Discussion Paper No. 783

CAN THE CONSUMPTION-FREE
NONEXPECTED UTILITY MODELSOLVE THE RISK PREMIUM PUZZLE?
AN EMPIRICAL STUDY
OF THE JAPANESE STOCK MARKET

Myong-Il Kang

June 2010

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

Can the Consumption-Free Nonexpected Utility Model Solve the Risk Premium Puzzle?
An Empirical Study of the Japanese Stock Market

Myong-Il Kang †Korea University

June 17, 2010

Correspondence: M Kang, Assistant professor, Department of Business Administration, Korea University,
1-700 Ogawa-cho, Kodaira, Tokyo 187-8560, JAPAN. Tel: +81-42-341-1331. Fax: +81-42-344-1300. E-mail:mkang@korea-u.ac.jp.
†

This paper is a part of the visiting research of the Institute of Social and Economic Research, Osaka University.

My special thanks go to S. Ikeda for helpful comments, and I am also grateful to Y. Fukuta, K. Hirata, K.
Kubota, H. Nakaota, K. Nishina, M. Ohnishi, F. Ohtake, K. Oya, Y. Tanigawa, and participants at the 2004
Annual Meeting of the Japanese Economic Association, Okayama University, for beneficial discussions. I
acknowledge a financial support by the Grant-in-Aid for JSPS Fellows (188689), the Ministry of Education,
Culture, Sports, Science and Technology.

1

Abstract

This paper investigates whether the consumption-free two-beta intertemporal capital asset-pricing model
developed by Campbell and Vuolteenaho (2004) is able to solve the risk premium puzzle in the Japanesestock market over the period 1984–2002. Using the cash flow and discount rate betas as risk factors, themodel is able to explain about half of the market returns by selection of suitable vector autoregression
variables. On this basis, the model proposed solves the risk premium puzzle in Japan, thereby suggestingthat Japanese investors are less risk averse than US investors. However, a model including only the cash
flow beta better explains returns than a model with both betas. The analysis also tests and rejects thesimple capital asset-pricing model in Japan.

Key words: Risk premium puzzle, Nonexpected utility, CAPM
JEL classification: G122

1. Introduction

Since Mehra and Prescott (1985) first identified the risk premium puzzle, many researchers haveinvestigated whether the Lucas (1978) and Breeden (1979) form of the consumption-based capital
asset-pricing model (C–CAPM) is compatible with the Japanese stock market. Using Hansen’s (1982)
Generalized Method of Moments, Hamori (1992) showed that the power utility type C–CAPM exhibits
good performance with low-risk parameters while Hamori (1994) verified that the Epstein and Zin (1989,
1991) nonexpected utility type C–CAPM explains returns better in the Japanese equity market. Conversely,
Tanigawa (1994) and Hori (1996) retested these models using the Hansen and Jagannathan (1991) boundtest and rejected both. Nakano and Saito (1998) also applied these models to three Japanesemarkets—stock, land, and bonds—and verified their poor performance. Importantly, all of these models
explicitly contain a consumption variable in the pricing kernel, and thus could not avoid the harmful
effects arising from the use of aggregate consumption data: often incriminated as the cause of the risk
premium puzzle because of aggregation bias, the infrequent reporting of consumption, sampling error, andsmoothing associated with seasonal adjustment.
To avoid these problems with the use of aggregate consumption data, Campbell and Vuolteenaho(2004) develop a consumption-free intertemporal capital asset-pricing model (hereafter, CV model)
assuming Epstein–Zin nonexpected utility. They solve the discrete-time version of Merton’s ICAPM byusing a dividend ratio model (Campbell, 1988a) and return decomposition (Campbell, 1991). The induced
model includes two risk factors, the cash flow beta and the discount rate beta, both of which areendogenously determined. The former measures the correlation between asset returns and unexpectedfluctuations in future cash flows (cash flow news) while the latter measures future discount rates (discountrate news). Campbell and Vuolteenaho (2004) decompose unexpected market returns into two components
by assuming that the market variables follow a first-order vector autoregression (VAR) process, and findthat the model empirically solves the risk premium puzzle with a low-risk aversion parameter in the US
stock market.
The focus of this paper is whether the CV model also solves the risk premium puzzle in Japan. For
this purpose, we empirically investigate the validity of the CV model for Japanese stock returns, and3

compare it with a factor model and the simple capital asset-pricing model (CAPM). We select fivevariables as VAR state variables suitable for the Japanese data and estimate two betas as risk factors. The
main contribution is that we demonstrate that the CV model is valid in Japan with high adjusted R-squared
values (52.2% and 24.6%), and solve the risk premium puzzle with low values of the relative risk aversion(RRA) parameter (2.80 and 2.05). Given that the estimated RRA is lower than in the US, we conjecturethat Japanese investors are less risk averse than investors in the US. We also find that a single-factor model
only including a cash flow beta can successfully explain Japanese stock returns and reject the CAPM.
The remainder of the paper is organized as follows. Section 2 introduces the CV model. Section 3
discusses the variables used as state variables in the VAR, generates data on the two news variables, andestimates their betas. We also empirically analyze the Japanese stock market by comparing the CV modelwith the factor model and the CAPM, and estimate the RRA coefficient. Section 4 provides the conclusion.

2. ModelConsider a stock that pays dividends Dt 1 at the end of the period. Letting Pt denote the price ofthe stock at time t, returns Rt are:

Pt 1

Rt 1

Dt 1
Pt

.

(1)

Taking logarithms of both sides of equation (1) and using a Taylor expansion, the log of Rt , rt , can be
expressed approximately as linear in the logs of Pt and Dt 1 :

rt 1
where

1 /(1 exp (d t

k

pt 1

pt )) ; k(1

)d t 1ln( ) (1pt ,) ln(1 /(2)1) ; and pt and d t 1 denote thelogarithms of Pt and Dt 1 , respectively.
We solve equation (2) forward iteratively. By taking expectations and subtracting d t from bothsides, we obtain the familiar Campbell and Shiller (1988a) formula:

pt

dt

k
1

j

Et
j 0

4

dt 1 jrt 1 j ,(3)wheredt 1 ( dt 1

d t ) denotes the log of dividend growth. This formula explains that the log of theprice dividend ratio at time t depends on expectations at time t of the discounted sum of future dividend
growth minus the discount rate.
We follow Campbell (1991) in decomposing unexpected returns into two of its component parts byusing (3). Substituting equation (3) for pt and pt 1 in (2) and rearranging obtains:rt 1

Et rt 1( Et 1jEt )dt 1 j( Et 1j 0

N CF ,t 1
where( Et 1

N CF ,t 1 (

j

Et )

j

Et )

rt 1 jj 1

N DR ,t 1 ,(4)

d t 1 j ) denotes news about future cash flows andj 0

N DR ,t 1 ( ( Et 1

j

Et )

rt 1 j ) denotes news about future discount rates.1 Equation (4) implies thatj 1

unexpected returns are composed of two parts: changes during the period from t to t + 1 in expectations of
future cash flows

d t 1 j j 0 and discount rates rt 1 j j 1 . Let rMe ,t represent the excess return inperiod t over the risk-free rate on the market portfolio. We define the betas as follows:

Cov (ri ,t , N CF ,t )i ,CFVar (rMe ,tCov (ri ,t , N DR ,t )andEt 1 rMe ,t )i , DR

Var (rMe ,t

E t 1rMe ,t ).

(5)

Because discount rate news has a negative sign, the sum of the two betas equals the market beta:
i,M

i ,CF

i , DR

Campbell and Vuolteenaho (2004) refer to

.
i,CF

(6)
as the cash flow beta andi, DR

as the discountrate beta.2 Equation (6) indicates that we can decompose the market beta into the cash flow anddiscount rate betas.
We close the model by specifying the utility-maximizing behavior of consumers. Consider an

1‘News’ is used to describe the revision of expectations during the two periods.

2Campbell and Vuolteenaho (2004) also refer to the cash flow beta as the ‘bad beta’ and the discount rate

beta as the ‘good beta’.

5infinitely lived representative consumer. He or she chooses the stochastic process of consumption C t .
Assume that the nonexpected utility function U proposed by Epstein and Zin (1989, 1991) gives
consumer preferences,1

U ( C t , E t (U t 1 ))wheresatisfies

(1

1

) /(1

(1

),

1

)C t

( E t (U

1
t 1

1

))

,

(7)

represents the relative risk aversion (RRA) coefficient,
the time discount factor. Letting Wt denotethe elasticity of intertemporal substitution (EIS), andwealth holding at time t, the budget constraint is given by Wt 1

(1 R p ,t 1 )(Wt

C t ) . The

representative consumer maximizes (7) subject to the budget constraint. The first-order condition is givenby the Euler equation,1C( t 1)
Ct

Et

1

1(1 R p ,t 1 )(1)(1 Ri ,t 1 ).

(8)

In equation (8), the pricing kernel—or intertemporal marginal rate of substitution (IMRS)—is givenbyC( t 1)Ct

1

1(1 Rp,t 1)(1), and is shown to depend on two factors, consumption growth and market

returns. The resulting two-factor structure enables us to examine the asset pricing implications of bothnews items ( N CF and N DR ). Note that in the case of= 1, the pricing kernel depends solely on market

returns, i.e., the model reduces to CAPM, whereas when=1 /, the pricing kernel depends solely on

consumption growth, so that the C–CAPM holds.3
By assuming that consumption growth and asset returns follow a joint lognormal distribution, thelogarithmic Euler equation is obtained from (8) as follows:

Et (ri ,t 1 ) r f ,t 1

2
i ,t

2

Cov t (ri ,t 1 , rp ,t 1

Et r p,t 1 ) (1

)Cov t (ri ,t 1 , N p, DR ,t 1 ) . (9)Substituting (4) into (9) yields:

3With Epstein–Zin preferences, we can generally express the pricing kernel as the weighted product ofconsumption growth and market returns.

6

Et (ri ,t 1 ) r f ,t 1

2i ,tCov t (ri ,t 1 , N p,CF ,t 1 ) Covt (ri ,t 1 , N p , DR ,t 1 ) ,

2

(10)

which in turn can be rewritten using (6) as:

E t ( ri , t 1 )2i ,tr f ,t 1

2
p ,t

2

i , CF p , t2
p ,ti , DR p , t .

(11)Equation (11) indicates that two risk factors, the cash flow beta and the discount rate beta, determine theequity risk premium i . The risk price of the cash flow beta israte beta is

2p ,tand the risk price for the discount2
p ,t . The risk price of the cash flow beta is thus larger than the discount rate beta when the

RRA coefficient is greater than one.

3. Empirical analysis

In this section, we use Japanese stock market data to examine: (i) whether the CV model is valid in
the Japanese stock market compared with the factor model and the CAPM, and (ii) how large the RRA is
in Japan. We conduct the empirical tasks as follows. First, we generate data on the cash flow and discountrate news by estimating a VAR model. We also show that the VAR variables used in this study are moresuitable for explaining Japanese economic data than those used by Campbell and Vuolteenaho (2004) inthe US. Second, using the news data, we estimate the cash flow and discount rate betas for various
portfolios. Third, we regress portfolio returns on these betas to test the empirical validity of the models andto estimate the value of the RRA coefficient.

3.1. Data description and news and beta estimation

To construct data on cash flow and discount rate news, we estimate a VAR model as follows:

zt 1
where

zt denotes an m

a

zt

t 1,

(12)

1 state vector, the first element of which is market portfolio returns with theother elements being specified later, a is an m

1 constant vector,

7

is an mm VAR coefficientmatrix, andis the m

t 1

1 error term or shock vector.

N CF ,t 1(e1

are constructed as affine transformations of the shock vectort 1:Upon estimation of the VAR process, the news data

N DR,t 1

e1

t 1

N CF ,t 1
where
an m

(I

(e1

e1 ) t 1 and N DR,t 1

e1

t 1,

e1 ) t 1

and

(13)

) 1 maps VAR shocks to news, I denotes the m m identity matrix, and e1 is

1 vector with one in the first element and zero otherwise.
For the VAR variables in z, we first try four variables; the excess returns on the market index (ER),the term yield spread (YS), the price–book value ratio (PBR), and the value yield spread of small stocks(VS). We construct ER by taking the difference in stock returns and the risk-free rate. For stock returns, we
use the Total Index of the DAIWA Stock Index 2 (DSI–2, hereafter) from the website of the Daiwa
Institute of Research Ltd. For the risk-free rate, we use the monthly GENSAKI Rates (the rate in the
repurchase agreement market) from the Financial and Economic Statistics Monthly published by the
Research and Statistics Department of the Bank of Japan.4 YS is the difference between short- andlong-term yields on the Nikkei Bond Indices at the end of the month. PBR is the average value of theprice–book value ratios computed from all listed companies on the First Section of the Tokyo Stock
Exchange. This data are from the Monthly Statistics Report published by the Tokyo Stock Exchange. The
ratio is log transformed. VS is the difference in small index returns for value and growth stocks from theDSI–2. The data series span the period 1984:1–2002:12. Table 1 provides descriptive statistics for the statevariables. Table 3 reports the results of the VAR estimation using the four variables. Although TY and YS
4

The reference base for the DSI indices is the end of December 1983. There are four major DSI indices: (1) a

Total Index that includes all securities listed on six markets (Tokyo, Osaka, and Nagoya Stock Exchanges,
JASDAQ, TSE Mothers, and Hercules); (2) Style Indices, including large, small, value, and growth indices; (3)Sector Indices that correspond to various industrial sectors; and (4) Other Indices, which include stock indicesfor large nonfinancials and financials, and a nonfinancials total index. All of these indices are derived byweighting the total returns of composite stocks by their market. All of these indices have two types, DSI–1 andDSI–2: the former is based on floating shares and latter on all listed shares. For more details, see the Web site of
Daiwa Capital Market Indices at http://www.dir.co.jp/InfoManage/datarsc.html.

8

have large values of adjusted R-squared, the system overall has only a few significant coefficients. More
importantly, ER has a negative adjusted R-squared and no significant coefficients. The poor performanceof the VAR estimation clearly indicates that these four VAR variables are unable to capture theexpectations among market participants and may be inappropriate for the purposes of our analysis.
To improve the performance of the VAR, we add the following two variables instead of VS: thegrowth rate of business failure (DEF) and bond yields (BY). DEF is the year-on-year growth rate ofbusiness failures obtained from Tokyo Syoko Research (TSR). BY are the three-month GENSAKI rates atmonth end for three-month contracts. These are from the monthly report published by the Japan Securities
Dealers Association, then transformed into real terms and taking the three-month moving average. Table 4shows the results of the VAR using these five variables. By adding new two variables, the number ofsignificant coefficients and the value of the adjusted R-squared both improve. In particular, ER now has
three significant coefficients and a positive adjusted R-squared of 1.69.
We can compute the residuals using the estimated VAR coefficients and then decompose them into
cash flow and discount rate news. Tables 5 and Table 6 provide descriptive statistics for the news
calculated with the four-variable and five-variable VARs, respectively. Using the news data calculated
above, we can compare the performance of the four-variable and five-variable VARs. Because cash flow
news is the sum of discount rate news and the residuals of RP according to equation (13), the larger the
VAR unpredictability, the greater the magnitude of the RP residuals and, as a consequence, the larger the
cash flow news. Table 7 presents a comparison of the absolute sum, absolute average, and squared sum ofboth news calculated using four and five variables. As cash flow news for four variables is much larger
than for five variables, we suspect that the four state variables have poorer prediction performance than thefive state variables.
Using Equation (13), we decompose the variance of returns into three terms as follows:

Var (rt 1

E t rt 1 ) Var ( N CF ,t 1 ) Var ( N DR ,t 1 ) 2Cov ( N CF ,t 1 , N DR ,t 1 ) .

(14)This expression indicates that we can decompose the variance of expected returns, i.e., variance of total
news, into variance and covariance of both types of news. Table 8 provides a comparison of both VARs
using the variance decomposition of news. In the case of four variables, the variance of cash flow news andcovariance of news unnaturally consists of a greater portion of total news, while with five variables, total

9

news decomposes well into both types of news. Accordingly, we use the news estimated by applying theVAR with five variables.
Next, we estimate the cash flow and discount rate betas. From definition (5) of the betas, these are
estimated using the following equations:

ˆ

i ,CF

Cˆ ov(ri ,t , Nˆ CF ,t )and ˆ i , DRˆˆˆVar ( N CF ,t N DR ,t )Cˆ ov(ri ,t , Nˆ DR ,t )Vˆar ( Nˆ CF ,t Nˆ DR ,t )(15)

We use 43 DSI–2 indices for the asset return data: 33 sector indices, 7 Daiwa sector indices, and 3 otherindices.5 We estimate the betas for these assets using the news data obtained above. The results areincluded in Table 9. On average, the discount rate beta is larger than the cash flow beta, and the correlation
coefficient between the betas takes a positive and low value of 0.187. These features are similar to the US
findings in Campbell and Vuolteenaho (2004).

3.2. Tests for asset-pricing models

Using these betas, we empirically compare three asset-pricing models: the factor model, the CVmodel, and the CAPM. Following Campbell and Vuolteenaho (2004), we assume three assumptions forequation (11). First, simple returns Et Ri,t 1

R f ,t 1 are used instead of log-returns on the left-hand side.

Second, the moments are invariant throughout time, so that unconditional moments can replace conditional
moments. Finally, the stock portfolio is a proxy for the market portfolio.6 Equation (11) can then be
rewritten as follows:

E Ri

Rf

2
M

i , CF M

2M

i , DR M.

(16)

Using the estimated betas as explanatory variables, we represent the regression equation for the CV model
as:

Rie

g0

g1 ˆi ,CFg 2 ˆi , DR

ei ,

5

See Footnote 4 for a short description of these indices.

6

For explicit expression of the third assumption, we insert subscript p into M.

10

(17)

where Rie

Ri

R f is the simple mean of excess returns on asset i and the slope parameters g 1 andg 2 are the prices of the risk factors. From equation (17), the ratio g1 g 2 equals the RRA coefficient.

Following Campbell and Vuolteenaho (2004), each model is estimated in two different regression
forms: the first with an unrestricted zero beta, and the second with a restriction that zero beta equals the
GENSAKI rate. Each model includes White’s heteroskedasticity consistent covariances. We also report the
95% critical value of a bootstrap using 2,500 simulated realizations.
We start by estimating the two-factor model with the cash flow and discount rate betas. We do this byregressing asset returns on both betas without imposing any restrictions on the risk prices. The results ofthese estimations are in the second and third columns of Table 10. The risk price of the cash flow beta issignificantly positive whereas the risk price of the discount rate beta is insignificant with a large adjusted
R-squared. Based on these results, we doubt that we could explain asset returns better using thesingle-factor model with a cash flow beta, so we regress returns on the cash flow and discount rate betas
separately. Table 11 shows the results. In the single-factor specification, the cash flow beta is still
significant and exhibits a value of adjusted R-squared larger than even the two-factor cases. In contrast, thediscount rate beta remains insignificant. These findings suggest that only the cash flow beta significantly
explains asset returns.
We next examine the CV model by running a regression with a restriction on the risk price of the
discount rate beta, g 2 =2 7
M.

The results are included in the fourth and fifth columns of Table 10. The

estimated slope parameter g 1 , which is the risk price of the cash flow beta, is significantly positive,
implying that the CV model significantly predicts asset returns. The last row of Table 10 provides the RRA
coefficient calculated by= g1 g 2 . This is 2.80 with an unrestricted zero beta and 2.05 with a restrictedzero beta. These values are lower than in the US case and indicate that Japanese investors may be less risk
averse than US investors.8 It is also noteworthy that we could solve the risk premium puzzle with thislow-risk aversion parameter by applying the model to Japanese data. The results lead us to the conclusionthat the CV model is useful for solving the risk premium puzzle in the Japanese stock market.
2
M = 0.00326 computed from DSI–2.

7

This restriction is from equation (11). In our data sets,

8

In the US case in Campbell and Vuolteenaho (2004), RRA equals 8.6 and 7.0, respectively.

11

Lastly, we examine the CAPM with the restriction that both risk prices are equal, g1

g2 .9 The sixthand seventh columns of Table 10 report the results. Although the estimated coefficient is significantly
positive, the value far exceeds average market portfolio returns; that is, the estimated risk price issignificantly higher than that required by the CAPM specification.10 Accordingly, we conclude that asingle-factor model with a market beta only marginally explains asset returns.

4. Conclusion

This paper investigates whether the consumption-free CV model better explains Japanese stock
returns than the factor model and the traditional CAPM, and whether we can solve the risk premium puzzle,
at least in Japan, using this model. In the analysis, we selected five VAR state variables (RP, YS, PBR,
DEF, and BY) as being more suitable for Japanese data than the four variables used in the comparable US
study. Using the estimated VAR coefficients, we decomposed unexpected returns into two components,and estimated the cash flow beta and the discount rate beta. We found the discount rate beta to be larger,
on average, than the cash flow beta, and their low and positive correlation coefficient is consistent with the
US case. We then tested three types of asset-pricing models: a two-factor model with two betas, the CVmodel, and the traditional CAPM.
The results of this analysis are as follows. Firstly, the single-factor model including only the cash
flow beta better explained Japanese stock returns rather than a two-factor model including both betas.
Second, the CV model is valid in the Japanese stock market, though with a somewhat lower adjusted
R-squared than that found with the single-factor model. On this basis, we can solve the risk premium
puzzle as the risk aversion parameter lies below three. Moreover, as the value of RRA is smaller than incomparable US studies, the implication is that Japanese investors are less risk averse than US investors.
These results support previous findings by Hamori (1992, 1994) that the risk premium puzzle does notarise in Japan. Third, consistent with many previous studies, we reject the CAPM.

9This restriction is from CAPM theory and the definition of betas in Equation (5).

10The average of the excess market portfolio returns is 0.00062 in our data set.

12

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14

Table 1
Descriptive statistics of the four VAR state variables

ER

YS

PBR

VS

Mean

0.000619

0.000600

0.785574

0.003447

Sterr.

0.003857

0.000032

0.030512

0.001586

Median–0.001299

0.000653

0.741937

0.003226

Stdev.

0.058235

0.000484

0.460718

0.023947

Variance

0.003391

2.35E-07

0.212261

0.000573

Kurtosis0.688647–0.384242–1.014469

2.756984

Skewness

0.016203–0.425616

0.098127–0.158592

Range

0.375825

0.001996

1.791759

0.199153

Min.

–0.209114–0.000488–0.105361–0.095524

Max.

0.166711

0.001508

1.686399

0.103630

Sum

0.1411250.136722

179.1109

0.785828

Note: This table shows the descriptive statistics of the VAR state variables. The sample period
1984:01–2002:12 comprises 228 monthly data points. ER is the excess return on the DSI–2 total stockindex with all listed stocks. YS is the term yield spread of the Nikkei Index of Bond Yields. PBR is theaverage value of the price to book value ratio (in logs) of all stocks trading in the First Section of theTokyo Stock Exchange. VS is the value yield spread of small stocks, which is the difference between the
DSI–2 small-value and small-growth indexes. Sterr. is the standard error and Stdev. is the standard
deviation.

15

Table 2
Descriptive statistics of the five VAR state variables

ER

YS

PBR

DEF

BY

Mean

0.000619

0.000600

0.785574

0.026984

0.001788

Sterr.

0.003857

0.000032

0.030512

0.016161

0.000102Median–0.001299

0.000653

0.741937–0.007281

0.001629

Stdev.

0.058235

0.000484

0.460718

0.244022

0.001535

Variance

0.003391

2.35E–07

0.212261

0.059547

0.000002

Kurtosis0.688647–0.384242–1.014469

0.906710–0.527424

Skewness

0.016203–0.425616

0.098127

0.873182–0.122364

Range

0.375825

0.001996

1.791759

1.221223

0.006956Min.

–0.209114–0.000488–0.105361–0.407945–0.001908Max.

0.166711

0.001508

1.686399

0.813278

0.005048Sum

0.1411250.136722

179.1109

6.152348

0.407580

Note: This table shows the descriptive statistics of the VAR state variables. The sample period
1984:01–2002:12 comprises 228 monthly data points. ER is the excess return on the DSI–2 total stockindex with all listed stocks. YS is the term yield spread of the Nikkei Index of Bond Yields. PBR is theaverage value of the price to book value ratio (in logs) of all stocks trading in the First Section of theTokyo Stock Exchange. DEF is the growth rate of business failures calculated as the year-on-year rate. BY
is the bond yield trading with repurchase agreement at month-end, with a term to maturity of three months,transformed into real terms and a three-month moving average. Sterr. is the standard error and Stdev. is thestandard deviation.

16

Table 3
VAR parameter estimates using four variables

ER
ER(–1)
YS(–1)PBR(–1)
VS(–1)C
Adj. R-squared

YS

PBR

VS

0.034895(0.51071)
9.167112(1.07960)
0.003957(0.43922)–0.140170(–0.85815)–0.007837(–0.73386)

0.000054(0.41495)
0.974357***(60.0024)-0.000008(–0.49236)-0.000060(–0.19102)
0.000019(0.92775)

0.099180(1.27987)
5.844833(0.60691)
0.997770***(97.6439)
0.033829(0.18261)–0.006800(–0.56143)

0.009471(0.34700)
1.238651(0.36517)
0.001303(0.36212)
0.250333***(3.83651)
0.000949(0.22250)–0.69%

94.70%

97.94%

4.69%

Note: This table provides the OLS parameter estimates for a first-order VAR model including a constantterm (C), the risk premium (ER), the term yield spread (YS), the price–book value ratio (PBR), and thevalue yield spread of small stocks (VS). The sample periods for the dependent variables 1984:02–2002:12
comprise 227 monthly data points. · (-1) is the explanatory variable of the VAR and denotes a lag of one
period. Adj. R-squared denotes the adjusted R-squared. The first row for each variable is the estimatedcoefficients. The values in parentheses are t-values.
*** denotes significance at the 1% level, ** at the 5% level, and * at the 10% level.

17

Table 4
VAR parameter estimates using five variables

ER (–1)
YS (–1)PBR (–1)
DEF (–1)
BY (–1)
C
Adj. R-squared

ER

YS

PBR

DEF

BY

0.029732[0.44259]
6.907166[0.81570]–0.018503[–1.49368]–0.036879**[–2.12304]
7.211536**[2.13043]–0.001084[–0.09707]

0.000063[0.49303]
0.978928***[60.6790]-0.000026[–1.09293]
0.000050[1.51829]
0.012449*[1.93038]
0.000006[0.28377]

0.084837[1.11092]
3.635542[0.37768]
0.977109***[69.3886]–0.039937**[–2.02243]
6.282213[1.63257]
0.000844[0.06652]

0.028358[0.24599]–17.87396[–1.23002]–0.004198[–0.19747]
0.911260***[30.5691]–3.461354[–0.59586]
0.021503[1.12218]

0.000542[1.15694]–0.142301**[–2.41014]
0.000018[0.20801]-0.000040[–0.33078]
0.945719***[40.0688]
0.000162**[2.07685]

1.69%

94.86%

97.98%

83.55%

93.09%

Note: The table provides the OLS parameter estimates for the first-order VAR model including a constantterm (C), the risk premium (ER), the term yield spread (YS), the price–book value ratio (PBR), the growthrate of business failure (DEF), and the bond yields (BY). The sample periods for the dependent variables
1984:02–2002:12 comprise 227 monthly data points. · (-1) is the explanatory variable of the VAR anddenotes a lag of one period. Adj. R-squared denotes the adjusted R-squared. The first row for each variable
is the estimated coefficients. The values in parentheses are t-values.
*** denotes significance at the 1% level, ** at the 5% level, and * at the 10% level.

18

Table 5
Descriptive statistics for cash flow and discount rate news as generated by the four-variable VAR

DR news

CF news

Mean

0.000000

Mean

0.000000

Sterr.

0.003275

Sterr.

0.005921

Median–0.001416

Median–0.000947

Stdev.

0.049342

Stdev.

0.089211

Variance

0.002435

Variance

0.007959

Kurtosis1.071481

Kurtosis0.908227

Skewness

0.072473

Skewness

0.132476

Range

0.341018

Range

0.591441

Min.

–0.169527

Min.

–0.296546

Max.

0.171491

Max.

0.294895

Sum

0.000000

Sum

0.000000

Note: This table provides descriptive statistics for the cash flow (CF) and discount rate (DR) news
generated from the four-variable VAR with elements RP, YS, PBR, and VS. Sterr. is the standard error andStdev. is the standard deviation.

19

Table 6
Descriptive statistics for cash flow and discount rate news generated by the five-variable VAR

DR news

CF news

Mean

0.000000

Mean

0.000000

Sterr.

0.003332

Sterr.

0.002700

Median0.000074

Median–0.002155

Stdev

0.050211

Stdev

0.040679

Variance

0.002521

Variance

0.001654

Kurtosis0.945681

Kurtosis–0.350219

Skewness

0.022871

Skewness

0.107653

Range

0.333853

Range

0.204112Min.

–0.167265

Min.

–0.105049

Max.

0.166588

Max.

0.105049

Sum

0.000000

Sum

0.000000

Note: The table provides descriptive statistics for cash flow (CF) and discount rate (DR) news generated
from the five-variable VAR with elements RP, YS, PBR, DEF, and BY. Sterr. is the standard error andStdev. is the standard deviation.

20

Table 7
Absolute sum, absolute average, and sum of squares of news

CF news

DR news

Four variables

Five variables

Four variables

Five variables

Absolute sum

15.13506

7.50625

8.31925

8.64082

Absolute average

0.06667

0.03307

0.036650.03807

Sum of squares

1.798640.374

0.550220.56979

Note: The table provides the absolute sum, absolute average, and sum of squares for news
generated by the four and five-variable VARs, respectively. Absolute sum is the sum of theabsolute value of news; absolute average is the average of the absolute value of news; sum ofsquares is the sum of the squared value of news.

21

Table 8
Variance decomposition of returns

Four variables

Real value
Ratio

Var(total news)

Var(CFN)

Var(DRN)–2Cov(CFN.DRN)

0.00341.00000.00802.37250.00240.7258–0.0070–2.0890

Var(total news)

Var(CFN)

Var(DRN)–2Cov(CFN.DRN)

0.00331.00000.00170.50760.00250.7733–0.0009–0.2797

Five variables
Real value
Ratio

Note: The table provides the variance decomposition for unexpected stock returns, i.e., total news, using
four- and five-VAR state variables, respectively. Each column ‘Real value’, i.e., ‘Var (total news)’, ‘Var
(CFN)’, ‘Var (DRN)’, and ‘–2 Cov (CFN, DRN)’, are given as each terms of equation Var (rt+1 - Et rt+1) =Var (NCF,t+1) + Var (NDR, t+1) - 2Cov (NCF, t+1, NDR, t+1). Dividing ‘Real value’ by the variance of total news
gives ‘Ratio’ (by definition sums to one).

22

Table 9
Beta of each index
Indices
33 sectors

Portfolio classification
Fishery, Agriculture & Forestry
MiningConstruction
Foods
TextilesPulp & Paper
Chemicals
Pharmaceutical
Oil & Coal Products
Rubber Products
Glass & Ceramic Products
Iron & Steel
Nonferrous Metals
Metal Products
Machinery
Electric Appliances
Transportation Equipment
Precision Instruments
Other ProductsElectric Power & Gas
Land Transportation
Marine Transportation
Air Transportation
Warehousing & Harbor
Information & Communication
Wholesale Trade
Retail Trade
Banks
Securities
Insurance
Other FinanceReal Estate
Services

23

CF β
DR β
Total β
0.210
0.617
0.827
0.290
0.698
0.988
0.063
0.043
0.106
–0.085 –0.178–0.262
0.176
0.591
0.767
0.316
0.669
0.985
0.101
0.065
0.166
–0.142 –0.173–0.316
0.140
0.606
0.746
0.325
0.858
1.183
0.169
0.048
0.217
0.116 –0.275–0.159
0.107
0.770
0.877
0.055
0.877
0.932
0.123 –0.025
0.098
0.177 –0.170
0.007
0.125
0.559
0.683
–0.003
0.834
0.831
0.083
0.045
0.128
0.341 –0.483–0.141
0.200
0.470
0.670
–0.026
1.240
1.214
0.052
0.065
0.116
0.259 –0.582–0.323
0.322
0.761
1.082
0.107
1.338
1.445
–0.093 –0.194–0.2870.439 –0.778–0.338
0.820
1.121
1.941
0.010
1.372
1.382
–0.520 –0.332–0.8520.415 –0.648–0.233
0.838
0.985
1.823

Table 9
Beta of each index –continued

Indices

Portfolio classification

CF β

DR β

Total βDaiwa 7 sectors

Material
Manufacturing
Miscellaneous Manufacturing
Transportation & Utility
Services
Miscellaneous Non-Manufacturing
FinancialLarge Non-Financials
Large Financials
Non-Financials Total Index–0.109–0.5990.312
0.972–0.005–0.661
0.557
0.974
0.010
–0.678
0.146
–

1.289
–0.320–0.7330.885
1.394–0.211–0.7770.829
1.405–0.195
0.334
–

1.180
–0.919–0.4211.858
1.389–0.871–0.2201.803
1.415–0.8730.480
0.187

OthersAverage
Correlation coef.

Note: The table provides the value of the betas for each index. ‘CF β’ denotes the cash flow beta and ‘DR β’denotes the discount rate beta. ‘Total β’ denotes the sum of the two betas. ‘Correlation coef.’ denotes thecorrelation coefficient of the two betas.

24

Table 10
Regression tests for the three asset-pricing models
Factor Model–0.00169***NA[0.00046]
NA

CV model–0.00251***NA[0.00051]
NA

CAPM–0.00151**
NA[0.00073]
NA–0.00088–0.00269

NANA–0.00155–0.00356NANA–0.00013–0.00297

NANA

g1
Std.error
95% BS interval
Upper
Lower

0.01012***[0.00085]

0.00900***[0.00126]

0.00912***[0.00090]

0.00668***[0.00123]

0.00294***[0.00088]

0.00213***[0.00076]

0.012070.008890.01159
0.00687

0.01108
0.007480.009270.004470.004810.001430.00372
0.00074g2
Std.error
95% BS interval
Upper
Lower

0.00036[0.00044]–0.00048[0.00049]

0.00326NA

0.00326NA

0.00294***[0.00088]

0.00213***[0.00076]

0.00126–0.00044

0.00051–0.00145

NA
NA

NA
NA

0.004810.001430.00372
0.00074

Adj. R-squared
RRA coef.

70.82%
NA

60.08%
NA

52.17%
2.80

24.55%
2.05

28.42%
NA

21.24%
NA

g0
Std.error
95% BS interval
Upper
Lower

Note: The table shows estimated risk prices for the factor model with two betas, the CV model, and the CAPM.
g0, g1, and g2 are regression estimates of the constant term, the risk price of the cash flow beta, and the risk
price of the discount rate beta, respectively. All regressions include White Heteroskedasticity Consistent
Covariances. The factor model is regressed with no restriction, the CV model with g2 = 0.00329, and the
CAPM with g1 = g2. The table reports two regressions for each model, with and without a constant. ‘Std. error’denotes the standard error of estimated coefficient. ‘95% BS interval’ denotes the 95% confidence intervalwith bootstrap from 2,500 simulated realizations. ‘Upper’ is the upper critical value and ‘Lower’ is the lower
critical value. ‘Adj, R-squared’ is the adjusted R-squared of the regression. ‘RRA coef.’ is the relative risk
aversion coefficient calculated as γ = g1/g2. NA – not applicable.
*** denotes significance at the 1% level, ** at the 5% level, and * at the 10% level.

25

Table 11
Regression tests with individual betas

Cash flow beta
–0.00159***NA[0.00042]
NA

Discount rate beta
–0.00056NA[0.00076]NA–0.00084–0.00247NANA

0.00010–0.00193

NANA

g1
Std.error
95% BS interval
Upper
Lower

0.01024***[0.00089]

0.00870***[0.00110]

NA
NA

NA
NA

0.01238
0.00901

0.01127
0.00689

NA
NA

NA
NA

g2
Std.error
95% BS interval
Upper
Lower

NA
NA

NA
NA

0.00139[0.00096]

0.00105[0.00082]

NA
NA

NA
NA

0.00295–0.00075

0.00242–0.00077

Adj. R-squared

71.24%

60.43%

2.14%

3.16%

g0
Std.error
95% BS interval
Upper
Lower

Note: The table shows estimated risk prices for the single factor model with each beta. g0, g1, and g2 areregression estimates of the constant term, the risk price of the cash flow beta, and the risk price of the discountrate beta, respectively. All regressions include White Heteroskedasticity Consistent Covariances. Cash flow
beta is the single-factor model with only the cash flow beta, and discount rate beta only includes the discountrate beta. The table reports two regressions for each model, with and without a constant. ‘Std. error’ denotes
the standard error of estimated coefficient. ‘95% BS interval’ denotes the 95% confidence interval withbootstrap from 2,500 simulated realizations. ‘Upper’ is the upper critical value and ‘Lower’ is the lower
critical value. ‘Adj, R-squared’ is the adjusted R-squared of the regression. NA – not applicable.
*** denotes significance at the 1% level, ** at the 5% level, and * at the 10% level.

26