.151
0.663
0.225 -0.044
0.972
0.199 -0.137
0.396 -0.245
0.798
0.013
0.997
0.371 -0.748
0.969
0.323 -0.185
0.104 -0.022
0.730
0.040 -0.272 -0.128
0.275
1.273
0.149 -0.240
0.673 -2.009
0.858
0.286 -0.021
0.127 -0.077
0.916
0.288 -0.223 -0.002 -0.034
1.247
0.585
0.318
0.081 -0.851
1.111
0.324 -0.304
0.233 -0.415
0.903
0.538
0.039
0.411 -0.299
1.049
0.516 -0.223
0.175 -0.085
0.981
0.175 -0.186 -0.176 -0.090
0.838
0.051 -0.061
0.096
0.024
0.821
0.062
0.010 -0.334
0.082
0.830
0.280 -0.026
0.002
0.068
0.705 -0.485 -0.448
0.491 -0.591
0.615 -0.058
0.238
0.225 -0.239
1.212
0.167
0.016
0.545 -0.722
1.508
0.658
1.242
0.342
5.726
1.079
0.351 -0.657
0.462 -0.616
1.413 -0.227
0.002 -0.521 -0.371
1.232
0.250
0.013
0.048 -0.345
0.882
0.355 -0.400
0.070 -0.031
1.561 -0.705
0.732
0.517
0.184
1.695 -0.351 -0.090
0.294 -0.456
1.267 -0.328 -0.096
0.182 -0.041
1.155
0.473
0.275 -0.146
0.052
1.183 -0.085 -0.244
0.496 -0.687
1.745
0.385 -0.188 -0.727 -0.395
1.096
0.054 -0.022
0.031 -0.156
The samples are all listed firms in the First Section of the Tokyo Stock Exchange. The number of the firms is 1,475 and the
estimation period is from September 1977 through December 2003. We use CAPM and unconditional and conditional Fama
and French three-factor models to estimate the expected excess return model with monthly data. The industry classification is
based on Tokyo Stock Exchange 33 way industry classifications. The individual loading estimates are aggregated for each
industry using value weighting with the data as of end of December 2003.
27
Table III: Basic Statistics and the Correlation Structure of
Portfolio Risk Factors and Macroeconomic Variables
(January 1980 - December 2003)
Panel (a) Basic statistics
PLG
PLC
EVW
SMB
HML
Min.
-4.379 -2.632 -20.664 -13.387 -10.531
1st. Qu. -0.720 -0.497 -2.885 -2.222 -1.160
Median
0.178
0.005
0.218
0.172
0.688
Mean
0.159 -0.016
0.200
0.088
0.689
3rd. Qu.
1.045
0.516
3.251
2.866
2.173
Max.
4.154
2.888 18.626 14.506 13.760
S.D.
1.388
0.871
5.180
3.747
3.094
Panel (b) Correlation Matrix
PLG
PLC
EVW
SMB
HML
PLG
0.000
0.998
0.133
0.176
PLC
0.315
0.051
0.856
0.069
EVW
0.000 -0.111
0.638
0.000
SMB
0.085
0.010
0.027
0.000
HML
0.077
0.103 -0.249
0.208
INF
0.005
0.073 -0.001 -0.034
0.047
CMR
0.042
0.122 -0.002
0.037
0.016
ITS
0.043 -0.078
0.071 -0.063 -0.061
M2CD
0.084 -0.007
0.089 -0.170
0.118
INF
-1.043
-0.225
0.101
0.136
0.394
1.996
0.512
CMR
0.000
0.035
0.334
0.320
0.533
1.058
0.256
ITS
-1.910
0.288
0.780
0.674
1.103
1.820
0.647
M2CD
-0.013
-0.002
0.003
0.005
0.010
0.041
0.010
INF
0.924
0.196
0.985
0.548
0.411
CMR
0.460
0.031
0.966
0.517
0.784
0.000
ITS
0.444
0.168
0.210
0.265
0.284
0.007
0.000
M2CD
0.140
0.895
0.118
0.003
0.037
0.348
0.004
0.086
0.258
-0.152
-0.053
-0.582
0.164
-0.098
(First Quarter 1980 - Second Quarter 2003)
Panel (c) Basic statistics
GDPG GDPC CPG
CPC
Min.
-1.453 -2.147 -3.939 -2.077
1st. Qu. 0.122 -0.820 0.122 -0.795
Median 0.597 -0.011 0.497 -0.136
Mean
0.602 -0.010 0.597 -0.010
3rd. Qu. 1.027 0.604 1.114 0.526
Max.
2.678 2.243 3.148 4.317
S.D.
0.849 1.008 0.952 1.002
Panel (d) Correlation matrix
GDPG GDPC CPG
CPC
GDPG
0.004 0.000 0.001
GDPC
0.293
0.076 0.000
CPG
0.680 0.185
0.000
CPC
0.332 0.631 0.519
EVW
0.018 -0.255 -0.066 -0.257
SMB
0.064 -0.029 -0.001 0.003
HML
-0.036 0.061 -0.011 -0.106
INF
-0.079 0.183 -0.291 -0.041
CMR
0.233 0.222 0.210 0.142
ITS
-0.085 -0.360 -0.045 -0.203
M2CD
0.277 -0.025 0.213 -0.039
EVW SMB
HML INF
CMR ITS
M2CD
-34.165 -25.961 -17.544 -0.778 0.000 -1.013 -0.013
-4.868 -3.515 -0.727 -0.100 0.034 0.283 0.002
2.090 0.508 1.947 0.200 0.294 0.740 0.012
0.562 0.209 2.247 0.320 0.307 0.650 0.014
7.405 4.896 5.546 0.704 0.521 0.993 0.021
22.155 15.901 21.898 3.091 1.039 1.787 0.050
10.091 7.046 6.391 0.676 0.262 0.636 0.014
EVW SMB
HML INF
CMR ITS
M2CD
0.865 0.540 0.728 0.452 0.025 0.416 0.007
0.014 0.783 0.561 0.079 0.032 0.000 0.815
0.528 0.991 0.919 0.005 0.043 0.666 0.040
0.013 0.980 0.310 0.694 0.174 0.051 0.714
0.894 0.093 0.869 0.833 0.412 0.808
0.014
0.000 0.598 0.599 0.180 0.635
-0.175 0.370
0.552 0.808 0.269 0.534
0.017 0.055 0.062
0.000 0.000 0.839
0.022 0.055 0.025 0.536
0.000 0.001
0.086 -0.140 -0.116 -0.384 -0.613
0.012
0.026 -0.050 -0.065 0.021 0.330 -0.259
Panel (a) and (b) are monthly data and (c) and (d) are quarterly data. EVW, SMB, and HML are three factor
portfolios in Fama and French unconditional model. PLC, GDPC, and CPC are cyclical components of
seasonally adjusted production index, gross domestic product, and per capita real consumption with H-P filter
applied. INF is inflation rate, CMR is the call rate, ITS is the term structure (long term JBG bond minus short
time Financial bills) and M2+CD is change in money supply.
28
Table IV: Lead and Lag Relationship between the Growth Rate of GDP
and the Equity Premium of Industries
CE(t-4) CE(t-3) CE(t-2) CE(t-1)
0.010
0.011
0.012
0.001
0.000
0.000
0.111
0.136
0.153
0.009
0.011
0.012
0.018
0.003
0.001
0.059
0.090
0.113
0.011
0.012
0.012
0.001
0.000
0.000
0.120
0.132
0.140
0.037
0.044
0.047
0.004
0.001
0.000
0.087
0.120
0.138
0.042
0.043
0.044
0.002
0.001
0.000
0.095
0.112
0.126
-0.009 -0.013 -0.016
0.264
0.084
0.036
0.014
0.032
0.047
0.028
0.031
0.032
0.002
0.001
0.000
0.101
0.121
0.131
0.020
0.020
0.018
0.373
0.376
0.421
0.009
0.009
0.007
0.026
0.026
0.027
0.002
0.002
0.001
0.101
0.100
0.111
0.032
0.034
0.036
0.013
0.009
0.006
0.065
0.073
0.081
0.026
0.025
0.026
0.017
0.016
0.010
0.060
0.061
0.070
0.012
0.013
0.014
0.021
0.012
0.004
0.056
0.067
0.087
0.015
0.015
0.016
0.003
0.002
0.001
0.094
0.100
0.110
0.016
0.022
0.024
0.074
0.015
0.006
0.034
0.063
0.081
0.063
0.068
0.063
0.001
0.000
0.001
0.108
0.125
0.105
-0.045 -0.041 -0.044
0.052
0.089
0.075
0.041
0.031
0.034
0.009
0.010
0.013
0.129
0.081
0.026
0.025
0.033
0.053
0.011
Coef.
0.001
p-value
R-squared 0.111
0.008
Mining
Coef.
0.031
p-value
R-squared 0.050
Construction
0.011
Coef.
0.001
p-value
R-squared 0.113
Foods
0.036
Coef.
0.005
p-value
R-squared 0.084
Textiles & Apparels
0.044
Coef.
0.002
p-value
R-squared 0.097
Pulp & Paper
-0.007
Coef.
0.419
p-value
R-squared 0.007
0.027
Chemicals
Coef.
0.003
p-value
R-squared 0.089
Pharmaceutical
0.021
Coef.
0.334
p-value
R-squared 0.010
Oil & Coal Products
0.029
Coef.
0.001
p-value
R-squared 0.121
Rubber Products
0.032
Coef.
0.014
p-value
R-squared 0.064
Glass & Ceramics Products Coef.
0.028
0.014
p-value
R-squared 0.064
Iron & Steel
0.011
Coef.
0.030
p-value
R-squared 0.050
Nonferrous Metals
0.015
Coef.
0.003
p-value
R-squared 0.094
Metal Products
0.013
Coef.
0.170
p-value
R-squared 0.020
Machinery
0.059
Coef.
0.003
p-value
R-squared 0.095
Electric Appliances
-0.043
Coef.
0.058
p-value
R-squared 0.039
Transportation Equipment Coef.
0.009
0.120
p-value
R-squared 0.026
Fishery & Agriculture
29
CE(t) CE(t+1) CE(t+2) CE(t+3) CE(t+4)
0.012
0.013
0.013
0.013
0.013
0.000
0.000
0.000
0.000
0.000
0.153
0.173
0.182
0.187
0.168
0.012
0.013
0.015
0.015
0.016
0.001
0.001
0.000
0.000
0.000
0.107
0.126
0.148
0.161
0.169
0.012
0.012
0.013
0.013
0.013
0.000
0.000
0.000
0.000
0.000
0.147
0.152
0.164
0.177
0.172
0.050
0.051
0.052
0.053
0.053
0.000
0.000
0.000
0.000
0.000
0.153
0.164
0.169
0.175
0.175
0.044
0.048
0.049
0.051
0.052
0.000
0.000
0.000
0.000
0.000
0.125
0.151
0.161
0.168
0.180
-0.017 -0.012 -0.005 -0.002 -0.003
0.024
0.113
0.472
0.780
0.740
0.055
0.028
0.006
0.001
0.001
0.032
0.035
0.035
0.034
0.034
0.000
0.000
0.000
0.000
0.000
0.128
0.152
0.149
0.138
0.137
0.012
0.012
0.009
0.000 -0.001
0.605
0.596
0.716
0.992
0.956
0.003
0.003
0.001
0.000
0.000
0.026
0.027
0.031
0.037
0.035
0.002
0.001
0.000
0.000
0.000
0.098
0.108
0.137
0.192
0.173
0.040
0.048
0.052
0.056
0.058
0.002
0.000
0.000
0.000
0.000
0.102
0.146
0.168
0.196
0.206
0.027
0.030
0.034
0.037
0.039
0.009
0.003
0.001
0.000
0.000
0.073
0.093
0.118
0.136
0.151
0.014
0.016
0.020
0.019
0.016
0.004
0.001
0.000
0.000
0.001
0.089
0.111
0.169
0.156
0.111
0.017
0.018
0.018
0.019
0.018
0.001
0.000
0.000
0.000
0.000
0.115
0.134
0.136
0.143
0.136
0.022
0.022
0.025
0.026
0.028
0.012
0.011
0.005
0.004
0.002
0.068
0.069
0.086
0.090
0.105
0.055
0.056
0.055
0.058
0.060
0.006
0.006
0.007
0.005
0.003
0.079
0.082
0.079
0.086
0.094
-0.041 -0.030 -0.026 -0.016
0.004
0.111
0.252
0.323
0.529
0.876
0.028
0.015
0.011
0.005
0.000
0.013
0.015
0.015
0.017
0.017
0.027
0.010
0.007
0.004
0.003
0.053
0.071
0.078
0.091
0.099
(continued)
CE(t-4) CE(t-3)
Coef.
0.041 0.043
p-value
0.017 0.013
R-squared 0.061 0.066
Other Products
Coef.
0.010 0.019
p-value
0.589 0.321
R-squared 0.003 0.011
Electric Power & Gas
Coef.
0.031 0.030
p-value
0.009 0.008
R-squared 0.073 0.073
Land Transportation
Coef.
0.033 0.033
p-value
0.000 0.000
R-squared 0.131 0.131
Marine Transportation
Coef.
-0.003 -0.002
p-value
0.628 0.722
R-squared 0.003 0.001
Air Transportation
Coef.
0.096 0.008
p-value
0.010 0.575
R-squared 0.070 0.003
Warehousing
Coef.
0.018 0.016
p-value
0.001 0.002
R-squared 0.114 0.101
Communication
Coef.
0.018 0.016
p-value
0.006 0.014
R-squared 0.080 0.064
Wholesale Trade
Coef.
0.017 0.017
p-value
0.009 0.009
R-squared 0.072 0.073
Retail Trade
Coef.
0.012 0.013
p-value
0.017 0.015
R-squared 0.061 0.063
Banks
Coef.
-0.001 -0.005
p-value
0.908 0.347
R-squared 0.000 0.010
Securities
Coef.
0.013 0.013
p-value
0.002 0.001
R-squared 0.101 0.116
Insurance
Coef.
0.014 0.011
p-value
0.056 0.093
R-squared 0.039 0.030
Other Financing Business Coef.
0.010 0.010
p-value
0.001 0.000
R-squared 0.118 0.127
Real Estate
Coef.
0.018 0.019
p-value
0.004 0.001
R-squared 0.084 0.107
Services
Coef.
0.020 0.022
p-value
0.006 0.002
R-squared 0.079 0.097
VW
Coef.
0.021 0.020
p-value
0.004 0.005
R-squared 0.086 0.082
Precision Instruments
CE(t-2) CE(t-1) CE(t) CE(t+1) CE(t+2) CE(t+3) CE(t+4)
0.047
0.007
0.077
0.032
0.092
0.030
0.027
0.015
0.063
0.032
0.000
0.128
-0.001
0.875
0.000
0.002
0.801
0.001
0.016
0.001
0.105
0.013
0.037
0.046
0.016
0.013
0.065
0.014
0.009
0.071
-0.009
0.097
0.030
0.015
0.000
0.141
0.010
0.094
0.030
0.011
0.000
0.143
0.019
0.001
0.118
0.023
0.001
0.117
0.020
0.006
0.078
0.048
0.006
0.080
0.033
0.088
0.031
0.024
0.028
0.052
0.032
0.000
0.129
0.002
0.721
0.001
0.002
0.747
0.001
0.015
0.001
0.108
0.012
0.067
0.036
0.018
0.006
0.080
0.015
0.006
0.079
-0.007
0.171
0.020
0.015
0.000
0.154
0.012
0.048
0.042
0.011
0.000
0.148
0.019
0.000
0.127
0.025
0.000
0.134
0.020
0.005
0.083
0.051
0.004
0.086
0.033
0.098
0.030
0.026
0.017
0.061
0.033
0.000
0.139
0.004
0.500
0.005
0.002
0.743
0.001
0.015
0.002
0.105
0.012
0.075
0.035
0.019
0.004
0.088
0.016
0.005
0.085
-0.002
0.725
0.001
0.016
0.000
0.162
0.013
0.027
0.053
0.011
0.000
0.145
0.020
0.000
0.134
0.026
0.000
0.142
0.021
0.003
0.093
0.057
0.002
0.106
0.040
0.052
0.041
0.026
0.020
0.059
0.035
0.000
0.152
0.004
0.470
0.006
0.005
0.502
0.005
0.016
0.001
0.114
0.012
0.065
0.037
0.021
0.002
0.106
0.018
0.002
0.106
-0.001
0.897
0.000
0.016
0.000
0.162
0.015
0.015
0.064
0.011
0.000
0.151
0.020
0.000
0.142
0.027
0.000
0.153
0.024
0.001
0.113
0.061
0.001
0.117
0.034
0.103
0.030
0.027
0.017
0.062
0.035
0.000
0.159
0.008
0.167
0.021
0.010
0.199
0.018
0.017
0.001
0.125
0.011
0.106
0.029
0.024
0.000
0.138
0.019
0.001
0.120
0.002
0.665
0.002
0.016
0.000
0.160
0.017
0.004
0.089
0.010
0.000
0.141
0.021
0.000
0.151
0.029
0.000
0.168
0.025
0.000
0.129
0.061
0.001
0.114
0.034
0.119
0.027
0.034
0.003
0.099
0.037
0.000
0.177
0.012
0.054
0.042
0.005
0.526
0.005
0.017
0.000
0.140
0.010
0.154
0.023
0.026
0.000
0.168
0.020
0.001
0.127
0.003
0.525
0.005
0.015
0.000
0.146
0.020
0.001
0.117
0.010
0.000
0.133
0.023
0.000
0.178
0.030
0.000
0.176
0.027
0.000
0.150
0.071
0.000
0.143
0.045
0.038
0.049
0.038
0.001
0.128
0.037
0.000
0.177
0.010
0.093
0.032
-0.006
0.466
0.006
0.019
0.000
0.158
0.009
0.163
0.022
0.026
0.000
0.165
0.021
0.001
0.130
0.003
0.630
0.003
0.014
0.001
0.117
0.023
0.000
0.159
0.010
0.000
0.136
0.024
0.000
0.190
0.029
0.000
0.168
0.029
0.000
0.165
CE(・) is the expected equity premium of industries used as an independent variable with lead and lags and
dependent variables and dependent variable is GDP growth rate over the previous quarter. The observation
period is from first quarter of 1980 through second quarter of 2003.
30
Table V: Lead and Lag Relationship between the Growth Rates of
Consumption per Capita and the Equity Premium of Industries
CE(t-4) CE(t-3) CE(t-2) CE(t-1)
0.010
0.010
0.011
0.007
0.005
0.002
0.077
0.081
0.097
0.010
0.011
0.012
0.034
0.012
0.006
0.048
0.067
0.078
0.011
0.011
0.012
0.005
0.004
0.002
0.082
0.087
0.103
0.041
0.046
0.047
0.006
0.002
0.002
0.078
0.097
0.101
0.045
0.046
0.048
0.006
0.003
0.001
0.080
0.092
0.108
-0.010 -0.010 -0.008
0.279
0.276
0.360
0.013
0.013
0.009
0.026
0.028
0.031
0.015
0.008
0.004
0.063
0.074
0.088
0.010
0.016
0.017
0.689
0.545
0.518
0.002
0.004
0.005
0.024
0.025
0.030
0.015
0.010
0.002
0.063
0.070
0.100
0.040
0.042
0.046
0.010
0.006
0.003
0.069
0.079
0.094
0.030
0.030
0.032
0.018
0.016
0.007
0.059
0.061
0.076
0.012
0.012
0.014
0.038
0.035
0.017
0.046
0.048
0.061
0.014
0.014
0.016
0.016
0.016
0.005
0.062
0.062
0.081
0.017
0.020
0.024
0.127
0.056
0.023
0.025
0.039
0.055
0.048
0.050
0.055
0.041
0.032
0.018
0.044
0.049
0.059
-0.040 -0.026 -0.024
0.147
0.355
0.410
0.023
0.009
0.007
0.010
0.011
0.014
0.154
0.113
0.032
0.022
0.027
0.049
0.010
Coef.
0.007
p-value
R-squared 0.077
0.010
Mining
Coef.
0.034
p-value
R-squared 0.048
Construction
0.011
Coef.
0.008
p-value
R-squared 0.074
Foods
0.041
Coef.
0.007
p-value
R-squared 0.077
Textiles & Apparels
0.047
Coef.
0.006
p-value
R-squared 0.078
Pulp & Paper
-0.012
Coef.
0.206
p-value
R-squared 0.017
0.026
Chemicals
Coef.
0.017
p-value
R-squared 0.061
Pharmaceutical
0.020
Coef.
0.453
p-value
R-squared 0.006
Oil & Coal Products
0.023
Coef.
0.023
p-value
R-squared 0.055
Rubber Products
0.037
Coef.
0.018
p-value
R-squared 0.059
Glass & Ceramics Products Coef.
0.027
0.040
p-value
R-squared 0.045
Iron & Steel
0.013
Coef.
0.028
p-value
R-squared 0.051
Nonferrous Metals
0.015
Coef.
0.015
p-value
R-squared 0.062
Metal Products
0.014
Coef.
0.216
p-value
R-squared 0.017
Machinery
0.051
Coef.
0.029
p-value
R-squared 0.051
Electric Appliances
-0.042
Coef.
0.120
p-value
R-squared 0.026
Transportation Equipment Coef.
0.011
0.107
p-value
R-squared 0.028
Fishery & Agriculture
31
CE(t) CE(t+1) CE(t+2) CE(t+3) CE(t+4)
0.011
0.011
0.012
0.012
0.011
0.002
0.003
0.001
0.002
0.002
0.097
0.094
0.114
0.106
0.101
0.012
0.012
0.013
0.013
0.014
0.011
0.008
0.004
0.005
0.003
0.069
0.077
0.089
0.087
0.095
0.012
0.012
0.012
0.012
0.012
0.001
0.002
0.001
0.001
0.003
0.108
0.105
0.113
0.109
0.098
0.048
0.048
0.050
0.047
0.045
0.001
0.002
0.001
0.003
0.004
0.106
0.105
0.114
0.098
0.091
0.046
0.047
0.047
0.043
0.044
0.002
0.002
0.001
0.004
0.003
0.099
0.106
0.108
0.091
0.095
-0.010 -0.009 -0.006 -0.010 -0.013
0.272
0.329
0.504
0.274
0.143
0.013
0.011
0.005
0.014
0.024
0.031
0.034
0.033
0.032
0.032
0.005
0.002
0.003
0.005
0.006
0.084
0.103
0.094
0.087
0.085
0.020
0.027
0.029
0.020
0.025
0.459
0.323
0.297
0.483
0.383
0.006
0.011
0.012
0.006
0.009
0.029
0.028
0.030
0.032
0.030
0.004
0.006
0.003
0.002
0.004
0.088
0.082
0.094
0.106
0.092
0.046
0.049
0.048
0.047
0.045
0.002
0.001
0.002
0.002
0.003
0.096
0.110
0.103
0.101
0.094
0.031
0.031
0.034
0.032
0.034
0.010
0.011
0.006
0.008
0.006
0.072
0.070
0.082
0.076
0.085
0.013
0.015
0.017
0.016
0.015
0.030
0.015
0.005
0.010
0.011
0.051
0.064
0.087
0.073
0.072
0.017
0.018
0.018
0.018
0.017
0.004
0.002
0.002
0.003
0.005
0.088
0.098
0.099
0.097
0.088
0.024
0.024
0.029
0.025
0.026
0.021
0.022
0.006
0.019
0.014
0.057
0.057
0.082
0.061
0.068
0.058
0.065
0.068
0.070
0.071
0.015
0.007
0.005
0.004
0.003
0.063
0.079
0.086
0.092
0.096
-0.015 -0.004 -0.010 -0.008
0.003
0.611
0.908
0.737
0.789
0.910
0.003
0.000
0.001
0.001
0.000
0.013
0.015
0.017
0.017
0.016
0.047
0.024
0.012
0.013
0.018
0.043
0.055
0.068
0.067
0.063
(continued)
Coef.
p-value
R-squared
Other Products
Coef.
p-value
R-squared
Electric Power & Gas
Coef.
p-value
R-squared
Land Transportation
Coef.
p-value
R-squared
Marine Transportation
Coef.
p-value
R-squared
Air Transportation
Coef.
p-value
R-squared
Warehousing
Coef.
p-value
R-squared
Communication
Coef.
p-value
R-squared
Wholesale Trade
Coef.
p-value
R-squared
Retail Trade
Coef.
p-value
R-squared
Banks
Coef.
p-value
R-squared
Securities
Coef.
p-value
R-squared
Insurance
Coef.
p-value
R-squared
Other Financing Business Coef.
p-value
R-squared
Real Estate
Coef.
p-value
R-squared
Services
Coef.
p-value
R-squared
VW
Coef.
p-value
R-squared
Precision Instruments
CE(t-4) CE(t-3) CE(t-2) CE(t-1)
0.044
0.030
0.050
0.006
0.801
0.001
0.023
0.094
0.030
0.033
0.003
0.094
-0.002
0.758
0.001
0.101
0.021
0.056
0.016
0.013
0.065
0.014
0.062
0.037
0.017
0.035
0.047
0.012
0.047
0.042
-0.004
0.584
0.003
0.013
0.008
0.075
0.017
0.042
0.044
0.010
0.004
0.086
0.017
0.025
0.054
0.020
0.018
0.060
0.019
0.025
0.054
0.047
0.021
0.056
0.012
0.605
0.003
0.027
0.044
0.043
0.033
0.002
0.100
-0.001
0.905
0.000
0.001
0.936
0.000
0.016
0.009
0.071
0.013
0.081
0.033
0.017
0.028
0.051
0.013
0.033
0.049
-0.005
0.411
0.007
0.013
0.007
0.076
0.016
0.038
0.046
0.010
0.003
0.094
0.019
0.009
0.072
0.021
0.011
0.068
0.020
0.019
0.058
0.052
0.011
0.068
0.021
0.343
0.010
0.027
0.041
0.045
0.032
0.002
0.095
0.001
0.934
0.000
-0.003
0.725
0.001
0.015
0.008
0.074
0.011
0.145
0.023
0.018
0.020
0.057
0.014
0.022
0.056
-0.006
0.355
0.009
0.013
0.004
0.085
0.015
0.038
0.046
0.011
0.001
0.109
0.019
0.006
0.078
0.022
0.007
0.077
0.021
0.015
0.063
0.051
0.013
0.065
0.031
0.168
0.021
0.028
0.029
0.051
0.034
0.001
0.110
0.005
0.501
0.005
-0.003
0.752
0.001
0.016
0.003
0.089
0.010
0.181
0.019
0.021
0.007
0.077
0.015
0.015
0.063
-0.001
0.879
0.000
0.015
0.002
0.103
0.017
0.016
0.061
0.011
0.001
0.107
0.022
0.001
0.115
0.025
0.002
0.099
0.024
0.005
0.084
CE(t)
0.050
0.016
0.062
0.040
0.086
0.032
0.030
0.021
0.057
0.033
0.002
0.103
0.005
0.449
0.006
-0.004
0.607
0.003
0.015
0.006
0.079
0.009
0.237
0.015
0.020
0.008
0.074
0.016
0.015
0.064
0.001
0.845
0.000
0.014
0.002
0.097
0.016
0.023
0.056
0.011
0.001
0.106
0.021
0.002
0.105
0.024
0.003
0.091
0.024
0.004
0.087
CE(t+1) CE(t+2) CE(t+3) CE(t+4)
0.056
0.008
0.075
0.051
0.032
0.050
0.029
0.025
0.055
0.032
0.003
0.095
0.005
0.484
0.005
-0.001
0.892
0.000
0.015
0.007
0.079
0.009
0.267
0.014
0.021
0.006
0.081
0.017
0.010
0.071
0.000
0.983
0.000
0.014
0.004
0.091
0.015
0.033
0.049
0.011
0.001
0.108
0.020
0.003
0.097
0.025
0.003
0.096
0.025
0.003
0.092
0.055
0.012
0.069
0.048
0.048
0.043
0.027
0.042
0.046
0.033
0.002
0.102
0.008
0.268
0.014
0.003
0.758
0.001
0.016
0.006
0.083
0.008
0.278
0.013
0.023
0.003
0.093
0.018
0.007
0.080
0.002
0.753
0.001
0.015
0.002
0.102
0.015
0.035
0.049
0.010
0.002
0.100
0.020
0.003
0.097
0.026
0.002
0.104
0.026
0.002
0.100
0.052
0.021
0.059
0.046
0.068
0.037
0.028
0.037
0.049
0.032
0.003
0.095
0.009
0.218
0.017
0.000
0.983
0.000
0.015
0.008
0.076
0.008
0.332
0.011
0.023
0.003
0.096
0.019
0.007
0.079
0.002
0.767
0.001
0.013
0.008
0.078
0.015
0.037
0.048
0.010
0.004
0.089
0.019
0.004
0.089
0.026
0.002
0.099
0.026
0.003
0.096
0.059
0.011
0.073
0.051
0.045
0.045
0.027
0.044
0.046
0.033
0.003
0.098
0.006
0.386
0.009
-0.002
0.818
0.001
0.015
0.007
0.080
0.007
0.346
0.010
0.022
0.005
0.087
0.019
0.007
0.079
-0.001
0.864
0.000
0.012
0.015
0.066
0.015
0.037
0.049
0.010
0.004
0.090
0.018
0.006
0.084
0.026
0.003
0.098
0.025
0.004
0.093
CE(・) is the expected equity premium of industries used as an independent variable with lead and lags and
dependent variables and dependent variable is per capita real consumption growth rate over the previous quarter.
The observation period is from first quarter of 1980 through second quarter of 2003.
32
Table VI: Relationship between the Cyclical Components of Production and GDP and
Lagged Industry Equity Premium
Cycle of Production Index(λ=6400)
Cycle Components of GDP（λ=1600)
CE(t-12)CE(t-9) CE(t-6) CE(t-3) CE(t) CE(t-4) CE(t-3) CE(t-2) CE(t-1) CE(t)
Fishery & Agriculture
Coef.
3.71
4.03
3.74
3.16
2.77
7.65
6.55
6.13
4.83
3.37
p-value
0.14
0.11
0.13
0.20
0.26
0.13
0.19
0.22
0.33
0.50
R-squar 0.01
0.01
0.01
0.01
0.00
0.02
0.02
0.02
0.01
0.00
Mining
Coef.
2.67
4.37
4.95
5.18
5.23 12.69 13.10 13.32 12.12 10.47
p-value
0.38
0.14
0.09
0.07
0.07
0.04
0.03
0.02
0.04
0.08
R-squar 0.00
0.01
0.01
0.01
0.01
0.05
0.05
0.05
0.05
0.03
Construction
Coef.
4.67
3.15
1.43
0.57 -0.23 11.33
9.25
7.30
5.44
4.20
p-value
0.07
0.22
0.57
0.82
0.93
0.03
0.07
0.15
0.28
0.41
R-squar 0.01
0.01
0.00
0.00
0.00
0.05
0.03
0.02
0.01
0.01
Foods
Coef.
-1.99
4.39 10.23 10.22
9.77 15.78 20.79 26.45 26.53 24.35
p-value
0.84
0.65
0.28
0.28
0.30
0.43
0.30
0.19
0.19
0.23
R-squar 0.00
0.00
0.00
0.00
0.00
0.01
0.01
0.02
0.02
0.02
Textiles & Apparels
Coef.
6.39
6.80
8.73 14.29 20.02 34.56 29.61 25.98 20.96 18.97
p-value
0.56
0.51
0.38
0.14
0.04
0.13
0.17
0.21
0.29
0.34
R-squar 0.00
0.00
0.00
0.01
0.01
0.02
0.02
0.02
0.01
0.01
Pulp & Paper
Coef.
-2.17 -10.37 -14.95 -11.84
1.74 -9.44 -17.77 -21.36 -18.65 -11.67
p-value
0.72
0.07
0.01
0.03
0.75
0.46
0.15
0.07
0.10
0.31
R-squar 0.00
0.01
0.02
0.02
0.00
0.01
0.02
0.03
0.03
0.01
Chemicals
Coef.
9.67
8.78
7.96
7.69
8.74 25.60 22.50 18.58 13.11
8.13
p-value
0.16
0.20
0.24
0.25
0.19
0.07
0.11
0.18
0.35
0.57
R-squar 0.01
0.01
0.00
0.00
0.01
0.04
0.03
0.02
0.01
0.00
Pharmaceutical
Coef.
20.21 14.22
5.02 -1.68 -2.05 -37.30 -38.20 -38.57 -41.07 -43.66
p-value
0.22
0.38
0.76
0.92
0.90
0.27
0.26
0.26
0.23
0.21
R-squar 0.01
0.00
0.00
0.00
0.00
0.01
0.01
0.01
0.02
0.02
Oil & Coal Products
Coef.
4.70
2.43
1.55
6.55
3.73 32.48 23.16 18.11 15.49 13.46
p-value
0.48
0.71
0.81
0.29
0.54
0.01
0.08
0.16
0.23
0.30
R-squar 0.00
0.00
0.00
0.00
0.00
0.06
0.03
0.02
0.02
0.01
Rubber Products
Coef. -10.51 -11.07
-8.47
0.64 15.87 27.47 28.96 32.35 35.57 39.67
p-value
0.31
0.28
0.40
0.95
0.11
0.18
0.15
0.11
0.08
0.05
R-squar 0.00
0.00
0.00
0.00
0.01
0.02
0.02
0.03
0.03
0.04
Glass & Ceramics ProductCoef.
7.48
1.66 -3.71 -4.76 -0.44 29.72 22.26 18.61 17.21 18.66
p-value
0.38
0.84
0.64
0.54
0.95
0.08
0.19
0.26
0.28
0.25
R-squar 0.00
0.00
0.00
0.00
0.00
0.03
0.02
0.01
0.01
0.01
Iron & Steel
Coef.
5.56
4.84
2.43
0.59
4.92 15.51 16.62 17.11 16.21 14.25
p-value
0.16
0.22
0.53
0.87
0.18
0.05
0.03
0.03
0.04
0.07
R-squar 0.01
0.00
0.00
0.00
0.01
0.04
0.05
0.05
0.05
0.04
Nonferrous Metals
Coef.
2.82
2.72
2.30
4.00
6.22
4.62
4.93
5.20
5.05
4.97
p-value
0.48
0.49
0.55
0.29
0.10
0.56
0.53
0.50
0.51
0.52
R-squar 0.00
0.00
0.00
0.00
0.01
0.00
0.00
0.00
0.00
0.00
Metal Products
Coef.
16.37 15.28
8.86
5.21
0.15 54.78 49.78 43.60 33.02 25.02
p-value
0.02
0.03
0.19
0.43
0.98
0.00
0.00
0.00
0.01
0.07
R-squar 0.02
0.02
0.01
0.00
0.00
0.15
0.13
0.10
0.06
0.04
Machinery
Coef.
52.91 40.49 15.62 -9.33 -25.73 49.79 41.49 28.99 11.83
1.19
p-value
0.00
0.01
0.30
0.54
0.09
0.10
0.18
0.35
0.70
0.97
R-squar 0.04
0.02
0.00
0.00
0.01
0.03
0.02
0.01
0.00
0.00
Electric Appliances
Coef.
4.74 -2.78 -2.87 -3.55 -0.35 60.09 59.71 59.56 60.53 74.22
p-value
0.76
0.85
0.85
0.81
0.98
0.08
0.09
0.09
0.10
0.05
R-squar 0.00
0.00
0.00
0.00
0.00
0.03
0.03
0.03
0.03
0.04
Transportation EquipmentCoef.
1.06
0.45 -0.94 -1.99 -0.25 13.84 11.76 11.43 11.05
9.75
p-value
0.81
0.92
0.83
0.64
0.95
0.12
0.19
0.20
0.21
0.27
R-squar 0.00
0.00
0.00
0.00
0.00
0.03
0.02
0.02
0.02
0.01
33
(continued)
Cycle of Production Index(λ=6400)
Cycle Components of GDP（λ=1600)
CE(t-12)CE(t-9) CE(t-6) CE(t-3) CE(t) CE(t-4) CE(t-3) CE(t-2) CE(t-1) CE(t)
Precision Instruments Coef.
8.22
5.17
0.34 -2.79
2.85 32.84 31.62 32.10 31.17 32.99
p-value
0.49
0.66
0.98
0.81
0.80
0.21
0.23
0.23
0.25
0.23
R-square 0.00
0.00
0.00
0.00
0.00
0.02
0.02
0.02
0.01
0.02
Other Products
Coef.
30.94 18.82
8.96
4.83
0.79 89.79 98.80 91.74 75.69 65.74
p-value
0.01
0.12
0.45
0.68
0.95
0.00
0.00
0.00
0.01
0.03
R-square 0.02
0.01
0.00
0.00
0.00
0.10
0.12
0.11
0.07
0.05
Electric Power & Gas Coef.
9.19 -0.94 -10.46 -16.97 -14.12 24.85 11.62
2.03 -2.28
0.50
p-value
0.29
0.91
0.21
0.04
0.08
0.17
0.51
0.91
0.89
0.98
R-square 0.00
0.00
0.01
0.01
0.01
0.02
0.00
0.00
0.00
0.00
Land Transportation Coef.
3.43
3.04
2.80
3.72
4.94 18.99 15.39 12.81 11.78 12.74
p-value
0.64
0.67
0.69
0.59
0.47
0.19
0.29
0.37
0.40
0.37
R-square 0.00
0.00
0.00
0.00
0.00
0.02
0.01
0.01
0.01
0.01
Marine TransportationCoef.
-2.50 -2.55 -1.88 -0.72
0.80 18.66 17.96 18.31 18.77 17.25
p-value
0.53
0.52
0.64
0.86
0.84
0.03
0.04
0.04
0.03
0.05
R-square 0.00
0.00
0.00
0.00
0.00
0.05
0.05
0.05
0.05
0.04
Air Transportation
Coef.
10.05
8.58
3.03 -6.17
3.41 53.25 19.93 11.94 10.45
6.25
p-value
0.21
0.11
0.51
0.16
0.43
0.35
0.35
0.32
0.35
0.58
R-square 0.01
0.01
0.00
0.01
0.00
0.01
0.01
0.01
0.01
0.00
Warehousing
Coef.
2.37
0.17 -1.34 -1.85 -0.07
6.94
3.58
2.00
0.80
0.83
p-value
0.56
0.97
0.72
0.62
0.98
0.41
0.66
0.80
0.92
0.91
R-square 0.00
0.00
0.00
0.00
0.00
0.01
0.00
0.00
0.00
0.00
Communication
Coef.
3.50
2.36
2.19
2.57
4.26 -16.76 -17.92 -17.98 -16.49 -13.98
p-value
0.47
0.62
0.65
0.59
0.37
0.09
0.07
0.07
0.10
0.16
R-square 0.00
0.00
0.00
0.00
0.00
0.03
0.04
0.04
0.03
0.02
Wholesale Trade
Coef.
-1.86 -3.54 -4.33 -2.41
2.38 14.27 12.95 12.37 13.47 14.49
p-value
0.72
0.48
0.38
0.62
0.63
0.17
0.20
0.22
0.18
0.15
R-square 0.00
0.00
0.00
0.00
0.00
0.02
0.02
0.02
0.02
0.02
Retail Trade
Coef.
1.72
0.72
0.01 -0.25 -0.33 10.52 10.72 11.28 11.52 11.95
p-value
0.63
0.84
1.00
0.94
0.93
0.18
0.18
0.16
0.16
0.15
R-square 0.00
0.00
0.00
0.00
0.00
0.02
0.02
0.02
0.02
0.02
Banks
Coef.
-10.29 -15.94 -12.29 -3.52
3.81 -2.05 -3.20 -0.06
7.77 13.20
p-value
0.01
0.00
0.00
0.37
0.33
0.81
0.70
0.99
0.35
0.11
R-square 0.02
0.05
0.03
0.00
0.00
0.00
0.00
0.00
0.01
0.03
Securities
Coef.
7.38
7.66
7.38
7.44
5.98 11.00 10.30
8.60
5.65
2.76
p-value
0.02
0.01
0.01
0.01
0.04
0.08
0.10
0.16
0.36
0.66
R-square 0.02
0.02
0.02
0.02
0.01
0.03
0.03
0.02
0.01
0.00
Insurance
Coef.
-2.31 -3.44 -1.39
4.82
0.77
8.86
7.16
7.64 10.86 13.71
p-value
0.64
0.44
0.74
0.23
0.85
0.42
0.47
0.41
0.23
0.14
R-square 0.00
0.00
0.00
0.00
0.00
0.01
0.01
0.01
0.02
0.02
Other Fi ncing BusineCoef.
2.66
1.89
1.08
0.26 -0.08
5.26
4.68
3.91
2.64
1.57
p-value
0.23
0.39
0.62
0.91
0.97
0.24
0.29
0.38
0.55
0.72
R-square 0.00
0.00
0.00
0.00
0.00
0.01
0.01
0.01
0.00
0.00
Real Estate
Coef.
3.98
4.11
2.99
4.56
6.82 17.86 17.07 14.46 11.36 10.48
p-value
0.40
0.37
0.49
0.28
0.10
0.06
0.07
0.11
0.19
0.23
R-square 0.00
0.00
0.00
0.00
0.01
0.04
0.04
0.03
0.02
0.02
Services
Coef.
5.88
6.15
5.07
4.43
4.53 25.83 24.37 21.83 18.15 14.72
p-value
0.26
0.23
0.32
0.38
0.36
0.02
0.02
0.04
0.09
0.18
R-square 0.00
0.00
0.00
0.00
0.00
0.06
0.05
0.04
0.03
0.02
VW
Coef.
2.16 -2.10 -4.86 -4.07
0.17 13.91 11.21
9.94 10.22 11.82
p-value
0.70
0.70
0.37
0.45
0.97
0.22
0.32
0.37
0.36
0.29
R-square 0.00
0.00
0.00
0.00
0.00
0.02
0.01
0.01
0.01
0.01
34
CE(・) is the expected equity premium of industries used as an independent variable with lags and dependent
variables are cyclical components of monthly production index and quarterly GDP. The monthly data covers
from January 1980 through December 2003 and the quarterly data covers from first quarter of 1980 through
second quarter of 2003.
35
Table VII: Sector Wise Estimates of Fama and French Model and the Relationship
between the Cyclical Components of Output and Lagged Equity Premium
(a) Factor Loadings of Sectors aggregated from Individual Estimates
β
0.899
1.019
0.949
0.712
0.994
0.861
0.986
0.990
Consumption Goods
Investment Goods
Commerce
Finance
Transportation
Utility
Real Estate
VW
βM
0.935
1.119
1.047
0.753
1.074
0.911
1.020
1.011
βSMB βHML
0.631
0.428
0.887
0.645
0.730
0.766
0.538
0.312
0.845
0.505
0.534
0.365
0.820
0.302
0.676
0.288
(b) The Business Cycle Predictive Power of
Consumption Goods
Investment Goods
Commerce
Finance
Transportation
Utility
Real Estate
VW
CE(t-12) CE(t-9)
4.589
0.618
0.001
1.024
0.760
0.000
-0.061
0.986
0.000
-9.561
0.064
0.011
-2.745
0.604
0.001
-4.942
0.509
0.001
-0.480
0.877
0.000
-1.089
0.819
0.000
Coef.
12.607
p-value
0.178
R-squared 0.006
Coef.
2.219
p-value
0.516
R-squared 0.001
Coef.
1.033
p-value
0.774
R-squared 0.000
Coef.
-4.473
p-value
0.391
R-squared 0.002
Coef.
-2.004
p-value
0.712
R-squared 0.000
Coef.
3.688
p-value
0.630
R-squared 0.001
Coef.
0.742
p-value
0.817
R-squared 0.000
Coef.
2.059
p-value
0.671
R-squared 0.001
γM
γ 0SMB γ 1SMB γ 0HML γ 1HML
0.899
0.651
0.015
0.272 -0.576
1.074
0.921 -0.208
0.415 -0.759
1.015
0.768 -0.157
0.589 -0.487
0.744
0.550 -0.037
0.246 -0.275
1.028
0.891 -0.315
0.366 -0.450
0.900
0.559
0.200
0.288 -0.742
1.010
0.844 -0.217
0.242 -0.313
0.996
0.689 -0.214
0.224 -0.339
Sector Equity Premium
CE(t-6)
-2.137
0.813
0.000
-0.310
0.925
0.000
-0.709
0.840
0.000
-8.395
0.102
0.009
-1.803
0.727
0.000
-12.341
0.093
0.009
-1.716
0.570
0.001
-3.203
0.493
0.002
CE(t-3) CE(t) CE(t-4) CE(t-3)
-4.829 -1.731 45.387 40.589
0.589 0.845 0.018 0.034
0.001 0.000 0.059 0.047
-0.471 0.654 9.406 7.977
0.885 0.840 0.169 0.236
0.000 0.000 0.020 0.015
-0.066 2.663 4.000 5.237
0.985 0.439 0.599 0.492
0.000 0.002 0.003 0.005
-1.856 6.851 5.134 2.999
0.717 0.177 0.624 0.774
0.000 0.006 0.003 0.001
0.667 4.511 13.650 12.595
0.896 0.373 0.210 0.238
0.000 0.003 0.017 0.015
-16.301 -12.559 17.809 7.498
0.024 0.081 0.254 0.626
0.016 0.010 0.014 0.003
-1.358 0.501 3.489 2.515
0.648 0.865 0.589 0.692
0.001 0.000 0.003 0.002
-2.556 1.241 13.334 11.134
0.580 0.787 0.175 0.252
0.001 0.000 0.020 0.014
CE(t-2)
34.251
0.072
0.034
7.039
0.289
0.012
7.356
0.337
0.010
4.876
0.640
0.002
12.429
0.235
0.015
0.262
0.986
0.000
1.177
0.850
0.000
10.054
0.296
0.012
CE(t-1)
26.393
0.165
0.021
6.086
0.355
0.009
9.723
0.207
0.017
10.611
0.308
0.011
12.325
0.232
0.015
-2.195
0.884
0.000
0.948
0.876
0.000
9.921
0.299
0.012
CE(t)
25.261
0.188
0.019
5.553
0.401
0.008
13.154
0.095
0.030
14.144
0.176
0.020
12.731
0.220
0.016
1.446
0.924
0.000
1.423
0.815
0.001
10.937
0.255
0.014
CE(・) is the expected equity premium of sectors used as an independent variable with lags and dependent
variables are cyclical components of monthly production index and quarterly GDP. The monthly data covers
from January 1980 through December 2003 and the quarterly data covers from first quarter of 1980 through
second quarter of 2003.
36
Cyclical Components of Production Index
4.0
-0.05
4.2
0.0
4.4
0.05
4.6
Trend Components of Production Index
1980
1985
1990
1995
2000
2005
1975
1980
1985
1990
1995
2000
Year
Year
Trend Components of GDP
Cyclical Components of GDP
2005
12.7
-0.02
12.9
0.0
0.01
13.1
1975
1980
1985
1990
1995
2000
1980
Year
1985
1990
1995
2000
Year
Figure 1: The Trends and Cyclical Components of Production Index and GDP in Japan
Production Index is for the period of January 1980 to December 2003 and GDP is for the period of First
Quarter 1980 to Second Quarter 2003. Applied
λ values are 6400 and 1400, respectively. Both series are
seasonally adjusted real values.
37
10
6
2
4
Equity Premium (in %)
8
Consum ption G oods
Investm ent G oo ds
Com m erce
Finance
Transp ortation
Utility
Real Estate
1980
1985
1990
1995
2000
Year
Figure 2: Time Series Pattern of Sector-wise Equity Premium
The samples are all listed firms in the First Section of the Tokyo Stock Exchange. The number of the firms is
1,475 and the estimation period is from September 1977 through December 2003. We use conditional Fama and
French three-factor models to estimate the expected excess returns with monthly data. We formed seven
sector-wise expected premiums; consumption goods, investment goods, commerce, finance, transportation,
utility, and real estates. The classification definition is as explained in Section VI a. in the main text of the paper.
The individual loading estimates are aggregated for each sector using value-weighting with the data as of end of
December 2003.
38
0
-5
-15
-10
Regression Coefficients
5
10
C o n s u m p t io n G o o d s
In v e s t m e n t G o o d s
C o m m e rc e
F in a n c e
T ra n s p o r t a t io n
U t ilit y
R e a l E s t a te
-12
-10
-8
-6
-4
-2
0
Lags
Figure 3: The Regression Coefficients of Future Production on Sector-wise Equity Premium
The expected equity premiums of seven sectors are used as independent variables with lags and dependent
variable is cyclical component of monthly production index and quarterly GDP. The monthly data covers from
January 1980 through December 2003 and the quarterly data covers from first quarter of 1980 through second
quarter of 2003.
39
30
20
0
10
Regression Coefficients
40
Consumption Goods
Investment Goods
Commerce
Finance
Transportation
Utility
Real Estate
-4
-3
-2
-1
0
Lags
Figure 4: The Regression Coefficients of Future GDP on Sector-wise Equity Premium
The expected equity premiums of seven sectors are used as independent variables with lags and dependent
variable is cyclical component of quarterly GDP. The quarterly data covers from first quarter of 1980 through
second quarter of 2003.
40