Modern Economy, 2011, 2, 701-705
doi:10.4236/me.2011.24078 Published Online September 2011 (http://www.SciRP.org/journal/me)
Exploring the Priced Factors in ICAPM in Japan
Chikashi Tsuji
Graduate School of Systems and Information Engineering, University of Tsukuba, Ibaraki, Japan
Received May 7, 2011; revised July 1, 2011; accepted July 10, 2011
Abstract
This paper investigates the priced factors in the Intertemporal Capital Asset Pricing Model (ICAPM) in the
Tokyo Stock Exchange (TSE) in Japan. Focusing on the time-varying covariance risks derived by the multi-
variate Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model, we find new priced
state variables in Japan. That is, our empirical tests reveal that in the TSE, the time-varying covariance be-
tween market return and illiquidity measure and that between market return and the log change of the sea-
sonally adjusted industrial production are statistically significantly priced state variables in the ICAPM.
Keywords: EGARCH-in-Mean Model, GARCH Model, GARCH-in-Mean Model, ICAPM, Multivariate
GARCH Model
1. Introduction
Merton [1] developed the Intertemporal Capital Asset
Pricing Model (ICAPM). ICAPM is a linear factor mo-
del with wealth and state variable that forecast changes
in the distribution of future stock returns. Several stu-
dies such as [2], [3], [4], [5] and [6] tested this model in
the US. However, in Japan, the pricing test of this
ICAPM has little been conducted. Hence, our objective
is to investigate the priced state variables in Merton’s
ICAPM in the Tokyo Stock Exchange (TSE).
This paper’s novel characteristics are as follows. First,
although we examine the ICAPM employing the similar
approach of Lundblad [7], we focus on the covariance
risks instead of volatility risk as in [7].
Second, we clarify new priced time-varying covari-
ance risks that are related to illiquidity measure and in-
dustrial production. This is our most significant contribu-
tion in this paper.
The rest of the paper is organized as follows. Section 2
concretely describes Merton’s ICAPM, Section 3 ex-
plains the data, Section 4 presents the empirical results,
and Section 5 summarizes the paper.
2. Theory and Research Design
Lundblad [7] concretely documents Merton’s ICAPM as
follows:
2
,,, ,
,
WW WF
tMt ftMtMFt
WW
JW J
Er rJJ

 
  



(1)
where rM,t is the market return, rf,t denotes the risk-free
rate, σ2
M,t denotes the variance of market return, σMF,t is
the covariance between market return and other state
variable. In addition, [−JWWW/JW] denotes the investors’
risk aversion, and [−JWF/JW] is the coefficient that adjusts
market risk premium in response to the changes of σMF,t.
Further, J(W(t), F(t), t) is the utility function which is
related to investors’ wealth, W(t), and state variable, F(t).
(The subscripts of W and/or F mean partial differentia-
tions by them.)
More concisely, for our empirical tests, we can write
the ICAPM simpler as follows:
2
,, , ,.
M
tftMMtCMFtt
rr

 

 (2)
To focus on the covariance risks, we first examine the
following model (3):
,, ,,
M
tft CMFtt
rr



 (3)
where the conditional variance of market return follows
GARCH (1, 1) model ([8]) as the following model (4):
22
,0112,1
.
MttMt

2


  (4)
We next examine the ICAPM more rigorously by in-
cluding the variance of market return as model (2), and
where the conditional variance of market return follows
Generalized Autoregressive Conditional Heteroskedas-
ticity (GARCH) (1, 1) model (4) or Exponential GARCH
(EGARCH) (1, 1) model ([9]) (5). That is, we estimate
model (2) as GARCH-in-mean model or EGARCH-in-
mean model.

C. TSUJI 702
 
22 11
,0123 ,1
,1 ,1
ln ln
tt
Mt Mt
Mt Mt

 

 



  





(5)
For calculating the time-varying covariance risks in-
cluded in models (2) and (3), we use the multivariate
GARCH model ([10,11]).
3. Data
The full sample period of our data is from April 1985 to
December 2009. We first compute the market risk pre-
mium: rM,t − rf,t. Where rM,t is the market return, which is
calculated using Tokyo Stock Price Index (TOPIX)
(from TSE), and rf,t is the rates of the one-month nego-
tiable Certificate of Deposit (CD) (from Bank of Japan
(BOJ)).
We also construct the following five covariance vari-
ables, CILLIQ, CDDY, CDEF, CDTERM, and CLCIP
by using ILLIQ, DDY, DEF, DTERM, and LCIP, re-
spectively. Where ILLIQ denotes the absolute value of
return of the TSE First Section stocks (from TSE) di-
vided by the total trading volume of the TSE First Sec-
tion stocks (from TSE), DDY is the first difference of the
dividend yield of the TSE First Section stocks (from
TSE), DEF denotes the default spread between the yields
of the long-term Nikkei Bond Index (from Nikkei, Inc.)
and 10-year government bonds (from Quick Corp.), and
DTERM means the first difference of the yield spread
between the yields of 10-year government bonds (from
Quick Corp.) and the one-month CD rates (from BOJ).
Finally, LCIP is the log change of the seasonally ad-
justed industrial production (from Ministry of Economy,
Trade and Industry). We then compute the above five
variables, CILLIQ, CDDY, CDEF, CDTERM, and CLCIP,
which are the covariances between market return rM,t and
ILLIQ, DDY, DEF, DTERM, and LCIP, respectively.
Again, these time-varying covariance risks are from the
multivariate GARCH model.
4. Empirical Results
This section describes the characteristics of our data and
empirical results for the ICAPM pricing in Japan. First,
Table 1 exhibits the descriptive statistics of five vari-
ables, ILLIQ, DDY, DEF, DTERM, and LCIP. Table 1
shows that all variables are generally slightly positively
skewed and possess excess kurtosis in comparison with
the normal distribution. DDY and DTERM are the first
differences of the raw variables because they have unit
roots in the augmented Dickey-Fuller (ADF) tests. Table
2 displays the correlation coefficients among the above
five variables. This table shows that the five variables are
little correlated each other.
The empirical results of ICAPM pricing in Japan are
exhibited in Tables 3 to 5. Table 3 reports the results of
our base tests by using model (3) and the GARCH (1, 1)
model (4). As described, market risk premium equation
(3) includes the covariance variables derived by the mul-
tivariate GARCH model. Table 3 indicates that CILLIQ
(time-varying covariance between market return and the
illiquidity measure) and CLCIP (time-varying covariance
between market return and the log change of the season-
ally adjusted industrial production) are statistically sig-
nificantly priced in ICAPM in the TSE.
Further, we implement two kinds of robustness checks.
First, Table 4 exhibits the results of ICAPM pricing by
using the GARCH-in-mean model. That is, we here in-
corporate both variance and covariance risks derived by
the multivariate GARCH model into ICAPM as shown in
(2), and where market return variance follows the
GARCH (1, 1) model (4). Table 4 again indicates that
CILLIQ and CLCIP are statistically significantly priced
in ICAPM in Japan.
Finally, we further perform the robustness checks by
using the EGARCH-in-mean model. Namely, again we
include both variance and covariance risks from the mul-
tivariate GARCH model in ICAPM (2), and where mar-
ket return variance follows the EGARCH (1, 1) model
(5). Table 5 again exhibits that CILLIQ and CLCIP are
Table 1. Descriptive statistics of state variables.
Results of April 1985 to December 2009
ILLIQ DDY DEF DTERM LCIP
Mean 0.295 0.004 0.218 0.002 0.047
Median 0.170 0.000 0.191 −0.008 0.197
Maximum 2.193 0.420 1.497 1.128 4.485
Minimum 0.0004 −0.380 −0.572 −1.349 −8.969
Std. Dev. 0.328 0.068 0.262 0.294 1.739
Skewness 2.097 0.469 1.139 0.022 −1.490
Kurtosis 9.042 10.805 7.409 6.288 9.676
Observations 297 296 297 296 297

C. TSUJI703
Table 2. Correlation coefficients of state variables.
Results of April 1985 to December 2009
ILLIQ DDY DEF DTERM LCIP
ILLIQ 1.000
DDY 0.080 1.000
DEF 0.217 −0.008 1.000
DTERM 0.032 −0.137 −0.086 1.000
LCIP −0.030 −0.186 −0.118 −0.013 1.000
Table 3. ICAPM tests by GARCH model.
Results of April 1985 to December 2009
Model 1 Model 2 Model 3 Model 4 Model 5
Coef. 0.879**
CILLIQ p-value 0.001
Coef. 0.258
CDDY p-value 0.862
Coef. 1.131
CDEF p-value 0.240
Coef. −0.357
CDTERM p-value 0.693
Coef. −0.547**
CLCIP p-value 0.032
LL −883.475 −884.171 −886.453 −884.113 −886.233
SC 6.045 6.070 6.065 6.070 6.064
LL denotes log likelihood and SC is Schwarz criterion. ** denotes the statistical significance at the 5% level, and * denotes the statistical significance at the
10% level.
Table 4. ICAPM tests by GARCH-in-mean model.
Results of April 1985 to December 2009
Model 1 Model 2 Model 3 Model 4 Model 5
Coef. 0.010 0.044 0.004 0.010 0.009
MV
p-value 0.400 0.200 0.726 0.465 0.481
Coef. 0.945**
CILLIQ
p-value 0.000
Coef. 5.698
CDDY p-value 0.185
Coef. 1.174
CDEF p-value 0.243
Coef. −0.841
CDTERM p-value 0.410
Coef. −0.478*
CLCIP p-value 0.100
LL −883.098 −883.232 −886.384 −883.861 −885.713
SC 6.062 6.083 6.084 6.087 6.079
LL denotes log likelihood and SC is Schwarz criterion. ** denotes the statistical significance at the 5% level, and * denotes the statistical significance at the
10% level. MV means market variance.

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Table 5. ICAPM tests by EGARCH-in-mean model.
Results of April 1985 to December 2009
Model 1 Model 2 Model 3 Model 4 Model 5
Coef. 0.005 −0.011 −0.002 0.002 0.003
MV p-value 0.713 0.719 0.850 0.860 0.801
Coef. 0.924**
CILLIQ p-value 0.001
Coef. −1.026
CDDY p-value 0.790
Coef. 1.032
CDEF p-value 0.299
Coef. −0.702
CDTERM p-value 0.484
Coef. −0.531*
CLCIP p-value 0.062
LL −879.557 −880.421 −882.786 −880.263 −885.102
SC 6.057 6.083 6.079 6.082 6.094
LL denotes log likelihood and SC is Schwarz criterion. **denotes the statistical significance at the 5% level, and * denotes the statistical significance at the 10%
level. MV means market variance.
statistically significantly priced in ICAPM in the TSE.
Therefore, we understand that these two time-varying
covariance risks are stably priced in the TSE regardless
of the model types.
To sum up, time-varying co-movements of market re-
turns and market illiquidity are important dynamics for
the market risk premium in the TSE. Further, we under-
stand that time-varying covariance between market re-
turn and industrial production is also important as the
determinant of the market risk premium in the TSE.
5. Conclusions
This paper explored the priced state variables in ICAPM
in the TSE. Differently from the US previous study of [7],
we focus on the time-varying covariance risks derived by
the multivariate GARCH model. Our empirical examina-
tions derived following interesting new findings.
First, for the TSE, we clarify that the time-varying
covariance between market return and illiquidity mea-
sure is one of the strongly priced state variables in Mer-
ton’s ICAPM.
Further, the time-varying covariance between market
return and the log change of the seasonally adjusted in-
dustrial production is also the priced state variable in the
ICAPM in Japan. These two variables’ statistical signi-
ficance is empirically robust regardless of the testing
model types.
As above, new robust findings demonstrated in this
paper will contribute to the body of academic researches
of asset pricing in the field of financial economics. We
consider that future related works using other data may
be also valuable, and these works are our future tasks.
6. Acknowledgements
The author acknowledges the generous financial assis-
tance of the Japan Society for the Promotion of Science
and the Zengin Foundation for Studies on Economics
and Finance. In addition, I thank the anonymous referee
for the constructive comments to refine this paper. Fur-
thermore, I greatly appreciate the invitation of the Edi-
tors to write to this journal.
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