Switching Volatility and Dynamic Linkages among International Real
Estate Securities Markets
Kim Hiang LIOW1 and Qing YE2
July 2012
Abstract
The primary contribution of this study is to assess the dynamic linkages among international real
estate securities markets from a volatility regime switching perspective from January 1990 to January
2012. The estimation of a univariate three-state SWARCH model reveals the existence of more than
one volatility regime over the last 20 years and there is a significant volatility increase during the
crises periods for all markets examined. However, the identified high volatility regime appears
short-lived. Based on the SWARCH results, we find that the dynamic linkages among the markets are
positively dependent on volatility regime. Specifically, the market correlations, Granger lead-lag
relations, aggregate variance spillover index, foreign market influence and variance-covariance matric
have intensified as market volatility increases during this period. Moreover, the evolution of market
linkages among international real estate securities markets is influenced significant by both a time
trend and a volatility regime factor. Our volatility regime and non-linear market linkage results are
preliminary; but indicative. They imply that risk-reduction via international diversification in real
estate securities markets may hold true in low volatility period. Consequently portfolio managers need
to understand and implement volatility state-dependent optimal asset allocation in order to better
advise their clients.
;Keywords:
International real estate securities markets; volatility regime, state dependent; market;
linkages, SWARCH; variance spillover index; variance-covariance matrix
1
Professor in real estate finance and investment, Department of Real Estate, National University of
Singapore, email: rstlkh@nus.edu.sg
2
PhD student, Department of Real Estate, National University of Singapore
1
1.
INTRODUCTION
Correlation and volatility are at the heart of international diversification. While the extant
literature has documented that correlations have changed over time, there is also evidence that market
correlations tend to increase during periods of high volatility and thus implies that risk-reduction via
international diversification may hold true only in low volatility periods. Karolyi and Stulz (1995) find that
co-variances are high when returns on the national stock indices are high and when markets fluctuate.
Hence, variance, correlation and co-variance could be both time- and state-varying and consequently the
diversification benefits could be varying over time, as well as depends on the states of economy. Modeling
how this conditional volatility, correlation and covariance evolve over time is thus important in portfolio
management. While the conventional ARCH-GARCH models have been popularly used to characterize the
volatility of stock returns, they have also been criticized as inappropriate in modeling the high persistence
of conditional volatility in the presence of structural changes in the volatility process during the
examination period (Lamoureux and Lastrapes, 1990). Motivated by this line of thought, in this paper, we
use a more sophisticated approach to model the volatility of nine developed securitized real estate return as
a stochastic process whose conditional variance is subject to regime change. In particular, we employ
switching ARCH models, known as SWARCH models, introduced by Hamilton and Susmel (1994) to
endogenously determine periods of high, low and average volatility for each market and assess the
behavior of correlation/covariance matrices and spillover effects under different volatility regimes during
these periods. In essence, the SWARCH model incorporate Markov-switching and ARCH models to
control the structural changes and mitigate the high persistence of variance in ARCH models.
This article is thus an addition to the already large body of literature on volatility regime. However,
there are few aspects of our study which are different and represent improvements over the extant literature.
Research on volatility persistence and regime switching has so far concentrated on national /international
stock markets. This paper is probably the first to explore the issue of dynamic market linkages in
international developed real estate securities markets from a structural break and non-linear perspective,
and in particular in using the SWARCH methodology of Hamilton and Susmel (1994). With increasing
significance of real estate securities in international investors’ mixed asset portfolio, our study is
particularly meaningful in understanding and implementing state-dependent optimal asset allocation.
Specifically, we are interested in the following issues. First, does a three-regime volatility setting (i.e. low,
medium and high volatility) exist in these real estate securities markets, similar to the stock market in the
2
United States?3 This implies that we allow for the existence of three regimes, namely high, medium and
low volatility. This approach will allow us provide better evidence for the existence of high volatility
during extreme events. Second, as a result of the SWARCH estimation, periods of high, medium and low
volatility are determined for each market, thereby lead to the determination of common volatility regimes
for all markets examined. The behavior of correlation and covariance matrices between the markets during
these periods can then be investigated under the three common volatility regimes (as defined by the
SWARCH model) via three questions: (2a) Does the degree of market interaction and co-movement
intensify during the period of high volatility as revealed by the state-dependent correlation and lead-lag
relations between the sample real estate securities markets? (2b) Do the variance spillovers increase
between the markets during periods of high volatility? Are foreign markets able to explain more of a
domestic market’s behavior during periods of high volatility? (2c) Is the covariance matrix of the
international developed real estate securities markets stable as the markets move from low to medium or
high volatility states? (2d) Are real estate securities return volatilities both time- and state-varying? Our
non-linear approach to carefully assess the changes of dynamic linkages among the major real estate
securities markets under three volatility states should be more pragmatic in today’s volatile financial
markets and contribute to the conventional linear market integration literature in international real estate
investing. From a practical perspective, portfolio managers will be able understand better the multilateral
interaction existing across the international real estate securities markets which could be more volatile than
the respective stock markets. Moreover, there is no a priori reason why real estate securities should display
similar volatility regime characteristics to general equities.
The paper is organized as follows: Section 2 provides a short discussion of previous empirical
research. Section 3 describes the research sample and preliminary data characteristics. This is followed by
Section 4 that gives a brief introduction to modeling time series using the SWARCH approach and Variance
decomposition methodology. Section 5 presents an empirical application of the SWARCH model and other
dynamic market linkage results. The final section will sum up the results.
2.
BRIEF LIERATURE
In the present context, a regime change is associated with a significant shift in the fundamental
3
Hamilton and Susmel (1994) presented a three volatility regime model that adequately pictures the stock market in
the United States.
3
relation of conditional volatility in securitized real estate, and there is a probability in each time period that
a volatility switch would happen from one regime to another. For example, the effect of 1997 Asian
Financial crisis was to reduce real estate returns and to increase real estate volatility and correlation with
other asset classes (Kallberg et al.2002); while prior to the crisis, the opposite occurred. Following the
work of Hamilton (1989) on switching regime, Cai (1994) and Hamilton and Susmel (1994) propose a new
ARCH model, the switching ARCH or SWARCH model, to incorporate the fact that volatility is both timeand state-varying and assume that the parameters of the ARCH model depend on a discrete number of
regimes, where the switch between regimes is governed by a discrete state Markov process.4 One key
advantage of the SWARCH model is the ability to objectively date the states of the economy. In our context,
we date different states for each real estate securities series and thereafter determine the common volatility
states for all series to provide a non-linear perspective on the dynamics of international real estate market
linkages.
Empirically, Hamilton and Susmel (1994) test their SWARCH model using weekly returns on the
New York Stock Exchange and find that their model implies a much lower level of volatility persistence
than standard ARCH specifications without regime shifts. Ramchand and Susmel (1998) use a SWARCH
technique to model the relation between correlation and variance in a conditional time- and state-varying
framework. They also develop a bivariate SWARCH model in a state-varying covariance framework. They
find that the correlations between the US and other world markets are on average 2 to 3.5 times higher
when the US market is in a high variance regime. Their findings provide great support to the hypothesis
that volatility persistence is linked to regime swifts and structural changes. Susmel (2000) fits an
exponential SWARCH model to his sample of eight international stock markets. He finds evidence of
switching volatility for the US, Canada, the UK and Canada. Edwards and Susmel (2001) use weekly Latin
American stock market data to analyze the behavior of volatility through time. They also apply both
univariate and bivariate SWARCH models and find that high volatility periods are short-lived. Other
evidence also shows strong volatility co-movements across countries. Using a SWARCH model on his
sample of five major stock markets, Jochum (2001) finds that international variance-covariance matrix is
not stable and the changes in the matrix are dependent on the volatility regimes. Finally, Li (2007) uses the
SWARCH technique to identify the volatility state of international stock markets. The author then
considers four possible state combinations of individual and world stock markets to examine the
4
See also Section 4 on a brief discussion regarding the SWARCH methodology.
4
relationship between international diversification and market volatility.
In contrast, similar effort to use a SWARCH approach on international real estate securities
markets is rare despite the increasing significance of public real estate in investors’ mixed asset portfolios.
Previous studies on regime switching focuses mainly on return (Maitland-Smith and Brooks (1998),
Kallburg et al. 2002, Liow et al. 2005). One notable exception is by Liow et al. (2012) who apply Bai and
Perron (2003)’s multiple structural break technique to identify multiple volatile regimes in international
real estate securities markets. On the dynamic market linkage issue, Cotter and Stevenson (2006) use a
multivariate VAR-GARCH model to examine the time-varying conditional volatilities and correlations in
the daily US REIT and equity return series. Michayluk et al. (2006) develop an asymmetric covariance
model to examine the daily volatility spillover effect and time-varying correlation dynamics between the
USA and UK securitized real estate markets. Relying on a DCC-GJR-GARCH (1, 1) model, Liow et al.
(2009) examine the correlation and volatility dynamics of international securitized real estate markets. Case
et al. (forthcoming) use the DCC-GARCH model to examine dynamics in the correlation of returns
between public traded REITs and non-REIT stocks. Their results indicate that REIT-stock correlations form
three distinct periods over 1972-2008. Finally, Liow et al. (2011) develop a multivariate regime-dependent
asymmetric dynamic covariance (MRDADC) model to detect the presence of significant mean-volatility
linkages across five major real estate securities markets under different volatility regimes which are derived
from using the Bai and Perron (2003)’ multiple structural break methodology.
3.
RESEARCH SAMPLE AND DATA
This research includes nine major public real estate markets from three continents; North America
(the US), Europe (France, Germany, the UK and Italy) and Asia-Pacific (Australia, Japan, Hong Kong and
Singapore). These nine public real estate markets represent about 80% of the global securitized real estate
market capitalization and have the world’s most significant listed real estate equity markets in the respective
regions. Moreover, these nine economies have a developed capital market to enable the growth of the broader
stock and public real estate markets. The US has the world’s largest real estate market, which is also the most
transparent public real estate market. Listed property companies have a long history in Europe. Among them,
the UK is the European’s largest public real estate market. Germany has a long history of indirect real estate
vehicles such as open-ended funds, closed-ended funds and listed real estate companies. In the Asia-Pacific
5
region, Japan as a major world economy has a long tradition of listed real estate, with some of the world’s
largest “real estate development” companies such as Mitsubishi Estate and Mitsubishi Fudosan. Together
with the US, Australia is one of the two most matured public real estate markets, with its listed property trusts
(LPTs) as a highly successful indirect real estate investment vehicle. Hong Kong and Singapore have track
record of listed real estate companies that have been contributing a relatively important role in the respective
local stock market indexes. Finally, REITs have been successfully established in all nine public real estate
markets.
The real estate data are weekly FTSE EPRA/NAREIT total return indices maintained by the
European Public Real Estate Association (EPRA). These global real estate series are established to track the
performance of listed real estate companies and REITs worldwide, as well as act as performance measure of
the overall market. We use weekly as opposed to monthly data since we need enough time-series
observations to be able to estimate the different volatility states but without the noise of daily data. The
data cover the period from January 1990 to January 2012 and are in terms of local dollars, for a total of
1150 observations and describe periods of major changes in the economy and international real estate
capital markets that can cause volatility to behave very differently. They include the Mexican peso crisis of
1994-1995, 1997-1998 Asian financial crisis, Russian financial crisis in August 1998, Brazil financial crisis
starting in early 1999, the bursting of the technology bubble in March 2000, the 9/11 terrorist attacks in
2001, stock market downturn in October 2002, the invasion of Iraq in March 2003, the Chinese stock
market drop in February 2007, the 2007-2008 Global financial crisis and the 2010 European sovereign debt
crisis, etc. all of which had clear observed effects on volatilities of international financial markets. Finally,
the weekly closing prices are used to calculate the weekly percentage returns.
Table 1 reports univariate return statistics for the nine real estate market indices. Few observations
are available. The mean of all return series are not significantly different from zero. There exists a
considerable degree of first-order auto-correlation (rho). The extreme values are very significantly larger
than the average returns for all markets. The coefficients of skewness and kurtosis reflect non-normality in
the data, suggesting the use of a -distribution in the subsequent model estimation to take account of this
characteristic. Finally, there is significant evidence of volatility clustering as confirmed by the ARCH test
results.
(Table 1 here)
6
4.
METHODOLOGY
Our analysis comprises two main parts. The first part involves search for the existence of volatility
regime switching. We hypothesize that there exists a structural break in volatility for each of the real estate
securities markets under examination, and employ the Markov Switching ARCH (SWARCH) methodology
developed by Hamilton and Susmel (1994) to determine endogenously the volatility structural break point
(s) in each market. As a result of the SWARCH estimation, in the second part we examine the dynamic
linkages among the markets with state-dependent returns, state-dependent correlations, state-dependent
lead-lag relations, state-dependent variance spillover, and state-dependent variance-covariance. Thus, this
SWARCH specification permits us to examine the dynamic linkage among the real estate securities markets
in a non-linear fashion. Moreover, the combination of the various results will allow us conclude with
greater confidence on whether changes in the real estate securities market linkages are positively dependent
on the volatility regime. We explain briefly two key empirical procedures below:
4.1
SWARCH modeling
As an improvement to the much used ARCH methodology to model the volatility of financial time
series, Hamilton (1989) proposes a new approach to model the behavior of financial time series which
show sudden changes in their levels at a certain point of time. Such shifts are traditionally described by
changes in the constant of the process:
(1)
Where the dummy
is used to model the change in the level of the AR (1) process assumed for the
variable . To allow the complete time series model to include a description of the process governing the
transition between different regimes, the behavior of the observable variable
is described by the
unobservable realization of the regime (state) variable . Equation (1) thus becomes:
(2)
Where
indicates
when
and
when
.
The volatility state is assumed to be the outcome of an unobserved first-order K-state Markov
process. Specifically, a Markov chain models the behavior of a random variable , which can take on only
7
integer values
and whose possibility of realizing a certain value
by the past value
is fully determined
. Each transition probability number p ij is the probability that state i is followed
by state j. Under this specification, the transition probabilities p
probabilities are specified in a
ij
are constant. The resulting transition
matrix :
The sum of elements in each and every column in the above matrix should be equal to1
Build on the above foundation, Cai (1994) and Hamilton and Susmel (1994) propose an
application of a Markov chain specification to switching volatility estimation, where the ARCH process is
modeled for the behavior of the residuals
of a zero-mean first-order auto-regression for the variable .
(3)
To capture the regime-dependent changes in the residuals , the conditional variance is written as:
(4)
Here
is assumed to follow a standard ARCH-( ) process,
(5)
Where
is a zero-mean and unit variance i.i.d. sequence, and
follows:
(6)
if
then multiplied by the constant
and
for
when
. The underlying ARCH-( ) variable
, and multiplied by constant
when
is
and
so on.
Finally, Hamilton and Susmel label the above switching volatility estimation methodology a
(switching autoregressive conditional heteroskedasticity) SWARCH (n, q) model (
where n denotes the number of possible volatility states and q the number of ARCH lags.
8
SWARCH (n, q))
4.2
Variance decomposition test and aggregate spillover analysis
To address issue (2b) regarding the multilateral interaction changes between the real estate
securities markets subject to volatility regime, a vector auto-regression (VAR) analysis is appropriate to
quantify the amount of return variance which is attributable to the local market and how much of a
market’s volatility reflects information transmitted from foreign markets. A variance decomposition test
follows to determine explicitly how much of the movement in one market can be explained by other
markets in terms of the percentage of the forecast variance of that market. Finally, the variance
decomposition results further allow us aggregate spillover effects across markets into a single spillover
measure. Following the latest generalized VAR procedure developed by Diebold and Yilmaz (2012), we
construct a variance spillover index (which is insensitive to the order of the markets) to measure and
compare the degree of linkages in return volatilities among the real estate securities markets under three
different volatility regimes (i.e. low, medium and high volatility states). In Essence, a total variance
spillover index measures what proportion of the volatility forecast error variances comes from spillovers.
We would expect that the total variance volatility index the highest during high volatility period to reflect
intensification of the co-movement of the real estate securities markets
5
RESULTS
5.1
Volatility state determination
Table 1 implies that the use of an underlying t-distribution (instead of normal) is appropriate. We
proceed to model the conditional volatility for each real estate securities market by using the univariate
SWARCH framework to examine the change effect in the variance regime. For our case we choose to
consider the case that the stochastic variable s t takes the values of 1, 2 and 3.5 The univariate SWARCH (3,
2) model with three regimes and two autoregressive coefficients in the variance equation is the best
specification based on the maximum value of the log-likelihood function. Maximum-likelihood estimation
is adopted with all standard errors computed from the heteroscedasticity-consistent variance-covariance
matrix. Table 2 reports the estimated AR (1) – SWARCH (3, 2) - t for each market.6 The results are
5
We estimate an AR (1) – GARCH (1, 1) model to examine whether there are significant ARCH effects in the real
estate securities data. The results (not reported in order to conserve space) provide evidence that are significant ARCH
effects for all series.
6
We also estimate separately an EGARCH model (results not reported) that requires the inclusion of a leverage term
9
generally robust to changes in the starting values and represent a single local maximum. As a result of the
leptopkurtic return distribution, the degree of t-distribution: t (d.f.) is found to be significant for all nine
return series, ranging from 5(Germany) to 24(Hong Kong). A number of interesting results can be observed
from Table 2.
(Table 2 here)
First, the coefficients
significant coefficient
and
on the lagged squared residuals are generally significant and a
on the leverage term
each in four markets (HK, JP, SG and US) shows
that a previous drop in the return subsequently increases the volatility.
Second, the values of
,
and
indicate the relative magnitude of variance at the three
volatility states. Taking the Australia (AU) FTSE EPRA/NAREIT return index as an example, a change
from state 1 to state 2 implies a rise in the variance by dividing
(3.565) over
(1.352), which is
2.637; and for a change from state 1 to state 3 indicates a change by a factor of 16.995 (22.977 /1.352). For
all nine markets the significant switch between the different volatility regimes implies a considerable
change in the market risk. On average, a jump from regime 1 into regime 2 implies roughly a 2.90 times
[7.164 (gv2) /2.469 (gv1)] increase in risk, while the risk during regime 3 is up to almost 12.9 times
[30.861 (gv3) /2.469 (gv1)] than during regime 1 over the study period. Thus we take the regimes 1, 2, 3 as
the low, medium and high volatility regimes, respectively. The amount of this shift indicates the effect of
omitted structural changes as one main reason for the high degree of volatility persistence found in
traditional ARCH models. Moreover, the Wald test statistics reported in Table 3 show that the null
hypothesis that there is no switch in the volatility process (i.e. either
,
or
) could be rejected for all markets. Thus, for each of the real estate securities markets it is
possible to distinguish among a “high”, a “medium” and a “low” volatility regime.
(Table 3 here)
Third, we measure the proportion of time the market remains in a particular regime from the
SWARCH model. This is derived from the transition probability estimates that measure the magnitude of
persistency observed in which data stay in one state - higher values suggest length of stay is likely to be
in the variance equation and the lagged returns in the mean equation of the model.
10
longer. Results for the probability matrices for each market 7 reveal that the values in the main diagonals of
some matrices are close to 1, implying that a certain state is quite persistent and tends not to change once it
has been reached. Consequently, changes between regimes are relatively infrequent in some markets. For
example in Singapore, the transition probability of staying in low volatility regime is 0.682, which means
this regime is expected to last for (1 - 0.682)-1 = 3.1 weeks on average; regime 2 is expected to last for
(1-0.942)-1 = 17.2 weeks; while regime 3 is expected to last for (1-0.569)-1= 2.3 weeks . Taking the nine
markets as a proxy for global real estate securities market, the average length of staying in state 1 (low
volatility) is about 4.1 weeks (average p11=0.756). Similarly, the average length of staying in state 2
(medium volatility) is about 6.4 weeks (p22 =0.843) and about 9.7 weeks (p33 = 0.897) in state 3 (high
volatility), respectively. Finally, the value of
in the (UK) matrix means that the transition
from high volatility regime to low volatility regime has either not taken place in the period or has very low
probability of occurrence. Further, these zero values (or values close to zero) are very often found in
or
, suggesting high volatility state is from the medium volatility regime and it is unlikely that market
can jump to high volatility regime directly from low volatility regime. This finding is consistent with
investors’ behavior.
Fourth, the estimates of the smoothed probability provide a useful means to examine volatility
shifts in different real estate securities markets. We adopt Hamilton’s (1989) procedure for dating regime
changes that classifies an observation as being in regime i if the smoothed probability: Prob (st =i /rT,
rT-1…rT-3) is bigger than 0.5. Figure 1 plots the smoothed probability in the first through third panel in
Regime 1 (low volatility), Regime 2 (medium volatility) and Regime 3 (high volatility), respectively for
the real estate securities markets in the sample.
(Figure 1 here)
A visual examination of the volatility switching patterns across markets is derived from Figure 1.
Based on the smoothed probability estimates, we observe that the volatility switching behavior in one
market differs from one other. Almost all real estate securities markets, except France and to a lesser degree
the US, are more apt to shift between the three volatility regimes, implying that their adjustments are
relatively sensitive to a broader set of market information. In contrast, real estate securities markets in
7
P (i, j) is the probability of moving from i to j.
11
Australia, Singapore, the UK and the US have shorter-lived high volatility state. Figure 1 also allow us
track regime switching in the markets in response to different economic/financial crisis. During the Asian
financial crisis /Russia financial crisis /Brazil crisis periods, real estate securities markets in Hong Kong,
Japan, Singapore, Germany and Italy were largely responsive to the crises and remained in the high
volatility regime for different durations. In contrast, all nine real estate securities markets remained highly
volatile during periods of global financial crisis which was triggered by the securitized real estate factor (i.e.
subprime crisis). Thus, there are some volatility synchronization phenomena across the real estate securities
markets during these financial crises (high volatility periods). In recent time, a majority of the markets have
switched to a high volatility regime again in response to the European sovereign debt crisis which is
on-going at present.
Finally, based on individual markets’ volatility states, we allow periods to be determined during
which the majority of the markets display a specific volatility behavior. For a same date, the prevailing
volatility regime of the period is determined if five of the nine markets are simultaneously in the same
volatility state (regime 1, regime 2 or regime 3). Observations that do not meet this criterion are excluded
from this analysis. Repeating this procedure for all dates thus split all observations into three samples
belonging to three volatility states, which yield 538 observations (51.2%) for low volatility state, 324
observations (28.2%) for medium volatility state and 147 observations (12.8%) for high volatility states,
with another 141 observations (12.3%) excluded from this classification. Thus volatility regime 1 (low
volatility) is by far the most common in the real estate securities market. We further note that 87.7% of all
observations describe periods during which the majority of the markets are in a particular state. This result
implies that similar to stock markets, real estate securities markets are dependent on the volatility regime
and tend to change regime simultaneously. Table 4 lists the periods corresponding to the common three
volatility states for our sample of nine international developed real estate securities market. We observe the
real state securities markets are in State 3 (high volatility) in three periods: March 1998 – December 1998
(Asian financial crisis); October 2007 – July 2009 (global financial crisis); and August – November 2011
(European sovereign debt crisis). In contrast, they are in state 1 (low volatility) and state 2 (medium
volatility) in 6 and 10 periods, respectively.
(Table 4 here)
Based on the SWARCH results, we are inclined to conclude that a three-volatility-regime setting
[AR (1) - SWARCH (3, 2)] could adequately describe the volatility dynamics in international developed
12
real estate securities markets. The estimates from the SWARCH model have provided valuable pieces of
information and as such are followed up in depicting the market correlation, lead-lag relations, variance
decomposition analysis and co-variance matrix in international real estate securities markets in the
following sections.
5.2
Market returns under three different volatility regimes
Table 5 analyzes the behavior of market returns under different volatility regimes. Results indicate
that the average return is highest for the UK and the US during periods of low volatility. Other seven real
estate securities markets report the highest average returns during periods of medium volatility, ranging
from 0.014% (Germany) to 0.373% (Hong Kong). In addition, the average returns of all nine markets are
negative during periods of high volatility, ranging from -1.083 % (Italy) to -0.324% (Hong Kong). Finally,
there is evidence for the presence of leverage effect, with the average return falls and the standard deviation
(risk) increases when the regimes shift from a medium to high level of volatility.
(Table 5 here)
5.3
State-dependent market correlations
Figure 2 provides an overall picture where the average amount of correlation between the nine
markets is calculated under the three volatility regimes as defined by the SWARCH model. As observed,
the markets are always positively correlated. The highest average correlation coefficient is found during the
period from August 10th, 2011 to November 9th, 2011 when most markets are in high volatility state. The
correlation coefficient is as high as 0.74. Periods in lower volatility regime tend to have lower correlation
bars. Results using non-parametric Mann-Whitney test on equal correlation between the markets over the
three volatility regime is reported in Table 6. As the test results reject significantly the null hypothesis of
equal correlation coefficients against the alternative that the correlations are higher in higher risk periods,
we are inclined to conclude that an upward move in the volatility regime is accompanied by an upward
move in the correlation coefficients between the markets, thereby causing the variance-covariance matrix
to be unstable regardless of the volatility regimes observed.
(Figure 2, Table 6 here)
Table 7 provides the bivariate correlations for the 36 market-pairs under different volatility
regimes. As the numbers indicate, average correlation in state 2 (0.2989) is about 68.7% higher than in
13
state 1 (0.1754); and is about 87% higher in state 3 (0.5589) than in state 2 (0.2989). Individual pair
analyses reveal that except for two cases from state 1 to state 2 (AU-SG and ITA-SG), all other correlations
are the highest in state 3 (high volatility), ranging between 0.413 (UK-SG) and 0.781 (HK-SG). Further
evidence indicates that of the 36 market-pairs, there are, respectively, 11 (from low to medium) and 22
(from medium to high) cases that report a more than 100% increase in market correlation. The highest
increase in correlation is 375.3% (low to medium: HK and JP) and 331.1% (medium to high: AU and FR),
respectively. One possible implication that these correlation coefficients are relatively high during the high
volatility period implies that risk-reduction via international real estate securities diversification could
possibly hold true in low volatility period. Consequently, the benefits of portfolio diversification have to be
carefully assessed in the context of volatility regime switching.
(Table 7 here)
5.4
State-dependency and Granger Causality
Table 8 summarizes the Granger-causality test results among the sample real estate securities
indices. A significant Granger-causality in international real estate securities markets may indicate
intensified market integration. During state 1 of low volatility (column 2), there exists only eight
significant unilateral causality F statistics (p<0.05). The number of significant unilateral F decreases
marginally to 7 during state 2 (medium volatility). Then in high volatility state (state 3), there are five cases
of significant bilateral causality and six cases of unilateral causality, respectively. Specifically there exist
some feedback relations between the US and UK, the US and FR, the UK and GER, FR and GER, as well
as between the UK and JP. This finding is significant: while there is no feedback relation between the
markets in the low and medium volatility periods, there exists a feedback relationship among the US, UK,
FR and German real estate securities markets, as well as between the UK and Japan during periods of high
volatility.
(Table 8 here)
Overall, in addition to market correlation, the causality relation is found to have intensified during
the high volatility period. Hence, we have preliminary established a significant positive relationship
between increases in market risk and degree of market linkage between the sample real estate securities
markets.
14
5.5
State dependent variance spillover index and foreign market influence
Table 9 reports the variance decomposition results based on a nine-variable VAR model under
three volatility regimes. The last column, “contribution from others”, calculates the percentage of market
return variance not explained domestically. In addition, the aggregate variance spillover index is computed
as the sum of all variances in the 9 x 9 matrix minus the sum of the diagonal variances. The volatility
spillover table thus provides an approximate “input-output” decomposition of the total variance spillover
index (Diebold and Yilmaz, 2012). Similar to the above market correlation and lead-lag relation analyses,
we are interested to find out whether the total (aggregate) variance spillover and individual ‘contribution
from other” are the highest during high volatility periods. If that is the case, than we can add another piece
of evidence to argue that the degree of market linkage among the major real estate securities markets
increases during periods of increased market volatility.
(Table 9 here)
As the numbers indicate, with a 12-week (4 months) forecast variance, about 23.50 % of the
forecast error variances are due to spillovers among the markets during periods of low volatility (Panel A). .
Similarly, the aggregate variance spillover index is 43.30% (state 2- Panel B) and 77.50% (state 3 – Panel
C), respectively. Turning to the “contribution from others” (foreign market influence) analysis, as the
market volatility increases, the average amount of the influence of the foreign markets rises significantly
from 23.6% (state 1) to 44.44% (state 2) and finally to 77.4% (state 3). In addition, the influence of the
foreign markets rises significantly for all nine markets investigated. For the world’s most matured real
estate securities market in the US, international influences account for about 18% of its innovations during
low risk periods. This percentage increases to 52% and 81% as the volatility jumps to regime 2 and regime
3, respectively.
Further evidence indicates the increases in the foreign market influence are between 6%
(JP) and 40% (GER) and between 19% (FR) and 43% (AU) when the volatility jumps from regime 1 to
regime 2 and regime 2 to regime 3, respectively.
Based on these “innovation accounting” results, we are inclined to conclude that the co-movement
and hence the degree of market linkages have intensified as the markets become more volatile. This is
further consistent with the state dependent market correlation and lead-lag relations findings reported
above.
5.6
State dependent variance-covariance matrix
15
In addition to examining the pair-wise co-movement between the markets using correlation
coefficient, we use the Box-M procedure to assess the stability of the complete variance-covariance matrix
under the three volatility regimes as defined by the SWARCH model. Results in Table 10 indicate that the
hypothesis of equal covariance structure under the three volatility regimes is always rejected, implying that
the variance-covariance matrix is unstable regardless of the volatility regimes observed. Thus, we are
inclined to conclude that the volatility regime shift variable is an important factor in explaining the changes
in the international covariance matrix in real estate securities markets. The implication is that in a volatile
market period, international portfolio investors should refrain from relying a constant variance-covariance
model to support their asset allocation decisions.
(Table 10 here)
5.7
Influence of regime shift and time trend in international correlation matrix
Our results indicate that correlation increases in high volatility periods. Further, we are interested
to know whether this positive relationship between correlation and volatility holds in the presence of time
trend and global stock market volatility. In our context, higher correlation implies higher market linkage
and greater integration among the real estate securities markets. This higher correlation is probably
positively dependent on volatility regime and time trend. An example of time trend is the evolution in the
globalization of financial markets which has resulted in the development of real estate securitization over
the past two decades. While the volatility regime shift variable is normally associated with financial crises,
the time trend variable indicates the globalization process which is evolving through time.
To formally test the relationship between market correlation (CORR) and volatility regime
(REGIME) and time trend (TIME) after controlling for global stock return volatility (GSVOL) on the
relationship, the following regression model will be investigated:
CORR t = b0 + b1*(REGIME) t + b2*(TIME) t + b3*(GSVOL) t + error t (Model A)
Where “CORR” describes the rolling average correlation over all nine real estate securities
markets and is created by rolling a window of 52 weekly observations in one-step increment over the full
study period (Figure 3). “REGIME” is the regime volatility variable which takes the values 0, 1, 2 ,3 for
the undetermined regime, low volatility regime, medium volatility regime and high volatility regime,
respectively, as defined by the SWARCH (3, 2) model; “TIME” is the time trend variable as defined by
t=1, …..1150. The inclusion of the global stock risk factor (GSVOL) is required to control for the world
16
stock market effect on the real estate securities markets’ correlation as real estate securities market is part
of the global stock market, Furthermore any residual relationship found between correlation and the two
independent variables could be reasonably attributed to the real estate securities markets per se with the
global stock return volatility factor controlled. This volatility variable is derived by squaring the MSCI
weekly global stock return over the same period.
In addition, we run another regression model specified by:
CORR t = b0 +b1*S2 + b2*S3 +b3*Su+b4*(TIME) t + b5*(GSVOL) t + error t (Model B)
Where volatility regime is represented by S1, S2, S3 and Su (periods of medium, high and
undetermined regimes) as defined by the SWARCH model; S1 (low volatility regime) is treated as the base
regime (b0) in order to minimize the influence of multicollinearity, Table 11 contains the regression results.
(Table 11 here)
As the numbers from Model A indicate, the influence of the “REGIME” variable on average
correlation is significantly positive and the coefficient has the expected positive signs. Similarly, Model B
indicates the constant (proxy for S1) and the influence of S2 and S3 are significantly positive, implying that
any change from volatility regime 1 will increase the average correlation. The results also indicate the
average correlation coefficient is a positive function of a linear time trend. The time factor adds
significantly to the explanatory power (R2) of the two models (i.e. from 0.153 to 0.611 in Model A; from
0.345 to 0.657 in Model B). Finally, the global stock market risk factor is significantly positive. However,
its presence in the two models does not yield any significant improvement in the results over the last two
decades. In addition, both the regime and time trend variables remain high significantly positive even after
the effect of global stock return volatility has been controlled for. This result implies that real estate
securities could display volatility regime and time trend characteristics that are different from those of the
global stock market
Based on the results obtained, we are inclined to conclude that the evolution of market linkages
among international real estate securities markets is influenced significant by both a time trend and a
volatility regime swift variable. Over the last two decades, both factors explain approximately up to 66% of
the changes in the international correlation matrix in our sample of nine developed real estate securities
markets. Moreover, real estate securities market could display significant volatility regime and time trend
17
characteristics that are different from those of the global stock market.
6.
CONCLUSION
In this paper we use weekly return data of nine developed real estate securities markets (the US,
France, Germany, the UK, Italy, Australia, Japan, Hong Kong and Singapore) from January 1990 to January
2012 to analyze the behavior of volatility through time, as well as the resulting state-dependent dynamic
linkages among the sample markets over the study period. The first part involves an analysis for the
existence of volatility regime switching by applying the SWARCH methodology developed by Hamilton
and Susmel (1994) to study for structural breaks in volatility of the sample markets over the full period. To
this end we develop a SWARCH (3, 2) model to allow for the existence of the three regimes, namely low,
medium and high volatility regimes. As a result of the SWARCH estimation, in the second part we assess
the dynamic linkages among the markets with state-dependent returns, state-dependent correlations,
state-dependent lead-lag relations, state-dependent variance spillover, and state-dependent covariance
analysis. To this end, we implement the Granger causality test, non-parametric Mann-Whitney test,
variance decomposition analysis and Box-M test to examine the behavior of the variables under the three
volatility regimes.
The overall results of the univariate three-state SWARCH models reveals the existence of more
than one volatility switching regime in the sample real estate securities markets during the last 20 year and
a significant increase in volatility during the crises periods for all the markets under examination. We
further find that the dynamic linkages among the markets are positively dependent on volatility regime.
There are four significant findings; (a) Market correlations and Granger lead-lag relations have intensified
in the high volatility period; (b) The aggregate variance spillover index as well the dependence on the
foreign market behavior increases for all markets as market volatility increases; (c) Consequently, the
international variance-covariance matrix is unstable regardless of the volatility regimes observed; and (d)
the evolution of market linkages in international real estate securities markets is influenced significant by
both a time trend and a volatility regime swift variable. Over the last two decades, both factors are able to
explain approximately up to 66% of the changes in the international real estate securities market correlation
matrix.
Our volatility regime and non-linear market linkage results are preliminary; but indicative. They
imply that risk-reduction via international diversification in real estate securities markets may only hold
18
true in low volatility period. Consequently portfolio managers need to implement state-dependent
optimal asset allocation in order to better advise their clients. Further studies using a bivariate
SWARCH model can help validate the various issues raised in this study. Moreover, a bivariate
SWGARCH methodology, similar to of Gray (1996), is useful to capture possible shifts in both ARCH and
GARCH terms, as well as to analyze between regime independence and correlation/covariance within a
time-varying setting in an international environment.
19
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21
Table 1
Descriptive statistics of weekly stock market returns for 9 real estate securities markets
AU
FR
GER
HK
ITA
JP
SG
UK
US
Mean (%)
0.017
0.090
-0.009
0.138
-0.065
-0.071
-0.003
-0.033
0.114
S.D (%)
2.043
2.128
2.848
3.893
3.394
3.768
3.983
2.609
2.423
Kurtosis
19.588
7.988
8.419
7.127
8.760
4.542
11.300
10.501
11.455
Skewness
-1.513
-0.683
-0.713
-0.388
-0.677
0.033
-0.505
-0.823
-1.012
Min (%)
-20.263
-12.957
-17.530
-26.565
-23.390
-17.861
-36.414
-20.293
-17.040
Max (%)
14.730
9.790
14.980
19.125
13.852
19.751
20.519
13.526
12.089
rho(1)
0.027
0.2031
0.2731
0.2351
0.248
0.1751
0.2001
0.226
0.2171
JB test
136221
12821
15041
8451
16781
1141
33501
28251
36211
ARCH(5)
131.51
147.31
221.11
62.91
105.51
43.21
93.71
217.71
353.91
Legend: Australia (AU), France (FR), Germany (GER). Hong Kong (HK), Japan (JP), Singapore (SG), United
Kingdom (UK), United States (US). Rho (1) is the first-order autocorrelation. *, - indicates statistical significance at
the 1% level
22
Table 2
Results for SWARCH (3, 2) estimation for securitized real estate markets
AU
FR
GER
HK
ITA
JP
SG
UK
US
0.0922
0.0982
0.011
0.1541
0.037
-0.005
0.124
0.071
0.1911
(0.039)
(0.041)
(0.042)
(0.000)
(0.063)
(0.089)
(0.078)
(0.055)
(0.043)
0.0961
0.3221
0.2601
0.2741
0.2431
0.1921
0.2381
0.2761
0.2231
(0.030)
(0.028)
(0.030)
(0.002)
(0.029)
(0.030)
(0.030)
(0.031)
(0.028)
0.028
0.1591
0.2472
-0.1001
0.1901
-0.0422
0.051
0.028
0.022
(0.048)
(0.057)
(0.109)
(0.000)
(0.070)
(0.019)
(0.045)
(0.075)
(0.048)
0.034
0.0372
0.083
-0.0291
0.053
0.011
0.0803
0.032
0.0972
(0.037)
(0.041)
(0.054)
(0.000)
(0.041)
(0.030)
(0.043)
(0.039)
(0.041)
0.027
0.023
0.068
0.1921
0.042
0.1212
0.1173
0.120
0.2641
(0.061)
(0.076)
(0.123)
(0.045)
(0.089)
(0.056)
(0.062)
(0.078)
(0.084)
1.3521
1.3391
0.6041
4.7211
1.9811
5.2601
3.2851
2.3381
0.9891
(0.142)
(0.101)
(0.114)
(0.158)
(0.331)
(0.664)
(0.401)
(0.202)
(0.136)
3.5631
4.4051
2.4921
14.1851
5.1981
12.2901
10.7751
9.1561
2.4161
(0.613)
(1.342)
(0.665)
(0.194)
(0.702)
(1.248)
(1.280)
(1.348)
(0.327)
22.9771
14.0081
11.4431
49.1001
26.4631
28.8161
41.8641
69.8111
13.2681
(4.648)
(3.195)
(2.775)
(7.295)
(4.953)
(5.003)
(8.607)
(24.154)
(2.373)
7
8
5
24
10
14
8
21
8
Transition matrix:
Australia:
France:
Germany:
Hong Kong:
Italy:
Japan:
Singapore:
UK:
23
US:
SWARCH (3, 2) model:
The underlying ARCH residual is multiplied by
if the process is in regime 2, and so on.
if the process is in regime 1, multiplied by
if
and
if
. The
constant in the ARCH equation is fixed at 1 as the normalization.
Standard errors are in brackets. 1, 2 and 3 indicate 1%, 5% and 10% levels of significance, respectively.
24
Table 3 Test of the null hypothesis that there is no switch in the volatility process
AU
FR
GER
HK
ITA
JP
SG
UK
US
16.161
5.022
55.501
34.991
23.911
34.901
31.561
30.791
19.411
18.821
9.861
24.071
37.091
29.261
18.751
15.871
7.571
24.521
21.901
14.771
35.861
65.941
35.411
33.301
22.321
9.251
31.651
Notes: the statistics reported are for Wald test which are asymptotically X 2(1). *, ** - indicates statistical significance
at the 1% and 5% level respectively
Table 4
Classification of three volatility regimes common to all real estate securities markets
Low volatility regime
Medium volatility regime
High volatility regime
02/07/1990 – 03/21/1990
03/13/1991 – 03/27/1991
05/08/1991 – 07/30/1997
01/24/2001 – 08/15/2001
12/03/2003 – 04/26/2006
08/04/2010 – 06/22/2011
04/25/1990 - 05/01/1991
02/03/1999 – 08/25/1999
11/03/1999 – 01/17/2001
08/22/2001 – 11/22/2001
03/12/2002 – 04/23/2003
07/09/2003 – 11/26/2003
06/28/2006 – 05/30/2007
07/25/2007
08/05/2009 – 04/28/2010
06/29/2011 - 07/06/2011
03/14/1998 – 12/02/1998
10/24/2007 – 07/29/2009
08/10/2011 – 11/09/2011
25
Table 5
Descriptive statistics (%) of market returns under three volatility regimes
AU
FR
GER
HK
ITA
JP
SG
UK
US
Low volatility state (538 week)
Mean
0.126
0.159
0.134
0.273
0.002
0.175
0.165
0.188
0.299
S.D.
1.209
1.525
1.908
3.042
2.241
3.111
2.634
1.876
1.418
Min
-3.780
-5.539
-11.316
-14.661
-6.758
-10.774
-10.901
-6.805
-8.280
Max
4.386
5.602
9.708
9.801
9.632
19.751
10.712
6.374
5.695
0.180
0.190
0.122
0.273
Medium volatility state: (324 weeks)
Mean
0.179
0.198
0.144
0.373
0.224
S.D.
1.551
1.741
2.743
3.466
2.970
3.664
3.660
2.158
2.092
Min
-5.778
-5.616
-11.635
-10.237
-10.009
-9.024
-11.183
-7.913
-7.004
Max
5.656
9.790
10.722
11.143
13.852
11.399
14.424
8.828
8.383
High volatility state: (147 weeks)
Mean
-0.778
-0.348
-0.556
-0.324
-1.062
-0.741
-0.485
-1.083
-0.729
S.D.
4.274
3.739
4.995
5.874
6.046
5.238
6.314
4.775
4.862
Min
-20.263
-12.957
-17.530
-11.460
-23.390
-17.861
-13.579
-20.293
-17.040
Max
14.730
8.208
14.980
19.125
12.319
11.821
20.519
13.526
12.089
Note: Returns are in local currency
26
Table 6
Non-parametric Mann-Whitney test on equal correlation between real estate securities
returns over three regimes (1, 2, 3)
Notes:
Regime 1 vs Regime 2
Regime 2 vs Regime 3
Regime 1 vs Regime 3
933
707
667
-4.2853
-7.2811
-6.8306
Rejected at 5%
Rejected at 5%
Rejected at 5%
sample 1 = (Au, Fr, Ger,…, US|1)
sample 2 = (Au, Fr, Ger,…, US|2)
sample 3 = (Au, Fr, Ger,…, US|3)
Mann-Whitney
-test:
with r1 the sum of ranks for the first population
The alternative for the test is the one-sided hypothesis that the location of population 2 is higher than that of
population 1. A rejection of the null hypothesis implies a rise in correlation.
27
Table 7
Correlation in market returns under three volatility regimes
Correlation
Low Volatility
Medium Volatility
High Volatility
AU-FR
AU-GER
AU-HK
AU-ITA
AU-JP
AU-SG
AU-UK
AU-US
FR-GER
FR-HK
FR-ITA
FR-JP
FR-SG
FR-UK
FR-US
GER-HK
GER-ITA
GER-JP
GER-SG
GER-UK
GER-US
HK-ITA
HK-JP
HK-SG
HK-UK
HK-US
ITA-JP
ITA-SG
ITA-UK
ITA-US
ITA-SG
ITA-UK
JP-US
SG-UK
SG-US
UK-US
Average
0.2105
0.0877
0.2006
0.1497
0.1329
0.2272
0.2452
0.2551
0.1926
0.1921
0.2624
0.1655
0.2079
0.3110
0.2092
0.0776
0.1721
0.0479
0.0796
0.1015
0.1025
0.1560
0.0652
0.4132
0.2278
0.1721
0.0295
0.2084
0.1805
0.1174
0.1283
0.1965
0.1314
0.2748
0.1566
0.2272
0.1754
0.2802
0.2251
0.2075
0.1517
0.2160
0.1756
0.3163
0.2927
0.3650
0.2173
0.3565
0.2135
0.2234
0.5196
0.3305
0.2593
0.2449
0.1556
0.2528
0.3537
0.3366
0.1788
0.3099
0.6004
0.3522
0.2222
0.1390
0.1088
0.4004
0.1825
0.3266
0.3089
0.2020
0.2915
0.3220
0.4025
0.2989
0.6459
0.5155
0.4431
0.4388
0.5282
0.4662
0.5455
0.5190
0.7778
0.5232
0.7257
0.5904
0.5092
0.7548
0.6693
0.5193
0.6396
0.6412
0.4831
0.6187
0.6594
0.4437
0.6760
0.7805
0.4446
0.4849
0.4592
0.4690
0.4980
0.5129
0.6311
0.5139
0.5214
0.4113
0.4444
0.6147
0.5589
28
Table 8
Granger causality test under three volatility regimes
Low volatility
Medium volatility
High volatility
US-UK
N
N
B (UK to US: 5%; US to UK: 1%)
US-FR
U (US to FR: 5%)
N
B (FR to US: 1%; US to FR: 5%)
US-GER
N
N
N
US-ITA
N
N
N
US-JP
N
N
U (US to JP: 1%)
US-AU
N
U (US to AU: 1%)
U (AU to US: 5%)
US-HK
N
N
N
US-SG
N
N
N
UK-FR
U (UK to FR: 5%)
N
N
UK-GER
N
N
B (GER to UK: 1%; UK to GER: 5%)
UK-ITA
N
N
N
FR-GER
N
N
B (GER to FR: 5%; FR to GER: 5%)
FR-ITA
N
N
N
GER-ITA
N
N
N
JP-AU
N
N
N
JP-HK
U (HK to JP: 5%)
N
N
JP-SG
N
N
N
AU-HK
N
U (HK to AU: 5%)
N
AU-SG
N
U (SG to AU: 5%)
N
HK-SG
N
U (HK to SG: 5%)
N
UK-JP
U (UK to JP: 5%)
N
B (JP to UK: 5%; UK to JP: 1%)
UK-AU
N
U (UK to AU: 5%)
U (AU to UK: 1%)
UK-HK
U (UK to HK: 5%)
N
N
UK-SG
U (UK to SG: 1%)
N
N
FR-AU
U (AU to FR: 5%)
U (FR to AU: 1%)
N
FR-JP
N
N
U (FR to JP: 5%)
FR-HK
N
N
N
FR-SG
U (SG to FR: 5%)
N
N
GER-AU
N
U (GER to AU: 5%)
U (AU to GER: 1%)
GER-JP
N
N
U (GER to JP: 5%)
GER-HK
N
N
N
GER-SG
N
N
N
ITA-JP
N
N
N
ITA-AU
N
N
N
ITA-HK
N
N
N
ITA-SG
N
N
N
Overall
8 U, 28 N
7 U, 29 N
5 B, 6 U, 25 N
Notes: Results from the bivariate Granger causality test under the three volatility regimes are summarized in three
categories: (a) N: no causality; (b) U: one-way causality and (c) B: two-way causality. The percentage figure included
under the U and B categories is the significant level of the test statistic (p<1% or p<5%)
29
Table 9
regimes
Decomposition of variance and total spillover index under three volatility
Panel A: Low volatility state
AU
FR
GER
HK
ITA
JP
SG
UK
US
From others
Au
78.2
2.3
0.7
3.3
1.4
0.9
4.1
4.7
4.4
22
Fr
5.4
65.0
2.8
2.2
5.5
2.4
3.1
8.3
5.3
35
Ge
0.8
3.0
89.7
0.6
2.4
0.2
0.7
0.7
1.8
10
HK
3.4
2.8
0.4
71.1
0.9
0.6
10.6
6.0
4.1
29
It
1.8
4.6
2.5
3.5
78.8
0.1
4.1
3.1
1.4
21
JP
2.6
1.5
0.3
0.4
0.5
85.6
0.9
5.1
3.1
14
SG
3.9
2.7
0.3
13.6
2.3
1.6
63.8
8.3
3.5
36
UK
4.8
5.8
1.2
2.6
1.9
1.7
3.6
73.4
4.9
27
US
6.8
2.4
0.5
1.5
0.8
0.7
1.2
3.6
82.4
18
29
25
9
28
16
8
28
40
29
212
108
90
98
99
95
94
92
113
111
23.5% (Total spillover index)
Contribution to others
Contribution including own
Panel B: Medium volatility state
AU
FR
GER
HK
ITA
JP
SG
UK
US
From others
Au
66.5
9.8
5.3
1.5
2.6
1.6
3.0
5.0
4.7
33
Fr
8.4
39.3
12.5
3.8
6.7
1.8
2.9
15.3
9.3
61
Ge
4.8
10.7
50.0
3.3
7.1
1.8
3.5
11.5
7.2
50
HK
3.2
2.6
3.3
55.8
0.8
3.9
21.6
6.6
2.4
44
It
4.4
7.6
7.2
2.8
60.5
0.3
1.0
11.7
4.6
40
JP
1.5
1.2
2.4
3.7
0.6
80.3
5.2
2.7
2.5
20
SG
5.4
1.2
1.6
22.4
0.3
6.1
54.5
5.0
3.6
46
UK
2.5
11.3
8.3
6.1
13.6
2.0
2.7
46.2
7.4
54
US
3.7
9.5
8.6
3.4
4.4
1.4
3.6
7.9
57.6
42
Contribution to others
34
54
49
47
36
19
43
66
42
389
Contribution including own
100
93
99
103
97
99
98
112
99
43.3%(Total spillover index)
Panel C: High volatility state
AU
FR
GER
Au
24.1
10.7
8.1
Fr
7.5
19.8
11.9
Ge
6.9
13.8
18.6
HK
5.8
9.2
It
5.5
JP
HK
ITA
JP
SG
UK
US
From others
9.3
6.8
10.7
8.0
10.6
11.7
76
10.5
11.9
8.0
8.2
10.9
11.3
80
10.7
10.3
11.6
9.1
8.7
10.4
81
6.3
27.0
7.4
12.2
18.0
7.2
6.9
73
12.9
10.0
11.1
24.8
9.3
12.7
6.1
7.6
75
9.8
8.4
8.3
16.0
7.5
22.4
11..9
7.2
8.5
78
SG
4.4
7.6
6.9
22.5
8.0
10.4
27.8
6.4
6.1
72
UK
8.9
14.7
10.7
10.0
7.8
8.7
8.3
19.3
11.6
81
US
10.3
13.0
10.9
10.3
7.6
10.7
8.2
10.4
18.7
81
Contribution to others
59
90
73
100
67
82
84
67
74
697
Contribution including own
83
110
92
127
92
104
112
87
93
77.5%(Total spillover index)
30
Table 10
Test of stability of covariance matrices over three volatility states using Box’s M
Box’s M
Significance
Cov (Au, Fr, Ger,…,US|1)=Cov (Au, Fr, Ger,…,US|2)
263.1418
0.0000
Cov (Au, Fr, Ger,…,US|1)=Cov (Au, Fr, Ger,…,US|3)
1565.2548
0.0000
Cov (Au, Fr, Ger,…,US|2)=Cov (Au, Fr, Ger,…,US|3)
651.4282
0.0000
Cov (Au, Fr, Ger,…,US|1)=Cov (Au, Fr, Ger,…,US|2)
=Cov (Au, Fr, Ger,…,US|3)
1717.9362
0.0000
Notes: The Box M test statistic is given by:
with
where
is the variance-covariance matrix for volatility state i.
is the number of samples, where the equality of the matrices is tested.
is the size of sample
minus 1.
31
Table 11
Regression results
Model A
CORR t = b0 + b1*(REGIME) t + b2*(TIME) t + b3*(GSVOL) t + error t
“CORR” describe the average correlation over all nine real estate securities markets and is created by rolling a
window of 52 weekly observations in one-step increment over the full study period.
“REGIME” is the regime volatility variable which takes the values 0, 1, 2 ,3 for the undetermined regime , low
volatility regime, medium volatility regime and high volatility regime, respectively, as defined by the SWARCH (3, 2)
model.
“TIME” is the time trend variable as defined by t=1, …..1150.
“GSVOL” is the global stock market return volatility variable, and is derived by squaring the MSCI weekly global
stock return over the same period.
Dependent
variable
0.180**
CORR
0.076**
0.026
0.028
0.039
**
0.036
**
0.153
0.0003
**
0.0003
**
0.611
16.944
** *
**
0.617
#
Notes: the residuals are corrected using the Newey-West (1987) method. , and indicate 1%, 5% and 10% levels of significance.
Model B
CORR t = b0 +b1*S2 + b2*S3 +b3*Su+b4*(TIME) t + b5*(GSVOL) t + error t (Model B)
Where volatility regime is represented by S1, S2, S3and Su (periods of medium, high and undetermined regimes)
as defined by the SWARCH model, S1 (low volatility regime) is treated as the base regime (b 0) in order to minimize the
influence of multicollinearity,
Dependent
variable
Avcorr
0.202**
0.114**
0.294**
0.135**
0.066
**
#
0.164
**
0.048
*
0.065
**
0.159
**
0.047
*
0.037
0.035
** *
#
0.345
0.0003
**
0.0003
**
0.657
7.409
*
0.657
Notes: the residuals are corrected using the Newey-West (1987) methods , and indicate 1%, 5% and 10% levels of significance.
32
Figure 1
Smoothed probability graphs from AR (1) – SWARCH (3, 2)
France
Germany
Hong Kong
Italy
Japan
33
Australia
UK
Singapore
US
34
Figure 2
Average correlations between the nine real estate securities markets under three volatility
states
Notes:
The average correlation between the nine market returns is calculated for each of the sub-periods. Low state, Medium
state and High state describe the correlation during periods that are attributed to volatility regime 1, 2 and 3 (low,
medium and high), respectively For a same date, the prevailing volatility regime of the period is determined if five of
the nine markets are simultaneously in the same volatility state (regime 1, regime 2 or regime 3). Observations that do
not meet this criterion are excluded in this analysis..
Figure 3
The average weekly correlation between the nine real estate securities
markets
Notes: The correlation coefficient between the 9 markets is calculated on a rolling basis using window size= 1 year
and step= 1 week.
35