INTERDEPENDENCE AND CAUSAL LINKAGES OF GLOBAL
STOCK AND MAJOR REAL ESTATE MARKETS
Kim Hiang LIOW, Department of Real Estate, National University of Singapore
Associate Professor (Dr) Kim Hiang LIOW
Department of Real Estate
National University of Singapore
4 Architecture Drive
Singapore 117566
Tel: (65)65163420
Fax: (65)67748684
Email: rstlkh@nus.edu.sg
17 April 2006
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INTERDEPENDENCE AND CAUSAL LINKAGES OF GLOBAL
STOCK AND MAJOR REAL ESTATE MARKETS
Abstract
This study assesses the interdependence and causal linkages across six major public real estate markets
and global stock market since 1990. Using weekly returns of FTSE EPRA/NAREIT series, a multivariate
EGARCH model with constant correlation coefficients and causality-in- variance tests, we find
international real estate markets are generally correlated in returns and volatilities contemporaneously
and with lags. Causality in mean and variance are detected in some real estate markets and the MSCI
global stock market, with dynamic adjustments take place on average between one and two weeks Using
the vector autoregression technique, we find that different markets’ volatility response to shocks from
different sources seems to be diverse. Whilst the conditional volatility of the MSCI global stock market
appears to affect the volatilities of the real estate markets significantly, the negligible cross-impact of some
real estate markets support the notion that international real estate markets are still fairly segmented.
Finally, by implementing the various statistical tests with two shorter sub-sample periods (pre- and postAsian financial crisis periods), we find that the causal interactions among the major real estate /global
stock markets under crisis circumstances differ from those in stable times. In particular, significant change
in the patterns and significances of the market interdependence over the two sub-periods have been
detected as both the stock and real estate markets experienced periods of stability and volatility in the 90’s.
This knowledge would help fund managers in managing their exposure in international real estate markets,
after controlling for the global stock market influence, and constructing better asset allocation models.
1.
INTRODUCTION
This study examines the interrelationship among the public real estate markets of Australia,
Japan, Hong Kong and Singapore as well as the relationship between each of these four markets and
the larger and more developed markets of the US and UK and global stock market since 1990s. Prior
literature has studied real estate correlation and diversification issues extensively in international stock
markets and some causality and interaction issues related to real estate data to a lesser extent. This
paper distinguishes itself from previous real estate studies in at least three aspects. First this paper is
unique in that it investigates simultaneously the interdependence of six major real estate markets and
the global stock market. The focus on the six real estate markets is of significant interest to the world
investors and policy markets. Furthermore, as these sample countries have leading capital markets in
the Asian and world economy, the inclusion of the global stock market allows the relationship
between pairs of real estate variable to be more fully specified when a whole system of seven series is
studied as a dynamic system. Second, in contrast to many real estate studies that examine
interdependence in returns only, we also focus on the relationship in return volatilities. The knowledge
of how volatility between two real estate markets is important in that the second moment or variance
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is directly linked to information flow as well as providing insights concerning the characteristics and
dynamics of real estate asset prices. Third, rather than estimating separate univariate GARCH models,
we employ multivariate GARCH methodology to model the volatility of the seven markets
simultaneously and ensure that they are estimated over a common range. Through the use of a
MGARCH model instead of estimating seven separate univariate GARCH models, we are able to
capture the co-movement of volatility across the seven markets as well as evaluating the causal
relationships in returns and return volatilities between any pairs of market throughout the study.
The first part looks at correlations and causal relationships in returns and return volatilities.
Specifically, causality tests and results provide investors with additional insights into how and when
information is impacted on different real estate markets and the global stock market and design more
objective pricing models with the appropriate lag structure. Regulators may also use the causality
results to identify the foreign market(s) that drive(s) movements in the domestic real estate market and
take appropriate corrective measures. In this paper we employ the causality-in-variance test developed
by Cheung and Ng (1996) to uncover causal relations in returns and return volatilities with regard to
the direction of causality as well as the number of leads/lags involved. So far, no research has
examined the causality in variance issue in international real estate investments.1 The second part
examines the dynamic responses of each market to shocks in volatilities. As correlation and causality
analyzes do not reveal anything about the transmission dynamics in the presence of unexpected shocks,
a vector autoregressive (VAR) analysis is employed to quantify the temporal precedence in real estate
and stock market return volatilities. Finally, we are also interested in finding out if inter-market
relationships vary significantly as the markets go into and out of financial crisis (e.g. 1997-98 Asian
financial crisis). By implementing the various tests with two shorter sub-sample periods (pre- and
post-crisis periods), we examine if the pattern and significance of the market interdependence has
changed over the two sub-periods as both the stock and real estate markets experienced periods of
stability and volatility.2
Our study is organized as follows. Section 2 contains a selective literature review. This is
followed by an explanation of the research data and methodology in Sections 3 and 4 respectively.
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Section 5 discusses the empirical results and implications. The last section concludes the study with a
summary of the main results.
2.
RELATED LITERATURE
Of late, there has been increasing interest in the causation in conditional variance across stock
market price movements. Such studies are considered in the wider context of the dynamic linkages
between national stock markets.3 The study of causation pattern in variance provides useful insights
into the relationship between information flow and volatility and the characteristics and dynamics of
financial asset prices (Cheung and Ng, 1996). Together with evidence regarding the causality in mean,
the overall results will yield a more complete picture regarding the dynamics of interactions among
the financial markets involved. The policy implication regarding causality would clearly be important,
as the evidence would suggest that financial market policies of one country should not be
implemented without taking into account the impacts on other markets (say, in Asian or European
regional real estate markets), and vice versa. From the institutional investors’ perspective, there would
be little diversification benefits in the short-term if two markets are causally linked in both returns and
volatilities.
Cheung and Ng (1996) develop a test for causality-in-variance (CIV) that allow researchers to
assess how a market evaluates and assimilates new information, and examine the temporal dynamics
of return volatilities across national stock markets. The CCF testing procedure does not require
modeling of the dynamics of the interaction of the series involved. Instead it is based on the residual
cross-correlation function (CCF) and is robust to distributional assumptions. The null hypothesis of no
causality in variance is tested through asymptotic normal t statistic. Mathematically, given two
stationary time series X t and Yt , the first task is to impose a conditional mean and variance
specification for the time series. Then the squared standardized residuals ( ε t and ξ t ) are estimated
2
2
for series X t and Yt , namely:
U t = {( X t − μ x ,i ) 2 / hx ,t } = ε t
2
4
Vt = {(Yt − μ y ,t ) 2 / h y ,t ) = ξ t
Where
2
μ and h are the conditional mean and variance of the time series respectively. Assume
further rUV (k ) and rεξ (k ) are the sample cross-correlations of the squared standardized residuals and
standardized residuals at lag k respectively.
The CCF testing procedure is employed to test the hypothesis of no causality in variance
against the alternative hypothesis of causality at lag k. Given that T is the number of time series
observations, the CCF-statistic is give by:
CCF − statistic = T * rUV (k )
Similarly, to test the null hypothesis of no causality in mean against the alternative hypothesis
of causality at lag k, the CCF statistic is given by:
CCF − statistic = T * rεξ (k )
To-date, the CCF testing methodology has been applied in some studies on stock markets,
foreign currency markets and interest rate markets. Hu et al (1997) examine the CIV and volatility
spillover effects among two developed markets (US, Japan) and four emerging markets in the South
China Growth Triangular (Hong Kong, Taiwan, Shanghai and Shenzhen). Employing the CCF
methodology, they find significant relationships among the variances of the markets and that there is a
feedback relationship between the Hong Kong and the US stock markets. In a study that covers five
Pacific-Rim stock markets and the US stock market returns with the CCF testing procedure plus a
TARCH model, a MGARCH specification and VAR analyzes, Tay and Zhu (2000) find that in most
instances there is bi-directional causality (both) in mean and variance among the markets. Furthermore,
the dynamic adjustment of the market return volatilities can take as much longer time than expected.
In a foreign exchange study, Kanas and Kouretas (2002) examine the issue of mean and variance
causality across four Latin American markets over 1976 -1993. Using an EGARCH-M model and the
CIV methodology, they find substantial evidence of causality in both mean and variance with the
causality in mean largely driven by the causality in variance. Alaganar and Bhar (2003) employ the
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CCF testing procedure to examine the linkages between the financial sector returns and interest rates
of the G7 countries. They demonstrate that the CIV procedure is able to model the direction and lags
in information flow between two time series. They are able to find feedback effects both at the mean
and the volatility level. Caporale et al (2002) provide some empirical evidence on the casual
relationship between stock prices and exchange rates volatility in four East Asian countries using daily
data from January 1987 to March 2000 by appealing to the MGARCH methodology with BEKK
representation. They also analyze the effects of the 1997 East Asia crisis by splitting the sample in two,
before and after the onset of the crisis. Finally, Fujii (2005) reveals significant causal linkages in mean
and variance both within the Asia and Latin America regions and across the two regions. His rolling
CCF results further indicate that the significance of the causality varies considerably over time and
causal linkages tend to strengthen particularly at the time of major financial crisis.
As for real estate studies, key findings of previous work are that diversification into
international real estate provides a way of achieving an efficient portfolio by a reduction in the
variance of returns and an enhancement of portfolio performance. Additionally, diversification across
different markets and regions can result in more efficient portfolios. For example, Eichholtz (1995)
compares the diversification benefits derived from international real estate investments to those of
international stock and bond investments and concludes that property shares are less strongly
correlated than common stock and bond returns across national boundaries. Similarly, several studies
on emerging market securities also conclude that international real estate securities offer
diversification benefits for a real estate portfolio. Using quarterly and monthly data separately in two
studies, Lu and Mei (1999) and Hu and Mei (1999) examine the return-generating process of property
indices in ten emerging markets (Argentina, China, Hong Kong, Indonesia, Malaysia, Philippines,
Peru, Singapore, Thailand and Turkey), and find that property indices are more volatile than their
respective market indices and US NAREIT index. Additional diversification benefits to invest in
emerging market property securities beyond that associated with international stocks are found, but
correlations are higher during times of high volatility. On the contrary, research studies on real estate
market volatility and its transmission across international real estate markets are relatively limited and
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none of them has examined the issue of causality-in-variance since 1990.. The lack of research in this
area is a peculiar oversight, given the increase in indirect global property investment over the last
decade and it is these market interdependence and causal linkage issues that this study can make a
meaningful contribution.. Garvey et al (1991) examine the linkages between securitized real estate
markets of Australia, Japan, Singapore and Hong Kong on both short and long-term basis. The short
term analysis covers linkages in both mean and variance of the return series using Granger causality
and GARCH models that incorporate volatility spillovers. They find little evidence of co-movements
or influences between the markets on a bivariate basis. Stevenson (2002) investigates the influences
on volatility in the US REITs. He finds that the volatility in equity REITs has significant influence on
other sub-sectors of the REIT market. More recently, Liow et al (2005) examine the long-term and
short-run relationships in mean and variance spillover effects across four Asian property stock markets
(Japan, Hong Kong, Singapore and Malaysia) and four European real estate stock markets (the UK,
France, Germany and Italy). Their evidence of minimal cointegration, weak mean transmission and
little cross-volatility spillovers among the Asian and European real estate stock markets imply that
diversification opportunities exists among the regional public real estate markets. However, they do
not examine the issue of causality in mean and variance across the real estate markets. Additionally,
Liow (2006) focuses on the dynamics of volatility persistence and systematic risk in Asian-Pacific real
estate markets. Again, the issues of interdependence in term of the causal links among the returns and
variances among the real estate markets were not investigated. Recently, Michayluk et al. (2006)
construct synchronously priced indices of securitized property listed on NYSE and LSE and then
examine dynamic information flows between the two markets. They show that the real estate markets
in these two countries experience significant interaction on a daily basis, and the positive and negative
news impact the markets differently.
3.
RESEARCH DATA
As in many previous academic real estate studies, we use returns on real estate stocks to
proxy for real estate asset performance. This choice is mainly justified by the availability of longer
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time series data and higher frequency data (such as monthly and weekly) for real estate stocks. Whilst
the adequacy of this proxy has been extensively debated amongst real estate practitioners and
researchers, it remains the only substantive “real estate” series appropriate for any rigorous statistical
analysis.
We include six major public real estate markets and a global stock market for a US-based
investor. Apart from the popularly known US and UK real estate markets that have different
institutional and market structures from the developing economies, the remaining four are Asia-Pacific
markets of Singapore, Hong Kong, Japan and Australia. These six countries are (major) trading
partners with one another, and thus that these markets may be (strongly) integrated. Japan is the
premier economy in the Asia region, and therefore a potential driver for the regional economy. It has a
long history of public real estate. Other countries like Australia, Hong Kong and Singapore have track
records of listed real estate companies that play a relatively important role in general stock market
indexes. In particular, Australian securitized real estate sector is a leading player in global real estate.
The UK real estate market plays a key role in the European property market. Moreover, the six
markets represent about 91 percent of the global securitized real estate market and have the world’s
most significant listed real estate markets in the respective regions (UBS Investment Bank, 2003).
The real estate data are weekly FTSE EPRA/NAREIT total return indexes maintained by the
European Public Real Estate Association (EPRA). These global real estate series are designed to track
the performance of listed real estate companies and REITs worldwide. The series act as a performance
measure of the overall market (www.epra.com). All six real estate index series are extracted from
Datastream and the sample period is from 29 December 1989 till 10 February 2006 the longest period
for which all weekly data indexes are available.4 Weekly real estate stock returns (R) are obtained by
taking the logarithmic difference of the stock index (P) times 100. That is, R t = 100 * (log P t – log P t
– 1).
All data are expressed in US dollars. Figure 1 displays the real estate index movement over the
study period. The world stock market equity index is compiled by MSCI and is also obtained from the
Datastream. The MSCI world market index is widely used by international fund managers for asset
allocation decisions and performance measurement as well as used by researchers in academic studies.
8
(Figure 1 here)
To provide a general understanding of the nature of each market return, Table 1 contains
sample characteristics of the weekly real estate stock returns and the global stock market returns over
the full sample period from 5 January 1990 – 10 February 2006. The descriptive statistics include
mean, standard deviation, coefficient of variation and the measures of skewness, kurtosis and
normality.
(Table 1 here)
Of the real estate index series, the US has the highest average weekly return (0.293 percent)
and is followed by Australia (0.258 percent); while Japan has the lowest average mean (0.002 percent)
Judging from the sample standard deviations, Singapore, Japan and Hong Kong are characterized by a
higher unconditional volatility (range between 5.14 percent and 4.40 percent) compared to the USA
1.82 percent), Australia (2.04 percent) and UK (2.40 percent). Consequently, the US, Australia and
UK markets also have the three lowest coefficients of variation (i.e. risk per unit of return). The MSCI
world stock index has an average weekly mean return and standard deviation of 0.098 percent and
1.91 percent, respectively. Except for Japan and the UK, all four other markets are negatively skewed
(between -0.275 for Australia and -0.430 for the US). These negative skewness coefficients are all
statistically significant at the one percent level. The kurtosis measure is more than three in all weekly
return series (between 3.506 for Australia and 21.90 for Singapore). The distribution of returns has
thus fat tails compared with the normal distribution. Finally, the MSCI world market index is
negatively skewed (-0.226), exhibit significant kurtosis (5.032) and fail the test of normality at the
one-percent level (Jacque Bera values of 151.81).
The presence of inter-temporal dependencies in the returns and squared returns are tested by
using Ljung-Box portmanteau test (LB). The LB statistic tests the hypothesis that autocorrelations up
to the nth lags are jointly statistically significant. The calculated LB statistics, given by LB-Q (5), LBQ (20), LB-Q2 (5) and LB-Q2 (20) are also reported in Table 1. As can be seen, except for the MSCI
global market index, the hypothesis of linear independence in mean return is firmly rejected at the ten
percent level or better for Hong Kong, Singapore and Japan and partially rejected for the US, UK and
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Australia, implying that the conditional mean of the distribution of real estate stock returns is probably
a function of either past returns or past residuals. On the contrary, independence of the squared return
series is partially accepted at the ten percent level for the UK only. Except for the UK, The LB
statistics for the squared returns are several times higher than that of returns themselves in other five
real estate markets and the MSCI world index. The implication is that higher-moment dependencies
are much more pronounced. Finally, the results for the augmented Dickey Fuller (ADF) and the
Phillips and Peron (PP) tests presented in Table 1 depict that a unit root is present in the logarithm of
all real estate stock indexes and the MSCI world index. On the contrary, the hypothesis of a unit root
is rejected for each of the return series. Consequently, further investigation of the short-term dynamics
of the real estate markets and the global stock market requires first differencing.
4.
RESEARCH METHODOLOGY
Our empirical procedures contain four major steps. They are briefly explained below.
First, we conduct a usual preliminary examination of the correlation in raw returns and return
volatilities (proxied by mean squared deviation). The correlation structure provides a rough measure
of interdependence and is probably the most important feature from the point of view of investors and
portfolio mangers. Pearson Correlation analysis has been frequently used in the initial literature on
international stock market linkages.
Second, GARCH models are used to study the stochastic behavior of return series and, in
particular, to explain the behavior of volatility over time (Bollerslev et al. 1992). In addition, Nelson
(1991)’s exponential GARCH (E-GARCH) model specifies the conditional second moments of
returns to allow for asymmetric effects of market news on the volatility function. These univariate
GARCH or EGARCH models can be extended into a multivariate framework (MGARCH or
MEGARCH). This extension allows all variables to be considered simultaneously over a common
range, i.e. volatility in all markets is analyzed as a whole system. One key advantage of the MGARCH
(/MEGARCH) specification is that they permit time-varying conditional covariances as well as
variances; thus allow for possible interactions within the conditional mean and variance of two or
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more financial series. In what follows, we estimate a MEGARCH model suggested by Bollerslev
(1990) that assume the correlations in the conditional volatilities are constant. This constant
correlation (CC) specification has generally a well-behaved likelihood function as well as limiting the
number of estimation of coefficients to a workable level. The model can be estimated by the
maximum likelihood method. The AR (p) - MEGARCH (1, 1) model is represented by the following
equations:
6
Ri ,t = β i , 0 + ∑ β i , j R j ,t −1 + ξ iσ i2,t + ε i ,t
for i, j = 1,2,…7,
(1)
j =1
⎧
⎫
6
σ i2,t = exp⎨α i , 0 + ∑ α i , j f j ( z j ,t −1 ) + γ i ln(σ i2,t −1 )⎬
j =1
⎩
f j ( z j ,t −1 ) = z j ,t −1 − E z j ,t −1 + δ j z j ,t −1
(
(
)
)
σ i , j ,t = ρ i , j σ i ,t σ j ,t
⎭
for i, j = 1,2,…7,
(2)
for i, j = 1,2,…7,
(3)
for i, j = 1,2,…7 and i ≠ j .
(4)
Equation (1) describes the returns of the seven markets as an autoregression (AR) each where
the conditional mean in each market is a function of pass own returns as well as a time dummy D
97
that takes a value of one for the period July 1997–August 1998 and zero otherwise. The intent is to
control for regime swifts in many Asian real estate markets following the eruption of Asian financial
crisis in July 1997 (Liow et al. 2005). Finally, while the 1997 Asian financial crisis may have had
effects reaching beyond the Asian regions, that issue is beyond the scope of this study. Hence the
dummy is not included in the mean equations for UK and USA.
Equation (2) explains the EGARCH representation of the variance term ε t . According to the
EGARCH representation, the conditional variance of the returns in each market is an exponential
function of past own, cross-market standardized innovations and past own conditional variance. The
persistence of volatility is measured by γ i . The unconditional variance is finite if
γ i < 1 . If γ i = 1 ,
then the unconditional variance does not exist, and the conditional variance follows an integrated
process of order one.
The particular function form of f j ( z j ,t −1 ) is given in Equation (3), which captures the
ARCH effect, and is asymmetric function of past standardized innovations. The term
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(
)
z j ,t −1 − E z j ,t −1 measures the magnitude effect. If the magnitude of z j ,t −1 is greater than its
(
)
expected value, E z j ,t −1 , the impact of z j ,t −1 on
positive. Finally, the term
σ i2,t will be greatly positive, providing that α i, j is
δ j z j ,t −1 measures the asymmetric volatility transmission mechanism
(Koutmos, 1996)
Equation (4) provides the conditional covariance specification, which captures the
contemporaneous relationship between the returns of the seven markets. This specification implies
that the covariance of market i and j to be proportional to the product of their standard deviations.
This assumption greatly simplifies estimation of the model and it is a plausible one for many
applications (Bollerslev et al., 1992). The coefficient
ρ i, j is the cross-market correlation coefficient
of the standardized residuals between two markets. Statistically, the significant estimates of
ρ i, j
indicates that time-varying volatilities across market i and j are correlated over time.
The BFGS algorithm provided by RATs is used to produce the maximum likelihood estimates
and their corresponding asymptotic standard errors with a Student-t fat tailed distribution. Finally, the
Ljung-Box Q statistic is computed to test the null hypothesis the MEGARCH model is correctly
specified, or equivalently, that the noise terms are random.
Third, once the appropriate AR(p)-MEGARCH (1, 1) model is identified, we employ the
causality-in-variance test developed by Cheung and Ng (1996) to detect causal relations and identify
patterns of causation in the first and second moments respectively. Here, the sample cross-correlations
(CCF) of the resulting standardized residuals and squared residuals standardized at k-lags are
determined. The cross-correlation function (CCF) of these standardized residuals and squaredstandardized residuals are used to test the null hypothesis of no causality in mean and variance
respectively.
Finally, we employ the conventional VAR method5 to conduct a dynamic analysis of the
conditional volatilities to shocks originating from various markets through impulse response and
variance decomposition analyses. Here, a kth VAR of the conditional volatilities can be written as:
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ht = c + Φ 1 ht −1 + Φ 2 ht − 2 + .... + Φ k ht − k + vt …………..(5)
where c denotes a (7x1) vectors of constant, Φ j is a (7x7) matrix of autoregressive
coefficients for j =1,2…..p, and vt ~ i.i.d. N (0, Ω) where Ω is a (7x7) symmetric positive definite
matrix, ht is a (7x1) vector of conditional volatilities derived from the MEGARCH estimation.
Through impulse response functions, we are able to trace the effect of one standard deviation
shocks in the conditional variances of each foreign market has upon the domestic market. The
normalized impulse response is the ratio of moving average coefficients and the respective standard
errors and will be reported in this study. The normalized coefficients illustrate how long and to what
extent each market’ volatility reacts to unanticipated changes in the other markets. We use the
generalized impulse response function (Pesaran and Shin, 1998) to decompose the error components.
One key advantage of this method is it is not dependent on the ordering of the variables in the VAR
system, thus doing away with the need to first conduct Granger causality analysis determine an
appropriate causal order of the variables in the VAR system.6 Through variance decomposition, we
would be able to examine the composition of the conditional volatilities [h (t) vectors from the
MEGARCH estimation] with regard to the extent they are affected by own shocks as well as by
shocks from other markets. The results will thus indicate the relative importance of the various
markets in causing the volatility fluctuations of that market.
5.
RESULTS
5.1
Correlations in Returns and Volatilities
The sample correlations of the real estate stock returns and return volatilities are first
estimated. They provide a rough measure of market interdependence. The low correlation between
returns of international real estate markets has been regarded as an incentive to hold internationally
diversified real estate portfolios. In Table 2, the correlation matrices are calculated for the return (first
row) and mean squared deviation of the returns (second row) (used to represent return volatilities).
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This is because international real estate markets might be related through their returns, or their return
volatilities or both.
(Table 2 here)
As the numbers indicate, correlations between the returns of all real estate markets are
between low and moderate ranges. Here we see that the highest and lowest correlation in returns,
respectively, are 0.581 (between Singapore and Hong Kong) and 0.096 (between Japan and the US),
and only one other pair’s correlation coefficient is slightly above 0.30 (0.303, between Australia and
the UK). The bivariate return correlations between the MSCI world stock index and all real estate
markets are higher; but on average still moderate; ranging between 0.336 (MSCI and Australia) and
0.458 (MSCI and the US). Next, the correlation coefficients for the mean squared deviations (return
volatilities) are comparatively lower. Here we see that only three pairs of the 21 markets’ pair-wise
correlation coefficients are higher in return volatilities than in returns (i.e. Singapore and HK, Japan
and the US and UK and the US). Again, Singapore and Hong Kong report the highest correlation
coefficient of 0.762. On the contrary, Singapore and the UK are not correlated at all (correlation =
0.022) even though the UK is the largest foreign investor by stock of total foreign direct investment.7
Overall, our findings are generally in agreement with what appears in the literature. We are able to
derive a conclusion that similar to stock markets, international real estate markets show small to
moderate correlation in returns, but some markets are not independent because they are related
through their second moments.
5.2
M-EGARCH Estimation Results
Maximum likelihood estimates with conditional t–distribution of the multivariate
specification,8 those of the Constant Conditional Correlation AR (p) - EGARCH model for the full
sample period are presented in Table 3.9
(Table 3 here)
The log-likelihood value of 13506.34 is large enough to suggest that the estimated model is
able to capture the temporal dependence of volatility reasonably well. All seven index returns display
14
a significant volatility persistence coefficient (between 0.928 for Australia and 0.995 for the UK).
Consistent with expectation, we find a significant and negative Asian financial crisis coefficient (D97)
each for Hong Kong, Japan and Singapore real estate markets. Finally, with some minor exceptions,
the estimated ARCH values, Ljung-Box statistics for the standardized and squared standardized
residuals indicate the AR (p) - MEGARCH (1, 1) model has been adequately specified.
The constant conditional correlation coefficients are given by the sample correlation matrix
and are set out in Table 3, under the heading CCC. Just as we have found previously in Table 2,
although all conditional volatility correlation coefficients are higher than the unconditional ones as
well as highly significant, the markets are only moderately correlated in variances with each other.
Among the real estate markets, Hong Kong and Singapore remains as the most strongly correlated pair
with a correlation of 0.472, and is followed by the UK-Hong Kong pair with a correlation coefficient
of 0.305. All other real estate market pair-wise correlations range between 0.102 and 0.301.
Additionally, Hong Kong, Singapore, Japan and Australia real estate markets are more correlated with
the UK than with the US. However, there is one interesting twist. Unlike the insignificant
unconditional correlation found previously (in Table 2) between Singapore and the UK, the
conditional correlation in variance between these two markets is now 0.282, which is statistically
significant at the one percent level. Finally, the six pairwise correlations between the MSCI world
market and real estate markets range between 0.357 and 0.452, which are higher than those of real
estate market, except between Hong Kong and Singapore.
Table 4 presents the MEGARCH model estimates for the pre-and post-Asian crisis time
periods. 10 Focusing our attention on the correlation estimates in volatilities, the conditional
contemporaneous correlation relationships are more or less similar to those reported for the full
sample period (shown in Table 3), with 20 pairs each of correlation coefficients statistically significant
at the one percent level for the two sub-periods. Further comparisons reveal that the post-crisis period
witnesses a stronger volatility correlation relationship for 16 of the 21 pairs, and that the numbers of
pairs of real estate markets that have a correlation coefficients larger than 0.30 are 1 (pre-crisis) and 4
(post-crisis) respectively. This could have been the results of the contagion effects of the financial
15
crisis. Conversely, the post-crisis volatility correlations between US-Hong Kong, UK-Japan, USJapan, MSCI – Japan and MSCI– UK have weakened (considerably) compared with the pre-crisis
period. Among the real estate markets, the strongest volatility correlation for the pre-crisis and postcrisis period occurred between Hong Kong and Singapore (0.381for pre-crisis and 0.531 for postcrisis).
(Table 4 here)
5.3
Causality
The standardized residuals and squared standardized residuals for each market are extracted
from the MGARCH models to implement the CCF tests for cross-market causality in mean and
variances. The results are reported in Tables 5(a) and 5(b) for the full sample period. These reported
statistics are for causality at a specific lag k. Lags are measured in weeks, which range from -10 to +
10. The test results are organized by market pairs and lag order. For a pair of markets, a significant
test statistic with lag k < 0 should be interpreted that the return/variance of the first market causes that
of the second market in mean/variance with a k–period lag. 11 Similarly, if the test statistic is
significant with k > 0, then the second market’s return / variance is said to cause the first market in
mean / variance with a kth lag. A significant test statistic with k = 0 indicates contemporaneous
causality.
Since these CCF tests for all markets will generate a voluminous amount of information, we
provide in Table 6 a combined summary of the causality patterns among the returns and return
volatilities. Out of the 420 t-statistics that indicate lead-lag relationship (from Tables 5a and 5b), the
results show that there are 44 (10.48%) and 50 (11.9%) significant cases of causality in mean (CIM)
and causality in variance (CIV). Although the majority of lead-lag linkages happened at k = 1,
statistical significant causal effects can arise from observations as long as 10 weeks ago for some
market pairs. Additional evidence reveals that in five cases there are bi-lateral (i.e. feedback) CIM and
bi-directional CIV among the returns (AU/HK, AU/MSCI, HK/SG, HK/MSCI and UK/US). In
another three cases of CIV where the contemporaneous correlations are weak and not statistically
16
significant (JP/SG, JP/UK and JP/US), the correlations at other lags are statistically significant. For
example, the t-statistic for the contemporaneous correlation in variance between the real estate
markets for Japan and Singapore is merely 1.102, which is statistically insignificant; but the t-statistics
for correlations are, respectively, 2.141 (lag 1), 2.853 (lag3), 2.497 (lag 7) and 5.589 (lag 8) and all are
statistically significant at the one percent level. The implication is that one-week and three-weeks
lagged variances of the Japan’s real estate returns causes the variances of Singapore’s real estate
returns, and longer lags of variances (weeks 7 & 8) of the Singapore’s returns causes the variances of
Japanese returns. Interestingly, although Singapore and the USA markets are moderately correlated in
their contemporaneous returns and variances, both markets are not correlated at all through lead-lag
linkages. Another interesting observation is that our results support significant mean transmission
from Hong Kong into the UK, Singapore into Japan and Singapore into the USA despite the UK,
Japan and the USA being dominant real estate markets. Hence it is plausible for mean return to be
transmitted from the smaller market to the dominant market, a finding which appears to contra most of
the previous stock market research (e.g. Janakiramanan and Lamba, 1998). Finally, the MSCI global
market has strong degree of interdependence in returns and volatilities with all real estate markets.
The most pronounced relationships are between MSCI and Australia and between MSCI and Hong
Kong; both pairs reported both feedback CIM and CIV in their returns / volatilities.
(Tables 5a, 5b and 6 here)
To examine the evolution of cross-market linkages over time and the influence of 1997-98
Asian financial crisis on the relationships, Tables 7(a)-7(b) and 8(a)-8(b) presents the CCF t-statistics
for the pre-crisis and post-crisis periods respectively. Some useful comparisons regarding the
significances and patterns of CIM and CIV between the pre-crisis and post-crisis periods are presented
in Tables 9, 10(a) and 10(b). As the causal structures between all market-pairs are diverse and thus
difficult to generalize, we will attempt to make few general observations only.
Whilst all markets maintain their significant relationships in the contemporaneous returns in
both periods (20 out of 21 pairs), the number of significant contemporaneous volatility pairs increases
considerably from 7 pairs in the pre-crisis period to 18 pairs in the post-crisis period. Additionally,
17
Figures 2 and 3 indicate that the contemporaneous correlation coefficients in returns (variances) are
significantly higher for 15 pairs (20 pairs) in the post-crisis period. It is thus evident that the
contemporaneous linkages in returns and return volatilities across the real estate markets and between
each real estate market and the global stock market have strengthened considerably in the post-crisis
period due possibly to contagion effects of the financial crisis, a finding which is consistent with those
reported in Table 4 and prior stock market studies.
[Tables 7(a), 7(b), 8(a), 8(b), 9, 10(a) and 10(b) here]
(Figures 2 and 3 here)
Another insightful aspect of our results is that the lead-lag linkages among the markets appear
to be unstable over the two sub-periods. In Table 9 where three categories of causality are analyzed
(i.e. bilateral causality, one-way causality and no causality at all) the post-crisis period witnesses
changes in the CIM relationship for 14 pairs (66.7%); the corresponding number is 13 (61.9%) for the
CIV relationship. Only four market pairs (JP/US, SG/UK, SG/US and SG/MSCI)’ causal linkages in
both returns and return volatilities remain stable throughout the two periods. This finding is similar to
some previous stock market studies indicating that the 1997-98 Asian financial crisis has brought
changes to the inter-relations of stock markets (and in our case, real estate markets) over time.
5.4
Dynamic responses of the conditional volatilities
A VAR moving average system describes the dynamic interdependence of the seven markets
included in the model. In the present context, the seven conditional variance series (Figure 4) obtained
from the MEGARCH (1, 1) estimation for the full period are used for a VAR model that performs
dynamic analyses using impulse response and variance decomposition techniques. The response
patterns are simulated by introducing one standard deviation shocks to each of the markets in the
system over different time horizons. The decomposition of variance of forecast errors of the
conditional volatility of the given market indicates the relative importance of the foreign markets’
shocks in causing the fluctuations in the conditional volatility of the subject market.
(Figure 4 here)
18
Table 11 shows the parameter estimates obtained from fitting a VAR model for the full
sample period. Based on the maximum log-likelihood and minimum AIC criteria, we determine the
lag order of the VAR model to be two.12
(Table 11 here)
The variance decomposition of the conditional volatilities for the full sample period for 1week, 4-week, 8-week, 12-week, 16-week, 20-week and 24-week horizons are reported in Table 12.
First, the majority of the global stock market volatility is explained by shocks originated in its own
market. At the horizon of 24 weeks, the proportion of its own volatility is over 85 percent with the
Japanese real estate market explain only about 6.6 percent of the volatility variation in the global stock
market. In contrast, the rest of the real estate markets have very weak or negligible influences over the
MSCI global stock market volatility. Second, Australian real estate market is not affected by the other
real estate markets except for Singapore and to a lesser degree, the MSCI world stock market. Whilst
the MSCI world stock market maintains its influence of between 2.3 and 2.92 percent over a 24 week
horizon, Singapore real estate market shocks starts to gradually increase the volatility in the Australian
market from the eighth week onward. Its impact reaches about 5.5% in 24 weeks.
(Table 12 here)
In the case of Hong Kong, the MSCI global stock market again has the largest lagged
impacts on Hong Kong real estate market volatilities. Its impact starts to explain just over 10 percent
of HK return volatility in three weeks and reaches about 11.6% in 24 weeks. The Australian real estate
market is the only other market that has a weak influence over time on HK real estate market as well.
In contrast, the rest of real estate markets (including Singapore) have very minimal influence on the
return volatilities for HK real estate market. Fourth, results for Japan shows that the MSCI global
stock market, Hong Kong and Singapore real estate markets have some lagged impacts on the
Japanese real estate market volatilities. The impacts occur very gently and in 24 weeks, the proportion
of the variation in the Japanese market explained by the global stock market, Hong Kong and
19
Singapore real estate markets are, respectively, about 8.7 percent, 6.5 percent and 6.3 percent; with the
remaining 3.2% market volatilities explained by the Australia, UK and US real estate markets.
The Singapore real estate market, however, is substantially affected by Hong Kong real estate
market and the impact occurs fairly quickly. In the first two weeks, HK market volatility innovation
explains about 35 percent of the variations of Singapore real estate market volatility. This influence
increases to about 46.7% in 24 weeks, even exceeds the proportion of shocks to its own market
(37.1%). At this horizon, the MSCI global stock market and Australian real estate markets contribute
about 8.8 percent and 4.3 percent of volatility innovation, respectively, to the volatility of the
Singapore real estate market. In contrast, the rest of the real estate markets have very minimal
influence on the Singapore real estate market volatility
Finally, the MSCI global stock market has the largest lagged impacts on the UK and USA
real estate market volatilities. In the case of the UK, the MSCI impact starts with about 5.0 percent in
week 1 and gradually increases to 10.0 percent in 24 weeks. At this horizon, about 81.2% of the UK
market volatility is explained by shocks originated in its own market, with another 4.7 percent and 2.4
percent, respectively, contributed by the Japanese and Hong Kong real estate markets. In contrast, the
remaining three markets (Australia, US and Singapore) explain less than one percent to the UK market
volatility. For the USA real estate market, the MSCI global stock market accounts for 13.1 percent of
the variation in the USA market in 24 weeks. The Australian real estate market also contributes 12.2
percent of the variation in the USA market as well.
To sum up, the variance decompositions have revealed several interesting evidence. First,
among the markets included in the VAR system, most of the short-term volatilities for the MSCI
global stock market and Australian real estate markets are explained by the shocks to their respective
own markets. Hence they are largely exogenous as their own innovations account for most of their
error variances. On the contrary, a significant portion (between 19 and 62 percents) of the Hong Kong,
Japanese, Singapore, UK and USA return volatilities is explained by the lagged impacts of shocks
from other markets. Second, the volatilities of the six major real estate markets are affected by the
global stock market. The MSCI global stock market appears to the main “exporter” of shocks to other
20
real estate markets and is only affected by the Australian, UK and USA real estate markets to a much
lesser degree. Third, among the six real estate markets, different markets’ response to shocks from
different sources appears to be diverse. There are many instances of lead-lag linkages in volatility
between any two markets, and is consistent with the causality results reported earlier. Singapore is the
most endogenous market with over 60 percent of its forecast error (in 24 weeks) explained by the
other markets in the system. This shows how open the Singapore real estate market is and how
vulnerable it is to shocks occurring in other leading real estate markets. Geographically and
economically close countries like Singapore and Hong Kong show strong volatility linkages in their
real estate markets. Whilst Hong Kong affects Singapore considerably with about 46.7 percent of
volatility innovations, Singapore real estate market accounts for only 0.23 percent of volatility of
Hong Kong real estate market. Furthermore, most of the other foreign markets’ volatility interactions
are only below 10 percent. The investment implication is clear. These major real estate markets are
still fairly segmented implying that institutional investors would likely to benefit from diversifying
public real estate portfolios internationally across Asia and the US/UK markets in the short- and /or
medium term.
(Table 12 here)
Table 13 reports the normalized impulse response coefficients of the markets in the system
over 1-week, 4-week, 8-week, 12-week, 16-week, 20-week and 24-week horizons. The numbers
demonstrate that shocks originating from all six real estate markets do not influence the behavior of
the MSCI global stock market significantly. The MSCI volatility response to one standard deviation
shocks from any real estate market in the system is very low on week 1 and is almost negligible on 24
weeks. As an example, the maximum MSCI volatility responses to a shock of one standard deviation
on week 1 from Hong Kong, USA, UK, Singapore, Australia and Japan are, respectively, 0.084, 0.084,
0.066, 0.064, 0.050 and 0.043. On the contrary, the results of the dynamic responses also indicate a
MSCI response of 0.410 on week 1, 0.218 on week 2, 0.162 on week3, 0.124 on week 4 and so on, to
its own one standard deviation shock, a magnitude much larger than that from any other real estate
21
markets. These responses indicate the global stock market behaves largely through its own internal
volatility dynamics in the system.
The numbers also indicate that the conditional volatilities of the six real estate markets are
affected weakly by the global stock market. For Australia, the maximum own-market response to a
shock of one standard deviation from other (foreign) markets on week 1 is 0.050 (from MSCI).
Similarly, the maximum (foreign market) responses for Japan (0.046), UK (0.065) and USA (0.085)
on week 1 are also with respect to one standard deviation shocks from the MSCI global stock market.
The volatility responses for Hong Kong and Singapore to one standard deviation shocks on week 1
from MSCI are of comparable magnitudes (0.083 for Hong Kong 0.065 for Singapore), although they
are not the highest. The peak coefficient (0.195) of Hong Kong’s response to shocks from Singapore
occurs on week 1. The impact of the shocks dies off quickly in about 24th week (0.027). We also see
that Singapore’s response to shocks from Hong Kong is the highest with a one-week lag (0.197) and
by week 24, the impact of the shocks become very negligible. Finally, various real estate markets’
volatility responses to their own domestic shocks range between 0.404 and 0.411, again a magnitude
much larger than any of the cross-volatility response coefficients.
To summarize, we find that the generalized impulse response analyses suggest almost the
same broad patterns of market interdependence as we find with variance decompositions. The
implication is evident. International real estate markets are affected by the global stock market in their
second moment. Although there are some volatility interactions among the real estate markets, most of
the interactions are quantitatively insignificant.
(Table 13 here)
Finally, Table 14 compares the variance decomposition results between the pre- and postcrisis periods. In the pre-crisis period, the MSCI global stock market index exerts significant influence
on Hong Kong, Japanese, Singapore, UK and US real estate markets but not vice versa. The largest
impact is on the US real estate market where its volatility innovation explains up to 36.2 percent of the
USA real estate market return volatility in 24 weeks. Among the real estate markets, Australia is
largely exogenous as its own volatility innovations are able to account for over 94 percent of its error
22
variances in 24 weeks. Furthermore, there is no major volatility interactions among the real estate
markets except those from Hong Kong to Singapore (about 26.2 percent in 24 weeks) and to a lesser
degree, from Japan to the USA (6.7 percent in 24 weeks). We witness a different situation in the postcrisis period. Here, we see that the MSCI global stock market is moderately affected by the Japanese
real estate market (about 11.4 percent in 24 weeks) but not vice versa. The global stock market also
affects Hong Kong (16.4 percent), UK (13.2 percent), USA (11.1 percent) and Singapore (10 percent),
respectively, in 24 weeks. Among the real estate markets, Australia is again largely exogenous as only
about 5.9 percent of its return volatility is accounted by other markets. There is a bilateral relationship
between the Hong Kong and Japanese real estate market. The magnitude of cross-volatility
transmission is, respectively, 11.6 percent (from Japan to Hong Kong) and 13.4 percent (from Hong
Kong to Japan). Singapore real estate market return volatility is affected by its own shocks and
volatility innovations from Japan (26.5 percent in 24 weeks) and Hong Kong (17.5 percent in 24
weeks). Finally, whilst the UK real estate market is only influenced by Australia with approximately
9.7 percent cross-volatility, the USA real estate market is largely unaffected by other real estate
markets.
(Table 14 here)
CONCLUSION
In this study, we examine the patterns and significances of dynamic interdependence and
casual linkages across six major real estate markets in the USA, UK, Japan, Australia, Hong Kong and
Singapore and the MSCI global stock market. We document the general direction and lead/lag
structure through mean- and variance-in-causality analyzes and furthermore, how conditional
volatilities are related and how important each market’s conditional volatility is to the rest. Finally, by
implementing the various statistical tests with two shorter sub-sample periods (pre- and post-Asian
financial crisis periods), we investigate whether the patterns and significances of the market interdependence have remained stable over the two sub-periods as both the stock and real estate markets
experienced periods of stability and volatility in the 90’s. This knowledge would help fund managers
23
in managing their exposure in the major real estate markets and constructing better asset allocation
models.
Following Cheung and Ng (1996)’s causality in variance technique, we find that all markets
show small to moderate correlations in returns; additionally some markets are not interdependent
because they are related through their second moments. There is some evidence of causality-in-mean
and /or causality-in-variance among the real estate/global stock markets and the majority of lead-lag
linkages happened at one week. The global stock market has strong causal relationships in returns and
volatilities with all real estate markets. Additionally, the causal linkages among all markets appear to
be unstable across the two sub-periods as only four market-pairs’ causal interactions in mean and
variance remain unchanged throughout the two sub-periods. Hence we conclude that the causal
linkages among the major real estate /global stock markets under crisis circumstances differ from
those in stable times. However, there is no conclusive evidence to suggest that the markets have
become more inter-dependent with each other in the post-crisis period. One possible reason is that
these markets are the world’s real estate market leaders at the respective continents (i.e. America,
Europe and Asia). Volatility shocks on each market can be temporary or highly persistent and that
each real estate market’s volatility is subject to the effects of movements in macroeconomic
fundamental. As a possible future extension, it would be useful to examine the effects of
macroeconomic and financial variables when considering market linkages in volatility during stable
and crisis periods.
The results on the dynamic volatility response to external shocks analyses indicate that
different markets’ responses to shocks from different sources seem to be diverse. The MSCI global
stock market appears to be the main “exporter” of shocks to other real estate markets. Geographically
and economically close countries such as Hong Kong and Singapore show strong interdependence in
their real estate market volatilities. However, most of foreign markets’ shocks only contribute to less
than 10 percent of each own market’s volatility.
To conclude, our study also underscores the complexity of inter-market relationships in mean
and particularly in volatility in at least two aspects: time-dependent market interdependence and
24
temporary/highly persistence in shocks on market linkages. These are some possible future extensions.
In the present context, the causality and interdependence evidence provide regulators with useful
information to understand own market’s mean and volatility position relative to other foreign markets;
i.e. whether it is “endogenous” or “exogenous”; identify relevant mean and volatility “drivers” and
take appropriate corrective measures to moderate fluctuations in market movements. Our statistical
evidence also provides institutional investors and fund managers with fresh insights into the
diversification potential of international real estate investing during stable and crisis periods after
controlling for the global stock market effect. This knowledge would further assist fund managers in
managing their exposure in international real estate markets and constructing better asset allocation
models.
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26
Table 1
Summary statistics of weekly real estate market and world stock returns
mean(%)
std dev(%)
Coefficient of variation
skewness
kurtosis
Jarque-Bara (JB)
LB-Q(5)
LB-Q(20)
LB-Q2(5)
LB-Q2(20)
ADF(I1)
PP(I1)
MSCI
Austraila Hong Kong
0.098
0.258
0.214
1.911
2.038
4.403
19.5
7.89922481 20.57476636
(0.226***) (0.275***)
(0.496***)
5.032***
3.506***
7.742***
151.81***
19.52***
719.56***
3.15
9.99*
15.62***
14.49
22.52
43.84***
70.88***
48.89***
35.76***
111.13*** 123.31***
118.73***
-28.88
-30.33
-26.79
-29.91
-30.33
-26.91
Japan
0.002
4.92
2460
0.442***
4.575***
114.26***
9.15*
32.21**
68.21**
133.32**
-31.77
-31.76
Singapore
UK
US
0.074
0.159
0.293
5.144
2.401
1.816
69.5135135 15.1006289 6.19795222
(0.865***)
0.032
(0.430***)
21.90***
4.684***
4.349***
12622***
99.54***
419.05
27.33***
11.05*
11.28**
48.53***
20.63
25.89
110.34***
9.08*
58.69***
164.04***
26.42
73.21***
-29.34
-26.35
-26.81
-29.37
-26.35
-26.88
Notes: Weekly returns are from January 5, 1990 to Feb 10, 2006 (841 weeks) for MSCI world stock
market and public real estate markets of Australia, HK, Japan, Singapore, the UK and the US. LB-Q (5),
LB-Q (20), LB-Q2 (5) and LB-Q2 (20) are the Ljung-Box test statistics for serial correlations in the returns
and squared returns, respectively. ADF and PP are, respectively, the augmented I (1) statistics for DickeyFuller and Phillips-Perron tests for unit roots. ***, **, * indicates two-tailed significance at the 1, 5 and 10
percent levels respectively.
Table 2
Correlations in returns (variances): 05/01/1990 – 06/02/2006
return (variances)
MSCI
Australia
Hong Kong
Japan
Singapore
MSCI
1
1
Australia
0.336***
0.186***
1
1
Hong Kong
0.454***
0.292***
0.287***
0.185***
1
1
Japan
0.424***
0.171***
0.171***
0.122***
0.221***
0.170***
1
1
Singapore
0.421***
0.209***
0.204***
0.107***
0.581***
0.762***
0.246***
0.106***
1
UK
US
UK
0.423***
0.351***
0.303***
0.103***
0.242***
0.079**
0.236***
0.022
0.230***
0.022
1
1
US
0.458***
0.431***
0.226***
0.123***
0.220***
0.162***
0.096***
0.116***
0.251***
0.093***
0.256***
0.280***
1
1
Notes: Numbers in brackets Pearson correlation coefficients in variance between the respect pairs. ***, **
indicates statistical significance at one and five percent levels respectively.
27
Table 3
Multivariate AR (p) – EGARCH (1, 1) estimates
of real estate market /MSCI returns (conditional t distribution)
5/1/1990 - 10/2/2006 (Entire sample period)
Constant Condtional Correlation (CCC)- MEGARCH (1,1)
Shape = 9.839 (t = 10.19***)
Log-likelihood = 13506.3443
MSCI(j=1)
AU (j=2)
HK(j=3)
JP(j=4)
SG(j=5)
UK(j=6)
Mean equation
constant
D97
variance equation
constant
arch
garch
CCC
pj1
pj2
pj3
pj4
pj5
pj6
Test on std residuals
Arch(10)[prob]
Q(10)[prob]
Q(20)[prob]
Q2(10)[prob]
Q2(20)[prob]
0.00187***
0.00297
0.00367***
-0.00321
0.00388***
-0.01214**
0.00175
-0.00823*
0.00306***
-0.01229*
0.00243***
n.a.
US(j=7)
0.07667***
n.a.
-0.15627*** -0.66591*** -0.38876*** -0.40295*** -0.28297*** -0.08641*** -0.31777***
0.09626*** 0.13501*** 0.14009*** 0.19461*** 0.13482*** 0.06731*** 0.12118***
0.98992*** 0.92768*** 0.95683*** 0.95847*** 0.97230*** 0.99521** 0.97206***
0.3570***
1.147[0.32]
13.345[0.21]
19.411[0.50]
10.494[0.40]
17.933[0.59]
0.548[0.87]
12.075[0.28]
24.313[0.23]
4.741[0.91]
15.193[0.77]
0.4394**
0.3006***
0.4661***
0.1649***
0.1771***
0.4185***
0.1930***
0.4723***
0.2043***
1.003[0.44] 2.025[0.028] 0.753[0.67]
12.204[0.27] 10.072[0.43] 7.341[0.61]
32.31[0.04] 17.20[0.64] 17.295[0.63]
10.433[0.40] 18.862[0.042] 7.495[0.68]
42.88[0.05] 29.169[0.084] 15.989[0.71]
0.4436***
0.3054***
0.2620***
0.2489***
0.2819***
0.4524***
0.2122***
0.2102***
0.1023***
0.2212***
0.2485***
1.828[0.053]
8.492[0.58]
12.952[0.88]
17.464[0.07]
25.449[0.18]
0.634[0.79]
10.108[0.43]
21.770[0.36]
6.935[0.73]
17.098[0.65]
***, ** - indicates statistical significance at the one and five percent levels
28
Table 4
Multivariate AR (p) – EGARCH (1, 1) estimates of real estate market /MSCI returns (conditional t distribution): pre- and post-crisis periods
5/1/1990 - 27/6/1997 (Pre-crisis period)
Constant Condtional Correlation (CCC)- MEGARCH (1,1)
Log-likelihood = 6596.6634
Shape = 11.068 (t = 8.36***)
MSCI(j=1) AU (j=2) HK(j=3)
JP(j=4)
SG(j=5)
UK(j=6)
US(j=7)
Mean eq
constant
0.0018***
variance eq
constant
-0.5434***
arch
0.0862***
garch
0.9431***
CCC
pj1
pj2
pj3
pj4
pj5
pj6
Test on std
residuals
Arch(10)[prob] 1.68[0.09]
Q(10)[prob] 18.01[0.06]
Q(20)[prob] 26.06[0.16]
Q2(10)[prob] 21.51[0.02]
Q2(20)[prob] 42.32[0.01]
0.0032*** 0.0054***
0.0044**
0.0035***
0.0041***
-3.0829*** -0.2635*** -1.1423*** -0.5120*** -0.0608*** -0.4691*** -0.1196** -7.9376*** -0.3389
-0.1967 -0.1995*
0.2272* 0.1196*** 0.2867*** 0.0801** 0.0740*** 0.1176*** 0.0862*** -0.0134
0.1457
0.0853 0.1167**
0.6358*** 0.9741*** 0.8533*** 0.9338*** 0.9995*** 0.9553*** 0.9936*** 0.2483 0.9658*** 0.9790*** 0.9836***
-3.3299
0.2158**
0.5964**
-9.7904
0.2243***
0.3207
0.415***
0.399***
0.327***
0.222***
0.333***
0.441***
0.235***
0.195***
0.066
0.231***
0.292***
1.15(0.32)
7.88[0.64]
12.63[0.89]
12.36[0.26]
22.22[0.33]
0.16(0.99)
9.99(0.44)
15.69[0.74]
1.97[0.99]
6.65[0.99]
0.281***
0.345***
0.262***
-0.0001
0.678***
0.120***
0.108**
0.0021***
0.403***
0.059
0.381***
0.193***
0.0019*
1/1/1999 - 10/2/2006 (Post-crisis period)
Constant Condtional Correlation (CCC)- MEGARCH (1,1)
Log-likelihood = 6096.7621
Shape = 12.962 (t=6.92***)
MSCI(j=1) AU (j=2)
HK(j=3)
JP(j=4)
SG(j=5)
UK(j=6)
US(j=7)
0.493**
0.204***
0.227***
0.258***
0.255***
0.0035*** 0.0023*** 0.0042***
0.439***
0.174***
0.214***
0.137***
0.206***
0.206***
0.384***
1.18[0.31] 1.76[0.07] 1.16[0.32] 0.84[0.59] 0.74[0.68] 0.32[0.98] 0.81[0.62] 1.28[0.18]
11.61[0.31] 7.59[0.67] 22.87[0.01] 5.16[0.88] 4.59[0.91] 12.07[0.28] 11.89[0.29] 5.32[0.87]
23.65[0.26] 28.08[0.11] 28.06[0.11] 10.28[0.96] 11.46[0.93] 26.74[0.14] 22.83[0.30] 10.70[0.95]
14.83[0.14] 15.89[0.11] 11.95[0.29] 7.28[0.70] 7.12[0.71] 3.30[0.97] 9.16[0.52] 27.15[0.02]
30.17[0.07] 21.83[0.35] 19.90[0.46] 19.47[0.49] 18.77[0.54] 8.88[0.98] 14.83[0.79] 42.02[0.12]
0.0031**
0.514***
0.318***
2.04[0.03]
16.91[0.08]
26.85[0.24]
32.80[0.01]
27.45[0.30]
0.0047***
0.287***
0.171***
0.228***
0.425***
0.292***
0.531***
0.225***
0.51[0.88] 1.23[0.27]
7.33[0.69] 11.12[0.35]
11.57[0.93] 19.46[0.49]
5.94[0.82] 13.06[0.22]
11.40]0.94] 15.77[0.73]
***, ** - indicates two-tailed significance at the one and five percent levels
29
Table 5(a)
Causality in mean results: 5/1/90 – 10/2/06 (full-sample period)
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
1
2
3
4
5
6
7
8
9
10
0.625
1.771*
-0.226
-1.629
-0.356
1.635
0.579
0.798
0.498
0.139
2.957**
0.069
0.023
1.322
-1.340
-0.454
-1.342
0.917
0.790
0.388
AU/JP 5.072** 1.849*
-1.473
0.014
-1.507
0.503
0.691
-0.691
-0.489
-0.819
-0.579
0.793
1.394
1.195
0.573
-0.908
-1.137
-0.608
0.732
-0.966
0.451
AU/SG 5.187**
0.741
-0.729 (2.173**) -0.694
0.975
-1.282
-0.006 2.144**
1.311
2.963** -0.778
0.555
0.709
-0.029
1.169
-0.532
0.804
1.539
0.457
0.356
-1.539
0.084
1.287
-0.165
-0.058
0.700
-0.072
0.541
-0.894
0.663
1.478
-0.506
-0.255
0.865
0.541
-0.723
0.987
-1.577
-1.010 (2.343**) 0.723
0.555
1.001
0.341
0.561
0.995
-0.269
-0.026
-0.547
0.376
-1.140
0.573
-0.680
0.214
0.451
-0.746
-0.822 2.155**
0.414
0.584
0.373 (1.854*) -0.376
-0.338
0.668
0.631
-0.122
Lag
0
AU/HK 8.170**
1.094
AU/UK 9.079** 2.858**
AU/US 6.307** 1.736* 2.589**
1.177
AU/WD 10.404** 3.541**
1.496
0.825 (2.592**) -0.255
HK/JP 5.694**
0.602
-0.720
-0.304
0.888
-0.521
-0.179
-1.516
-0.333
0.579
-0.567
1.123
1.131
1.065 (2.031**) 0.023
HK/SG 15.429** 1.823*
0.298
0.529
-0.266
-0.555
-0.955
-0.104
-0.590
0.622
0.373
HK/UK 7.479** 2.054**
0.651
0.376
0.891
-0.139
HK/US 6.515**
0.978
0.868
-0.613
-1.293
0.443
-1.331
-1.134
0.095
-0.312
0.078
-0.257
0.877
-0.012
2.873**
1.325
-0.425
-0.402
-0.046
0.200
0.793
0.758
-0.029
-0.454
-0.182 (2.291**) -0.205 2.199** -0.396
-0.582
0.576
-0.191
0.570
0.570
0.295
-0.474
-0.521
-1.513
0.642
-0.492
-0.127
1.776*
-0.706
0.509
0.764
0.174
1.962**
0.908
-0.347
-1.325
0.385
-1.123
1.577
0.822
1.125
HK/WD 12.837** 2.893**
0.694
0.341
-0.654
-0.310
1.238
-0.454
-0.179
0.911
0.547
0.292
1.881*
-0.833
-0.862
0.176
0.179
-0.318
-0.674
0.521
JP/SG 6.385** -1.366
-0.784
-0.385
-1.490
0.246
-1.018
-1.423
0.003
1.525
0.587
1.180
1.797*
-0.393
0.324
-0.139
0.165
-0.136
1.568
0.477
0.422
JP/UK 7.354** 2.190**
1.438
1.421
1.180
-0.069
1.368
-0.376
1.386
0.801
-0.793
-0.451
-0.671
-0.052
-0.052
0.865
0.793
0.009
0.356
-0.784
-0.446
JP/US 3.136**
-1.189
1.125
1.287
0.472
-0.017
0.561
-1.128
1.473
1.458
1.073
0.176
0.156
-0.312
1.528
0.182
0.043
-0.370
-0.671
0.376
0.527
JP/WD 13.314** 1.496
0.529
-0.226
-0.550
1.290
-0.853
0.353
0.729
0.095 (2.902**) 1.007
-0.168
0.353
0.958
-1.206
-0.341
-1.059
-0.162
0.842
-0.133
SG/UK 7.762** 3.165**
1.224
-0.260
-0.437 2.239**
1.180
-1.140
1.727* 2.228** -0.550
0.321
-1.273
-0.634
0.191
0.503
0.041 (1.687*) 0.451
0.772
0.142
SG/US 7.033**
0.023
1.276
-0.515
-0.243
0.231
-1.635
-0.020
1.765*
1.134
0.787
-0.159
1.441
0.631
0.035
1.447
1.247
1.117
-0.509
-0.402
SG/WD 12.012** 3.449** 1.771*
-0.226
-0.761
-0.179
0.989
-0.295
1.490
2.653** -0.246
1.701*
0.955
-0.900
-0.987
-0.448
-0.159
-1.201
0.043
1.056
0.509
UK/US 7.808** 2.352**
0.579
0.150
-0.446
0.532 (1.892*) -0.081
1.151
1.956*
0.385
-0.107
1.036
1.322
1.817*
0.518
0.506
0.182
0.691
-1.068
-0.026
UK/WD 13.051** 1.149
-1.293
-0.009
-1.218
0.697
-0.443
0.165
1.383
-0.689
-1.044
1.918*
0.657
0.179
0.347
-0.286
0.625
-0.804
0.923
0.081
0.081
US/WD 13.499** 0.150
1.392
0.165
1.597
0.495
1.493
-0.269
-0.197
-0.599
-0.712
0.367
0.801
0.145
-0.564
-1.189
-1.030
-0.532
0.179
1.123
-0.414
0.984
Notes: Each entry gives the causality in mean t-statistics between the real estate / global stock markets of the countries noted in the first column. The six real
estate markets are Australia (AU), Hong Kong (HK), Japan (JP), Singapore (SG), the UK and the USA; the global stock market (WD) is represented by the
MSCI World Index. The lag k denotes the number of weeks by which the return of the first market lags or leads that of the second market. A negative (positive)
value of k indicates lags (leads). Significant t-statistics with k<0 suggests that the first market causes the second market. Significance with k>0 indicates causality
in the opposite direction. ***, ** - indicates statistical significance at one and five percent levels.
30
Table 5(b)
Causality in variance results: 5/1/90 – 10/2/10 (full-sample period)
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
1
2
3
AU/HK 4.360**
1.256
-1.279
1.209
-1.175
0.327
-1.435
1.250
0.411
-1.360
-0.067
1.504
-0.845
0.584
1.828*
0.657
0.249
-1.070
Lag
0
4
5
-0.683 2.610**
7
8
1.389
-1.513
9
10
-0.715 (1.655*)
-1.267
-0.145
-0.758
-1.027
1.909*
1.510
0.746
0.515
1.412
1.079
0.243
-0.119
-0.333
1.397
-0.599
AU/SG 2.121** 2.951** -0.778 2.627**
0.194
-0.255
-1.293
1.765*
1.820*
0.142
-1.096
0.307
-0.651
0.145
-0.393
0.535
0.159
1.551
-1.444
-0.159
-1.079
AU/UK 4.450**
1.204
0.156
-0.527
-0.249
0.610
-1.146
0.373
-0.576 (1.996**) -1.050 2.555** 2.060** -0.388
0.894
0.240
AU/US 2.902**
1.177
0.029
-0.231
0.038
-0.078
-0.642
-0.278
-0.657 (1.739*) -1.371
AU/WD 5.731**
0.353
0.295
0.663
-1.241
-0.370
-0.715
1.042
-0.347
HK/JP 3.370**
0.385
AU/JP
2.485** -0.084
6
0.865
0.804
0.639
-0.171
-1.042
0.622
0.506
0.382
0.133
1.516
0.744
0.266
2.115** -0.338
-0.101
0.437
0.095 (1.753*) -0.084
0.214
-0.243
0.084
1.426
1.559
2.332** -1.565
1.290
-0.020
-0.515
-0.330
0.107
-0.249
0.061
1.522
-0.078
-0.139
-0.139
-0.527
-0.932
-0.237
0.185
0.822
-0.286
-0.367
-0.784
0.428
2.245**
0.038
-0.906
1.490
0.000
HK/SG 18.215** 0.365
-0.278
-0.778 3.072** -0.639
0.041
-0.396
0.200
-0.761
-0.527
1.389
0.356
HK/UK 3.628**
-0.405
0.385
-0.243
-0.260
0.605
-0.793
0.830
-1.510
0.634
1.713* 4.695** -0.781
-0.451
-0.926
1.166
-0.419
0.998
-0.663
-1.331
HK/US 3.668** 1.993** -0.605
1.516
-0.107
0.417
0.547
0.257
-0.110
-1.632
1.215
1.585
-0.856
-0.706
0.677
0.495
-1.206
-0.220
-0.914
0.477
0.573
-1.328
-0.402
0.396
-0.252
1.230
2.720** 1.672*
-0.492
2.222**
1.050
1.805*
HK/WD 7.675** 2.155**
0.284
-0.564
-0.518
-0.845
1.073
1.672*
0.949
-0.017
1.664* 2.115**
1.580
-0.448
1.285
-0.712
0.639
1.102
2.141**
0.657
2.853**
1.195
-0.599
-0.463
-0.770
0.830
-0.344
0.995
-0.489
0.851
0.009
-0.284
-0.211
-0.984 2.497** 5.589**
JP/UK
0.804
0.197
-0.150
-0.474
1.455
-0.853
0.124
1.811*
0.124
-1.125
-0.315
0.744
0.081
-0.281
-0.153 3.232**
0.498
0.017
1.366
1.669
-0.176
JP/US
-0.122
0.495
0.405
1.134
-0.466
1.687*
1.189
0.038
0.729
-1.056
-0.336
-0.934
0.130
-0.521
-0.009 4.473**
0.385
0.107
0.026
-0.486
-0.746
JP/WD 4.774**
0.746
-0.906
0.683
1.241
0.515
-0.240
-0.133
1.001
0.457
0.272
1.785*
1.519
-0.315
0.041
0.871
0.868
0.914
0.894
0.654
-0.203
SG/UK 1.768*
-0.260
-0.365
0.443
-0.113
-0.553
0.610
-0.961
0.087
-0.833
-0.414
1.826* 3.538** -0.197
-0.336
-0.532
0.139
-0.414
0.489
-0.628
-0.775
SG/US 2.184**
0.608
-0.110
-0.124
1.004
0.093
0.182
0.052
-0.307
-0.492
0.796
1.435
0.393
-0.032
-0.593
-0.272
-0.373
-0.289
-0.758
-0.558
-0.906
SG/WD 5.086**
1.053
0.307
-0.012
0.865
-0.064
-0.150 2.242**
0.162
-0.593 2.031**
1.192
-0.448
-0.023
1.467
-0.524
0.017
0.278
-0.156
-0.712
-0.544
1.125
0.463
-0.324
-0.451
0.113
0.865
0.292
0.029
-0.917 4.354** -0.457
-0.639
-0.729
0.003
-1.267 (1.730*) 0.237
0.208
-0.286
UK/WD 11.428** 3.191** 2.083**
1.065
0.223
-0.362
0.469
1.328
0.451
-0.642
-0.952 2.346**
0.726
-0.880
0.307
-0.393
-0.981
-1.230
-1.042
-1.039
-0.535
US/WD 11.598** 2.936**
1.177
1.177
0.506
0.116
-0.489
-0.443
-0.113
-1.499 3.813**
0.767
0.443
2.236**
0.411
-0.093
-0.356
-0.862
-0.443
-0.660
JP/SG
UK/US 10.924** 3.775**
1.337
Notes: Each entry gives the causality in variance t-statistics between the real estate / global stock markets of the countries noted in the first column. The six real
estate markets are Australia (AU), Hong Kong (HK), Japan (JP), Singapore (SG), the UK and the USA; the global stock market (WD) is represented by the
MSCI World Index. The lag k denotes the number of weeks by which the variance of the first market lags or leads that of the second market. A negative (positive)
value of k indicates lags (leads). Significant t-statistics with k<0 suggests that the first market causes the second market. Significance with k>0 indicates causality
in the opposite direction. ***, ** - indicates statistical significance at one and five percent levels.
31
Table 6
Summary of causality patterns: full sample period (5/1/90-10/2/06)
Australia
Australia
HongKong
Japan
Singapore
UK
US
MSCI
CIM
CIV
CIM
CIV
CIM
CIV
CIM
CIV
CIM
CIV
CIM
CIV
CIM
CIV
0,-1
0, -10
0
0, -3
0, -1
0
0
0,-1,-2
0
0, -7
0,-1,-5
0, -7
Hong Kong
0, -2
0, -5
0,-1
0,-3,-4
0, -1
0, -4
0
0,-1,-2
0,-2,-7
0,-1,-2
0,-1
0, -1
Japan
0, -1
0, -8
0
0, -8
0, -1
-7,-8
0
-5
0
-5
0
0, -1
Singapore
0,-4,-9
0,-1,-3,-7,-8
0,-1
0, -4
0
-1,-3
0, -7
0,-1,-2
0
0
0,-1
0
UK
0, -1
0, -9
0,-1,-7,-9
0
0,-1
-7
0,-1,-5,-8,-9
0
0,-4
0,-1,-7
0,-1
0, -1
US
0,-1,-6
0, -9
0
0, -1
0
-5
0, -9
0
0,-1,-6,-9
0, -1
MSCI
0,-1,-4
0, -10
0,-1
0,-1,-7,-10
0, -10
0
0,-1,-2,-9
0,-7,-10
0
0,-1,-2
0
0, -1
0
0, -1, -4
Notes: This summary is constructed based on the results reported in Table 5(a) (causality in mean – CIM)
and Table 5(b) (causality in variance – CIV). 0 indicates contemporaneous correlation between two markets
exist. –k indicates the presence of correlation at lag k. For example: 0,-2 in the first cell of the Hong Kong
column indicates there is contemporaneous relation between the means of the Australia and Hong Kong
real estate markets, and the mean return of the Australia market at lag 2 has an impact on the current mean
return of the Hong Kong market
32
Table 7(a)
Causality in mean results: 5/1/90 – 27/6/97 (pre-crisis period)
-2
-3
-4
-5
-6
-7
-8
-9
-10
1
2
3
4
5
6
7
8
9
10
AU/HK
Lag
4.100** -0.057
0
-1
1.525
0.748
-1.544
0.521
0.218
2.672**
0.366
2.467**
0.795
1.664*
-0.498
1.064
-1.021
-0.352
-0.726
-1.328
1.064
1.418
-0.193
AU/JP
2.353** 2.227** -1.310
0.201
0.732
-1.013
-0.240
-1.096
-1.411
1.348
-0.606
0.089
2.075**
0.173
0.539
0.033
-0.193
-0.751
0.417
-1.060
-0.429
0.773
0.942
0.437
-1.399
0.053
0.376
0.474
-0.429 2.841**
1.316
1.277
-0.151
0.002
-0.035
0.445
1.422
-1.574
1.434
0.690
-0.340
AU/UK
3.718** 1.798*
-1.310
0.053
-0.370
1.253
0.106
1.617
1.521
0.565
0.626
-0.582
-0.476
0.797
0.061
-0.706
-0.810
0.883
-0.374
-1.100
1.289
AU/US
3.470**
0.110
0.734
-1.009
0.338
-1.639
-0.236
-0.061
0.946
0.370
-0.429
0.728
-0.651
-0.610
0.421
-0.661
-0.724
1.566
-0.268
0.720
AU/WD
5.253** 2.221** -1.121
0.818 (2.048**) 0.002
-0.423
-0.090
0.492
0.885
0.212
0.584
0.846
0.667
-0.128
-0.541
0.063
-0.203
1.355 (1.818*) 0.360
HK/JP
2.154**
0.244
0.277
0.797
-0.584
-0.230
0.559
0.645
1.111
2.308** -1.106 (1.957*) 0.130 (2.630**) -1.586
0.177
-1.119
-0.033
-0.134
0.576
-1.174
HK/SG
8.152**
0.063
1.367
-0.338
0.437
0.262
0.120
1.108
-0.069
-0.008
1.497
-0.110
0.612
1.568
0.336
-0.124
-0.942
HK/UK
4.426** 1.708*
1.560
0.470
0.779
-0.329
0.157
-1.096
-0.714 2.506** -0.506
HK/US
4.322** -0.285
0.395
0.787
0.002
-0.663
-0.468
0.710
1.108
0.155
0.866
-0.679
AU/SG
0.911
0.885
-0.441
0.207
0.761
-0.492
-0.041
0.207
-0.136
0.486
0.610
-0.938
-0.773
-0.704 (1.942*) 0.712
-1.576
1.845*
-1.237
-0.468
-0.547
-1.027
1.672*
-0.100
1.171 (1.739*) -0.502
0.515
-0.462
0.677
-0.710
HK/WD 6.877**
1.098
1.100
-0.285
0.374
0.793
-0.031 2.485** -0.026
-0.834
JP/SG
3.814**
0.919
-0.124 (2.567**) (1.727*) 0.403
-0.551
-0.423
-0.169
1.283
0.852
2.593**
JP/UK
5.075** 2.068**
1.194
0.659
-1.147
1.397
-0.443
0.637
1.729*
-0.165
0.669
JP/US
2.988** 2.217**
0.515
-1.007
-1.414 2.190** -0.582
1.955*
0.344
-0.470
-0.797
0.081
JP/WD 13.411** 1.710*
0.301
0.177 (1.794*) 1.076
-1.265
0.301
0.911
0.409 (3.814**) 1.613
1.121
SG/UK
4.957** 2.492**
0.850
0.114
-0.643
1.509
0.708
0.307
-0.297
1.674*
0.171
1.385
1.430
SG/US
4.296**
1.391
-0.724
1.363
-0.201
0.159
0.081
0.232
-0.205
0.498
0.087
-0.877
1.662*
SG/WD
8.032** 1.649*
1.727*
0.384
-0.753
-0.374
-0.004
1.586
0.445
1.436
UK/US
3.954**
1.123
-0.765
-1.051
0.057
-0.321
-1.499
-0.840
-0.035
-0.586
-0.051
0.724
UK/WD 9.752**
0.454
-1.007
-0.395
-0.230
0.618
-0.927
-0.264
1.316
-0.757
9.039** -0.631
1.346
0.214
0.710
-0.049
0.610
2.003**
0.012
0.818
US/WD
0.124
-1.627
-1.119
0.708 (1.865*)
0.049
-0.502
0.421
0.360
-0.547
0.246
0.671
0.275
-1.265
0.321
0.970
1.784*
-0.480
-0.462
1.710*
0.163
-0.753
1.210
0.944
0.822
-0.079
0.478
-0.159
0.171
0.919
-0.090
1.206
0.653
-0.370 (2.040**) -0.157
0.964
1.279 (2.801**)
-0.620
0.246
0.140
-0.614 (2.188**) 0.104
0.224
-0.456
-0.295
0.513
-0.185
1.058
1.218
1.326
0.151
-1.021
1.826*
-1.446
-1.350
-0.081
0.014
-0.773
-0.179
1.371
-1.104
0.529
0.220
1.039
1.072
0.506
1.308
0.317
0.710
-1.133
-1.121 2.252**
0.993
0.675
-0.321
-0.382
1.145
0.655
0.114
0.797
-0.083
-0.474
0.203
0.622
-0.470
0.043
0.096
0.795
0.205
0.214
-1.129
2.638** -0.907
0.787
2.268** -1.106
Notes: Each entry gives the causality in mean t-statistics between the real estate / global stock markets of the countries noted in the first column. The six real
estate markets are Australia (AU), Hong Kong (HK), Japan (JP), Singapore (SG), the UK and the USA; the global stock market (WD) is represented by the
MSCI World Index. The lag k denotes the number of weeks by which the return of the first market lags or leads that of the second market. A negative (positive)
value of k indicates lags (leads). Significant t-statistics with k<0 suggests that the first market causes the second market. Significance with k>0 indicates causality
in the opposite direction. ***, ** - indicates statistical significance at one and five percent levels.
33
Table 7(b)
Causality in variance results: 5/1/90 – 27/06/97 (pre-crisis period)
Lag
0
-1
-2
AU/HK
0.289
-0.179
-0.565
-0.238 (1.822*) 1.117
-3
-4
-5
-6
-7
-8
-9
-10
1
2
3
-0.590
0.488
-0.594
-0.008
0.732
-0.415
-1.279
1.519
4
5
-0.490 2.160**
6
7
8
9
10
0.952
1.351
-0.946
0.026
-1.348
AU/JP
0.016
1.953*
0.285
-0.716
-1.078
-0.067
0.545
-1.060
0.797
0.537
-0.218
0.696
2.020**
0.708
-0.018
0.096
-0.616
1.391 (1.991*) 1.393
-0.504
AU/SG
-0.364
1.804*
-0.407
-0.407
1.212
-0.179
-1.161
0.014
-0.687
0.964
-0.470
-0.089
-0.604
0.342
-0.449
0.413
-0.270
1.420
-1.102
AU/UK
-0.549
0.826
-0.750
0.366
0.057
0.338 (1.749*) 2.172**
0.409
-1.127
-1.161
0.417
0.287
0.293
-0.031
1.318
0.689
-1.076
1.987** -0.879
-1.072 2.347**
AU/US
0.508
1.505
0.704
0.035
1.503
-0.954
-0.022
-1.534
-0.624
-1.070
0.130
-1.351
-0.240
-0.047
0.830
-0.102
0.338
-0.006
0.748
-0.321
AU/WD
1.176
0.722
-0.476
-0.130
-0.561
0.014
0.069
-0.055
1.174
1.414
-1.076
-1.477
1.407
0.588
0.488
0.142
1.249
1.361 (1.682*) -0.130
0.671
HK/JP
1.393
-0.610
0.466
-0.647
-0.344
-0.151
-0.388
-0.519
-0.936
-0.122
-1.348
0.277
0.498
0.445
0.954
-0.063
0.476
1.774*
1.058
-0.698 2.913**
HK/SG
6.724**
0.570
0.862
-0.502
0.360
-1.210
-0.199
-1.041
-0.193
-0.925
-0.771
0.999
0.342
-0.677
1.076
0.944
-0.155
-0.004
-0.340
HK/UK
0.134
-0.087
-1.031
-0.824
-0.915
-0.667
0.624
-0.559
1.678*
-0.860
1.418
-0.065 2.620** -0.787
1.692*
-0.942 2.441** -0.218
1.365
0.281
-0.397
2.398** -1.127
0.671
-0.832
2.939** 1.961**
HK/US
0.830
0.140
-0.205
1.405
0.035
0.348
-0.291
-0.118
0.346
-0.844
0.035
0.012
HK/WD
3.864**
0.370
0.427
-0.687
0.395
-0.895
0.244
-0.346
-0.871
-0.222
-0.582
-0.578 3.124**
0.134
0.873
0.216
JP/SG
0.673
0.474
-0.059 2.886**
0.490
-0.087
-0.256 2.101** 3.063** -0.094
0.736
-1.037
0.860
-0.128
0.173
JP/UK
-0.083
0.938
1.680*
-0.781
0.124
0.578
-0.631
-0.020
-0.537
1.070
1.035
0.128
-0.372
JP/US
0.327
1.505
0.431
1.489
0.799
0.364
1.430
-0.260
-0.415
-0.917
0.028
-1.306
0.612
JP/WD
9.163**
0.073
0.334
1.564
SG/UK
0.612
0.311
-0.565
-0.472
1.991** -0.995
0.102
1.971**
3.714** 2.097** -0.746
0.370
2.750** 2.673** -0.763
-0.232
0.464
0.500
-0.146
1.509
2.406** 2.115** 1.967** -0.799
-1.049
1.652*
0.903
-0.004
1.940* 2.311**
0.264
-0.445
0.234
-0.706
0.161
-0.537
-0.352
0.968
0.582
0.342
-0.364
0.472
1.204
1.074
1.239
1.127
1.084
-1.039
0.030
-0.059
-0.923
1.373
0.915
0.628
-0.586
0.435
-0.761
-0.633
-1.377
0.053
0.059
-0.724
-0.616
1.312
0.612
1.058
0.153
1.975*
0.073
0.614
-0.932
0.187
1.216
-0.146
-0.232
-1.214
SG/US
1.694*
1.200
0.832
-0.350 3.734**
0.767
-1.412
0.413
0.429
-0.885
1.580
0.063
1.273
1.645*
-0.209
1.051
0.380
SG/WD
3.803**
0.433
0.950
1.121
1.338
-0.372
0.425
1.033
-0.641
0.077
1.666*
0.297
1.202
2.994**
1.591
0.978
1.625
UK/US
0.659
2.388**
1.054
0.301
0.728
0.877
0.513
0.085
0.126
-0.075
0.313
0.612
-0.716
-0.183
0.112
-0.807
-0.537
-1.322
-0.108
0.661
0.012
UK/WD
4.688** 2.315**
0.793
-0.285
0.950
0.081
2.142** 2.327** 1.713*
0.761
0.901
-0.496
1.324
-1.643
1.322
-1.389
-0.138
-0.675
-0.472
-0.506
-0.004
US/WD
5.731**
0.106
0.596
0.744
0.409
1.062
-0.706 3.334**
0.362
0.059
1.869*
1.153
0.352
0.035
0.574
-0.033
-0.146
0.980
-0.061
0.976
0.325
2.654** 2.095** -0.452
0.201
Notes: Each entry gives the causality in variance t-statistics between the real estate / global stock markets of the countries noted in the first column. The six real
estate markets are Australia (AU), Hong Kong (HK), Japan (JP), Singapore (SG), the UK and the USA; the global stock market (WD) is represented by the
MSCI World Index. The lag k denotes the number of weeks by which the variance of the first market lags or leads that of the second market. A negative (positive)
value of k indicates lags (leads). Significant t-statistics with k<0 suggests that the first market causes the second market. Significance with k>0 indicates causality
in the opposite direction. ***, ** - indicates statistical significance at one and five percent levels.
34
Table 8(a)
Causality in mean results: 4/9/98 – 10/2/06 (post-crisis period)
-1
-2
-3
-4
-5
-6
-7
-8
-9
AU/HK 6.736**
Lag
0
1.423
0.253
-0.667
-1.105
-0.632
1.882*
-1.409
-1.034
-1.273
AU/JP
3.550**
1.248
-1.468
0.441
-1.056
0.642
1.368
AU/SG 6.283**
1.615
-0.742
-0.122 (2.135**) -0.120
1.837*
AU/UK 8.433** 1.848*
1.407
-1.489
0.094
0.257
-0.084
-1.215
2.211**
1.211
-1.258
-0.389
-1.101
0.759
0.347
0.693
0.457
0.267
0.275
0.757
1.185
-0.791
0.565
1.462 (1.682**) 1.016
1.342
-0.854
-0.840
-1.175
-1.258
1.387
-0.567
0.167
0.936
-1.652
-0.479
-1.330
AU/US 4.919**
1.220
AU/WD 7.972** 2.980** 1.678*
HK/JP
5.176** 2.192** (1.791**) 0.385
2
3
4
5
6
7
8
9
10
-0.006 1.995**
0.298
-0.691
1.650*
-0.679
-0.290
0.487
-0.473
0.188
0.408
0.614 (2.459**) 0.024
-0.806
0.595
-0.846
1.069
-0.467
-0.549
-1.403
0.806
0.365
0.137
0.840
-1.454 (2.070**) 1.974**
0.926
1.925*
-0.296
0.239
-0.102
0.173
0.430
2.058** -0.322
1.446
0.434
-0.375
0.724 (2.068**) 0.077
2.349**
0.667
-0.039
0.434
-0.540
-0.051
-0.545
-0.141
-1.458
-0.891
-0.184
-0.088
1.164
-0.057
0.349
-1.111
-0.463
-10
1
0.188
-0.545
0.047
0.061
0.320
-0.233
1.941*
-0.251
-0.967
-0.014
-0.139
0.822
1.224
-0.357
-0.381
0.557
-1.081
0.232
-0.438
0.010
0.198
-0.744 (1.666**) 1.819*
1.077
3.989**
1.122
0.245
0.135
0.133
0.930
0.850
0.133
-0.742
0.445
HK/UK 6.416** 1.970** -0.746
0.842
1.067
0.706
-0.522
-1.222
0.532
-0.265
0.865
-1.132
0.418
0.518
1.138
-0.752
-1.313
-0.799
0.047
HK/US 4.083**
0.296
0.571
-0.706
-0.194
0.440 (2.037**) 0.783
0.950
1.001
1.583
0.981
0.122
1.028
0.720
0.708
1.364
0.112 (2.121**) -0.271
HK/WD 10.189** 3.306** -0.700
0.453
-0.389
1.067
1.842*
-0.912
-0.944
0.210
1.503
0.932
0.557
-0.377
-0.512
0.879
-0.806 (1.715*) -0.084
-0.390
0.355
-0.336 (1.748**) 0.700
1.360
0.604
1.007
-0.410
-0.436
0.445
0.237
0.852
0.175
-1.479
0.838
0.135
0.310
1.071
-0.320
-0.169
-0.826
-0.024
-0.757
-0.108
-0.151
0.918
0.963 (1.854*) -1.943
0.712
-1.052
HK/SG 11.116** 1.946*
0.610
-0.151
-0.785
0.748
1.466
JP/SG
5.184** -0.506
-1.128
0.055
JP/UK
4.317**
1.097
0.498
1.674* 2.111**
0.300
JP/US
1.230
-0.671
-0.147
0.545
0.708
-0.483
0.037
0.757
1.191
1.472
-0.702
0.716
-1.373
1.578
0.494
-0.355
-0.273 (1.780*) -0.120
0.553
JP/WD
5.637**
0.481
-0.818
-0.671
0.818
1.111
0.312
0.481
0.593
-0.467
-0.365
0.283 (1.929**) 0.082
1.128
-0.734
0.799
-0.257 (2.500**) 0.573
2.402**
-0.167
SG/UK 6.665**
1.264
0.404
-0.404
0.188
1.880*
0.228
-0.948
0.983
0.997
-0.241
0.306 (2.296**) -1.222
0.408
0.330
0.665
-0.610
-0.646
1.791*
0.712
SG/US
0.410
0.347
0.455
-1.032
-0.006
0.628
-1.160
0.184
1.550
1.126
1.444
-1.395 2.149**
0.801
0.190
1.042
0.257
-0.481
-1.366
-0.047
SG/WD 8.608** 3.210**
0.430
-0.940
-0.775
0.665
1.570
0.477
1.285
1.099
-0.398
1.452
-1.040
-0.192
0.075
-0.563
0.506
-0.595
-0.808
1.167
2.164**
UK/US 6.550** 2.337**
1.140
0.775
-0.748
0.956
-0.822
1.114
1.432
2.614**
0.636
-0.334
0.137
1.315
2.262** -0.304
-0.328
-0.632
0.210 (2.667**) -0.039
UK/WD 8.455** 1.758*
-0.810
-0.077
-0.161
1.264
0.889
1.073
0.135
-0.885
-0.204
0.714
-0.881
-0.518
0.901
-0.634
-1.209 (1.803*) -0.118
-1.277
0.147
US/WD 9.002**
0.561
0.418
1.393
0.483
1.315
-1.352
-0.808
-1.631
-0.801
-0.589
0.080
-0.653
-1.181
-1.629
-1.307
1.370
0.351
4.899**
0.877
-0.836
-0.116
Notes: Each entry gives the causality in mean t-statistics between the real estate / global stock markets of the countries noted in the first column. The six real
estate markets are Australia (AU), Hong Kong (HK), Japan (JP), Singapore (SG), the UK and the USA; the global stock market (WD) is represented by the
MSCI World Index. The lag k denotes the number of weeks by which the return of the first market lags or leads that of the second market. A negative (positive)
value of k indicates lags (leads). Significant t-statistics with k<0 suggests that the first market causes the second market. Significance with k>0 indicates causality
in the opposite direction. ***, ** - indicates statistical significance at one and five percent levels.
35
Table 8(b)
Causality in variance results: 4/9/98 – 10/2/06 (post-crisis period)
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
1
2
3
4
5
6
7
8
9
10
AU/HK 4.038**
Lag
0
1.032
0.208
-0.491
-1.599
-0.320
-0.318
0.767
-0.475
-1.617
-0.245
1.530
1.442
-0.595
-0.506
0.534
-0.608
-0.078
-0.673
0.573
-0.128
AU/JP
-0.116
0.905
-0.206
-0.445
-0.226
-0.441
0.292
1.175
-0.049
0.141
0.067
0.610
-0.024
-1.311
0.049
-0.377
-1.040
-0.343
0.263
0.300
AU/SG 3.767**
1.354
0.239
-0.804
-0.198
-1.346
-0.290
1.903*
-0.165
-0.496
-1.056
0.092
0.840
-0.993
-0.145
1.289
0.432
1.136
-1.342
0.363
-0.381
AU/UK 6.762**
0.616
0.920
-1.077
-0.801
0.569
0.208
-0.147
-0.494
-1.326
0.165
1.432
2.353** -1.140
1.044
0.098
-1.271
-0.232
-0.691 2.537** -0.371
AU/US 3.618**
0.418
0.377
-0.551
-1.046
0.224
-0.510
0.579
-0.165
-1.177 (1.646*) 0.314
0.485
-0.583
0.620
1.183
-1.132 2.245** -0.463
-0.775
0.192
AU/WD 5.904**
0.267
0.922
-0.106
-0.836
-1.056
-0.106
1.585
-1.585
0.067
1.615
-0.959
HK/JP
1.595
-1.458
0.857
0.642
-0.806
-0.200
0.718
-0.120
0.084
-1.807
5.429** 5.386**
1.146
0.371
1.138
0.365
-0.145
-0.547
-0.275
0.198
0.390
1.954*
-0.573
-0.487
-0.775
0.567
-0.457
-0.538
-0.700
0.188
0.253
HK/SG 10.406** 3.118**
0.441
-1.340
-0.771
-0.318
-0.481
-0.649
-0.031
-0.477
-0.744 7.105**
0.891
-0.799
0.122
1.252
1.075
-0.616
-0.369
-1.201
-1.034
HK/UK 5.822** 1.990** -0.357
0.055
-0.789
-0.540
-0.408
0.031
0.626
-0.390
-0.422 2.151** 2.688** -1.340
HK/US 6.663** 3.999** -0.263
-0.067
-0.977
-0.145
-0.824
-0.092
0.135
-1.101
0.251
HK/WD 8.465** 3.569**
-1.258
-0.373
-0.359
-0.644
0.006
-0.434
-0.379
2.980** 2.386**
0.194
-0.212
-0.924
0.438
-1.215
-0.383
-0.526
-0.593
-0.447
-0.498
-0.871
0.237
-0.789
-0.200
-1.107
-0.999
0.602
1.099
1.748*
0.306
-0.290
-0.697
0.004
0.230
1.542
1.638
0.549
-1.154
-0.408
-0.077
0.261
0.400
0.041
0.108
3.924**
JP/SG
3.083**
0.567
-0.871
0.469
-1.338
-0.039
-0.069
-0.810
-0.300
-0.387
0.137
6.540** 2.588**
JP/UK
1.458
0.196
-1.120
0.024
0.237
-1.024
-0.110
1.156
0.579
-0.693
-0.396
0.018
-0.290
-0.186
-0.175
0.351
-1.275
-0.247
1.815*
-0.975
JP/US
1.742*
0.334
0.226
-0.424
-1.116
-0.153
0.371
-0.557
0.494
-1.079
-0.914
0.192
0.483
0.027
-0.267 4.499** -0.296
0.043
-0.661
-0.459
-0.651
JP/WD
0.767
2.374** -0.812
0.078
-0.549
-0.871
-0.130
0.004
-0.216
-0.108
-0.479 2.590** 2.773** -0.485
-0.061
0.251
-0.267 1.995** -0.736
SG/UK 4.874**
SG/US
0.616
4.776** 2.804**
1.519
1.397
0.549
-0.485
0.441
-0.591
-0.500
1.024
-0.491
-0.763
-0.316
-0.834 2.831**
0.169
-0.630
-0.063
-0.659
0.524
-0.826
0.029
0.318
-0.824
0.893
-0.131
-0.059
0.383
1.083
-0.361
-0.777
0.343
-0.163 3.789**
0.781
0.022
-0.014
-0.675
-1.067
-0.928
-0.536
-0.512
-0.879
SG/WD 8.298** 1.752* 2.384**
0.220
0.100
0.577
0.049
0.020
-0.171
-0.310
-0.045 3.349** -0.141
0.177
-0.073
-0.451
0.328
-0.334
-0.534
-0.750
-0.897
UK/US 8.641**
1.381
-0.230
-0.538
-0.728
-0.294
0.757
0.740
-0.349
-0.983 3.024** -0.365
-0.198
-0.549
0.508
-0.983
-1.470
0.318
-0.165
-0.298
UK/WD 9.232**
0.905
1.262
0.926
-0.663
-0.308
-1.071
0.332
-0.206
-0.781
-0.842 2.716** -0.279
0.257
-0.775
-0.169
-1.309
-0.952
-0.889
-0.491
-0.249
US/WD 8.826** 1.809*
1.676*
0.512
0.624
0.249
-0.648
-1.270
-0.041
-0.818
-0.918 2.975**
-0.336
0.285
-0.726
-1.179
-0.781
-0.934
-0.606
-0.632
-0.306
0.469
Notes: Each entry gives the causality in variance t-statistics between the real estate / global stock markets of the countries noted in the first column. The six real
estate markets are Australia (AU), Hong Kong (HK), Japan (JP), Singapore (SG), the UK and the USA; the global stock market (WD) is represented by the
MSCI World Index. The lag k denotes the number of weeks by which the variance of the first market lags or leads that of the second market. A negative (positive)
value of k indicates lags (leads). Significant t-statistics with k<0 suggests that the first market causes the second market. Significance with k>0 indicates causality
in the opposite direction. ***, ** - indicates statistical significance at one and five percent levels.
36
Table 9
Direction of causality in mean and causality in variance: pre- and post-crisis periods
Market-pair
Australia / Hong Kong
Australia / Japan
Australia / Singapore
Australia / UK
Australia / USA
Australia / MSCI
Hong Kong / Japan
Hong Kong / Singapore
Hong Kong / UK
Hong Kong / US
Hong Kong / MSCI
Japan / Singapore
Japan/ UK
Japan / USA
Japan / MSCI
Singapore / UK
Singapore / USA
Singapore /MSCI
UK / USA
UK / MSCI
US / MSCI
Causality-in-mean
PRE-CRISIS POST-CRISIS
Bilateral
Bilateral
Bilateral
Uni-directional
Uni-directional
Bilateral
Uni-directional
Bilateral
No
Uni-directional
Bilateral
Uni-directional
Bilateral
Uni-directional
No
Bilateral
Bilateral
Uni-directional
Uni-directional
Bilateral
Bilateral
Bilateral
Bilateral
Uni-directional
Bilateral
Bilateral
Uni-directional Uni-directional
Bilateral
Uni-directional
Bilateral
Bilateral
Uni-directional Uni-directional
Bilateral
Bilateral
No
Bilateral
Uni-directional
Bilateral
Uni-directional
No
Causality-in-variance
PRE-CRISIS POST-CRISIS
Bilateral
No
Bilateral
No
Uni-directional Uni-directional
Bilateral
Uni-directional
No
Bilateral
Uni-directional
No
Uni-directional
Bilateral
Uni-directional
Bilateral
Bilateral
Bilateral
Uni-directional
Bilateral
Uni-directional
Bilateral
Bilateral
Uni-directional
Bilateral
Uni-directional
Uni-directional Uni-directional
Uni-directional
Bilateral
Uni-directional Uni-directional
Bilateral
Bilateral
Bilateral
Bilateral
Uni-directional Uni-directional
Uni-directional Uni-directional
Uni-directional
Bilateral
Notes: Based on the results reported in Tables 7(a) – 8(b), the direction of causality (in mean and variance)
for all 21 market pairs is classified into three groups, and the results for both pre- and post-crisis periods are
compared. “Bilateral” causality means there are lead-lag interactions between the two markets (i.e. from
lagged A to B and from lagged B to A); “Uni-directional” causality means either A causes B or B causes
(and not both): “No” means that there is no lead-lag interaction between the two markets.
37
Table 10 (a)
Causality in mean patterns: pre- and post-crisis periods
Australia
Australia
HongKong
Japan
Singapore
UK
US
MSCI
PrePostPrePostPrePostPrePostPrePostPrePostPrePost-
0, -1
0,-1,-4
0, -2
0
NIL
0,-1,-7
0
0,-2,-4
0
0
0, -9
0
Hong Kong
0,-7,-9
0, -6
0, -1, -3
0
0
0,-1
0, -9
0
0,-2,-7,-10
0, -9
0, -3
0, -8
Japan
0, -1
0, -8
0, -9
0,-1,-2,-10
0,-2,-9
0
0,-5,-8
0, -8
0
-8
0,-6,-10
0,-2,-8,-10
Singapore
-9
0,-4,-6,-8,-9
0
0,-1,-8,-9
0,-3,-4
0, -7
0, -7
0, -2,-9
0, -2
0, -3
0,-2
0, -10
UK
0, -1
0, -1
0,-1,-9
0, -1
0,-1,-9
0, -3,-4
0,-1,-9
0,-5
US
0
0, -2
0
0, -7
0,-1,-5,-7
NIL
0
0
0
0, -1,-9
0
0,-4,-9
0, -1
0, -7
MSCI
0,-1,-4
0,-1,-2,-4
0, -9
0,-1,-6
0,-1,-4
0
0,-1,-2,-9
0, -1
0
0, -1
0, -1
0
0
0
Notes: This summary is constructed based on the results reported in Tables 7(a) and 8 (a). 0 indicates
contemporaneous correlation between two markets exist. NIL indicates no relationship at all between the
two markets. –k indicates the presence of correlation at lag k. For example: 0,-7, -9 in the first cell of the
Hong Kong column (pre-crisis) indicates there is contemporaneous relation between the means of the
Australia and Hong Kong real estate markets, and the mean returns of the Australia market at lags 7- and 9week have an impact on the current mean return of the Hong Kong market in the pre-crisis period.
Table 10 (b)
Causality in variance patterns: pre- and post-crisis periods
Australia
Australia
HongKong
Japan
Singapore
UK
US
MSCI
PrePostPrePostPrePostPrePostPrePostPrePostPrePost-
-5
0
-2, -8
NIL
NIL
0
-7,-10
0,-2,-9
NIL
0, -10
-8
0
Hong Kong
-4
0
-7, -10
0, -1
0,-2-3
0, -1
-2,-4,-6
0,-1,-2
-2,-3,-7
0,-1,-2
0,-2,-6,-7,-8
0,-1
Japan
-1
NIL
NIL
0, -1
-7
0,-1,-2,-5
-7,-8
-9
NIL
0,-5
0
-1,-2,-9
Singapore
-1
0, -7
0
0, -1
-3,-7,-8
0
-6
0,-1
0,-3,-7,-8
0,-1
0,-3,-7,-8
0,-1
UK
-6, -7
0
-8
0, -1
-2, -4
NIL
NIL
0
NIL
0,-1
0
0,-1
US
NIL
0, -10
NIL
0, -1
-3
0
0, -4
0,-1
-1
0
MSCI
NIL
0
0
0, -1
0,-4,-5
-1
0, -10
0,-1-2
0,-1,-6,-7,-8
0
0
-1,-2
0,-1,-4
-1
Notes: This summary is constructed based on the results reported in Tables 7(b) and 8 (b). 0 indicates
contemporaneous correlation between two markets exist. NIL indicates no relationship at all between the
two markets. –k indicates the presence of correlation at lag k. For example: -4 in the first cell of the Hong
Kong column (pre-crisis) indicates there is no contemporaneous relation between the variances of the
Australia and Hong Kong real estate markets, and the return variance of the Australia market at lag 4-week
has an impact on the current return variance of the Hong Kong market in the pre-crisis period.
38
Table 11
Vector Autoregressive Estimates: 5/1/90 – 10/2/06
MSCI
0.939019
[ 24.3382]*
MSCI(-2)
0.04487
[ 1.17108]
AU(-1)
-0.003224
[-0.13579]
AU(-2)
0.007828
[ 0.32912]
HK(-1)
0.0095
[ 1.68495]*
HK(-2)
-0.007759
[-1.38146]
JP(-1)
0.003919
[ 1.56843]
JP(-2)
-0.001063
[-0.42672]
SG(-1)
-0.002653
[-0.85458]
SG(-2)
0.000376
[ 0.12094]
UK(-1)
0.007956
[ 0.24004]
UK(-2)
-0.026472
[-0.79518]
US(-1)
0.177891
[ 5.85865]*
US(-2)
-0.171584
[-5.67478]*
C
7.53E-06
[ 1.54565]
R-squared
0.980109
Adj. R-squared
0.979769
Sum sq. resids
5.29E-07
S.E. equation
2.54E-05
F-statistic
2886.014
Log likelihood
7657.505
Akaike AIC
-18.3054
Schwarz SC
-18.22048
Mean dependent
0.000366
S.D. dependent
0.000179
Determinant resid covariance
Log likelihood
Akaike information criterion
Schwarz criterion
MSCI(-1)
Australia
-0.055085
[-0.94805]
0.048385
[ 0.83855]
0.936922
[ 26.2085]*
-0.011951
[-0.33364]
0.000839
[ 0.09887]
-0.003681
[-0.43524]
0.001174
[ 0.31190]
4.49E-05
[ 0.01197]
0.007018
[ 1.50122]
-0.003948
[-0.84392]
0.046319
[ 0.92797]
-0.046856
[-0.93458]
0.046898
[ 1.02560]
-0.054826
[-1.20404]
3.30E-05
[ 4.50107]*
0.885058
0.883096
1.20E-06
3.83E-05
451.0038
7315.629
-17.48654
-17.40161
0.000427
0.000112
1.74E-58
47232.23
-112.8796
-112.2851
HongKong
0.09257
[ 0.30126]
-0.074562
[-0.24434]
0.274388
[ 1.45134]
-0.214902
[-1.13445]
1.011039
[ 22.5158]*
-0.058074
[-1.29827]
0.020789
[ 1.04457]
-0.013724
[-0.69166]
-0.047565
[-1.92393]*
0.04454
[ 1.80050]*
0.201405
[ 0.76297]
-0.218147
[-0.82276]
0.789645
[ 3.26533]*
-0.827158
[-3.43490]*
5.89E-05
[ 1.52007]
0.918253
0.916857
3.36E-05
0.000202
657.9219
5924.907
-14.15547
-14.07054
0.001732
0.000702
Japan
0.197849
[ 0.36367]
-0.104445
[-0.19332]
-0.405881
[-1.21259]
0.481385
[ 1.43532]
0.013281
[ 0.16705]
-0.034573
[-0.43655]
1.010169
[ 28.6694]*
-0.10778
[-3.06801]*
0.068704
[ 1.56961]
-0.025759
[-0.58815]
-0.018208
[-0.03896]
0.108376
[ 0.23087]
0.944668
[ 2.20640]*
-0.963882
[-2.26079]*
7.20E-05
[ 1.04848]
0.900566
0.898868
0.000105
0.000358
530.4757
5447.915
-13.01297
-12.92805
0.002417
0.001126
Singapore
-0.212607
[-0.39159]
0.28807
[ 0.53428]
0.186872
[ 0.55942]
-0.075385
[-0.22523]
0.159888
[ 2.01524]*
-0.099342
[-1.25693]
0.001806
[ 0.05137]
0.008785
[ 0.25057]
0.92231
[ 21.1138]*
0.015524
[ 0.35518]
-0.17314
[-0.37121]
0.004109
[ 0.00877]
1.224346
[ 2.86543]*
-1.227306
[-2.88449]*
1.79E-05
[ 0.26154]
0.950072
0.94922
0.000105
0.000358
1114.555
5449.607
-13.01702
-12.9321
0.002011
0.001587
UK
0.060304
[ 1.44762]
-0.054691
[-1.32204]
0.029813
[ 1.16318]
-0.026943
[-1.04914]
-0.002303
[-0.37836]
-0.00121
[-0.19961]
0.000436
[ 0.16151]
0.001739
[ 0.64662]
0.00138
[ 0.41167]
-0.001322
[-0.39411]
0.966742
[ 27.0141]*
0.021917
[ 0.60976]
0.085444
[ 2.60628]*
-0.086559
[-2.65144]*
4.52E-06
[ 0.86016]
0.978781
0.978419
6.17E-07
2.74E-05
2701.748
7593.472
-18.15203
-18.06711
0.000597
0.000187
US
0.07479
[ 1.63997]
-0.067342
[-1.48696]
-0.023014
[-0.82020]
0.064341
[ 2.28853]*
0.003477
[ 0.52170]
-0.004651
[-0.70065]
7.38E-05
[ 0.02499]
0.001314
[ 0.44622]
0.001313
[ 0.35786]
-0.002892
[-0.78765]
0.091267
[ 2.32958]*
-0.102044
[-2.59321]*
1.101469
[ 30.6898]*
-0.150368
[-4.20734]*
3.39E-06
[ 0.58949]
0.948411
0.94753
7.39E-07
3.00E-05
1076.772
7517.88
-17.97097
-17.88605
0.000314
0.000131
Notes: The number of the lags in the VAR is 2. T-statistics are indicated in the brackets. The 10% critical
value for a two-tailed test is 1.645. Statistical significance is denoted by *
39
Table 12
Variance Decomposition of forecast error of conditional volatilities (full-sample period)
Market
MSCI
Australia
HongKong
Japan
Singapore
UK
USA
Horizon (wks)
1
4
8
12
16
20
24
1
4
8
12
16
20
24
1
4
8
12
16
20
24
1
4
8
12
16
20
24
1
4
8
12
16
20
24
1
4
8
12
16
20
24
1
4
8
12
16
20
24
MSCI
100.00
95.48
92.91
90.61
88.54
86.72
85.12
2.92
2.90
2.77
2.63
2.52
2.44
2.38
8.08
10.87
11.55
11.70
11.69
11.64
11.58
2.19
3.98
5.39
6.49
7.39
8.13
8.74
4.75
6.32
7.41
8.05
8.45
8.67
8.79
5.03
8.53
9.27
9.53
9.69
9.85
10.03
8.06
12.22
13.33
13.58
13.52
13.35
13.14
Australia
0.00
0.02
0.20
0.47
0.75
1.00
1.20
97.08
96.24
95.33
94.12
92.73
91.30
89.95
1.54
2.82
3.72
4.45
4.96
5.28
5.46
0.19
0.09
0.41
0.97
1.56
2.08
2.51
0.48
1.03
1.85
2.66
3.35
3.89
4.28
0.24
0.62
0.74
0.82
0.87
0.90
0.92
0.01
0.24
2.12
4.91
7.76
10.24
12.22
Hongkong
0.00
0.31
0.25
0.19
0.15
0.12
0.11
0.00
0.19
0.30
0.44
0.64
0.92
1.26
90.38
84.67
82.87
81.94
81.32
80.88
80.57
1.20
2.54
3.49
4.32
5.09
5.80
6.45
31.99
37.80
41.08
43.23
44.75
45.87
46.71
0.01
0.04
0.35
0.85
1.40
1.94
2.43
0.27
0.40
0.24
0.29
0.46
0.66
0.83
Japan
0.00
0.71
2.30
3.86
5.11
6.01
6.62
0.00
0.05
0.19
0.34
0.45
0.52
0.56
0.00
0.21
0.53
0.82
1.05
1.21
1.32
96.41
92.22
88.18
84.31
80.81
77.83
75.38
0.00
0.05
0.24
0.48
0.68
0.82
0.91
0.01
0.21
1.10
2.16
3.14
3.97
4.65
0.03
0.14
0.65
1.23
1.73
2.09
2.32
Singapore
0.00
0.18
0.62
1.03
1.34
1.57
1.74
0.00
0.44
1.27
2.33
3.46
4.53
5.45
0.00
0.29
0.29
0.26
0.23
0.22
0.23
0.00
0.56
1.77
3.17
4.46
5.50
6.29
62.77
53.95
48.40
44.43
41.39
39.00
37.11
0.01
0.01
0.02
0.05
0.10
0.19
0.29
0.00
0.01
0.07
0.12
0.13
0.12
0.11
UK
0.00
0.02
0.10
0.43
0.96
1.67
2.53
0.00
0.09
0.08
0.07
0.07
0.08
0.11
0.00
0.12
0.11
0.09
0.08
0.09
0.10
0.00
0.02
0.06
0.08
0.08
0.08
0.08
0.00
0.01
0.11
0.35
0.70
1.14
1.64
94.71
89.83
87.73
85.91
84.20
82.63
81.21
0.40
1.36
1.13
0.90
0.78
0.79
0.91
US
0.00
3.27
3.62
3.42
3.15
2.90
2.69
0.00
0.09
0.07
0.08
0.14
0.21
0.29
0.00
1.02
0.92
0.74
0.66
0.68
0.75
0.00
0.59
0.70
0.67
0.62
0.59
0.56
0.00
0.84
0.90
0.79
0.68
0.60
0.56
0.00
0.76
0.79
0.70
0.60
0.53
0.47
91.23
85.62
82.46
78.97
75.63
72.76
70.46
Notes: The entries indicate the percentage of conditional volatility of returns of a particular market
displayed at the first column explained by conditional volatilities of returns of all markets.
40
Table 13
Generalized Impulse Response of all markets to
a one standard deviation shock in each of the markets
Market
MSCI
Horizon (wks)
1
4
8
12
16
20
24
Australia
1
4
8
12
16
20
24
HongKong
1
4
8
12
16
20
24
Japan
1
4
8
12
16
20
24
Singapore
1
4
8
12
16
20
24
UK
1
4
8
12
16
20
24
US
1
4
8
12
16
20
24
MSCI
0.410
0.218
0.162
0.124
0.098
0.079
0.064
0.050
0.031
0.021
0.013
0.009
0.006
0.004
0.083
0.068
0.054
0.039
0.029
0.022
0.016
0.044
0.044
0.043
0.037
0.032
0.028
0.025
0.065
0.055
0.047
0.039
0.031
0.024
0.020
0.065
0.062
0.052
0.043
0.034
0.030
0.027
0.085
0.072
0.061
0.043
0.031
0.024
0.017
Australia
0.050
0.034
0.028
0.025
0.022
0.020
0.018
0.407
0.183
0.095
0.063
0.045
0.036
0.027
0.049
0.042
0.030
0.024
0.020
0.017
0.014
0.020
0.013
0.018
0.019
0.019
0.019
0.019
0.031
0.030
0.026
0.024
0.021
0.019
0.017
0.025
0.025
0.018
0.014
0.012
0.011
0.010
0.017
0.026
0.037
0.037
0.037
0.035
0.033
HongKong
0.084
0.060
0.040
0.027
0.021
0.017
0.015
0.050
0.039
0.024
0.019
0.016
0.016
0.016
0.404
0.192
0.115
0.076
0.058
0.045
0.038
0.045
0.044
0.035
0.029
0.027
0.026
0.026
0.197
0.131
0.093
0.068
0.055
0.048
0.042
0.018
0.012
0.000
-0.004
-0.006
-0.007
-0.007
0.039
0.030
0.014
0.006
0.002
0.000
0.000
Japan
0.043
0.046
0.044
0.039
0.035
0.032
0.029
0.020
0.017
0.015
0.012
0.011
0.010
0.009
0.044
0.039
0.028
0.022
0.020
0.018
0.016
0.407
0.167
0.084
0.056
0.042
0.035
0.029
0.031
0.026
0.023
0.020
0.019
0.017
0.016
0.012
0.021
0.024
0.024
0.023
0.022
0.022
0.020
0.021
0.021
0.020
0.018
0.017
0.015
Singapore
0.064
0.038
0.018
0.011
0.007
0.005
0.004
0.031
0.038
0.037
0.033
0.030
0.028
0.027
0.195
0.104
0.071
0.051
0.038
0.031
0.027
0.031
0.048
0.049
0.044
0.040
0.036
0.034
0.411
0.204
0.132
0.091
0.068
0.054
0.044
0.012
0.011
0.005
0.002
0.002
0.002
0.002
0.029
0.019
0.007
0.002
0.001
0.001
0.002
UK
0.066
0.043
0.027
0.012
0.003
0.004
0.008
0.026
0.022
0.014
0.007
0.002
0.001
0.002
0.018
0.024
0.017
0.010
0.005
0.003
0.001
0.013
0.016
0.017
0.014
0.010
0.007
0.004
0.012
0.008
0.000
-0.006
-0.009
-0.012
-0.013
0.409
0.225
0.171
0.134
0.110
0.088
0.074
0.038
0.040
0.027
0.014
0.005
-0.001
-0.005
USA
0.084
0.087
0.058
0.040
0.030
0.024
0.020
0.017
0.016
0.005
0.000
-0.002
-0.003
-0.004
0.038
0.045
0.025
0.012
0.005
0.002
-0.001
0.020
0.032
0.021
0.014
0.011
0.008
0.007
0.029
0.039
0.025
0.016
0.011
0.007
0.004
0.036
0.043
0.030
0.020
0.015
0.013
0.011
0.411
0.190
0.116
0.073
0.052
0.039
0.031
Notes: The entries contain the normalized impulse response coefficients. The response patterns are simulated by
introducing one s.d. shocks in the system and tracing out the normalized responses of the markets in the system over
different time horizons.
41
Table 14
Variance Decomposition of forecast error of conditional volatilities (pre- and post-crisis periods)
Pre-crisis period: 5/1/90 - 27/6/97
Post-crisis period: 1/1/99 - 10/2/06
Lag(wks)
MSCI
Australia HongKong Japan Singapore
UK
USA
MSCI
Australia HongKong Japan Singapore
(a) Percentage of conditional volatility of MSCI World market returns explained by conditional volatilities of real estate market returns of
1
100.00
0.00
0.00
0.00
0.00
0.00
0.00
100.00
0.00
0.00
0.00
0.00
4
95.21
0.21
0.00
0.16
0.06
0.20
4.16
94.77
0.44
0.66
0.87
0.44
8
94.62
0.21
0.00
0.68
0.37
0.27
3.85
93.05
0.50
0.41
2.92
0.32
12
93.92
0.26
0.00
1.22
0.75
0.38
3.46
90.99
0.41
0.43
5.30
0.24
16
93.26
0.30
0.00
1.62
1.09
0.55
3.16
88.66
0.33
0.67
7.60
0.26
20
92.64
0.33
0.00
1.91
1.37
0.80
2.94
86.38
0.28
0.98
9.65
0.37
24
92.05
0.36
0.00
2.13
1.57
1.11
2.77
84.29
0.24
1.31
11.39
0.54
(b) Percentage of conditional volatility of Australian real estate market returns explained by conditional volatilities of market returns of
1
0.17
99.83
0.00
0.00
0.00
0.00
0.00
3.29
96.71
0.00
0.00
0.00
4
0.31
96.08
0.05
0.59
1.57
0.69
0.71
3.35
95.86
0.07
0.32
0.19
8
0.30
95.07
0.07
0.58
2.20
1.11
0.69
3.66
94.91
0.21
0.76
0.19
12
0.30
94.60
0.07
0.58
2.38
1.38
0.68
3.80
94.50
0.24
0.98
0.19
16
0.30
94.36
0.08
0.58
2.43
1.57
0.68
3.88
94.30
0.24
1.10
0.19
20
0.31
94.18
0.08
0.58
2.44
1.72
0.69
3.92
94.18
0.24
1.16
0.19
24
0.33
94.02
0.09
0.58
2.45
1.85
0.70
3.95
94.11
0.24
1.20
0.19
(c) Percentage of conditional volatility of Hong Kong real estate market returns explained by conditional volatilities of market returns of
1
3.77
0.00
96.23
0.00
0.00
0.00
0.00
13.43
1.96
84.61
0.00
0.00
4
4.86
0.11
94.44
0.20
0.21
0.07
0.11
15.58
5.10
74.66
3.22
0.01
8
4.85
0.14
94.15
0.27
0.29
0.11
0.18
15.63
5.82
71.60
5.21
0.02
12
4.65
0.18
93.84
0.29
0.64
0.20
0.21
15.74
5.71
69.60
7.03
0.04
16
4.42
0.22
93.49
0.27
1.02
0.36
0.22
15.94
5.57
67.76
8.71
0.06
20
4.21
0.27
93.10
0.26
1.36
0.60
0.22
16.17
5.43
66.08
10.23
0.08
24
4.03
0.31
92.65
0.24
1.63
0.93
0.22
16.42
5.30
64.58
11.57
0.10
(d) Percentage of conditional volatility of Japaneses real estate market returns explained by conditional volatilities of market returns of
1
18.67
0.08
0.00
81.25
0.00
0.00
0.00
0.04
0.71
8.35
90.90
0.00
2
17.33
0.20
0.08
81.17
0.11
0.01
1.11
0.63
0.66
10.68
87.86
0.03
8
24.13
0.98
0.10
73.35
0.36
0.16
0.91
1.84
0.90
13.14
82.93
0.05
12
27.22
1.19
0.16
69.83
0.51
0.23
0.87
2.55
0.86
13.48
81.68
0.05
16
29.29
1.22
0.24
67.48
0.64
0.27
0.85
3.36
0.85
13.59
80.67
0.06
20
30.77
1.21
0.32
65.81
0.76
0.28
0.84
4.21
0.85
13.54
79.83
0.06
24
31.88
1.20
0.40
64.56
0.85
0.29
0.83
5.06
0.84
13.37
79.12
0.07
UK
USA
0.00
0.74
0.50
0.40
0.35
0.31
0.29
0.00
2.07
2.30
2.24
2.13
2.02
1.92
0.00
0.06
0.10
0.11
0.12
0.12
0.12
0.00
0.16
0.17
0.18
0.18
0.18
0.18
0.00
0.13
0.31
0.44
0.52
0.58
0.61
0.00
1.29
1.41
1.43
1.44
1.43
1.43
0.00
0.10
1.05
1.25
1.31
1.32
1.31
0.00
0.05
0.10
0.13
0.17
0.20
0.22
42
Table 14 (Continued)
Pre-crisis period: 5/1/90 - 27/6/97
Post-crisis period: 1/1/99 - 10/2/06
Lag(wks)
MSCI
Australia HongKong Japan Singapore
UK
USA
MSCI
Australia HongKong Japan Singapore
(e) Percentage of conditional volatility of Singapore real estate market returns explained by conditional volatilities of market returns of
1
6.72
0.02
7.56
0.07
85.63
0.00
0.00
7.99
1.12
12.95
0.69
77.25
4
9.51
0.14
13.40
1.29
74.79
0.07
0.79
8.53
1.04
19.14
6.04
63.81
8
14.63
0.38
18.13
2.19
61.97
0.62
2.08
8.22
0.92
19.36
11.13
57.74
12
18.42
0.47
21.34
2.82
52.40
1.57
2.98
8.38
0.79
19.02
15.75
52.96
16
20.86
0.48
23.53
3.23
45.91
2.59
3.41
8.79
0.73
18.56
19.88
48.74
20
22.31
0.47
25.08
3.48
41.58
3.55
3.53
9.33
0.69
18.06
23.46
45.08
24
23.09
0.46
26.24
3.62
38.66
4.42
3.51
9.95
0.66
17.54
26.51
41.94
(f) Percentage of conditional volatility of UK real estate market returns explained by conditional volatilities of market returns of
1
3.83
0.17
0.15
0.90
0.10
94.85
0.00
10.66
2.97
0.47
0.14
0.19
4
6.62
1.26
0.38
0.52
0.07
90.66
0.48
13.26
9.58
0.92
0.24
1.12
8
9.09
1.36
0.62
0.30
0.04
87.55
1.04
13.17
9.79
1.48
0.54
1.14
12
11.38
1.24
0.88
0.27
0.04
84.64
1.55
13.20
9.76
1.88
0.70
1.13
16
13.62
1.10
1.15
0.25
0.07
81.82
1.99
13.20
9.75
2.05
0.79
1.13
20
15.82
0.98
1.41
0.22
0.11
79.09
2.36
13.20
9.75
2.13
0.83
1.12
24
17.99
0.88
1.66
0.19
0.17
76.44
2.67
13.20
9.74
2.16
0.85
1.12
(g) Percentage of conditional volatility of US real estate market returns explained by conditional volatilities of market returns of
1
7.35
0.14
0.05
1.05
0.04
0.34
91.04
11.50
0.25
1.46
0.00
0.24
4
15.30
0.12
0.34
4.20
0.06
0.24
79.75
11.01
0.49
2.27
0.31
0.74
8
21.14
0.15
0.69
5.50
0.08
0.26
72.18
11.06
0.50
2.33
0.37
0.82
12
26.03
0.18
1.09
6.16
0.11
0.30
66.13
11.08
0.50
2.35
0.39
0.88
16
30.14
0.20
1.47
6.50
0.16
0.35
61.18
11.09
0.50
2.35
0.39
0.91
20
33.52
0.21
1.81
6.66
0.20
0.42
57.18
11.10
0.50
2.36
0.39
0.93
24
36.24
0.21
2.11
6.72
0.24
0.50
53.98
11.11
0.50
2.36
0.39
0.94
UK
USA
0.00
0.53
1.67
2.14
2.35
2.43
2.45
0.00
0.90
0.96
0.96
0.95
0.95
0.94
85.56
74.47
73.45
72.89
72.64
72.53
72.48
0.00
0.42
0.43
0.44
0.44
0.44
0.44
4.08
4.74
4.74
4.74
4.73
4.73
4.73
82.48
80.45
80.17
80.07
80.02
79.99
79.96
Notes: The number of the lags in the VAR is 2
43
AUSTRALIA
HONG KONG
JAPAN
SINGAPORE
UK
2005-12-29
2005-6-29
2004-12-29
2004-6-29
2003-12-29
2003-6-29
2002-12-29
2002-6-29
2001-12-29
2001-6-29
2000-12-29
2000-6-29
1999-12-29
1999-6-29
1998-12-29
1998-6-29
1997-12-29
1997-6-29
1996-12-29
1996-6-29
1995-12-29
1995-6-29
1994-12-29
1994-6-29
1993-12-29
1993-6-29
1992-12-29
1992-6-29
1991-12-29
1991-6-29
1990-12-29
1990-6-29
1989-12-29
INDEX LEVEL
Figure 1
EPRA FTSE/NAREIT INDEXES
3500
3000
2500
2000
1500
1000
500
0
WEEK
USA
44
Figure 2: Comparison of t-statistics for contemporaneous conditional
correlation in mean: pre-and post-crisis periods
14.000
12.000
10.000
t-statistic
8.000
6.000
4.000
2.000
0.000
AU/HK
AU/JP AU/SG AU/UK AU/US AU/WD HK/JP
HK/SG HK/UK HK/US HK/WD JP/SG
JP/UK
JP/US
JP/WD SG/UK SG/US SG/WD UK/US UK/WD US/WD
Market pair
Pre-crisis
Post-crisis
Figure 3: Comparison of t-statistics for contemporanoues conditional
correlation in variance: pre- and post-crisis periods
12.000
10.000
8.000
t-statistic
6.000
4.000
2.000
0.000
-2.000
AU/HK
AU/JP
AU/SG AU/UK AU/US AU/WD HK/JP
HK/SG HK/UK HK/US HK/WD JP/SG
JP/UK
JP/US
JP/WD SG/UK SG/US SG/WD UK/US UK/WD US/WD
Market pair
Pre-crisis
Post-crisis
45
Figure 4
Conditional Volatility Graphs from the MEGARCH (1, 1) estimation
A us tralia real es tate market
Ho ng K o ng re al es tate market
.0010
Ja pa n rea l es tate market
.006
.009
.008
.0009
.005
.007
.0008
.004
.0007
.006
.005
.0006
.003
.004
.0005
.002
.003
.0004
.002
.001
.0003
.001
.0002
.000
100
200
300
400
500
600
700
800
.000
100
S ing ap ore rea l es ta te ma rke t
200
300
400
500
600
700
800
100
UK re al es ta te market
.0014
.0012
.010
.0012
.0010
.008
.0010
.0008
.006
.0008
.0006
.004
.0006
.0004
.002
.0004
.0002
.0002
100
200
300
400
500
600
700
800
300
400
500
600
700
800
700
800
US re al e s tate ma rke t
.012
.000
200
.0000
100
200
300
400
500
600
700
800
100
200
300
400
500
600
MS CI glo ba l s to c k market
.0010
.0009
.0008
.0007
.0006
.0005
.0004
.0003
.0002
.0001
100
200
300
400
500
600
700
800
46
Endnotes
1
Whilst the examination of causation in mean using Granger causality test has commonly appeared in
studies relating to financial market movements; the issue of variance causality has received less attention in
international finance.
2
In this study, the pre- and post-Asian financial crisis periods are arbitrary defined as 5/1/90-27/6/97 and
4/9/98- 10/2/06 respectively. In the second sub-period (i.e. post-crisis), in addition to the Asian financial
crisis, two other common shocks are the August 1998 Russian crisis and the January 1999 Brazilian
exchange rate crisis. Since our sample mainly comprises Asia real estate markets, we thus focus our
attention on the impact of Asian financial crisis on the cross-market linkages. Kallberg et al. (2002) note
that the 1997-98 Asian financial crisis has led to a reduction in real estate returns and an increase in real
estate market volatility and correlations following the crisis.
3
Many stock studies were conducted to investigate the benefits of international diversification and to
understand the transmission mechanisms across national /regional boundaries. Examples of the some most
recent studies include Engle and Susmei (1993), Hamos et al. (1993), Karolyi (1995) and Koutmos (1996),
among others.
4
Weekly data are employed in this study as the monthly sampling interval is considered too long a
measurement interval to capture the dynamics of volatility and the asymmetry of returns. Furthermore,
weekly returns represent a compromise between the many daily observations within a given calendar time
interval and the less severe measurement errors in monthly returns. For example, problems arising from
non-synchronized trading, rounding errors and bid-ask spreads should not as important in weekly return
data as in daily data.
5
The VAR methodology was developed by Sims (1980) with the purpose of estimating unrestricted
reduced-form equations that have uniform sets of lagged dependent variables as regressors. The VAR
model thus estimates a dynamic simultaneous equation system, free of a priori restrictions on the structure
of relationships.
6
Specifically, to obtain the decomposition, the innovations in the VAR system are usually orthogonolized
by Cholesky decomposition according to a causal ordering of the variables. However, Pesaran and Shin
(1998) propose an orthogonal set of innovations that does not depend on the VAR ordering for obtaining
the generalized impulse response function.
7
According to a Strait Times report (18/3/06), the UK is now the biggest investor in Singapore to the tune
of S$45.7 billion as at end of 2004. Further, the UK is Singapore second largest European trading partner
and a popular investment destination for Singapore companies.
8
The coefficient for the t-shape distribution is 9.839 (standard error is 0.965), which is statistically
significant at the one percent level. We estimate the model with BFGS and robust standard error
calculations written in RATs program. The estimates converge in 147 iterations.
9
The appropriate lag length (p) chosen for each market is based on the highest negative Akaike information
criterion (AIC). The resulting p values are 1 for MSCI, Australia, Japan, UK and US; 2 for Hong Kong and
4 for Singapore.
10
The coefficients for the t-shape distribution are, respectively 11.068 (t = 8.36) and 12.962 (t=6.92), for
the pre- and post-crisis models, which are statistically significant at the one percent level. Using RATs
estimation, the two models achieved convergence in 206 iterations (pre-crisis) and 134 iterations (postcrisis). Finally, the test statistics (ARCH and LB tests) indicate that the two models are adequately
specified.
47
11
A statistical significant level of 10% is adopted in this study.
12
The log-likelihood values are, respectively, 47228.83, 47232.23, 47212.64 and 47185.28 at lag orders 1,
2, 3 and 4. The AIC values are -112.853 (lag 1), -112.880 (lag 2), -112.851 (lag 3) and -112.804 (lag 4).
48