Market Segmentation and Pricing of
International Assets
Cathy(Qiao) Ning∗
April, 2004
Abstract
This paper investigates how conditional and unconditional forms of an
international multi-factor asset pricing model perform in explaining the
returns available to global investors. The assets considered are portfolios
of equities, bonds and currencies from several of the largest industrial
countries. We find evidence suggesting that international equity markets,
bond markets and currency markets are segmented. Therefore, we price
these assets using separate multi factor models. The factors we consider
are measures related to the level of equity market risk, currency market
risk, term structure risk, and default risk. To compare the performance
across different models, we estimate the Hansen-Jagannathan distances for
each model. Although we are unable to reject our unconditional models
∗ I would like to thank Prof. Stephen Sapp for his sufficient instruction. I also wish to
thank Prof. John Knight for his encouragement and useful suggestions, Prof. Joel Fried for
helpful discussion. Comments from the applied economics workshop also improve the paper.
All the errors are of myself.
1
for pricing equities, we do not find a significant role for our factors in
the unconditional models. Conditional models perform well for pricing
international equities with the term structure playing a significant role.
On the other hand, unconditional models perform well for bonds with
bond returns being explained by the default premium and equity market
risk premium, but conditional models perform poorly for bonds. For
currency returns, both the unconditional and conditional models indicate
that term structure risk and default risk have explanatory power.
1
Introduction
As the economies of the world have become increasingly global in nature, investors are able to invest in assets from around the world. Consequently both
academics and practitioners are interested in understanding how to explain the
returns on the set of international assets available to investors. In this paper, we examine several categories of international assets that are considered
by global investors, namely equities, bonds and currencies from several of the
largest industrial countries.
Trying to understand what factors influence the returns of assets has been the
focus of significant research for at least the past 40 years. The first attempts being related to the different versions of the Capital Asset Pricing Model (CAPM).
Among them, the Sharpe-Lintner-Black Capital Asset Pricing Model (CAPM)
2
is one of the most commonly used models by financial managers to assess the
risk of an investment. According to CAPM, the risk of an investment project is
measured by its correlation with the return on the market portfolio of all assets
in the economy, which is the systematic risk named beta. The expected return
for an asset has a linear relationship with the beta. Unfortunately numerous
empirical tests report that the CAPM does not fit cross-sectional asset pricing
data. For example, Fama and French (1992) find that cross sectional returns
can be explained by two persistent variables: size and book-to-market ratio,
while market beta has no explanation power in cross-sectional returns.
Possible explanations for the poor performance of the CAPM are provided
by some of the main critiques of the CAPM: 1) Roll’s (1977) critique that
market portfolio is unidentifiable. 2) Static CAPM fails to consider the effects
of time-varying investment opportunities in the calculation of an asset’s risk.
3) the Hansen-Richard (1987) critique that CAPM implies a conditional linear
factor model, which does not imply an unconditional model. The CAPM may
be true conditionally but may fail the unconditional testing. Therefore, CAPM
is a theoretical intuitive but not realistic model.
Since CAPM is unsatisfactory performed and not realistic, researchers have
developed many other more flexible and realistic models. Multifactor model
is one of them. In addition to the stock market risk, multifactor models take
into account many other sources of systematic risks that could influence the
asset returns. Besides, conditional multifactor models also solve the problem of
time-varying investment opportunities. And more, the multifactor models have
3
successfully explained the returns of domestic and global assets in the literature.
Many risk factors have been shown significant roles.
The domestic multifactor models tried to explain returns from stocks, bonds
and mutual funds. Chen, Roll and Ross (1996) introduce one of the earliest
popular multifactor models. They find that US stock returns can be explained
by some macro factors such as the term structure, expected and unexpected
inflation, industrial production, and default premium. Fama and French (1992
and 1993) propose the presently most popular multifactor models. They find
that stock returns are priced by firm specific factors such as firm size and bookto-market ratio. Chan, Karceski and Lakonishok (1998) investigate both macro
and firm specific risks factors in pricing stock returns and find a couple of
significant risk factors. Fama and French (1993) also find the explanation power
of multifactor models in bonds. Kryzanowski, Lalancette and To (1997) develop
the multifactor model to explain returns of mutual funds.
International multifactor models also tried to determine which risk factors
can explain global assets. Ferson and Harvey (1994) find that the world market
betas do not provide good explanation of cross-sectional difference of returns.
Multiple beta models provide an improved explanation of international equity
returns. Dumas and Solnik (1995) find both currency risk factors and world
market risk factor are significant in explaining world equity returns and foreign currency deposit returns. However international multifactor models are
relatively less developed than domestic ones.
In this paper, we investigate how multifactor models perform in explaining
4
the returns of the assets that are available to the global investors. Especially we
include foreign currencies as one category of available assets. In the literature of
international CAPM or multifactor models research, whether foreign exchange
risk is priced in the international equity asset returns receives a lot of attention.
See Solnik (1974), Sercu (1980), Stulz (1981). However, foreign exchange itself
is an important asset for investors. How to price it has not receive enough
attention that it deserves. By including currencies as assets, we actually extend
the investment opportunity set of global investors as global investors not only
invest in stocks and bonds, but also foreign currencies.
We examine the sources of the risks exposed by these international assets
and investigate several global economic risk factors including world equity market risk, foreign exchange risk, term structure risk, and default risk. We try
to answer the question as whether different international assets are priced by
the same risk factors. This depends on whether the assumption of market integration is true or not. International models usually assume the integrity of
international capital market although Korajczyck and Viallet (1992) indicate
evidence of market segmentation. We undertake a couple of tests to examine
the assumption of market integration.
We find evidence that international asset markets are actually segmented.
The segmentation in this paper means that different assets can not be priced the
same. Based on this, we analyze the returns of different international assets by
separate multifactor models. For each group of assets, we compare performance
of models with different risk factor specifications using Hansen-Jagannathan
5
(1996) distance measure (here after HJ-distance). Since HJ-distance approach
uses the same weighting matrix for different models, it allows us to compare
different models directly. If the model is correctly specified, the HJ-distance
should be zero.
Finally, in the empirical research of multifactor models, portfolios are usually
formed according to some attributes. However, according to Roll(1977), Lo
and Mackinlay(1990), FF(1996), and Brennan et al (1996), portfolio formation
processes are quite problematic. They find that same model with different
attribute-formed portfolios often lead to different inferences. In our study, we
use single asset such as one equity, bond and foreign currency for each country.
It can be viewed as a natural portfolio formed by the attributes of a country.
This naturally formed portfolio may avoid the problem caused by the artificial
portfolio formation process.
The main results of the paper are as following. The conditional models are
not rejected for equities and the world equity market risk factor can explain
the equity returns in the single factor model. But the significance of this factor
disappears when other risk factors are considered. Conditional models perform
well with the term structure risk factor being the only survived significant risk
factor with the presence of other factors in the explanation of equity returns.
Unconditional models perform well for bonds with significant explanation role
of term structure risk. But conditional models perform very poorly for bonds.
Both unconditional and conditional models indicate that foreign currency returns can be explained by term structure risk and default risk.
6
The paper is organized as follows. Part 2 describes the models and methodology. Part 3 describes and summaries the data.
Results are described and
discussed in Part 4. Part 5 summarizes our conclusions.
2
Models and Methodology
2.1
Unconditional models
According to CAPM, the beta multifactor model with K risk factors and N
assets is :
k
E[Rit ] = λ0 + ΣK
k=1 λk β i
where β ki =
cov(Rit ,Rtk )
V ar(Rtk )
(1)
is the factor loading, k=1,2 ....K
is the number
of factors, and i =1· · ·N is the number of assets. λk is the risk premium of
factor k. Rit is the gross return of asset i at time t. And Rtk is the return
of the kth risk factor at time t. Substitute expression of β ki into (1) and use
cov(Rit , Rtk ) = E[Rit Rtk ] − E[Rit ]E[Rtk ], we get:
E[Rit ] = λ0 + ΣK
k=1 λk
= λ0 + ΣK
k=1 λk
= λ0 + ΣK
k=1
cov(Rit ,Rk
t)
V ar(Rk
t)
E[Rit Rtk ]−E[Rit ]E[Rk
t]
V ar(Rtk )
λk E[Rit Rtk ]
V ar(Rk
t)
− ΣK
k=1
λk E[Rit ]E[Rk
t]
V ar(Rtk )
move all the terms except λ0 into left side of above equation. we get:
7
E[Rit ] − ΣK
k=1
λk E[Rit Rtk ]
V ar(Rtk )
+ ΣK
k=1
λk E[Rit ]E[Rtk ]
V ar(Rtk )
λ E[Rk ]
= λ0
λ Rk
k
k t
K
t
that is E[Rit (1 + ΣK
k=1 V ar(Rk ) − Σk=1 V ar(Rk ) )] = λ0
t
multiply
1
λ0
t
for both side, we get
λ E[Rk ]
λ Rk
k
k t
K
t
E[Rit ( λ10 + ΣK
k=1 λ0 V ar(Rk ) − Σk=1 λ0 V ar(Rk ) )] = 1
t
let δ 0 =
1
λ0
+
1
λ0
t
PK
λk E[Rtk ]
k=1 V ar(Rk
t)
λk
δ k = − λ0 V ar(R
k ) , for k=1...K,
t
then
k
E[Rit (δ 0 + ΣK
k=1 δ k Rt )] = 1N
(2)
for i=1· · ·N.
This is the stochastic discount factor form of multifactor CAPM. Here the
k
discount factor is dδ = δ 0 + ΣK
k=1 δ k Rt .
In the literature, factor models are most often applied to excess returns. Let
rit denote the excess return of asset i at time t. In the case of excess returns,
according to Cochrane (2002) page 256, the discount factor model will be:
k
E[rit (b0 + ΣK
k=1 bk Rt )] = 0
k
Where Rtk are returns of risk factors. As any multiples of (b0 + ΣK
k=1 bk Rt )
will fit the model, there is no way to separately identify b0 and bk ,Therefore,
the model is normalized as:
k
E[rit (1 + ΣK
k=1 bk Rt )] = 0
8
k
Where bk = − C0 V λar(R
k)
t
C0 = 1 +
PK
λk E[Rtk ]
k=1 V ar(Rk
t)
k
Then E[rit (1 + ΣK
k=1 bk Rt )] = E[wt (δ)] is the vector of pricing error, which
should be 0. The naturally convenient approach of estimation of the model
is the General Method of Moment (GMM). To do this, the quadratic form
E[wt (b)]0 G−1 E[wt (b)] is formulated, where G−1 is a positive definite matrix
(weighting matrix). b is chosen to make the pricing errors E[wt (b)] as small as
possible, by minimizing the quadratic form E[wt (b)]0 G−1 E[wt (b)].
It is well known that (V ar(wt (b)))−1 is the statistically optimal weighting
matrix, which produces estimates with lowest asymptotic variance. This is
formally shown by Hansen (1982). This weighting matrix also has the interpretation of paying less attention to pricing errors from assets with high variance of
k
rit (1 + ΣK
k=1 bk ft ). With this optimal weighting matrix, Hansen also shows that
the quadratic form has a χ2 distribution with degree of freedom (N-K), where
N is the number of moments and K is the number of parameters in the model.
We will only use this type of optimal GMM method for the test of the market
integration hypothesis based on stochastic discount factor models. However, it’s
inappropriate to use the optimal GMM approach to compare competing model’s
performance because the weighting matrix keeps changing across different models. We will use HJ-distance approach to compare model performance, which is
examined in the latter part of the paper.
9
2.2
Conditional Models
As the previous studies document that the poor empirical performance of CAPM
maybe because of inadequate allowances for time variation in the conditional
moments of returns. That is it fails to take into account the effects of timevarying investment opportunities. For the discount factor form of the model, the
discount factor dδ should be state dependent, which means it should incorporate
the conditional information. The conditional asset pricing model can be written
as follows:
k
E[(ri,t (1 + ΣK
k=1 bk Rt )|It−1 ] = 0
(3)
where It−1 is the information set at time t − 1 that investors use to price
assets.
By Cochrane (2001), one approach to incorporate conditional information
is to specify and estimate explicit statistical models of conditional distributions
of asset payoffs and discount factor variables. However, by this way, the number
of required parameters can quickly exceed the number of moments. And more
importantly, this explicit approach requires us to assume that investors use the
same conditioning information that we use. This is apparently not true. We
don’t observe all the conditional information as economic agents do. However,
asset price can summarize an enormous amount of information that only individual observes. To avoid assuming that investors only see the variables that we
include in an empirical investigation, we can incorporate conditional information by scaling factors with instruments that are likely to summarize variation
10
in conditional moments. By this way, the conditional model is transformed into
unconditional model. Let Zt−1 be the information variable set that summarizes
the It−1 .Then the moments can be formulated as following:
k
E[ri,t (1 + ΣK
k=1 bk Rt ) ⊗ Zt−1 ] = 0mN
(4)
where Zt−1 = {1, z1, z2 ......zm−1 }t−1 , and m is the number of conditional
variables.
This is actually:






E





[ri,t (1 +
k
ΣK
k=1 bk Rt )]
k
[ri,t (1 + ΣK
k=1 bk Rt )]z1,t−1
···
k
[ri,t (1 + ΣK
k=1 bk Rt )]zm−1,t−1



  0N 
 

 

  0 
  N 
=

 

  ··· 
 

 

 

0N
(5)
Which gives m × N moments and estimating K parameters. So there are
(m × N − K)over identifying moments.
let wt = {rit , Zt−1 }, yT = (wT0 , wT0 −1 , · · ·, w10 )0 be a vector containing all the
observations with sample size T. And let

k
[ri,t (1 + ΣK

k=1 bk Rt )]


 [r (1 + ΣK b Rk )]z
 i,t
1,t−1
k=1 k t
h(b, wt ) = 


···



k
[ri,t (1 + ΣK
k=1 bk Rt )]zm,t−1
The sample average value of h(b, wt ) is
g(b, yT ) = (1/T )
PT
t=1
h(b, wt ),
11












(6)
and the GMM objective function is
Q(b) = [g(b, yT )]0 SbT−1 [g(b, yT )]
With the assumption of no serial correlation,
P
δ, wt )][h(b
δ, wt )]0 },
SbT = (1/T ) Tt=1 {[h(b
The standard errors for bbT is:
b 0 = (1/T ) PT
where D
T
t=1
0
b−1 d −1
d
(1/T ){D
T ST DT }
∂h(b,wt )
|b=bb
∂b0
T
In the econometric context, Zt−1 is an instrument vector because it should
be uncorrelated with the error vector. Cochrane (2001) interprets the implications of the conditioning model as to include actively managed portfolios to the
analysis by adding instruments. This is in principle able to capture all of the
model’s predictions. Suppose there is only one conditional variable Zt−1 , the
investor decided on the amount of money to invest in each asset based on Zt−1
at the beginning of each period. Therefore the level of Zt−1 at the beginning
of each period is considered as an investment signal. Hence Zt−1 can be interpreted as time varying investment portion of the risky asset. The payoff (in
excess of risk free rate) of the actively managed portfolios is rt Zt−1 .
2.3
Testing of Market Segmentation
Method 1—othogonality condition test
Testing market segmentation is the same as testing subsets of othogonality conditions. The method we use to test whether a subset of othogonality
12
conditions holds is the one developed in Eichenbaum, Hansen, and Singleton (1988). Following the above notations, the whole pricing error vector is
k
1
rit (1 + ΣK
k=1 bk Rt ) ⊗ Zt−1 = ht . Partition the vector into two subvectors ht and
h2t . Here ht is N dimensional with N assets and parameter vector b0 , while
h1t and h2t are N1 , N2 dimension with N1 , N2 assets and K1 and K2 parameters
b10 , b20 respectively. The null hypothesis is :
if E[ht ] = 0 and E[h1t ] = 0,
then H0 : E[h2t ] = 0
Following the notation in the above section, assume that the matrices S0
b T : T ≥ 1} and
and D0 can be consistently estimated by { SbT : T ≥ 1} and {D
S0 is nonsingular. According to the orthogonality conditions, we partition D0 ,
S0 , S0−1 and gT as:
¯
¯
¯
¯
¯ D1 ¯
¯ 0 ¯
¯
D0 = ¯¯
¯
¯ D2 ¯
¯ 0 ¯
S0−1
¯
¯
¯
¯
= ¯¯
¯
¯
Se011
Se021
¯
¯
12 ¯
e
S0 ¯
¯
¯
22 ¯
e
S0 ¯
Where g1T (b1T ) = (1/T )
¯
¯
¯ S 11
¯ 0
S0 = ¯¯
¯ S 21
¯ 0
PT
t=1
S012
S022
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯ g (b )
¯ 1T 1T
gT = ¯¯
¯ g (b )
¯ 2T 2T
¯
¯
¯
¯
¯
¯
¯
¯
h1t , g2T (b2T ) = (1/T )
In order to implement this test, first,
PT
t=1
h2t
one chooses b0T to minimize the
objective function [gT ]0 SbT−1 [gT ]. Next, the estimator b1T is formed by using
only the first N1 orthogonality conditions that are presumed to hold under the
alternative hypotheses and the weighting matrix (SbT11 )−1 . Using both estimators
to calculate the distance
13
CT = T [gT (b0T )]0 SbT−1 [gT (b0T )] − T [g1T (b1T )]0 (SbT11 )−1 [g1T (b1T )]
(7)
Under null hypothesis, the asymptotic distribution of CT is χ2 with degrees
of freedom [N ∗ m − K − (N1 ∗ m − K1)], where m is the number of instruments.
If CT is statistically significant different from 0, the null hypothesis is rejected. This means that the stochastic discount factors used to price the two
groups of assets perform significantly differently. In the context of market segmentation, this means the market consisting of N2 assets is segmented from the
market consisting of the N1 assets.
Method 2—likelihood ratio test
Another formal test of market segmentation is obtained by comparing the
market prices of pricing risks. If the market is integrated, the prices should be
the same for different financial market. The null hypothesis here is that the
market is integrated, that is:
(1) H0:
beq = bex
(2)
H0:
bbd = bex
(3)
H0:
beq = bbd
where beq , bex , bbd are market pricing vectors for equities, currencies and
bonds respectively. To test these, we can use Wald test, Lagrangian multiplier
test and likelihood ratio test. As Monte Carlo simulations suggest that the
asymptotic distribution of the Wald test is a poorer approximation to its small
14
sample distribution than the other two tests, we use likelihood ratio test for our
case.
The likelihood ratio test statistic is
T = 2 ∗ (L(eb) − L(bb))
(8)
where bb is the unconstrained estimate of b and eb is the constrained estimate
of b such that H0 is true. L is the log likelihood function for the estimation
method used. Under the null hypothesis the test statistic is asymptotically
distributed as a χ2 random variable with r degrees of freedom, where r is the
number of constraints on the null hypothesis. The p-values reported for the
tests are computed from the distribution and are only asymptotically valid.
2.4
Comparison of model performance by HJ-distance
In order to compare the performance of different model, we can not use the optimal weighting matrix to calculate the pricing error because the weighting matrix
changes for different models and parameter values. We fix the weighting matrix
among different models for the same category of the assets. Following Hansen
and Jagannathan (1996), we use second-moment matrix G−1 = E[rt0 rt ]−1 as
weighting matrix for unconditional models, while G−1 = E[(rt ⊗ Zt−1 )0 (rt ⊗
Zt−1 )]−1 as the weighting matrix for the conditional models. The fixed weighting matrix allow us to compare the performance of models by the value of
the quadratic form E[wt (b)]0 G−1 E[wt (b)], whose square root is called HansenJagannathan distance (HJ-distance). Hansen and Jagannathan (1994) showed
that the value of the quadratic form is the squared distance from the candidate
15
stochastic discount factor of the given model to the set of all the discount factors
that price the N assets correctly. With this arbitrarily weighting matrix, the
quadratic form E[wt (b)]0 G−1 E[wt (b)] will asymptotically have a distribution
of weighted sum of χ2. Based on this, the HJ-distance of various models and
p-value of HJ-distance by the method of GMM can be calculated. The smaller
of the HJ-distance indicates better fit of the model.
3
Data and Summary Statistics
3.1
Data Sources and Data Specification
The international market consists of international equity market, currency market and bond market. The assets in these markets will be equities, foreign
currencies and bonds from each country. More specifically, we consider 4 industrialized countries with the largest market capitalization. They are US, United
Kingdom, Germany and Japan. Therefore, there are four equities, three foreign
exchanges and four bonds for the four countries.
All returns for assets are monthly excess returns. For equities, if equity
index for country i at time t is pit , rriskf ree is the one month US dollar risk-free
rate, then the excess return is rit =
ex
defined as: rit
=
pit −pi,t−1
pi,t−1
deposit
pex
)−pex
it (1+rit
i,t−1
pex
i,t−1
− rriskf ree . Currency returns are
− rriskf ree . Where pex
it is the exchange
deposit
rate of country i relative to US dollars at time t. rit
is the deposit rate of
currency i at time t. Bond returns are bond holding returns computed from the
long term government bond yield.
16
Data are from January 1982 to December 1998. The data for equity indices are from Morgan Stanley Capital International (MSCI) and they are all
expressed in US dollars. The bond indices are data stream total all lives government bond indices for each country. These data are from the last day of each
month. The monthly exchange rate data are from the Federal Reserve Board
and Economic Research Federal Reserve Bank of St. Louis (FRED).
In order to see whether the different international assets are priced the same,
we use standard international capital asset models following Dumas and Solnik
(1995). The world market risk factor is defined as world equity index returns.
The world equity index is from the MSCI. If purchasing power parity is violated,
then investing in foreign markets entails exposure to exchange rate risk. The
currency risk factor should be added. We will not break this into separate
factors for each country as Dumas and Solnik (1995) did. As they state that,
the separation of foreign exchange risk “ creates a potential problem since in
reality investors bear exchange risks from other currencies.” Following Ferson
and Harvey (1994), we use the returns on trade-weighted US dollar price of the
currencies of 10 industrialized countries the proxy of the currency risk factor.
The G-10 trade weighted currency index return is understood as the aggregate
measure of currency risk.
The selection of conditioning information is an important step. The instrumental variables should summarize the information that international investors
use to formulate prices. The conditional variables are selected by comparing
with the literature. Harvey (1991) uses following common instruments for world
17
equity market: 1. return of S&P 500 index, 2.dummy variable for January, 3.return difference of 3 month treasure bill and 1 month treasure bill, 4. return
difference of Baa corporate bond and Aaa corporate bond. Instruments in Dumas and Solnik (95) are: 1. constant,2.the excess rate of return on the world
index lagged one month,3. a January dummy,4. the US bond yield, 5.the dividend yield on the US index, 6. the one-month rate of interest on a Eurodollar
deposit. Santis and Gerard (98) use following instruments:1.a constant,2.the
dividend yield on the world equity index in excess of the one-month Eurodollar
rate,3. the change in the US term premium measured by the yield on the tenyear US Treasury note in excess of the one-month Eurodollar rate, 4.the change
in the one-month Eurodollar deposit rate, 5. the US default premium measured
by the yield deference between Moody’s Baa-rated and Aaa-rated bonds.
Dumas and Solnik document that the US bond yield, the US dividend yield,
and the Eurodollar rate are fairly strongly correlated, and all three are somewhat correlated with the lagged world equity return. Plus that the dividend
yield, the bond yield and short-term rate of interest may not be stationary.
Therefore, among these instruments, we only chose lagged world equity return
and Eurodollar rate.
Following the literature and also considering above discussions, we select
following instruments:
1. a constant
2.lagged world equity market return in excess of US risk free rate, denoted
as rmlag.
18
3. the US default premium measured by the yield deference between Moody’s
Baa-rated and Aaa-rated bonds, denoted as rdef.
4. the change in the US term premium measured by the yield on the ten-year
US Treasury note in excess of the US risk free rate, denoted as rtm11 .
5. the one-month rate of interest on a Eurodollar deposit, denoted as euro.
The Eurodollar deposit rate is the 1 month Eurodollar deposit rate bid at
11am London time from data stream. The US risk free rate should be one
month T-bill rate. As one month T-bill rate is not available in our time period,
we use three month T-bill rate from FRED instead. The available data of one
month rate and three month rate are compared and we find that the difference
is very small. All interest rates are divided by 12 to change the annually rate
to monthly rate.
3.2
Risk factor specification
Cochrane (2001) points out that: since we can always take linear combination
of factors to reduce the number of factors, the pure number of pricing factors is
not a meaningful question. However, sometimes, an economic interpretation of
the factors can be lost on taking a linear combination of the factors . He then
argues that clear economic foundation is important for factor models. Carefully
describing the fundamental macroeconomic sources of risk thus provides more
1 We also use GDP weighted risk free rate, default premium, term premium from the major
industrilized countries, the results are not good to interprete. The problem could be the noisy
of this type of weighted data.
19
discipline for empirical work.
In the literature, there are two basic approaches to identify factors. One
is to use statistic techniques to identify optimal risk factors such as Connor
and Korajczyck (1993). The other is to specify a set of macro economic factors
(state variables), for example, Chen, Roll and Ross (1988). We will use the later
approach to identify factors.
By Cochrane (2001), factor pricing models choose for factors according to
the following approximation:
0
0
t)
β uu0 (c(ct−1
) ≈ δ 0 + δ ft
Any variable that is good proxy for aggregate marginal utility growth is an
economically meaningful approximation. Directly speaking, investors are especially concerned about some special states of the economy in which their portfolios do not perform badly. The factor variables should be those of indication
or forecast of these “bad states”.
As consumption and marginal utility are related to the state of the economy, any variables that can measure the state of the economy are good candidate factors. Furthermore, consumption and marginal utility respond to news.
Therefore, any variable that forecasts changes in the investment opportunity set
or asset returns is a candidate factor. Consequently, macro economic factors as
state variables are proposed as pricing factors in the literature.
Following Dumas and Solnik (1995) and Ferson and Harvey (1994), we use
two market risk variables: equity risk factor and currency risk factor. In the
20
literature of multifactor asset pricing models, equally weighted or value weighted
equity market index returns are usually taken as the proxy for the market risk.
According to their argument, when we consider international assets, stock risk
is not the only source of market risk. Relative price change of currencies (foreign
exchanges) is another source of market risk. Therefore, it is necessary to consider
both equity market risk and currency market risk as the proxy of the world
market risk. The computation of these two factors are specified in the above
section.
Another two factors we considered are macroeconomic factors. Macroeconomic factors are systematic forces that can affect the asset prices by changing
the investment opportunities. Chen, Roll and Ross (1986) first investigate the
role of macroeconomic risk factors in the domestic multifactor models, followed
by numerous others. Ferson and Harvey (1994) use macroeconomic factors in
the international asset pricing models.
The first macroeconomic factor we considered is term structure. This factor
has been used by many authors such as Chen, Roll and Ross (1980), Ferson and
Harvey (1994), and Lettau and Ludvigson(2001). They argue that this factor
captures investors expectation of the trend of economy and it will influence
the asset returns by changing the time value of the future cash flows. It can
also forecasts “good” state or “bad” state of the economy. It is defined as the
difference between the yield on the seven-year US Treasury note and 3 month
treasure bill return denoted as rtm2t. We use seven year US treasury note
instead of long term government bond is because business cycle usually takes
21
about five to eight years.
The second macroeconomic factor considered is default risk. Chen, Roll
and Ross (1986) and Ferson and Harvey (1994) used this risk factor because
it has been argued that it captures the change of risk aversion of international
investors. It is also a forecast of “good” state or “bad” state. The increasing
of this premium indicates a ”bad” state. It is approximated by the difference
between Moody’s Baa corporate bond return and the Aaa corporate bond return
denoted as rdeft.
3.3
Data analysis and Summary Statistics
In order to have a basic idea about the behavior of different assets and the data
properties, we give a preliminary data analysis as following.
Figure 1 and Figure 2 give the trends in the international equity market and
bond market. They plot the equity index trend and bond index trend for the
four countries considered. The equity market shows upward trend while there
is no apparent trend for the bond market. Figure 3 and Figure 4 plot foreign
exchange rate against time. Foreign exchange market shows downward trends
indicating appreciation of U.S. dollars during this period. From these figures,
we can visually tell that these assets behave quite differently.
The description statistics are in Table 1. Panel A of the Table 1 gives the
statistics for excess returns of all assets considered. The mean of excess equity
returns are all positive. It’s interesting to see from the table that US equity
22
market has both lowest average return and volatility. This is consistent with
the financial theory of low risk low return. Japanese equity market has relatively
small mean and largest standard deviation. That means Japanese stock market
has relatively low return with highest risk. This unusual phenomenon may be
related to Japanese economic bubble. Other country’s market is consistent with
the financial theory of high return high risk. The autocorrelations of equities
are very small and not significant.
The means of bond index returns are all positive with standard deviations
much lower than those of equity returns, which indicates much more stable of
bond market. All bonds exhibit significant first order autocorrelation. But
the autocorrelations die out one month later. The currency deposit returns
have lower means and higher standard deviations than those of bonds, but
lower standard deviations than those of equities. Currency returns show similar
autocorrelation patterns as that of bonds. The fluctuations of returns in different
international markets can also be seen in figure 5, 6 and 7. The figures show
that there is no trend for the series and the volatilities of series do not change
much with time. By Dicky-Fuller test, all return series are stationary.
Panel B of Table 1 provides the descriptive statistics for risk factors. The
world equity index return has lower standard deviation than that of any country,
which indicates relatively low risk of world stock index return. This data does
not show significant autocorrelations. Similar to the world equity return, world
currency risk premium is lowest among all currency returns. It also shows
significant first order autocorrelation but dies out one month later. Figure 8
23
gives the fluctuation of these two terms. Term structure and default premium
show significant first order autocorrelation but dies out one month later as well.
Dicky-Fuller tests reject the null hypothesis of nonstationary of these series. The
volatilities of the term structure and default premium are much lower than the
world equity market index. Given their small volatilities, it would be hard for
the model to price the term premium and default premium. If they are priced,
that implies that they are really strong factors in predicting returns.
The descriptive statistics for instruments are in Panel C of Table 1. Notice
that lagged term premium, default premium, and excess Eurodollar returns have
much lower standard deviation than lagged world equity risk premium. Among
all instruments, lagged term premium and default premium show significant first
order autocorrelations but the autocorrelations die out one month later again.
Excess Eurodollar returns exhibit significant autocorrelations up to 4 lags. As
the autocorrelations decay very fast, we can judge all series are stationary. The
Dicky-Fuller tests also confirm this judgement. Therefore the assumption of
stationary data for GMM is satisfied.
In order to gauge the instruments predictive ability, various assets’ returns
are regressed on the instruments. The results are provided in Table 2. Though
the R squares are low, but several coefficients are significant. The equity market
risk premium is significant to predict the US, Japanese, and German bond returns. Term premium is significant in predicting most asset returns. Eurodollar
plays significant role in predicting Japanese bond returns and French currency
returns.
24
The correlations between pricing factors are presented in Table 3. Table
3 shows that correlations between factors are small except the correlation between term premium and default premium, which is -0.33421. There may have
some multicollinearity, but the collinearity is not perfect after implementing
multicollinearity diagnose.
4
Main Results
4.1
4.1.1
Test of Market Integration
Linear Regression
In order to have a rough idea about the relationship of assets and international
market risk factors: world equity risk factor (reqwd) and world currency risk factor (rexwd), all single assets (equity returns, bond returns and foreign exchange
returns) are regressed on these factors. The linear model for excess returns ri,t
is
ri,t = β 0 + β reqwd,i, ∗ reqwdt + β rexwd,i ∗ rexwdt
(9)
Where β 0 is the intercept term. The results are in Table 4. All R-squares
for equity and currency assets are very high ranging from 0.33 to 0.95 with
significant role of reqwd and rexwd for most single equities and currencies.
This indicates that world equity market risk premium and world currency risk
premium play significant roles in predicting single equity and currency returns
for different countries. However, the R squares for bonds are very low with only
25
reqwd being significant. The currency risks usually do not affect bond returns.
These also show that bond market is quite different from equity market and
exchange market.
Then, we do regressions for the conditional linear international model:
rt = β 0t + β 1t ∗ reqwdt + β 2t ∗ rexwdt
Following Lettau and Ludvigson (2001)’s arguments, β 0t , β 1t and β 2t are
time varying. That is
β 0t = β 01 + β 02 ⊗ Zt−1
β 1t = β 11 + β 12 ⊗ Zt−1
where
β 2t = β 21 + β 22 ⊗ Zt−1
Zt−1 is the conditional information set. As specified in the data
section, Zt−1 = {1, rmlag, rtm1, rdef }t . The explicit form of the conditional
model in our case is:
rti = β i0 + β i1 ∗ reqwdt + β i2 ∗ rexwdt + β i4 ∗ rmlagt + β i4 ∗ rdeft + β i5 ∗ rtm1t +
β i6 ∗ eurot
+β i7 ∗ reqz1 + β i8 ∗ reqz2 + β i9 ∗ reqz3 + β i10 ∗ reqz4
+β i11 ∗ rexz1 + β i12 ∗ rexz2 + β i13 ∗ rexz3 + β i14 ∗ rexz4
(10)
Where
reqz1 = reqwdt ∗ rmlagt−1 , reqz2 = reqwdt ∗ rdeft−1 , reqz3 = reqwdt ∗
rtm1t−1 , reqz4 = reqwdt ∗ eurot−1
rexz1 = rexwdt ∗ rmlagt−1 , rexz2 = rexwdt ∗ rdeft−1 , rexz3 = rexwdt ∗
rtm1t−1 , rexz4 = rexwdt ∗ eurot−1
rti is the return of asset i. The results are in Table 5. The conditional linear
model increases R squares for all the cases, which implies that conditional model
26
performs better than unconditional ones. It’s interesting that while world equity
risk factor plays an important role in predicting equity returns for different
countries, the currency risk factor is no longer significant in this market. Both
factors are still significant for currency returns as before. This difference implies
that there exists potential difference between international equity market and
exchange market. The term premium plays very significant role in the bond
market. This again shows that bond market is different from the other two
markets.
The formal test of market integration by conditional linear model is presented in Table 6. As linear model is the special case of nonlinear model, we
use likelihood ratio test method described in the methodology part. The null
hypothesis is market integration. That is to test the equality of the coefficients
for different assets. The null hypothesis is rejected for all cases. Therefore,
the linear models indicate that international equity market, bond market and
currency market are segmented.
4.1.2
Stochastic Discount Factor Models
1. Orthogonality Condition Test
We then test the null hypothesis of market integration by the international
stochastic discount factor models with the method of Eichenbaum, Hansen
and Singleton (1988) discussed earlier in 2.3. The international asset pricing
model proposed by Dumas & Solnik (1995) and others includes both a stock
27
market risk factor and a currency risk factor in the model. The inclusion of
currency risk factor is to incorporate the international market risk from the
relative changing of currency prices. The reason to use this model is that the
assets we are examining are international assets. They should expose to both
stock market risk and the foreign exchange risk.
The unconditional version of the model is:
E[rit ∗ (1 + b1 ∗ reqwdt + b2 ∗ rexwdt )] = 0
(11)
The results in Panel A of Table 7 shows that most unconditional models are
rejected. Only the models for equities and bonds are not rejected. But none
of the factors are significant for equities. Only the world equity risk factor is
significant for bonds. Overall, the unconditional models do not perform well for
international assets.
Then we investigate the conditional international models:
E[rit ∗ (1 + b1 ∗ reqwdt + b2 ∗ rexwdt ) ⊗ Zt−1 ] = 0
Where the conditional information variables in Zt−1 are the same as defined
earlier. The explicit form of the model is:

[ri,t ∗ (1 + b1 ∗ reqwdt + b2 ∗ rexwdt )]



 [r ∗ (1 + b ∗ reqwd + b ∗ rexwd )] ∗ rmlag
 i,t
1
t
2
t
t−1


E
 [ri,t ∗ (1 + b1 ∗ reqwdt + b2 ∗ rexwdt )] ∗ rtm1t−1


 [r ∗ (1 + b ∗ reqwd + b ∗ rexwd )] ∗ rdef

i,t
1
t
2
t
t−1


[ri,t ∗ (1 + b1 ∗ reqwdt + b2 ∗ rexwdt )] ∗ eurot−1


 
 
 
 
 
 
 
=
 
 
 
 
 
 
 

0N 


0N 



0N 
 (12)


0N 



0N
To simplify notation, we use E[ht ] = 0 to denote above equation system
(12).
28
The results are presented in Table 7 Panel B. The models are not rejected
for most cases, the coefficients for most cases are significant, which shows better
performance of conditional models. This indicates investors do use conditional
information. However, overall, this type of the model does not perform very well
in explaining asset returns we considered except equity returns. The p-value for
the objective function of currency assets is much smaller than that of equity
assets or bond assets. This indicates exchange assets performs quite differently.
The two-factor model fit currency returns data very poorly.
We then test the market integration hypothesis based on the conditional
model. We first assume that different international asset markets are integrated.
That is to assume the integration of the international equity market and the
bond market, integration of equity market with currency market, and the integration of the bond market with the currency market. So the hypothesis test
is:
Assume:
E[ht ] = 0
for the whole asset group of r consisting of the sub asset group
of r1 and r2
E[h1t ] = 0
for the sub asset group of r1
Test H0:
E[h2t ] = 0
for the sub asset group of r2
To check the robustness, we then test the alternative null hypothesis of the
market segmentation. The hypothesis test will be:
Assume:
29
E[ht ] = 0
for the whole asset group of r consisting of the sub asset group
of r1 and r2
E[h1t ] 6= 0
for the sub asset group of r1
Test H0:
E[h2t ] = 0
for the sub asset group of r2
Market integration tests are done for international conditional models. We
use Eichenbaum, Hansen and Singleton (1988)’s method of testing orthogonality
condition to test the null hypothesis of the market integration. The results are
in Panel A of Table 8. Both the null hypothesis of integration of equity market
and bond market and the integration of equity market and currency market are
rejected.
Then we undertake the test of the null hypothesis of the market segmentation. The results are in Panel B of Table 8. We can not reject any null
hypothesis, indicating that the three types of markets are segmented from each
other.
2.Likelihood ratio test
The likelihood ratio test results are presented in Panel C of Table 8. The
model is the same as in (12). The test method is dexcribed in section 2.3. The
null hypotheses of integration of the equity market and the currency market,
and the integration of the equity market and bond market are strongly rejected
with the p-value less than .0001. The null hypothesis of integration of bond
market and currency market is rejected with p value of 0.0002.
Therefore, the hypothesis of integration of the international equity market,
30
bond market and currency market is rejected. This means that we can not price
the three type of assets together. Next, we will price international equities,
bonds, and currency returns with separate multifactor models.
4.2
Pricing of International Assets by multifactor models
We use the multifactor models discussed in the model section to price our international assets. Factors considered are equity market risk factor (reqwd),
foreign exchange risk factor (rexwd), term structure factor (rtm2t) and the default premium factor (rdeft). These factors are discussed and defined in section
3 of the paper. HJ-distance is used to compare the performance of different factor models for each category of the assets. The unconditional and conditional
multifactor models are:
k
E[rit (1 + ΣK
k=1 bk Rt )] = 0
(13)
k
E[ri,t (1 + ΣK
k=1 bk Rt ) ⊗ Zt−1 ] = 0mN
(14)
where bk is the subset of {b1 b2 b3 b4 }, Rtk is the subset of {rexwd rtm2t
rdef t reqwd}t . Zt−1 is the conditional variable set described in section 2, that is
Zt−1 = {1 rmlag rtm1 rdef euro}t−1 . To be more explicitly, the unconditional
models are:
Model 1: E[rit (1 + b1 ∗ rexwdt )] = 0
Model 2: E[rit (1 + b4 ∗ reqwdt )] = 0
Model 3: E[rit (1 + b1 ∗ reqwdt + b4 ∗ reqwdt )] = 0
Model 4: E[rit (1 + b2 ∗ rtm2tt + b3 ∗ rdef tt + b4 ∗ reqwdt )] = 0
31
Model 5: E[rit (1 + b1 ∗ reqwdt + b2 ∗ rtm2tt + b3 ∗ rdef tt )] = 0
Model 6: E[rit (1 + b1 ∗ reqwdt + b2 ∗ rtm2tt + b3 ∗ rdef tt + b4 ∗ reqwdt )] = 0
Model 7: E[rit (1 + b2 ∗ rtm2tt + b3 ∗ rdef tt )] = 0
The correspondent explicit conditional models are:
Model 8: E[rit (1 + b1 ∗ rexwdt ) ⊗ Zt−1 ] = 0mN
Model 9: E[rit (1 + b4 ∗ reqwdt ) ⊗ Zt−1 ] = 0mN
Model 10: E[rit (1 + b1 ∗ reqwdt + b4 ∗ reqwdt ) ⊗ Zt−1 ] = 0mN
Model 11: E[rit (1 + b2 ∗ rtm2tt + b3 ∗ rdef tt + b4 ∗ reqwdt ) ⊗ Zt−1 ] = 0mN
Model 12: E[rit (1 + b1 ∗ reqwdt + b2 ∗ rtm2tt + b3 ∗ rdef tt ) ⊗ Zt−1 ] = 0mN
Model 13: E[rit+1 (1 + b1 ∗ reqwdt + b2 ∗ rtm2tt + b3 ∗ rdef tt + b4 ∗ reqwdt ) ⊗
Zt−1 ] = 0mN
Model 14: E[rit (1 + b2 ∗ rtm2tt + b3 ∗ rdef tt ) ⊗ Zt−1 ] = 0mN
The explicit form of the cross product is the same as in equation (12). For
the unconditional models, the common weighting matrix of the HJ-distances is:
G−1 = E[rt0 rt ]−1 . For the conditional model, the common weighting matrix for
HJ-distance is G−1 = E[(rt ⊗Zt−1 )0 (rt ⊗Zt−1 )]−1 . We examine these models by
their different combination of factors to pin down which factors are significant
in pricing different international assets.
4.2.1
Pricing of Foreign Exchange Rate Returns
We tried the above fourteen models to explain currency returns. Table 9 gives
the results for the unconditional models (model 1-5, model 7). The first 3
models are rejected with HJ-distance significantly different from zero. Model 4
32
and 5 are exactly identified cases with term structure and default premium being
significant factors. The two-factor model 7 has the statistically insignificant HJdistance of 0.6132, this is the smallest among all the competing models. The
p-value of 82.86% indicates that we can’t reject this two-factor model. The
model also indicate that term structure and default premium are significant in
pricing foreign exchange returns.
The comparison of conditional multifactor models are in Table 10. Model
8, 9, and 10 are rejected indicating that either world currency index risk nor
world equity index risk are not enough to price foreign exchange returns. The
next four models are not rejected with the four factor model having the lowest
HJ-distance of 3.7661, which is statistically not significantly different from zero.
Term structure and default premium keep playing significant role in pricing
foreign exchange returns. The world equity market risk also shows significance
in several cases.
Both unconditional and conditional classical and international models do
not work for pricing foreign exchange returns.The term structure risk factor
and default risk factor improve the models’ performance dramatically in both
unconditional case and conditional case. The extremely good performance of
models with term and default premium factors indicates that the cross sectional
exchange rate returns can be priced by these two terms. That is cross sectional
foreign exchange returns are explained by fundamental economic variables. The
sign for the coefficients of term premium and default premium are all negative,
which means the increase of exposure to these risks requires higher compensation
33
for returns.
Another striking result is that even though the equity market risk and currency market risk factor explain a significant portion of the time-series variability of single exchange returns, they have insignificant influence on pricing when
compared with the fundamental economic state variables. Therefore, market
force variables are dominated by economic state variables. Foreign exchange
returns are priced by systematic economic forces such as term risk and default
risk2 .
4.3
Pricing of International Equities
Next, we apply the above seven unconditional and the seven conditional models
to the international equities. Table 11 and Table 12 give the results. From
Table 11, we can not reject any unconditional model. However, none of the
factors are significant except the market equity risk factor in the single factor
model (model 2). The classical single market factor model is not rejected with
the p value of the HJ-distance of 84.8% and the equity market risk factor is
statistically significant. This result is consistent with that was found in Dumas
and Solnik (1995).
Shown in Table 12, the conditional models perform very well for equities.
None of the model is rejected. It looks like that investors do use conditional
2 Note that the term premium and default premium are from US data. The GDP weighted
aggregate world premium and default premium are tried to replace the above two factors.
We find that they are not significant factors. This might because that we are looking at
US investors, the currency returns are more related to US fundamental forces. The world
aggregate variables just add more noise, which lead bad fit of the models.
34
information in making equity investment decision. Both equity market risk
factor and currency market risk factor play significant role in the single factor
model. However, when the macro economics factors are added into the model,
none of the market risk factors showing any significant role. The term structure
factor is persistently significant in all models. Unlike the case of exchange
rate returns, default risk factor does not play any significant role in explaining
equity returns. The finding of the significant role of term structure factor and
powerlessness of market risk factor in explaining of equity returns confirmed
Chen, Ross and Roll’s (1986) result in explaining domestic equity returns. They
argue that the equity market risk factor may be captured by the significant
macro economic factor.
4.4
Pricing of International Bonds
We then fit the unconditional and conditional models (model 1 to model 14) with
international bonds data. Shown in Table 13, the unconditional models perform
ok for bonds. The single currency risk factor model (model 1) is rejected. The
other models are not rejected. The equity market risk factor is significant in the
models without macro economics factors (model 2 and model 3). The default
risk factor is significant in the models that the equity risk factor is not included
(model 5 and model 7). It seems that simultaneously including both market
risk factor and default risk factor will hurt the model fit. This can be seen
from the not significant of any factor in model 4 and model 6. Our findings of
unconditional models for bonds are consistent with those of Fama and French
35
(1993) and Erb, Viskanta and Harvey (1996).
From Table 14, we can see that the conditional models perform poorly for
bond returns. All the models considered are rejected. The HJ-distances are
much bigger than the models for equities and currencies. And they are all significantly different from zero. The poor performance of the conditional models
for bonds seems to indicate that, unlike investing in risky assets, investors do
not update the conditional information when they make decision on investing
in fixed-income assets. This also indictes that bonds are risk free assets that
can not be explained by risky factors.
5
Conclusion
According to capital asset pricing theory, asset pricing models should price any
assets. However, should we price all international assets using the same stochastic discount factor model? In this paper, we examine the performance of
unconditional and conditional models for all international assets. We find that
there exists market segmentation in the international asset market. Given this,
we explain the foreign exchange rate returns, international equity returns and
bond returns with separate multifactor models. Different stochastic discount
factor models are examined and it is found that some fundamental economic
state variables term premium and default premium are significant factors in
pricing cross sectional returns of foreign exchanges. Market risk terms in international models play no significant role in predicting cross sectional return of
36
exchange rate. Unconditional models are not rejected but there is no persisitent
significant factor. Conditional models perform well for pricing international equities with the term structure playing a significant role. On the other hand,
unconditional models perform well for bonds with bond returns being explained
by the default premium and equity market risk premium, but conditional models
perform very poorly for bonds.
37
References:
Bekaert, G. and Hodrick, R.J., 1992, Characterizing predictable components
in excess returns on equity and foreign exchange markets, Journal of Finance
47, 467-51.
Brennan, M.J., Chordia, T. and Subrahmanyam, S., 1998, Alternative factor
specifications, security characteristics, and the cross-section of expected stock
returns, Journal of Financial Economics 49, 345-373.
Brennan, M.J. and Subrahmanyam, A., 1996, Market microstructure and
asset pricing on the compensation for illiquidity in stock returns. Journal of
Financial Economics 41, 341-364.
Chan, Louis K.C., Karceski, J. and Lakonishok, J., June 1998, The risk and
return from factors, Journal of Financial and Quantitative Analysis, Nol. 33,
No. 2.
Chen, N.F., Roll, R.and Ross, S. A., Jul., 1986, Economic forces and the
stock market, Journal of Business, Vol. 59, Issue 3, 393-403.
Cochrane, J.H., 2001, Asset Pricing, Princeton University Press.
Connor, G. and Korajczyk, T., 1993, A Test for the number of factors in an
approximate factor model. Journal of Finance 48, 1263-1291.
Dumas, B. and Solnik, B.,June 1995, The world rice of foreign exchange risk,
The Journal of Finance, Vol 47, No.2.
Eichenbaum, M. S., Hansen, L. P. and Singleton, K. J., Feb. 1988, A Time
Series Analysis of Representative Agent Models of Consumption and Leisure
Choice Under Uncertainty. The Quarterly Journal of Economics, Issue 1.
38
Elton, .E. J., Gruber, M. J. and Blake, C. R., Sep., 1995, Fundamental
economic variables, expected returns, and bond fund performance, The Journal
of Finance, Vol. 50, Issue 4, 1229-1256.
Erb, C. B., Viskanta, T. E. and Harvey, C. T., June 1996, The influence of
political, economic and financial risk on expected fiexed-income returns. Journal
of Fixed Income, Vol 6 No. 1.
Fama, E.F. and French, K.R., 1992, The Cross-Section of expected stock
returns, Journal of Finance 47, 427-465.
Fama, E.F. and French, K.R., 1993a, Differences in the risks and returns of
NYSE and NASDAQ stocks. Financial Analysts Journal 49, 27-41.
Fama, E.F. and French, K.R., 1993b, Common risk factors in the returns on
stocks and bonds. Journal of Financial Economics 33, 3-56.
Fama, E.F. and French, K.R., 1996, Multifactor explanations for asset pricing anomalies. Journal of Finance 51, 55-84.
Ferson, Wayne E. and Harvey, Campbell R., 1994, Sources of risk and expected returns in global equity markets. Journal of Banking & Finance 18,
775-803.
Harvey, C.R., March 1991, The world price of covariance risk, The Journal
of Finance, Vol. XLVI, No.1.
Hansen, Lars Peter, 1982, Large sample properties of generalized method of
moments estimators, Econometrica 50, 1029-1054
Hansen, Lars Peter, and Ravi Jagannathan, 1994, Assessing specification
errors in stochastic discount factor models, Technical working paper No. 153,
39
NBER.
Hansen, L and Richard, S., 1987, The role of conditioning information in
deducing testable restrictions implied by dynamic asset pricing models”, Econometrica 55, pp. 587-613.
Jagannathan, R.,Wang, Z.Y., Mar.1996, The conditional CAPM and the
cross-section of expected returns, Journal of Finance, Volume 51, Issue1, 3-53
Korajczyck, R.A., and C.J. Viallet, 1992, Equity risk premia and the pricing
of foreign exchange risk, Journal of International Economics, 199-220.
Kryzanowski, L., Lalancette, S. and To, M.C., Jun.1997, Performance attribution using an APT with prespecified macrofactors and time-varying risk
premium and betas, The Journal of Financial and Quantitative Analysis, Vol.
32, Issue 2 , 205-224.
Lettau, M. and Ludvigson, S., Dec., 2001, Resurrecting the CCAPM: A
Cross-Sectional Test When Risk Premia Are Time -Varying, Journal of Political
Economy, Number 6, Vol. 109..
Lo, A.W., MacKinlay, A.C., 1990, Data-snooping biases in tests of financial
asset pricing models. Review of Financial Studies 3, 431-468.
Roll. R., 1977, A critique of the Asset Pricing Theory’s tests: on past and
potential testability of theory, Journal Financial Economics 4, 129-176.
Santis,Giorgio De and Gerard, Bruno, 1998, How big is the premium for
currency risk, Journal of Financial Economics 49, 375-412.
Sercu, P., 1980, A generalization of the international asset pricing model,
Finance 91-135.
40
Solnik, B., 1974, An equilibrium model of the international capital market,
Journal of Economic Theory 8, 500-524.
Stulz, R. M., 1981, A model of international asset pricing, Journal of Financial Economics 9, 383-406.
41
Table 1
Summary Statistics
Requs, requk, reqgm and reqjp are excess equity index returns from U.S, United Kindom,
German and Japan. Rbdus, rbduk, rbdgm, and rbdjp are excess bond returns calculated from
long term government yields from these countries. Rexuk, rexgm, and rexjp are excess
exchange returns of British pound, German deutsche mark, Japanese yen (defined by the
currency one month deposit return compounded with variation of exchange rates). Reqwd is
the excess world equity index return. Rexwd is the G-10 trade weighted exchange index
return excess of risk free rate. Rmlag is the lagged term of reqwd. Rdef is the lagged
default premium defined as the difference of US Baa corporate bond returns and Aaa
corporate bond returns. Rtm1 is the lagged term premium defined by the difference between
ten year t-bill note return and three month t-bill return. Euro is the lagged one month
Eurodollar rate in excess of risk free rate. Rdeft is the default premium defined as the
difference between Baa corporate bond returns and Aaa corporate bond returns. Rtm2t is
the term premium defined as seven year Treasury bill return in excess of 3 month t-bill
rate. The ρi’s are autocorrelations lagged by i.
________________________________________________________
Nomber of Observations=202 (March 1982-December 1998)
_____________________________________________
Panel A: Excess Returns of Assets
variable
mean
0.0059705
0.0072959
0.0081282
0.0062159
Standard
deviation
0.04192
0.05537
0.06027
0.07055
requs
requk
reqgm
reqjp
ρ1
-.04665
-.05567
-.01547
0.07594
ρ2
-.00311
-.06790
0.04505
-.08691
ρ3
-.08244
-.04553
0.04073
0.06008
ρ4
-.14500
0.00292
0.08924
0.07157
ρ12
-.01722
-.08662
-.01936
0.01323
ρ24
0.12170
0.07093
0.01880
0.04844
rbdus
rbduk
rbdgm
rbdjp
0.0048974
0.0058049
0.0026792
0.0011409
0.02042
0.01904
0.01542
0.02375
0.39383*
0.28837*
0.35552*
0.14799*
0.01632
0.02746
0.06628
0.08736
0.01809
-.12576
0.06983
-.06910
0.01529
-.07233
0.01771
-.11418
-.07637
-.00114
-.02681
0.08223
0.02455
0.05091
-.09177
-.02379
rexuk
rexgm
rexjp
0.0035409
-0.0018599
-0.0047444
0.02729
0.02744
0.02944
0.32381*
0.30744*
0.33443*
-.05892
0.01475
0.02186
0.04698
0.07514
0.03880
0.01969
0.03425
-.04972
0.06728
0.06359
0.02298
-.02008
-.08093
-.02392
42
Panel B: Risk Factors
variable
mean
Standard
deviation
ρ1
ρ2
ρ3
ρ4
ρ12
ρ24
reqwd
0.0061388
0.04063
0.01196
-.03524
-.05235
-.04655
0.01047
0.14834
rexwd
-0.0057908
0.02239
0.31905*
0.00624
0.07467
0.01404
0.06217
-.07850
rtm2t
0.004897
0.02042
0.39383*
0.01632
0.01809
0.01529
-.07637
0.02455
rdeft
0.00097
0.00558
0.29563*
-.04098
0.04080
-.02898
-.04828
0.01577
Panel C: Instruments
variable
mean
rmlag
rtm1
rdef
euro
0.0004196
0.0048692
0.0010109
0.0004516
Standard
deviation
0.04118
0.02041
0.005566
0.000421
ρ1
0.02978
0.39876*
0.23704*
0.69591*
43
ρ2
-.03445
0.01401
-.06836
0.61132*
ρ3
-.03519
0.01424
-.10724
0.59173*
ρ4
-.02019
0.01284
-.01471
0.45857*
ρ12
0.00944
-.07751
-.10823
0.26146
ρ24
0.15097
0.02523
0.03125
0.22608
Table 2
Excess Returns Regressed on the Instruments
Regression: ri = a0 +a1*rmlag+a2*rdef+a3*rtm1+a3*euro
Where ri is an element of { requs requk reqgm reqjp rbdus
rbduk rbdgm rbdjp rexuk rexgm rexjp}
rmlag
rdef
rtm1
euro
Constant
Observations
R-squared
(1)
requs
-0.098
(1.32)
-0.108
(0.19)
0.426
(2.68)**
3.409
(0.48)
0.003
(0.56)
202
0.05
(2)
requk
-0.062
(0.62)
-0.373
(0.50)
0.349
(1.64)
-0.851
(0.09)
0.006
(1.07)
202
0.02
(3)
reqgm
-0.073
(0.68)
-1.304
(1.62)
0.438
(1.92)
-12.747
(1.26)
0.013
(2.05)*
202
0.05
(4)
reqjp
0.048
(0.39)
0.129
(0.14)
0.789
(2.98)**
5.891
(0.50)
-0.000
(0.06)
202
0.06
(5)
rbdus
-0.098
(2.94)**
-0.124
(0.49)
0.436
(6.14)**
1.697
(0.54)
0.002
(1.09)
202
0.20
Absolute value of t statistics in parentheses
* significant at 5%; ** significant at 1%
rmlag
rdef
rtm1
euro
Constant
Observations
R-squared
(7)
rbdgm
-0.045
(1.76)
-0.345
(1.77)
0.260
(4.73)**
-4.008
(1.63)
0.004
(2.32)*
202
0.15
(8)
rbdjp
-0.131
(3.19)**
0.329
(1.06)
0.304
(3.46)**
-7.828
(2.01)*
0.003
(1.19)
202
0.09
(9)
rexuk
0.011
(0.23)
0.498
(1.35)
-0.019
(0.18)
8.128
(1.75)
-0.001
(0.19)
202
0.02
(10)
rexgm
0.098
(2.01)*
0.232
(0.63)
-0.207
(1.99)*
4.451
(0.96)
-0.003
(1.07)
202
0.04
(11)
rexjp
-0.011
(0.22)
-0.270
(0.68)
-0.292
(2.61)**
5.585
(1.12)
-0.006
(1.78)
202
0.04
Absolute value of t statistics in parentheses
* significant at 5%; ** significant at 1%
44
(6)
rbduk
-0.043
(1.27)
-0.330
(1.29)
0.142
(1.96)
0.146
(0.05)
0.005
(2.67)**
202
0.04
Table 3
Correlation Coefficients of risk factors
Reqwd is the excess world equity index return. Rexwd is the G-10 trade weighted exchange
index return in excess of risk free rate. Rdeft is the default premium defined as the
difference between Baa corporate bond returns and Aaa corporate bond returns. Rtm2t is
the term premium defined as seven year Treasury bill return in excess of 3 month t-bill
rate.
reqwd
rexwd
rtm2t
rdeft
____________________________________________________________________
reqwd
1.00000
-0.21699
0.28674
-0.15635
rexwd
-0.21699
1.00000
-0.21343
0.22029
rtm2t
0.28674
-0.21343
1.00000
-0.33421
rdeft
-0.08536
0.08109
-0.33421
1.00000
________________________________________________________________________
Table 4
Regression of Each Single Asset on International Risk
Factors (Unconditional Model)
Regression: rit = β0 +βreqwd*reqwd+ βrexwd *rexwd
Where rit is the excess asset returns, and reqwd and rexwd are
international market risk factors.
reqwd
rexwd
Constant
R-squared
(1)
requs
0.848
(18.99)**
0.322
(3.97)**
0.003
(1.43)
0.64
(2)
requk
1.003
(15.98)**
-0.313
(2.75)**
-0.001
(0.26)
0.60
(3)
reqgm
0.819
(9.26)**
-0.178
(1.11)
0.002
(0.57)
0.33
(4)
reqjp
1.220
(14.36)**
-0.382
(2.48)*
-0.003
(1.00)
0.55
(5)
rbdus
0.132
(3.81)**
-0.116
(1.85)
0.003
(2.40)*
0.10
(6)
rbduk
0.146
(4.50)**
0.007
(0.12)
0.005
(3.73)**
0.10
Absolute value of t statistics in parentheses
* significant at 5%; ** significant at 1%
(7)
rbdgm
0.105
(3.95)**
0.009
(8)
rbdjp
0.100
(2.41)*
-0.134
(9)
rexuk
-0.020
(0.67)
0.942
(10)
rexgm
0.029
(2.68)**
1.207
(11)
rexjp
-0.109
(3.02)**
0.895
(0.19)
(1.78)
(16.99)**
(62.15)**
Const.
0.002
-0.000
0.009
0.005
(13.66)*
*
0.001
R-sqrd
(1.92)
0.07
(0.14)
0.05
(7.27)**
0.61
(11.27)**
0.95
(0.75)
0.53
reqwd
rexwd
Absolute value of t statistics in parentheses
* significant at 5%; ** significant at 1%
45
Table 5
OLS Regression of Each Asset on International Risk Factors
and Instrument Scaled Factors (Conditional)
Model: rit = β0 +βreqwd*reqwd+ βrexwd *rexwd + βrmlag*rmlag +βrdef *rdef
+βrtm1*rtm1 + βeuro*euro+βreqz1 *reqz1+βreqz2 *reqz2+βreqz3 *reqz3+βreqz4
*reqz4+βrexz1 *rexz1+βrexz2 *rexz2+βrexz3 *rexz3+βrexz4 *rexz4
Where
reqz1=reqwd*rmlag, reqz2=reqwd*rdef, reqz3=reqwd*rtm1, reqz4=reqwd*euro
rexz1=rexwd*rmlag, rexz2=rexwd*rdef, rexz3=rexwd*rtm1, rexz4=rexwd*euro
rit is the asset return from {requs, requk, reqgm reqjp rbdus rbduk
rbdgm rbdjp rexuk rexgm rexjp}t
reqwd
rexwd
rmlag
rdef
rtm1
euro
reqz1
reqz2
reqz3
reqz4
rexz1
rexz2
rexz3
rexz4
Constant(β0)
Observation
s
R-squared
(1)
requs
0.744
(10.73)**
0.217
(1.68)
-0.066
(1.25)
0.051
(0.15)
-0.005
(0.04)
0.333
(0.07)
0.842
(0.72)
-18.281
(1.53)
-4.199
(1.69)
239.320
(2.27)*
-0.332
(0.19)
13.105
(0.83)
-2.521
(0.50)
215.727
(1.08)
0.003
(0.90)
202
(2)
requk
0.943
(9.85)**
-0.068
(0.38)
-0.045
(0.62)
-0.171
(0.36)
-0.180
(1.18)
3.149
(0.51)
-0.485
(0.30)
18.524
(1.12)
-8.005
(2.33)*
123.169
(0.84)
-2.156
(0.88)
12.631
(0.58)
-9.494
(1.36)
-488.434
(1.77)
0.001
(0.22)
202
(3)
reqgm
0.896
(6.51)**
-0.060
(0.23)
-0.149
(1.43)
-1.162
(1.69)
0.146
(0.67)
-11.923
(1.34)
-1.793
(0.78)
29.715
(1.26)
-0.116
(0.02)
-228.710
(1.09)
-6.839
(1.94)
33.209
(1.06)
4.843
(0.48)
-359.477
(0.91)
0.010
(1.73)
202
(4)
reqjp
1.345
(10.16)**
-0.378
(1.54)
0.149
(1.48)
0.142
(0.22)
0.017
(0.08)
3.275
(0.38)
-0.005
(0.00)
22.592
(0.99)
11.602
(2.45)*
-290.958
(1.44)
1.750
(0.52)
-7.333
(0.24)
3.288
(0.34)
43.451
(0.11)
-0.007
(1.33)
202
(5)
rbdus
0.110
(2.18)*
-0.222
(2.37)*
-0.070
(1.84)
-0.132
(0.52)
0.357
(4.45)**
1.345
(0.41)
0.210
(0.25)
-5.695
(0.66)
1.395
(0.77)
-19.059
(0.25)
0.792
(0.61)
-8.506
(0.74)
2.754
(0.75)
274.664
(1.89)
0.001
(0.58)
202
(6)
rbduk
0.198
(3.91)**
0.000
(0.00)
-0.016
(0.42)
-0.391
(1.54)
0.096
(1.19)
0.335
(0.10)
0.803
(0.95)
-5.709
(0.66)
-0.782
(0.43)
-103.710
(1.35)
1.696
(1.31)
-11.555
(1.00)
2.582
(0.70)
17.790
(0.12)
0.005
(2.47)*
202
0.67
0.64
0.37
0.58
0.27
0.15
Absolute value of t statistics in parentheses
* significant at 5%; ** significant at 1%
46
reqwd
rexwd
rmlag
rdef
rtm1
euro
reqz1
reqz2
reqz3
reqz4
rexz1
rexz2
rexz3
rexz4
Constant
Observations
R-squared
(7)
rbdgm
0.086
(2.19)*
0.141
(1.94)
-0.035
(1.19)
-0.375
(1.92)
0.246
(3.95)**
-4.103
(1.63)
1.141
(1.74)
0.077
(0.01)
-1.265
(0.90)
-3.544
(0.06)
1.313
(1.31)
0.677
(0.08)
1.803
(0.63)
-232.546
(2.06)*
0.004
(2.48)*
202
0.23
(8)
rbdjp
0.068
(1.09)
-0.071
(0.61)
-0.114
(2.41)*
0.468
(1.49)
0.204
(2.04)*
-9.840
(2.44)*
-2.155
(2.05)*
-1.621
(0.15)
5.225
(2.33)*
-10.304
(0.11)
-0.555
(0.35)
1.982
(0.14)
1.758
(0.39)
-54.364
(0.30)
0.002
(0.89)
202
0.17
(9)
rexuk
-0.057
(1.21)
1.091
(12.47)**
-0.073
(2.04)*
0.385
(1.63)
0.205
(2.73)**
2.957
(0.97)
-0.115
(0.15)
-3.657
(0.45)
-0.870
(0.52)
20.615
(0.29)
-1.679
(1.39)
0.640
(0.06)
3.113
(0.91)
-362.174
(2.67)**
0.007
(3.81)**
202
0.64
Absolute value of t statistics in parentheses
* significant at 5%; ** significant at 1%
47
(10)
rexgm
0.038
(2.34)*
1.238
(40.77)**
0.047
(3.83)**
0.004
(0.05)
-0.049
(1.89)
-1.341
(1.27)
0.158
(0.58)
-0.919
(0.33)
0.464
(0.79)
-11.974
(0.48)
1.129
(2.70)**
-3.153
(0.85)
-1.343
(1.13)
-35.163
(0.75)
0.006
(8.51)**
202
0.96
(11)
rexjp
-0.124
(2.28)*
0.642
(6.36)**
-0.094
(2.30)*
-0.356
(1.31)
-0.073
(0.84)
2.476
(0.71)
-1.885
(2.07)*
-1.792
(0.19)
-1.501
(0.77)
38.902
(0.47)
-2.691
(1.93)
7.718
(0.63)
0.035
(0.01)
463.974
(2.97)**
0.001
(0.33)
202
0.59
Table 6 Likelihood Ratio Test of Market Integration
Using conditional Linear Models(OLS)
Model: ri = β0i +β1i*reqwd+ β2i *rexwd + β3i*rmlag +β4i *rdef +β5i*rtm1 +
β6i*euro+β7i *reqz1+β8i *reqz2+β9i *reqz3+β10i *reqz4+β11i *rexz1+β12i
*rexz2+β13i *rexz3+β14i *rexz4
Where
reqz1=reqwd*rmlag, reqz2=reqwd*rdef, reqz3=reqwd*rtm1, reqz4=reqwd*euro
rexz1=rexwd*rmlag, rexz2=rexwd*rdef, rexz3=rexwd*rtm1, rexz4=rexwd*euro
ri are the asset returns from equities={requs, requk, reqgm reqjp},
bonds={rbdus rbduk rbdgm rbdjp}, or foreign exchanges= {rexuk rexgm
rexjp}
eq, ex, bd are used in the superscript to stand for the case when
assets are equities, foreign exchanges and bonds respectively.
Null Hypothesis
H0: Market Integration
β keq= βkex
k=1,2,…14
β kbd= βkex
k=1,2,…14
β keq= βkbd
k=1,2,…14
Chisquare
P-value
Test
result
1651.6
<.0001
Reject H0
1034.0
<.0001
Reject H0
748.17
<.0001
Reject H0
Table 7
Panel Unconditional International Discount Factor Model
(GMM)
Model: E[rit*(1+b1*reqwdt+b2*rexwdt)]=0
Equities &
Currencies
-3.3068
Bonds &
Currencies
-16.9349
Equities
Bonds
Currencies
reqwd
Equities
& Bonds
-4.48719
-3.78811
-23.1666
-8.7833
t
(-1.98)*
(-1.59)*
(-3.41)**
(-1.43 )
(-2.40)*
(-0.97)
Rexwd
-0.16481
3.3417
-3.2661
-0.85659
-8.94839
1.9131
t
(-0.02 )
(0.89)
(-0.72)
(-0.09 )
(-0.36)
(0.33)
Chi-sqr
13.7576
14.9059
18.2378
0.6883
1.3965
9.6951
df
6
5
5
2
2
1
p-value
3.25
1.08
0.27
70.88
49.75
0.18
48
Panel B Conditional International Discount Factor Model
(GMM)
Model: E[rit*(1+b1*reqwdt+b2*rexwdt) ⊗ Zt-1]=0
Where Zt-1 ={1 rmlag rtm1 rdef euro}t-1
Equities &
Currencies
-4.4538
Bonds &
Currencies
-20.1681
Equities
Bonds
Currencies
Reqwd
Equities
& Bonds
-1.06273
-2.72981
-16.3543
-16.2093
t
-0.78
(-2.76)**
(-8.22)**
(-1.67)
(-4.41)**
(-3.33)**
Rexwd
21.93377
9.4983
-2.8416
13.8569
19.50077
-0.3790
t
(6.46)**
(3.08)**
(-0.78)
(2.49)*
(2.69)**
(-0.08)
Chi-sqr
47.0544
44.6509
42.5942
16.7476
27.3589
25.0789
df
38
33
33
18
18
13
p-value
14.89%
8.48%
12.24%
54.05%
7.25%
2.25%
Table 8
Panel A:
Testing of Market Integration
(Use Conditional international models)
Null Hypothesis: Market integration
E[ ht ]= 0 for whole assets group r
E[ ht 1]= 0 for asset group r 1
Test H0: E[ ht 2]= 0 for asset group r 2
Groups of Assets
r=equities & bonds
r 1 =equities
r=equities & currencies
r 1 =equities
CT = T * Obj − T * Obj 1
30.31
27.90
p-value
6.51%
Reject H0
Equities are segmented
from bonds
2.22%
Reject H0
Equities are segmented
from currencies
Test results
49
Panel B
Testing of Market Segmentation
(Use Conditional international models)
E[ ht ]= 0 for whole assets group r
E[ h1t ] ≠ 0 for asset group r 1
Test H0: E[ h 2 t ]=0 for asset group r 2
Groups of Assets
r=equities & bonds
r 1 =bonds
r=equities & currencies
r 1 =currencies
r=bonds & currencies
r 1 =currencies
CT = T * Obj − T * Obj 1
19.69
19.57
7.95
p-value
47.68%
Can not reject H0
Bonds are
segmented from
equities
48.50%
Can not reject H0
Currencies are segmented
from equities
61.93%
Can not reject H0
Currencies are
segmented from bonds
Test results
Panel C
Testing Market Integration: Likelihood Ratio Test
(Conditional International Models)
Model: E[rit*(1+b1*reqwdt+b2*rexwdt) ⊗ Zt-1]=0
Where Zt-1 ={1 rmlag rtm1 rdef euro}t-1
The parameters have superscript of eq, ex, bd when the asset groups are
equities, foreign exchanges and bonds respectively.
Null
Hypothesis(H0)
eq
i
b
=b ,
ex
i
i=1,2
bibd = biex
i=1,2
bieq = bibd
i=1,2,
Chi-square
P-value
Test result
18.94
<.0001
Reject H0
17.28
0.0002
Reject H0
29.77
<.0001
Reject H0
50
Table 9
Unconditional Discount Factor Models to Price
Foreign Exchange Rate Returns(GMM HJ-distance)
Model
Model
Model
Model
Model
Model
1:
2:
3:
4:
5:
7:
Where rit
E[rit*(1+b1*rexwdt)]=0
E[rit*(1+b4*reqwdt)]=0
E[rit*(1+b1*rexwdt +b4*reqwdt)]=0
E[rit*(1+b2*rtm2tt +b3*rdeftt+b4*reqwdt)]=0
E[rit*(1+b1*rexwdt +b2*rtm2tt +b3*rdeftt)]=0
E[rit*(1+b2*rtm2tt +b3*rdeftt)]=0
are the excess returns of foreign exchange rates.
models
1
rexwd
Rtm2t
rdeft
2
3
0.444911
(0.1)
4
5
4.986951
(0.61)
7
•
•
•
•
reqwd
3.124689
(1.00)
-40.6464
(-3.06)**
-30.9227
(-1.29)
-43.3902
(-3.46)**
-430.217
(-3.20)**
-513.886
(-2.62)**
-426.019
(-3.17)**
-7.06949
(-1.35 )
-6.5596
(-0.91)
3.46993
(-0.61)
HJ-distance
3.9539
(0.04%)
3.8487
(0.06%)
3.8473
(0.01%)
--0.6132
(82.86%)##
Numbers below the coefficients are t statistics. Numbers below the Objective*T is
the p- value.
* significant at 5%; ** significant at 1%.
# the model is marginally not rejected. ## the model is not rejected.
Model 4 and model 5 are exactly identified.
Table 10
Conditional Discount Factor Models to Price Foreign
Exchange Rate Returns (GMM HJ-distance)
Model 8: E[rit*(1+b1*rexwdt)
Model 9: E[rit*(1+b4*reqwdt)
⊗ Zt-1]=0mN
⊗ Zt-1]=0mN
⊗ Zt-1]=0mN
⊗ Zt-1]=0mN
+b2*rtm2tt +b3*rdeftt) ⊗ Zt-1]=0mN
+b2*rtm2tt +b3*rdeftt + b4*reqwdt ⊗ Zt-1]=0mN
+b3*rdeftt) ⊗ Zt-1]=0mN
Model 10: E[rit*(1+b1*rexwdt +b4*reqwdt)
Model 11: E[rit*(1+b2*rtm2tt +b3*rdeftt+b4*reqwdt)
Model 12: E[rit*(1+b1*rexwdt
Model 13: E[rit*(1+b1*rexwdt
Model 14: E[rit*(1+b2*rtm2tt
Where Zt-1 ={1 rmlag rtm1 rdef euro}t-1,
foreign exchange rates.
rit
51
are the excess returns of
models
rexwd
8
Rtm2t
rdeft
9
10
-1.43661
(-0.38)
11
12
-2.96099
(-0.80 )
-7.88826
(-1.83)
13
14
•
•
•
1:
2:
3:
4:
5:
6:
7:
Where rit
-30.2016
(-3.70 )**
-38.1823
(-4.26)**
-37.0173
(-4.13)**
-34.4687
(-4.50)**
-90.8306
(-2.30 )**
-98.5978
(-2.51)**
-84.0461
(-2.11)*
-98.9471
(-2.52)**
-12.5114
(-3.00)**
-13.6214
(-2.66 )**
-6.71597
(-1.51)
-11.5597
(-2.23)**
Unconditional Models to Price Equities
(GMM HJ-distance)
are the excess returns of equities.
rexwd
Rtm2t
rdeft
reqwd
10.10795
(1.30)
2
-1.51246
(-0.15)
3
4
5.238786
(0.64 )
14.19406
(0.70)
5
6
7
•
•
•
•
6.2731
(0.03%)
5.6913
(0.35%)
5.6789
(0.22%)
4.1859
(13.10%)#
4.3772
(8.47%)
3.7661
(22.30)##
4.4493
(10.04%)#
E[rit*(1+b1*rexwdt)]=0
E[rit*(1+b4*reqwdt)]=0
E[rit*(1+b1*rexwdt +b4*reqwdt)]=0
E[rit*(1+b2*rtm2tt +b3*rdeftt+b4*reqwdt)]=0
E[rit*(1+b1*rexwdt +b2*rtm2tt +b3*rdeftt)]=0
E[rit*(1+b1*rexwdt +b2*rtm2tt +b3*rdeftt + b4*reqwdt)]=0
E[rit*(1+b2*rtm2tt +b3*rdeftt)]=0
models
1
HJ-distance
Numbers below the coefficients are t statistics. Numbers below the Objective*T is
the p- value.
* significant at 5%; ** significant at 1%.
# the model is marginally not rejected. ## the model is not rejected.
Table 11
Model
Model
Model
Model
Model
Model
Model
reqwd
4.426294
(1.42)
-11.4505
(-0.53 )
-17.3035
(-1.41 )
-36.7172
(-0.87)
-18.5945
(-1,54)
36.01349
(0.17)
48.96388
(0.25)
106.1459
(0.46)
62.62337
(0.32)
-3.92133
(-2.25)**
-4.13565
(-1.84 )
-1.69914
(0.40)
5.142252
(0.48)
HJ-distance
2.0411
(24.42%)##
0.8979
(84.80%)##
0.8852
(67.59)##
0.6966
(48.61%)##
0.4797
(63.14%)##
-0.8010
(72.56)##
Numbers below the coefficients are t statistics. Numbers below the Objective*T is
the p- value.
* significant at 5%; ** significant at 1%.
# the model is marginally not rejected. ## the model is not rejected.
Model 6 is exactly identified.
52
Table 12
Conditional Models to Price Equities
(GMM HJ-distance)
Model 8: E[rit*(1+b1*rexwdt)
Model 9: E[rit*(1+b4*reqwdt)
⊗ Zt-1]=0mN
⊗ Zt-1]=0mN
⊗ Zt-1]=0mN
+b3*rdeftt+b4*reqwdt) ⊗ Zt-1]=0mN
+b2*rtm2tt +b3*rdeftt) ⊗ Zt-1]=0mN
+b2*rtm2tt +b3*rdeftt + b4*reqwdt ⊗ Zt-1]=0mN
+b3*rdeftt) ⊗ Zt-1]=0mN
Model 10: E[rit*(1+b1*rexwdt +b4*reqwdt)
Model 11: E[rit*(1+b2*rtm2tt
Model 12: E[rit*(1+b1*rexwdt
Model 13: E[rit*(1+b1*rexwdt
Model 14: E[rit*(1+b2*rtm2tt
Where Zt-1 ={1 rmlag rtm1 rdef euro}t-1,
equities.
models
8
rexwd
rit
Rtm2t
are the excess returns of
rdeft
14.23279
(2.37)**
9
10
9.868144
(1.42)
11
12
13
8.874375
(1.40)
10.58902
(1.53)
14
•
•
•
1:
2:
3:
4:
5:
6:
7:
Where rit
-24.577
(-2.56)**
-29.3933
(-0.63 )
-21.6194
(-2.84)**
-25.1567
(-2.62)*
-24.7276
(-3.39 )**
-31.9103
(-0.68)
-33.4578
(-0.71 )
-29.4322
(-0.63)
-3.96445
(-2.28)**
-2.53524
(-1.26)
-0.05623
(-0.02)
1.544422
(0.60)
HJ-distance
4.1274
(58.74%)##
4.1801
(55.79%)##
3.9297
(63.13%)##
3.3062
(86.01%)##
2.9944
(94.13%)##
2.9330
(92.89)##
3.3063
(89.92%)##
Numbers below the coefficients are t statistics. Numbers below the Objective*T
is the p- value.
* significant at 5%; ** significant at 1%.
# the model is marginally not rejected. ## the model is not rejected.
Table 13
Model
Model
Model
Model
Model
Model
Model
reqwd
Unconditional Models to Price bonds
(GMM HJ-distance)
E[rit*(1+b1*rexwdt)]=0
E[rit*(1+b4*reqwdt)]=0
E[rit*(1+b1*rexwdt +b4*reqwdt)]=0
E[rit*(1+b2*rtm2tt +b3*rdeftt+b4*reqwdt)]=0
E[rit*(1+b1*rexwdt +b2*rtm2tt +b3*rdeftt)]=0
E[rit*(1+b1*rexwdt +b2*rtm2tt +b3*rdeftt + b4*reqwdt)]=0
E[rit*(1+b2*rtm2tt +b3*rdeftt)]=0
are the excess returns of bonds.
53
models
rexwd
Rtm2t
rdeft
reqwd
31.66317
(2.74)**
1
2
-8.95283
(-0.49 )
3
4
-11.714
(-0.47)
-21.6641
(-0.85)
5
6
7
•
•
•
•
16.12245
(1.42)
11.5085
(0.92)
11.49941
(0.91)
14.13535
(1.25 )
259.8789
(1.72)
335.651
(2.32)**
258.2287
(1.71)
331.9337
(2.29)**
-17.4131
(-3.97)**
-20.0337
(-2.91)**
-12.4775
(-1.63)
-13.9537
(-1.78)
HJ-distance
3.4559
(0.76%)
1.9279
(29.37%)##
1.8635
(17.62%)##
0.8547
(39.27%)##
1.7808
(7.49%)#
-1.8428
(18.31%)##
Numbers below the coefficients are t statistics. Numbers below the Objective*T is
the p- value.
* significant at 5%; ** significant at 1%.
# the model is marginally not rejected. ## the model is not rejected.
Model 6 is exactly identified.
Table 14
Conditional Models to Price Bonds
(GMM HJ-distance)
Model 8: E[rit*(1+b1*rexwdt)
Model 9: E[rit*(1+b4*reqwdt)
⊗ Zt-1]=0mN
⊗ Zt-1]=0mN
⊗ Zt-1]=0mN
+b3*rdeftt+b4*reqwdt) ⊗ Zt-1]=0mN
+b2*rtm2tt +b3*rdeftt) ⊗ Zt-1]=0mN
+b2*rtm2tt +b3*rdeftt + b4*reqwdt ⊗ Zt-1]=0mN
+b3*rdeftt) ⊗ Zt-1]=0mN
Model 10: E[rit*(1+b1*rexwdt +b4*reqwdt)
Model 11: E[rit*(1+b2*rtm2tt
Model 12: E[rit*(1+b1*rexwdt
Model 13: E[rit*(1+b1*rexwdt
Model 14: E[rit*(1+b2*rtm2tt
Where Zt-1 ={1 rmlag rtm1 rdef euro}t-1,
models
8
rexwd
rit
Rtm2t
are the excess returns of bonds.
rdeft
9
10
-11.5889
(-3.50)**
10.03851
(1.14)
11
12
13
14
•
•
•
reqwd
21.23012
(3.01)**
12.13532
(1.43)
6.792538
(0.74)
-5.54962
(-1.07)
-7.47108
(-1.50 )
-4.58071
(-0.86)
-10.7773
(-2.45)**
6.01197
(0.15 )
1.869097
(0.05)
6.586573
(0.16)
-1.3869
(-0.03)
-8.76309
(-2.12)*
-7.93159
(-1.90)
-6.59386
(0.1487)
HJ-distance
6.8803
(0.03%)
6.6446
(0.09%)
6.5463
(0.08%)
6.4746
(0.07%)
6.5939
(0.04%)
6.4326
(0.05%)
6.7481
(0.03%)
Numbers below the coefficients are t statistics. Numbers below the Objective*T is
the p- value.
* significant at 5%; ** significant at 1%.
# the model is marginally not rejected. ## the model is not
rejected.
54
Figure 3
55
Ja
n9
Ja
n9
Ja
n9
Ja
n9
Ja
n9
Ja
n9
Ja
n9
Ja
n9
Ja
n9
Ja
n8
Ja
n8
Ja
n8
Ja
n8
Ja
n8
Ja
n8
Ja
n8
Ja
n8
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
Bond Indices
1/
29
8/ /19
31 82
3/ /19
3 82
10 1/1
/3 98
1 3
5/ /19
31 83
12 /1
/3 98
1 4
7/ /19
31 84
2/ /19
28 85
9/ /19
30 86
4/ /19
3 86
11 0/1
/3 98
0 7
6/ /19
30 87
1/ /19
31 88
8/ /19
31 89
3/ /19
3 89
10 0/1
/3 99
1 0
5/ /19
31 90
12 /1
/3 99
1 1
7/ /19
31 91
2/ /19
26 92
9/ /19
30 93
4/ /19
29 93
11 /1
/3 99
0 4
6/ /19
30 94
1/ /19
31 95
8/ /19
30 96
3/ /19
3 96
10 1/1
/3 99
1 7
5/ /19
2 97
12 9/1
/3 99
1/ 8
19
98
Indices
Figure 1
Equity Market
4000
3500
3000
2500
2000
wdeq
useq
ukeq
gmeq
jpeq
1500
1000
500
0
Figure 2
Bond Market
140
120
100
80
60
usbd
ukbd
gmbd
jpbd
40
20
0
Ja
n8
Ju 2
lJa 82
n8
Ju 3
l -8
Ja 3
n8
Ju 4
lJa 84
n8
Ju 5
lJa 85
n8
Ju 6
l -8
Ja 6
n8
Ju 7
lJa 87
n8
Ju 8
lJa 88
n8
Ju 9
l -8
Ja 9
n9
Ju 0
lJa 90
n9
Ju 1
l -9
Ja 1
n9
Ju 2
l -9
Ja 2
n9
Ju 3
lJa 93
n9
Ju 4
l -9
Ja 4
n9
Ju 5
l -9
Ja 5
n9
Ju 6
lJa 96
n9
Ju 7
l -9
Ja 7
n9
Ju 8
l -9
8
Exchange Rate
Figure 5
Time
56
Ja
n98
Ja
n96
Ja
n97
Ja
n94
Ja
n95
Ja
n92
Ja
n93
Ja
n90
Ja
n91
Ja
n88
Ja
n89
Ja
n86
Ja
n87
Ja
n84
Ja
n85
Ja
n82
Ja
n83
Exchange Rate
Deauche Mark and British Pound /US dollars
3.5
3
2.5
2
exukus
exgmus
1.5
1
0.5
0
Time
Figure 4
Japanese Yen/US Dollar
300
250
200
150
100
50
0
-0.0500
-0.1000
-0.1500
Time
57
Ja
n98
Ja
n96
Ja
n97
Ja
n94
Ja
n95
Ja
n92
Ja
n93
Ja
n90
Ja
n91
Ja
n88
Ja
n89
Ja
n86
Ja
n87
0.0000
09/30/98
03/31/98
09/30/97
03/31/97
09/30/96
03/29/96
09/29/95
03/31/95
09/30/94
03/31/94
09/30/93
03/31/93
09/30/92
03/31/92
09/30/91
03/29/91
09/28/90
03/30/90
09/29/89
03/31/89
09/30/88
03/31/88
09/30/87
03/31/87
09/30/86
03/31/86
09/30/85
03/29/85
09/28/84
03/30/84
09/30/83
03/31/83
09/30/82
03/31/82
-5.00
Ja
n84
Ja
n85
Ja
n82
Ja
n83
excess bond returns
Equity Returns
25.00
20.00
15.00
10.00
5.00
0.00
requs
requk
reqgm
reqjp
-10.00
-15.00
-20.00
-25.00
-30.00
Figure 6
Bond Returns
0.1500
0.1000
0.0500
rusbd
rukbd
rgmbd
rjpbd
-5.00
-10.00
-15.00
-20.00
58
09/30/98
03/31/98
09/30/97
03/31/97
09/30/96
03/29/96
09/29/95
03/31/95
09/30/94
03/31/94
09/30/93
03/31/93
09/30/92
03/31/92
09/30/91
03/29/91
09/28/90
03/30/90
09/29/89
03/31/89
09/30/88
03/31/88
09/30/87
03/31/87
09/30/86
03/31/86
09/30/85
03/29/85
09/28/84
03/30/84
09/30/83
03/31/83
09/30/82
03/31/82
Figure 7
Currency Deposit Returns
15.00
10.00
5.00
0.00
rexuk
rexgm
rexjp
-5.00
-10.00
-15.00
Figure 8
Risk Factors
15.00
10.00
5.00
0.00
reqwd
rexwd