An examination of common volatility in Asian
securitized real estate markets
Abstract
This study considers whether a group of eight Asian, UK and the US securitized real estate markets shows
similar time-varying volatility effects over the past 15 years, 1995-2009. We also examine, for comparison,
the presence of a common time-varying variance among four corresponding regional real estate securities
markets. Using a modified Johansen co-integration procedure with GARCH effects, the empirical results
indicate the presence of at least one common variance component, and thus partial volatility convergence,
among real estate securities markets in the Asian and international groups. Furthermore, some real estate
securities markets during the global financial crisis period are co-integrated in both their first and second
moments and demonstrate partial return and volatility convergence. Our analysis that focus in capturing the
common roots in the second moment whilst accounting for time-varying variance has important
implications for international real estate portfolio investment.
Keywords
Asian real estate securities markets; common volatility; GARCH-cointegration; portfolio diversification;
global financial crisis
1.
Background and Objectives of Research
Prior literature has focused on different aspects of international stock market interdependence and
integration from short run and long-term perspectives. While the short-run investigations focus on returns
and volatility spillovers as well as time-varying correlation dynamics across different markets (e.g. Hamos
et al. 1990; Yang, 2005), another strand of the literature considers long-run relationships and common
stochastic trends among different stock markets over time. In this regard, co-integration methodology has
been frequently applied to different international stock market datasets to detect the existence and dynamics
of long-run relationships and strength of the relationships among the stock markets (e.g. Chan et al 1992)
Moreover, Kasa (1992) and Manning (2002) investigate the presence of any common forces driving the
long-run return movement of the stock market indexes. This approach is superior because a combination of
common trends analysis and co-integration analysis provides investors with a more complete picture
regarding the degree of portfolio diversification benefits across the markets concerned.
Our paper extends this “common trend” interest to determine whether international securitized real
estate markets exhibit a similar common time-varying volatility over the period 1995-2009. Engle and
Susmel (1993) explicitly examine whether there is a common component driving the volatility among
international stock markets using the bivariate common feature test of Engle and Kozicki (1993). By the
1
same token, it is possible that a group of securitized real estate markets being investigated share a common
volatility component; and accordingly these markets are closely linked in the second moment (i.e. volatility
linkages) if this commonality exists. Given the unique features and comparable size of the global real estate
securities markets (relative to the global stock markets), they provide a unique and interesting research
setting. Securitized real estate is a hybrid of stock, bond and real estate. Moreover, due to its strong growth
and remarkable risk-adjusted performance over time, the securitized real estate sector has now been
recognized as an “essential:” asset class in mixed-asset portfolios (Dhar and Goetzmann, 2006), with
industry sources predicting the global real estate securities market capitalization to increase significantly
from $500 billion in 2004 to 1 trillion by 2010 (Newell et. 2005). However, in comparison to the
considerable amount of literature that has examined stock market and bond market integrations, far less is
known about the presence of common volatility and its implication for integration among international real
estate securities markets despite their remarkable growth over the past decade as well as the potential
importance of common time-varying volatility in international real estate diversification. This is where our
study intends to contribute.
This paper includes four areas of investigation. With a sample that covers the US, UK and eight
Asian real estate securities markets, including Australia, Japan, Hong Kong, Singapore, China, Taiwan,
Malaysia and the Philippines over a period of 15 years beginning January 1995 and ending December 2009,
first we search for long-term relationships in different groups that comprise these 10 national and 4 regional
real estate securities indices. Second, we test whether the real estate securities markets exhibit time-varying
volatility characteristics. Third, we address the issue of common time-varying volatility across the sample
national and regional real estate securities indexes using the modified multivariate cointegration test with
generalized autoregressive conditional heteroskedascity (GARCH) effects (henceforth termed as “GARCHcointegration”) developed by Gannon (1996). With the investigations conducted on both bivariate and
multivariate basis, we hope to detect the presence of a common time-varying volatility factor among the
real estate securities markets in different groupings. Finally, we repeat the common volatility analysis for
the last five years from January 2005 to Dec 2009. This period includes the peak of the global financial
2
crisis. 1 Following literature, if real estate securities markets have become more closely related in their
second moments in this “crisis” period, then it is possible that this period may be associated with more
common volatility components or a stronger common volatility factor compared with the full-period model.
It is noted even though the GARCH-cointegration test methodology, an extension of the bivariate
Engle and Kozicki (1993)’s “common-feature” methodology, has been employed in some stock, bond and
foreign exchange markets’ studies (e.g. Gannon, 1996; Alexakis and Apergis, 1996; Pan et al. 1999; Fan,
2003;Thuraisamy and Gannon, 2008) to our knowledge, this is the first study in the securitized real estate
arena that utilizes this multivariate “common feature” methodology to search for common volatility
components in international, and in particular, Asian real estate securities markets. Importantly, the level of
securitized property in Asia is about 12% which is significantly above that of the mature markets (e.g. US:
6 percent; UK: 5 percent) and the global levels (6 percent) (EPRA, 2008). With the growing economic
importance of the Asian countries, particularly China in recent years, we would expect this market
integration issue in Asia to become increasingly significantly enough in affecting the level of informational
efficiency due to the influence of globalization and real estate asset securitization.
Our analysis that involves capturing the common roots in the second moment whilst accounting
for time-varying common volatility has important implications for portfolio managers and policy makers.
Even though international real estate securities market indices are not co-integrated in the long-run, it is
still possible that the markets are linked together in the long run through their second moment (i.e.
volatility). Furthermore, if the markets are converging towards few common stochastic volatility
components over time, it would imply that the benefits arising from investing in international real estate
securities portfolio could be (significant) reduced due to the presence of one or more “common volatility”
in the cross-market relationships. This knowledge is likely beneficial to portfolio managers who should be
more cautious in understanding the cross-market return and volatility linkages in short-run as well as in the
long term. For policy makers, this additional knowledge on “common volatility” will be useful in their
policy formulation on cross-border real estate investment especially in periods of market turmoil such as
the currently ongoing global financial crisis.
1
The global financial crisis started in the US in the summer of 2007 with the bursting of sub-prime
mortgage market and rapidly propagated across different asset classes and financial markets. Consequently,
dramatic changes have taken place in the financial landscape and the global financial markets have been
seriously affected.
3
The outline of the paper is as follows. The next two sections review the existing literature and
describe the real estate securities market sample and data used in the analysis. The following section
explains the “common features” and “GARCH-cointegration” methodologies and outlines the empirical
procedures. Thereafter, we present the empirical results, while the last section presents some concluding
remarks.
2.
Related Literature
In line with the stock market literature, short-term studies on international real estate market
linkages focus on return correlations and volatility spillovers. Cotter and Stevenson (2006) use a
multivariate GARCH model to examine tine-varying conditional volatilities and correlations in the daily
USA REIT and equity prices. Michayluk et al (2006) investigate daily volatility spillover effects and timevarying correlation dynamics between the USA and UK securitized real estate markets. Liow et al (2009)
examine the time-varying correlation and volatility links of several national /regional securitized real estate
and stock markets. They find that real estate markets’ conditional volatilities and stock markets’ volatilities
are synchronous over time. Moreover, the international correlation structure of real estate securities and the
broader stock market are linked to each either. In another study, Liow et al (forthcoming) investigate the
dynamics and transmission of conditional return volatilities with multiple structural breaks using a
multivariate regime-dependent asymmetric dynamic covariance model. However, none of the above studies
has examined the issue of common time-varying volatility in the REIT/securitized real estate markets.
Another group of real estate researchers use multivariate co-integration technique to investigate
the nature and extent of long-term equilibrium relationships among international real estate securities
markets (e.g. Wilson and Okunev, 1996; Eichholtz et al, 1998; Garvey et al. 2001; Kleiman et al. 2002;
Liow et al. 2005; Yang et al. 2005; Yunus and Swanson, 2007 and Yunus, 2009). Nevertheless, these
studies focus only on the return co-integration among the markets. In so far as this study is concerned, we
locate four real estate studies that bear similar “common-feature” theme to our work. Bond and Hwang
(2003) identify the common (or permanent) component of volatility shared by both the UK securitized and
direct commercial property markets. Liow and Webb (2009) examine the existence of common return
factors in the securitized real estate markets of Hong Kong, Singapore, UK, and US over 1993-2003. Using
4
factor analysis and canonical correlation technique on the monthly data, they detect a common risk factor
which is moderately correlated with the global real estate market. Yunus (2009) investigates the dynamic
interdependence among the securitized real estate markets of Australia, France, Hong Kong, Japan,
Netherlands, UK, and US for the period 1990-2007. Using co-integration tests and common trends analysis,
she finds that international securitized real estate markets are becoming increasing integrated over time. In
addition, the US and Japanese markets are the sources of the common stochastic trends that drive the cointegrated markets toward the long-run equilibrium relationships. Finally, covering 12 real estate securities
markets over 1994-2006, Liow and Ibrahim (2010) in their recent study examine the correlation structure of
securitized real estate markets’ “permanent” and “transitory” volatility series using factor analysis. In
particular, the summary of the “permanent” volatility dynamics using factor analysis will indicate whether
the correlation in volatilities is caused by at least a “common factor “that spans across all real estate
“permanent” volatility series. They find that even though with the same numbers of “common factor”
derived from the “permanent” and “transitory” volatility series, their loadings are not similar and
consequently the long-run and short-term volatility linkages for some real estate securities markets are
different.
3.
Sample and data characteristics
Our sample consists of weekly securitized property market indexes for the US, the UK, Australia,
Japan, Hong Kong, Singapore, China, Taiwan, Malaysia and Philippines and four regional market indexes
for North America (NAM), Europe (EU), Asia-Pacific developed (ADEVEP) and Asia-emerging
(AEMERG). Each of the ten real estate securities markets is in different stages of development and has
different market capitalizations, institutional and regulatory frameworks, market transparencies, trading
systems and transaction costs. The data are from S&P Global Property database.2 The sample data consist
of 782 weekly total return indexes covering the period from 6 January 1995 to 26 December 2009, the
2
This S&P global property database, the latest international public real estate database in the market, is
designed to reflect components of the broad universe of investable international real estate stocks reflecting
their risk and return characteristics. In total, the database has indices (both capitalization weighted and float
adjusted) comprised of over 500 companies from more than 35 developed and emerging markets with a
minimum market value of $100 million (Serrano and Hoesli, 2009).
5
longest data period for which all 14 real estate indices are available in an international study.3 Weekly stock
returns are computed as natural logarithmic of the total return indexes relative, I t in successive weeks; i.e.
Ln( I t I t 1 ) . Using of weekly data hopes to avoid the problem of non-synchronous trading and short-term
correlations due to noise.
Some summary statistics for the 14 real estate securities market index returns are given in Table 1.
Over the full study period, the best weekly return performer is China (0.21%), and is followed by the US
(0.18%) and Hong Kong (0.15%). In contrast, the Taiwan real estate securities market has the worst return
performance and third highest volatility as revealed by its standard deviation of returns. Except for
Malaysia, the other three Asia-emerging markets are the most volatile with China tops the list (weekly
standard deviation is 5.84%); in comparison, Australia, the US and UK are the least volatile. On the
regional front, the NAM and EU markets have the best return and risk performances. Finally, the results
indicate that the distribution of return for all 14 real estate stock indexes is non-normal, characterized by
higher peakedness and fat tails relative to a normal distribution. Figure 1 plots the index movements of this
14 markets over the full study period.
(Table 1 and Figure 1 here)
4.
Methodology
The presence of GARCH effects (i.e. fat tailed and possible time-varying volatility) (Table 1)
could affect the standard co-integration tests in searching for common long-run stochastic trends.
Following Engle and Kozicki (1993)’s “common ARCH-feature” framework, the ARCH feature is said to
be common if a linear combination of two or more series do not display ARCH effects even though ARCH
is present in each of the individual series. If two series share a common volatility process, it is also an
indicator of integration between the two markets which are responding to similar factors that cause
volatility in their real estate securities markets. As an extension of the common ARCH-feature test which is
only applicable to bivariate market-pairs, we employ the GARCH-cointegration test developed by Gannon
(1996) to investigate whether our international securitized real estate data series (multivariate) share at least
3
Thailand and Indonesia are excluded from the study due to large number of missing time series data.
6
a common time-varying volatility. This methodology was utilized by Pan et al. (1999) and Fan (2003) in
their studies on Asia-Pacific stock markets. Additionally we conduct bivariate common volatility
investigations for all market-pairs in order to unravel any significant bivariate linkages that contribute to
the multivariate cross-market volatility relationships under examination. Following Gannon (1996), the
GARCH-cointegration test procedure is briefly explained below:
Starting from the multivariate test methodology for co-integration developed by Johansen (1988)
and Johansen and Juselius (1990), we have:
(1) Yt   

k 1
j 1
 j Yt  j  Yt k   t
Where Yt is an n-dimensional vector of real estate securities price indices;  and  are
coefficient matrices; if  has zero rank, no stationary linear combination can be identified. If the rank r of
 is greater than zero, there will exist r possible stationary linear combinations and  can be
decomposed into matrices
 and  , such that     . 
integrating vectors that cause equilibrium and
contains the coefficients of the r distinct co-
 contains the coefficients for the speed of adjustment for
the equation.
Equation (1) is reformulated as:
(2a) R0t   R1t   t (t=1,2…T); and
(2b) Yt 

(2c) Yt  k 

k 1
j 1
k 1
a 0 j Yt  j  R0t
a Yt  j  R1t
j 1 1 j
Then, a three-step modified co-integration test for common time-varying volatility is implemented
as outlined below:
Step 1: Generate R0t and R1t based on equations (2b) and (2c)
Step 2: Estimate the canonical correlations and derive the canonical weights
g1 j to g pj and
h1 j to h pj through equation (2a). Then, generate two new canonical variates, named U and V as
follows:
7
(3a) U j  g 1 j R0 jt   ........  g pj R0 pt
(3b) V j
 h1 j R1 jt  ......  h pj R1 pt
By construction, the variates U j and V j are created as linear combinations of original error terms
and hence have zero mean
Step 3: Estimate GARCH models for U and V for those significant canonical pairs from step 2:
(4a) U jt
 V jt   t
(4b) h jt   j   j  t 1   j ht 1
2
In the above, equation (4a) is equivalent to the standard ADF test for testing a unit root in
residuals from the co-integrating equation, with GARCH effects accounted for in calculating Uj. We
compare the t-value for the  coefficient in equation (4a) with the critical values derived from McKinnon
(1991). In our present context, if the computed t-statistic is less than the relevant critical values at the
conventional probability levels (1%, 5% and 10%), then the null hypothesis of no common volatility
component in securitized real estate markets cannot be rejected.
Empirically, we first test whether all individual series is stationary or not. In this paper, the
augmented Dickey-Fuller (ADF) and Kwiatkowski-Philips-Schmidt-Shin (KPSS) tests will be utilized.
Then we test for univariate ARCH effects in each market’s return. Using squared returns as a prosy for
realized volatility, we perform Engle’s (1982)’s Lagrange Multiplier (LM) test by regressing each squared
return on a constant and four lags of its own squared return as well as on a constant and eight lags of its
squared residual returns. These are the univariate ARCH (4) and ARCH (8) tests. In addition, the ARCH
test is conducted with multivariate information set that includes, respectively, one lagged (MARCH (1)),
four lagged (MARCH (4)) and eight lagged (MARCH (8)) squared returns of other markets. The null
hypothesis to be tested is that the series exhibits no ARCH effects. The test statistic, which has a chisquared distribution, is obtained by multiplying the regression R2 times the sample size (Engle, 1982).
Third, we conduct the GARCH-cointegration test for eight multivariate models (Model A: All-Asian;
Model B: All-Asian +US+UK; Model C: Asia-Pacific developed; Model D: Asia-Pacific developed +
8
US+UK; Model E: Asia-emerging; Model F: Asia-emerging + US+UK and Model G: Regional)4 as well
for all bivariate pairs. This will allow us closely examine which markets contribute to the co-integration
space in the context of common volatility. In addition, the possible influences of the US and UK markets
are investigated by including them in the co-integrating space.
5.
Results
The results of the unit root tests are presented in Table 2. Based on the ADF and KPSS tests, the
reported results indicate the rejection of non-stationarity in first (natural logarithmic) differences. Therefore,
all 14 real estate securities series, are integrated once, I (1)
(Table 2 here)
5.1
Johansen multivariate co-integration test results on long-run relationship
We first employ Johansen’s multivariate likelihood ratio co-integration analysis to investigate
whether the real estate securities markets are in long-run equilibrium. Table 3 presents the Johansen’s trace
and maximum eigen values together with the 5% critical values. As can be observed, since all test statistics
are below the 5% critical values, the three groups of real estate securities index series (Asian sample,
international sample and regional sample) are not co-integrated; implying there is absence of long-term comovement of the real estate securities markets under examination.
(Table 3 here)
5.2
ARCH tests and unconditional volatility correlation
Table 4 presents the ARCH test results for univariate [ARCH (4) and ARCH (8)] and multivariate
[MARCH (1), MARCH (4) and MARCH (8)] information set. As can be observed, the LM statistic
indicates that an ARCH (4) and ARCH (8) effect each is present in all 14 real estate securities series.
4
We follow S&P Property classification - Asia-Pacific developed (Australia, Japan, Hong Kong and
Singapore) and Asia-emerging (China, Taiwan, Malaysia and the Philippines). Please also refer to the S&P
Property database for the markets included in four regional groupings - North America (includes US and
Canada); Europe (includes UK and other European developed markets), Asia-Pacific developed (includes
AU/ JP/HK/ SG and others) and Asia-emerging (includes CH/TW/MA/PH and others)
9
Moreover, with the exception for Taiwan, the MARCH (1) /MARCH (4) /MARCH (8) tests provide
evidence of significant time-varying volatility at the 1% level in all real estate securities series.
(Table 4 here)
Table 5 provides the Pearson correlation results for the squared return (volatility) series for the full
period as well as for the global financial crisis period (Jan 05 – Dec 09). Panel A provides the correlation
coefficients for the 10 individual markets; Panel B contains the correlation estimates for the four regional
markets. For the full period, only two volatility correlations are higher than 0.5 (Singapore/Hong Kong;
UK/Australia) and only six correlation coefficients are higher than 0.3. In addition, there are three negative
correlation coefficients (Malaysia/Australia; Malaysia/US, Malaysia/UK) reported. Except for three pairs
(Australia/US and Australia/UK, Japan/UK), the correlations between the US/UK and other Asian
securitized real estate markets are lower than 0.3. During the global financial period (Jan05-Dec09),
correlations are higher for 40 pairs (89%) and five pairs’ correlation estimates are higher than 0.6. Except
for Australia, other seven Asian markets shows a higher correlation with the US and UK real estate
securities markets. For the regional estimates, while volatility correlations are between 0.19 (Asiaemerging/North America) and 0.63 (Asia-Pacific developed / Asia-emerging) for the full period, they are
between 0.18 (Asia-emerging/North America) and 0.778 (Asia-Pacific developed / Europe) over 2005-2009
that includes the global financial crisis period.
The volatility correlation results are in general agreement with what appears in the literature. In
contrast to international stock markets, international securitized real estate markets exhibit smaller return
correlations (Liow et al, 2009), however, some markets are interdependent through their second moments
(i.e. volatility). Moreover, it appears that there is a pattern of (much) higher volatility correlation among the
markets in “crisis” period, which is again in broad agreement with what is reported in the stock market
literature (Longin and Solnik, 1995). However, correlation analysis is not suitable for analyzing long-term
relationships because it utilizes return (or squared return) information and neglects information contained in
level data.
(Table 5 here)
5.3
Common time-varying volatility trends
10
Based on the three-step GARCH-cointegration methodology outlined in Section 4, Table 6
contains the full period results for 7 models. Because the Taiwan real estate securities market does not
exhibit a MARCH effect, the test is also conducted on both the cases of with and without Taiwan in four
appropriate groups.
(Table 6 here)
Based on the test results, there is evidence of two common co-integrating vectors (significant at
the 5% and 10% levels respectively) for the all-Asian group (Model A). Even when Taiwan is excluded
from the test (Model A1), there is evidence of at least one significant (at the 5% level) co-integration vector
for the Asian group. Thus it appears that the eight Asian real estate securities markets are linked together in
the long-run through some similar volatility processes. Furthermore, the GARCH-cointegration procedure
is able to uncover a strong (at the 1% level) common volatility link that exists among the four Asia-Pacific
developed markets (Model C); however the Asia-emerging group (Models E and E1: with and without
Taiwan) does not share similar volatility process.
When the US and UK markets are included in the three above Asian systems, the empirical results
indicate that, first, the ten real estate securities markets (Model B: 8 Asian +US+UK) share two (with
Taiwan) and three (without Taiwan) common time-varying volatility. Second, whilst adding the US and
UK markets to the Asia-emerging group failed to uncover a common volatility factor (with and without
Taiwan); up to two significant (at the 1% level) common volatility components are detected for Model D
(Asian-Pacific developed + US +UK).
Finally, when the GARCH co-integration is applied to the four regional markets, we are unable to
detect a common time-varying volatility among the four weekly indices because the t-statistic is not
significant at any conventional levels.
Results of the bivariate tests help identify those markets that contribute to the co-integration space.
Table 7 contains the bivariate GARCH co-integration results for all 45 real estate securities market pairs
(Panel A) and 6 regional-pairs (Panel B). Whilst all 6 regional-pairs have insignificant volatility links; there
are four significant bivariate market pairs each with a common time-varying volatility. These market pairs
are: Hong Kong/China; Hong Kong /Singapore; Singapore/ Philippines and Australia/UK; which produces
two combinations: (a) Australia and UK, and (b) China, Hong Kong, Singapore and Philippines. A further
11
GARCH co-integration on Set b (4-variate system) captures two significant common volatility effects {i.e.
t=4.808 (1%) and t = 3.912 (10%)}. Together with one significant volatility link detected for AU/UK (i.e.
System a), the results indicate that a group of six markets (HK, SG, CH, PH, AU, UK) are part of the longrun common volatility relationships in the International system (i.e. 8 Asian markets + US + UK); and
accordingly, the real estate securities markets of the US, JP, MAL and TW can possibly be excluded from
the volatility co-integration space. The implication is that diversification benefits are still available within
these excludable real estate securities markets (i.e. did not contribute the volatility co-integration space).
5.4
Common volatility during the global financial crisis period (Jan05 to Dec09)
In contrast to the full period co-integration results (section 5.1), the Johansen co-integration test
indicates that there are, respectively, three (International sample), one (Asian sample) and one (regional
sample) co-integrating relationships at the 5% level during the global financial crisis period, implying these
indexes exhibit some tendencies to move together in the long run. These results are in broad agreement
with the findings reported in Liow (2008) that real estate securities markets have become more
interdependent following some turbulence (such as Asian financial crisis) in the markets because of the
contagion effect.
To understand the impact of the global financial crisis on the dynamic cross-volatility
relationships, we repeat the GARCH co-integration tests on the same datasets covering the period from
Jan05 to Dec09. Table 8 provides the multivariate results. Three major differences are observed. First,
compared with the full period model, the group that is composed of four regional real estate securities
market shows a similar time-varying volatility during the global financial crisis period. Second, in contrast,
the Asia-Pacific developed system does not capture a common time-varying volatility effect, a result which
is not to be expected. Third, in two groups (All Asian + US + UK and Asia-Pacific developed + US + UK),
we observe higher t-statistics of the common-volatility coefficient ( ), implying the common volatility
effects are stronger among some markets of the two groups in the “crisis” period. Additional bivariate
results contained in Table 9 indicate that there are six significant volatility links (compared to four for the
full period model). A common factor that has a time-varying volatility is found in the HK/CH, HK/TW,
SG/PH, MA/UK, AU /UK and US/UK pairs. During this period, the US market as the principal source of
12
the global financial crisis contributes to the common time-varying volatility space mainly with the UK
market.
Summarizing, this global financial crisis period is associated with co-integration in the first
moment in three groups of real estate securities markets (Asian, International and Regional). Furthermore,
at least a common time-varying volatility each is detected in five groups of real estate securities markets
(Asian, international, Asia-developed +US/UK, Asia-emerging +US/UK and regional). Hence some real
estate securities markets during this “crisis” period are co-integrated in both their first and second moments
with other markets and demonstrate partial return and volatility convergence. Accordingly, international
portfolio diversification benefits are further reduced compared to the full period where no long-term return
co-movement could be detected.
(Tables 8 and 9 here)
6.
Conclusion
In the simple set up of this paper, we investigate whether there exists long-run equilibrium
relationships among the US, UK and eight Asian securitized real estate market indices, including Australia,
Japan, Hong Kong, Singapore, China, Taiwan, Malaysia and the Philippines as well as four broad regional
groups (Asia-Pacific developed, Asia-emerging, Europe and North America) over the past 15 years
spanning from January 1995 to December 2009. In contrast to the previous studies that evaluated only
long-run return interdependence, the focus of the current study is concerned with whether international, and
in particular, Asian real estate securities markets show a similar time-varying volatility. To our knowledge,
this is probably the first “common volatility” study and supplements prior securitized real estate literature
on return and volatility spillovers. In addition, we examine the impact of the global financial crisis on the
dynamics of return and volatility equilibrium relationships among the real estate securities markets.
Our empirical results indicate the presence of ARCH effects in almost all real estate securities
index series, indicating that their time-varying volatilities need to be incorporated in searching for volatility
equilibrium. Although different groups of real estate securities market indexes (Asian, international, Asiadeveloped, Asia-emerging and Regional) are not co-integrated in the long run (in their first moments), we
find three groups of real estate securities markets have long-term, common time-varying volatility. Our
GARCH co-integration tests reveal that the Asian, International and Asia-developed samples are linked
13
with at least one common time-varying variance factor. During the global financial crisis period (January
2005-December2009), we find that not only the real estate securities markets within the Asian,
international and regional groups display some tendencies to co-move in the long run, they are also linked t
through at least a long-term, common time-varying variance.
To conclude, our study indicates the presence of at least one common time-varying variance
component, and thus partial volatility convergence, among real estate securities markets that composed of
eight Asian markets, UK and the US. One important lesson to learn from this study is that any effort to
unravel the cross-market dynamics and extent of integration among international real estate securities
markets should consider both long–run return co-movement and common time-varying variance; from the
short term perspective should consider dynamic return correlation and volatility spillovers.
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16
Table 1
Market
Australia
Japan
Hong Kong
Singapore
China
Malaysia
Philippines
Taiwan
US
UK
Asian developed
Asian Emerging
Europe
North Americas
Table 2
Summary statistics on weekly real estate securities returns: Jan95-Dec09
Mean (%)
0.121
0.020
0.151
0.066
0.202
-0.060
0.018
-0.072
0.181
0.110
0.081
-0.071
0.156
0.180
Std dev(%)
2.672
4.567
4.561
4.961
5.843
4.494
5.140
5.007
3.318
3.069
Regional
3.217
3.783
2.377
3.235
Skewness
-2.093
-0.098
-0.396
-0.350
0.033
0.801
-0.012
-0.154
-0.421
-1.295
Kurtosis
20.641
4.279
7.347
12.747
5.041
11.347
5.498
5.135
15.033
11.182
-0.713
-0.417
-2.125
-0.409
8.789
6.037
17.161
15.176
1st difference
-17.565***
-30.874***
-26.608***
-13.247***
-27.945***
-26.536***
17.803***
-26.798***
-27.946***
-28.898***
Regional
-17.913***
-27.004***
-17.270***
-27.905***
level
2.552***
1.261***
1.742***
1.016***
2.232***
0.787***
0.668**
1.385***
2.993***
2.432***
first difference
0.413
0.095
0.049
0.115
0.096
0.216
0.126
0.241
0.104
0.261
1.728***
1.046***
2.864***
2.997***
0.074
0.306
0.216
0.104
Unit root tests
ADF
Market
Australia
Japan
Hong Kong
Singapore
China
Malaysia
Philippines
Taiwan
US
UK
Level
-2.107
-1.512
-1.500
-1.619
-0.640
-1.736
-1.561
-1.226
-1.393
-1.676
Asian developed
Asian Emerging
Europe
America
-1.446
-1.551
-1.511
-1.375
KPSS
Notes
ADF – the Augmented Dickey-Fuller test with a constant with test critical values as: -2.865 (5%) and -3.438 (1%). The
null hypothesis is that the time series has a unit root.
KPSS – the Kwiatkowski-Philips-Schmidt-Shin test with test critical values as: 0.463 (5%) and 0.739 (1%). The null
hypothesis is that the time series is stationary. ***- denotes statistical significance at the 1% level
17
Table 3
Results of Johansen multivariate co-integration tests: January 1995-December 2009
Trace
Ho
r =1
r<=1
r<=2
r<=3
r<=4
r<=5
r<=6
r<=7
r =1
r<=1
r<=2
r<=3
r<=4
r<=5
r<=6
r<=7
r<=8
r<=9
r =1
r<=1
r<=2
r<=3
Maximum Eigenvalue
5% CV
statistic
5% CV
Panel A: All Asian (8 markets)
142.41
159.53
37.51
52.36
104.91
125.62
32.32
46.23
72.58
95.73
24.06
40.08
48.52
69.82
20.61
33.88
27.91
47.86
15.13
27.58
12.78
29.79
5.37
21.13
7.41
15.49
5.06
14.26
2.36
3.84
2.36
3.84
Panel B: All Asian+US+UK (10 markets)
220.45
239.24
50.79
64.51
169.65
197.37
41.69
58.43
127.96
159.53
31.44
52.36
96.53
125.62
26.44
46.23
70.08
95.75
24.23
40.08
45.85
69.82
18.82
33.88
27.04
47.86
14.65
27.58
12.39
29.79
7.15
21.13
5.24
15.49
2.99
14.26
2.25
3.84
2.25
3.84
Panel C: Regional (4 groups)
34.94
47.86
17.89
27.58
17.06
28.79
7.53
21.13
9.53
15.49
6.64
14.26
2.98
3.84
2.98
3.84
statistic
Notes: r is the number of co-integrating vectors. The critical values are from Mackinnon-HaugMichelis (1999).
18
Table 4
ARCH tests for securitized real estate markets: Jan 1995 – Dec 2009
Market
US
UK
Japan
Australia
Hong Kong
Singapore
China
Taiwan
Malaysia
Philippines
ARCH(4)
134.520***
47.311***
16.366***
44.808***
9.936***
21.788***
5.734***
4.662***
14.286***
6.590***
North America
Europe
Asia-Pacific developed
Asia- Emerging
136.520***
29.304***
11.221***
9.472***
ARCH(8)
68.633***
34.544***
10.859***
31.980***
5.624***
11.608***
4.853***
5.439***
8.222***
4.415***
Regional
69.520***
22.323***
10.064***
7.078***
MARCH(1)
314.754***
199.006***
134.586***
171.223***
47.147***
30.921***
33.438***
9.727
65.04***
50.471***
MARCH(4)
428.284***
291.478***
197.38***
352.296***
111.829***
131.691***
62.312**
37.180
320.205***
86.481***
MARCH(8)
549.694***
467.742***
256.641***
387.921***
183.576***
226.568***
139.762***
83.983
371.574***
138.192***
305.463***
136.463***
120.508***
51.208***
400.052***
206.7***
144.906***
77.199***
514.895***
300.031***
188.781***
107.542***
 2 values (degree of freedom =4): 14.860 (99%), 11.143(95%), 9.488 (90%); critical  2 values (degree of freedom=10): 25.188(99%),
2
2
20.483(95%), 18.307(90%); MARCH (4): critical  values (degree of freedom=16): 32.467(99%), 28.845(95%), 26.296(90%); critical  values (degree of freedom=40):
2
2
66.766(99%), 59.342(95%), 55.759(90%); MARCH (8): critical  values (degree of freedom=32): 69.311(99%), 61.758(95%), 58.108(90%); critical  values (degree of
Notes: MARCH (1): (a) critical
freedom=82): 116.321(99%), 106.629(95%), 101.880(90%); ***, **, * - denotes statistical significance at the 99%, 95% and 90% confidence level
19
Table 5
Correlation results for the squared returns (volatilities)
Panel A
Australia
Japan
Hong Kong
Singapoere
China
Malaysia
Philipinnes
Taiwan
US
UK
Australia
1
0.493
0.595
0.525
0.372
0.050
0.546
0.205
0.456
0.504
Japan
0.391
1
0.727
0.542
0.565
0.152
0.604
0.305
0.329
0.391
Hong Kong
0.268
0.330
1
0.669
0.615
0.131
0.611
0.344
0.349
0.319
Singapore
0.169
0.204
0.771
1
0.491
0.146
0.547
0.475
0.256
0.314
China
0.247
0.256
0.311
0.293
1
0.299
0.525
0.349
0.100
0.165
Malaysia
-0.0027
0.113
0.286
0.444
0.154
1
0.203
0.062
0.008
0.019
Philipinnes
0.259
0.264
0.379
0.395
0.238
0.137
1
0.424
0.308
0.2567
Taiwan
0.091
0.141
0.107
0.092
0.112
0.043
0.081
1
0.138
0.114
US
0.482
0.261
0.165
0.092
0.081
-0.015
0.147
0.062
1
0.456
UK
0.519
0.307
0.159
0.115
0.105
-0.016
0.124
0.054
0.490
1
Panel B
Asia-Pacific Developed
Asia-Emerging
Europe
North America
Asia-Pacific Developed
1
0.751
0.778
0.376
Asia-Emerging
0.634
1
0.551
0.178
Europe
0.602
0.487
1
0.434
North America
0.306
0.192
0.469
1
Notes: Each correlation panel contains two reporting periods: Figures for the Upper triangle are the correlation coefficients for January 1995- December 2009 (full study
period); figures for the lower triangle are correlation coefficients for January 2005 – December 2009 (global financial crisis period):
20
Table 6
Results of Modified Multivariate Co-integration test with GARCH Effect for Securitized Real Estate Markets: Jan95- Dec 09 (Full-period)
Model
A
All Asian
N
8
A1
B
All Asian (w/out Taiwan)
All Asian +US+UK
7
10
B1
All Asian +US+UK (w/out Taiwan)
9
C
D
Asian developed
Asian developed+US+UK
4
6
E
E1
F
F1
G
Asian emerging
Asian emerging (w/out Taiwan)
Asian emerging+US+UK
Asian emerging+US+UK (w/out Taiwan)
Regional
4
3
6
5
4
R
1
2
1
1
2
1
2
3
1
1
2
1
1
1
1
1

0.1761
0.1759
0.1595
0.2263
0.1694
0.1743
0.1813
0.1594
0.1508
0.1795
0.1612
0.1094
0.1032
0.1342
0.1277
0.1042
t-stat
5.613**
5.047*
5.518**
7.077***
5.594*
6.018**
5.818**
5.323*
4.983***
5.347***
5.438***
3.712
3.287
4.287
4.142
3.801
10%
4.974
4.974
4.717
5.446
5.446
5.216
5.216
5.216
3.821
4.442
4.442
3.821
3.460
4.442
4.145
3.821
critical values
5%
5.529
5.529
5.002
5.730
5.730
5.501
5.501
5.501
4.110
4.729
4.729
4.110
3.752
4.729
4.433
4.110
1%
5.805
5.805
5.550
6.275
6.275
6.046
6.046
6.046
4.667
5.279
5.279
4.667
4.312
5.279
4.986
4.667
Notes: Based on S&P property - All Asian (Japan, Australia, Hong Kong, Singapore, China, Taiwan, Malaysia, Philippines); Asian developed (Japan, Australia, Hong Kong,
Singapore); Asian emerging (China, Taiwan, Malaysia, Philippines); Regional (North Americas, Europe, Asian developed, Asian emerging), N refers to the number of
markets; R refers to the canonical variates derived from step 2 (see methodology)-the maximum canonical correlation is used for the row of R=1; whereas the second highest
canonical correlation is used for the row of R=2;  is the portfolio weight coefficient in equation 4(a) with GARCH effect: (4a) U jt  V jt   t ; critical values are
derived from Table 2 in McKinnon (1991); ***, **, * - denotes statistical significance at the 1%, 5% and 10% level
21
Table 7
Results of Bivariate Co-integration test with GARCH Effect for Securitized Real Estate
Markets: Jan95- Dec 09 (Full-period)
Panel A
10 national markets
R=1 CH HK TW PH JP SG MA AU US UK CH HK TW PH JP SG MA AU US UK 0.0944 (3.084*) 0.0386 (1.210) 0.0621 (1.851) 0.0683 (2.088) 0.0672 (2.173) 0.0599 (2.129) 0.0292 (1.310) 0.0592 (2.553) 0.0419 (1.711) 0.0656 (1.876) 0.0778 (2.799) 0.0618 (1.876) 0.1063 (3.067*) 0.0537 (2.053) 0.0406 (1.537) 0.0281 (1.129) 0.0445 (1.684) 0.0865 (2.562) 0.0459 (1.385) 0.0308 (0.962) 0.0661 (2.557) 0.0371 (1.697) 0.0339 (1.291) 0.0419 (1.616) 0.0650 (2.073) 0.1216 (4.194***) 0.0729 (2.596) 0.0358 (1.499) 0.0449 (1.293) 0.0249 (0.888) 0.0708 (2.122) 0.0395 (1.539) 0.0400 (1.635) 0.0482 (1.369) 0.0533 (1.561) 0.0321 (1.632) 0.0365 (1.499) 0.0251 (1.030) 0.0242 (0.994) 0.0286 (1.292) 0.0367 (1.510) 0.0351 (1.334) 0.0285 (1.331) 0.0749 (3.380**) 0.0698 (2.268) Panel B
Four Regional markets
R=1 Asian –Pacific developed Asia‐emerging Europe North America Asian –Pacific developed Asia‐emerging ‐ ‐ ‐ ‐ 0.0735 (2.297) 0.0138 (0.508) 0.0210 (0.552) ‐ ‐ ‐ 0.0422 (1.470) 0.0526 (1.812) ‐ ‐ 0.0531 (2.704) ‐ Europe North‐America Notes: (a) These two tables present the  estimates, the portfolio weight coefficient and its t-statistics
(numbers in parenthesis), in equation 4(a) with GARCH effect: (4a) U jt  V jt   t ; (b) Based on
S&P property – Japan (JP), Australia (AU), Hong Kong (HK), Singapore (SG), China (CH), Taiwan
(TW), Malaysia (MA), Philippines (PH); R=1 refers to the first canonical variates derived from step 2
(see methodology)-the maximum canonical correlation is used for the row of R=1; critical values are
derived from Table 2 in McKinnon (1991) (10%: 3.061; 5%: 3.360 and 1%: 3.939); ***, **, * denotes statistical significance at the 1%, 5% and 10% level. The results indicate that only four pairs of
real estate securities markets have common volatility (HK/CH; HK/SG; SG/PH and AU/UK) (in bold)
22
Table 8
Results of Modified Multivariate Co-integration test with GARCH Effect for Securitized Real Estate Markets: January 2005- December 2009
(Global Financial Crisis period)
Model
A
B
Markets
All Asian
All Asian +US+UK
N
8
10
C
D
Asian developed
Asian developed+US+UK
4
6
E
F
G
Asian emerging
Asian emerging+US+UK
Regional
4
6
4
R
1
1
2
1
1
2
1
1
1

0.2904
0.4315
0.4067
0.2367
0.3024
0.2658
0.1527
0.2472
0.3151
t-stat
5.471**
10.503***
8.602***
3.556
7.134***
5.197***
2.611
5.247**
5.218***
10%
5.021
5.737
5.737
3.843
4.476
4.476
3.843
4.476
3.843
critical values
5%
5.318
6.036
6.036
4.139
4.772
4.772
4.139
4.772
4.139
1%
5.892
6.615
6.615
4.714
5.345
5.345
4.714
5.345
4.714
Notes: This table reports the common volatility results based on the modified co-integration test with GARCH effect from Jan 05 to Dec 09 which covers the global financial
crisis period. Based on S&P property - All Asian (Japan, Australia, Hong Kong, Singapore, China, Taiwan, Malaysia, Philippines); Asian developed (Japan, Australia, Hong
Kong, Singapore); Asian emerging (China, Taiwan, Malaysia, Philippines); Regional (North Americas, Europe, Asian developed, Asian emerging), N refers to the number of
markets; R refers to the canonical variates derived from step 2 (see methodology)-the maximum canonical correlation is used for the row of R=1; whereas the second highest
canonical correlation is used for the row of R=2;  is the portfolio weight coefficient in equation 4(a) with GARCH effect: (4a) U jt  V jt   t ; critical values are
derived from Table 2 in McKinnon (1991); ***, **, * - denotes statistical significance at the 1%, 5% and 10% level
23
Table 9
Results of Bivariate Co-integration test with GARCH Effect for Securitized Real Estate
Markets: January 2005- December 2009 (Global Financial Crisis period)
Panel A
10 national markets
R=1 CH HK TW PH JP SG MA AU US UK CH HK 0.2089 (3.318*) 0.1543 (2.931) 0.1253 (1.900) 0.0689 (1.938) 0.0863 (1.777) 0.1036 (2.156) 0.0671 (1.441) 0.0651 (1.207) 0.0584 (1.332) 0.1894 (3.304*) 0.0965 (1.662) 0.1138 (2.211) 0.0978 (2.145) 0.0903 (1.685) 0.0558 (1.183) 0.0535 (1.065) 0.0622 (1.384) 0.0922 (1.471) 0.0590 (0.882) 0.0590 (0.882) 0.1353 (2.565) 0.0577 (1.013) 0.0206 (0.349) 0.0535 (0.845) 0.8450 (2.868) 0.2031 (3.636**) 0.0966 (1.470) 0.0887 (1.471) 0.0857 (1.514) 0.1076 (1.825) 0.107 (2.487) 0.1380 (2.674) 0.0775 (2.146) 0.1115 (2.171) 0.1049 (2.217) 0.1082 (2.417) 0.0810 (1.902) 0.0266 (0.564) 0.0853 (2.003) 0.0667 (1.635) 0.1061 (2.456) 0.1235 (3.597**) 0.1421 (2.821) 0.1716 (4.238***) 0.1630 (5.201***) TW PH JP SG MA AU US UK Panel B
Four Regional markets
R=1 Asian –Pacific developed Asia‐emerging Europe North America Asian –Pacific developed Asia‐emerging ‐ ‐ ‐ ‐ 0.0011 (0.026) 0.0931 (1.991) 0.0659 (1.576) ‐ ‐ ‐ 0.0385 (1.023) 0.0062 (0.105) ‐ ‐ 0.1922 (5.043***) ‐ Europe North‐America Notes: (a) These two tables present the  estimates, the portfolio weight coefficient and its t-statistics
(numbers in parenthesis), in equation 4(a) with GARCH effect: (4a) U jt
 V jt   t ; (b) Based on S&P
property – Japan (JP), Australia (AU), Hong Kong (HK), Singapore (SG), China (CH), Taiwan (TW),
Malaysia (MA), Philippines (PH); R=1 refers to the first canonical variates derived from step 2 (see
methodology)-the maximum canonical correlation is used for the row of R=1; critical values are derived
from Table 2 in McKinnon (1991) (10%: 3.061; 5%: 3.360 and 1%: 3.939); ***, **, * - denotes statistical
significance at the 1%, 5% and 10% level. The results indicate that six pairs (HK/CH; HK/TW; SG/PH;
MA/UK; AU/UK AND US/UK) and one regional pair (EUR/NAM) of real estate securities markets have
common volatility in 2005-2009 (in bold)
24
Figure 1
Logarithmic Index Movements
7.0
6.5
6.0
5.5
5.0
4.5
4.0
1996
1998
2000
2002
US
JAPAN
HONG KONG
2004
2006
2008
UK
AUSTRALIA
SINGAPORE
7.0
6.5
6.0
5.5
5.0
4.5
4.0
3.5
1996
1998
2000
2002
ASIAN DEVELOPED
EUROPE
2004
2006
2008
ASIAN EMERGING
NORTH AMERICAS
25
7
6
5
4
3
2
1996
1998
2000
2002
China
Phillipines
2004
2006
2008
Malaysia
Taiwan
26