CORRELATION DYNAMICS IN INTERNATIONAL REAL
ESTATE SECURITY MARKETS
Introduction
There is extensive evidence that diversifying across national markets that are subject to
the low correlation of returns between them would enable investors to reduce their total portfolio
risk, without sacrificing return. In addition, the correlations that exist among the international stock
markets are themselves evolving through time (Longin and Solnik, 1995). This paper thus relates
the evolution of the structural behavior of the international correlation but within the context of the
real estate security markets, from the broader field of asset price microstructure.
Specifically, this paper focuses on the objective to investigate the correlation trends and
their changing dynamics for five major national real estate security markets (US, UK, Japan,
Hong Kong and Singapore), and three regional real estate security markets (Americas, Europe
and Asia). The five countries have well-developed mature real estate investment markets that
have public listed companies or funds owning property, which enable them to offer investors an
alternative indirect approach to investing in real estate. Given the significance of the five national
real estate security markets in the respective continents, it is therefore imperative to attain an indepth understanding the evolution of the structural behavior pertaining to the correlations of such
markets with each other and with the US market for portfolio decisions and asset allocation in
international investing. The approach we adopt in this paper is to explicitly model the dynamic
conditional multivariate distribution of the international real estate security returns, and to
examine the evidence of the time-varying conditional correlation over a long time period between
1984 and 2006. This is because the trends in a long period can be detected more easily than for
a period of only a few years. Compared with previous studies that have investigated the
unconditional correlation imputed over different sub-periods, we estimate an explicit and unique
model for the conditional correlation under a ‘Dynamic Conditional Correlation (DCC)’ model.
In addition, this paper adds to the existing literature, pertaining to asset price
microstructure and even beyond the price discovery concept, in at least two other aspects. First,
we examine the research question of whether the correlation movements of the real estate
security markets can be explained by movements in the stock market correlations relating to the
real estate security markets. Because the real estate security market is an imperative part of the
wider stock market (i.e. the public equity market), the real estate security markets can in turn
become increasingly correlated especially when the wider stock market returns themselves move
together. Hence, the real estate security market and the general stock market correlations may
well be linked. For example, the UK real estate security market may become increasingly
correlated with the US real estate security market at the same time that the UK and the US stock
markets become increasingly synchronized. Secondly, the issue of the evolution of the real estate
security market correlations over time is investigated with regard to the influences of the stock
market correlations and the market volatilities. In this second issue, we examine the research
question of whether the real estate security market correlation increases in periods of high market
volatility and in those periods involving a stock market crash and the recent 1997 Asian economic
crisis. The positive link between the real estate security market correlations, the stock market
correlations and their market volatilities implies that international diversification would be
significantly discouraged owing primarily to the diminishing benefits of portfolio diversification.
Similar to the unconditional correlation estimates of the real estate security market
returns, the corresponding conditional estimates indicate significantly lower correlations between
all the national and regional real estate security market returns than those between the stock
market returns themselves. There are significant variations and structural changes in the
correlation structure that have occurred within the sample period between 1984 and 2006. There
is a slight increase of the international correlation between the five major real estate security
markets over the past 22 years. However, some sample markets have not become increasingly
correlated among themselves.
We also find that there is a strong and positive connection
between the real estate security market correlation and the conditional volatilities. Finally, the real
estate security and the stock market correlations are linked.
Our study is organized as follows: a selective literature review is provided in the next
section, to be followed by a discussion of the required research sample and methodology. A
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discussion of the associated results and implications is then undertaken. The last section of this
paper concludes the study together with a summary of the main results.
Related Literature
Similar to common stocks, the benefits of the international diversification of real estate
stems from the low correlation between the national real estate markets. Eichholtz (1996a) has
favorably reported even significantly lower correlations between the national real estate returns
than those between the common stock or bond returns, as real estate markets are more often
affected by local factors. Nevertheless, there is evidence that real estate markets are becoming
more open and interdependent owing to rapidly increasing international capital flows, involving
global funds such as the Asian real estate investment trusts (REITs).
Longin and Solnik (1995) and Solnik (1996) reiterate the evidence that the international
stock market is evolving through time, and a pertinent concern is whether the international real
estate security market correlations have increased historically as market participants become
aware that a general increase in the market correlations can erode the benefit of international risk
diversification for real estate funds in the long run. The general level of international real estate
security market correlation can increase when global factors dominate domestic ones, and can
affect all financial markets (Longin and Solnik, 1995). Since the real estate security market is an
imperative part of the wider stock market, the increase in correlation among the national stock
markets and the national real estate security markets may well be synchronized. Solnik et al,
(1996) have found that the movements in the international stock market correlations do not follow
closely the movements in the international bond market correlations or vice versa. However,
virtually no such study has been conducted on the co-movements between the international real
estate security and the stock market correlations.
The stochastic properties of the stock market correlation measures have been
investigated by Kaplanis (1988), who fits time-series models to the rolling correlation measures of
the public market equities in 15 national markets. Her tests reject the hypothesis that the
correlation between these public-equity markets is constant. Longin and Solnik (1995) estimate a
multivariate GARCH model and test the null hypothesis that the correlation between equity
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markets is constant. They reject the model and conclude that the international stock market
correlation is not constant. Their conditional correlation results further indicate an increase of the
international correlation between stock markets over the past thirty years, and it is this
international correlation that rises in periods of high market volatility. Solnik et al (1996) also show
that the international stock market correlations vary over time and across countries in their study
of the correlations of six foreign stock markets with the US stock market. They find that although
the correlation of the individual foreign stock markets with the US stock market has increased
slightly over the past 37 years, it has not increased over the past 10 years. Finally, their results
also indicate that the international correlation increases in periods of high market volatility.
Consequently, increased international stock market correlations would result in diminishing
portfolio diversification benefits in an investment environment, when international portfolio risk
reduction and the diversification benefits are most needed by domestic investors. Yang (2005)
examines the international stock market correlations between Japan and four other Asian stock
markets, deploying Engle’s (2002) DCC analysis in the period between 1990 and 2003. Yang’s
results support the findings of earlier stock market studies that it is necessary to consider the
market condition when conducting international asset allocation.
While there are extensive studies on the dynamics of the international stock market
conditional correlations and portfolio diversification, far less attention has been devoted to such
studies in the real estate literature pertaining to the broader field of asset price microstructure,
inclusive of price discovery. This is mainly due to the lack of reliable and longer time-series for
real estate return data. In addition, many real estate studies focus on the unconditional correlation
measure. In a key study by Echholtz (1996a), it is found that significant lower correlations exist
between the national real estate security returns than those between the common stock or bond
returns. Some evidence of the instability of the international correlation and the covariance
structure of the property equity returns is reported by Eichholtz (1996b). As such and in deploying
asset allocation models to generate the optimal international real estate portfolio allocation,
Elchholtz (1996b) suggests the possibilities of utilizing time-varying covariances to adjust the
conventional portfolio models. Lu and Mei (1999) and Hu and Mei (1999) find some diversification
4
benefits through investing in emerging market property indexes but there is an unfavorable
asymmetry in the unconditional correlations between these indexes and the US index, i.e. the
unconditional correlations are higher during highly volatile periods. Gordon and Canter (1999) find
that the unconditional correlation coefficients, between the real estate stock indexes and the
wider public equity indexes in his sample of 424 securities from 14 countries, have not been
stable over time and that there is some evidence towards the integration or segmentation of
public-listed real estate with the broader public equity markets. Utilizing the Australian Property
Trust (LPT) data in the period between 1980 and 2000, Newell and Acheampong (2001) find that
the unconditional correlations between the LPTs and the common-stock shares vary considerably,
with an increased correlation between LPTs and the shares that is linked to the increased
volatility of the LPT and stock markets. Finally, Liow and Sim (2006) find that there is some
evidence of instability in the unconditional correlations between the US and the Asian real estate
security markets in the period between 1990 and 2003.
Data
We extract real estate security price indices from the Global Property Research (GPR)
database for five national markets, namely, the USA, the UK, Japan (JP), Hong Kong (HK) and
Singapore (SG); and for three regional markets, namely, America (AME), Europe (EUR) and the
Asia/Far East (ASI). The USA market, being the world’s largest, most mature and most
transparent securitized real estate market is an apparent choice. The UK is a major world
economy and is Europe’s largest property market. Japan is also a major world economy and has
a long history of public listed real estate. The remaining two Asian markets of Hong Kong and
Singapore have each enjoyed remarkably rapid economic growth in the past decade and both
have established good track records of securitized real estate investment and development
companies in their capital markets. As of 1st April 2006, the GPR General database includes 33
country indices, five regional indices and two world indices. In order for a country to be eligible to
be included in the GPR index, it must have listed property investment companies of sufficient size.
A firm must have had a market capitalization of more than USD 50 million as well as a minimum
of 75% of all revenues must come from equity real estate investment. Our sample includes
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monthly data from 1983:12 to 2006:03. Monthly real estate security returns (R) are obtained by
taking the natural logarithmic difference of the index times 100. The respective stock market
indices are compiled by the Morgan Stanley Capital Index (MSCI) and obtained from DataStream
on-line information system. The MSCI stock market indices are widely used by international fund
managers for asset allocation decisions and performance measurement as well as by
researchers for academic studies. Finally, all returns are expressed in local currency (currency
hedged) returns. This avoids the incorporation of currency movements into the analysis, and for
the concerned investor, it should make the findings more generalizable to all investors under the
assumption that they have the perfect hedging ability. Table 1 provides the mean and standard
deviation for all the data series. The mean real estate security returns per month vary from 0.72
percent (Europe) to 2.05 percent (Hong Kong). The monthly standard deviations range from 2.45
percent for Europe to 11.31 percent for Singapore.
(Table 1 here)
Table 2 reports the unconditional correlations of the national and the regional real estate
security market returns estimated in the period from 1984 to 2006. Similar numbers for the stock
markets are produced. The Bonferroni adjusted p-values are used to assess the statistical
significance of the correlation coefficients. For the real estate security markets, the coefficients
are significantly positive at the least at the five percent level (except for JP-SG and JP-HK),
indicating that the real estate security returns move in the same direction in the same month. The
highest coefficient is 0.590 (HK and SG) and the lowest is 0.094 (JP and HK) while the average
coefficient is around 0.291. With one exception (AME and EUR), each real estate security market
correlation is lower than its corresponding stock market correlation. The real estate security
market correlations vary from 0.094 to 0.590 while the stock market correlations vary between
0.295 and 0.783. These findings are in agreement with Eichholtz (1996a) who finds that the
national real estate return correlations are significantly lower than the national common-stock
return correlations. The fairly low to moderate levels of the international correlations among the
real estate securities suggest that national factors still strongly affect the local real estate security
prices.
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(Table 2 here)
The average correlations between (a) all the five real estate security markets; (b)
between the US and the other four markets and (c) between three Asian markets are plotted in
Figure 1. The correlations are estimated over a sliding window of 36 months (three years).
Although the correlations do not follow the same pattern for all the three averages, they fluctuate
over time. This provides a good visual support of the instability of the international real estate
securities across different national markets and regions.
(Figure 1 here)
Finally, we estimate the unconditional correlation matrix for the national and the regional
real estate security markets over five adjacent periods of 53 months, and test for the equality of
the correlation matrices over adjacent sub-periods as well as over the non-adjacent sub-periods
by the usual t-test, to see whether the difference between the averages is significant.1 Table 3
reports the results. As the numbers indicate, the null hypothesis of a constant correlation matrix is
rejected at the five percent confidence level in 5 out of the 10 national market comparisons and in
8 out of the 10 regional market comparisons. These results are broadly similar to the findings by
Eicholtz (1996b) that the international property share correlations are stable between some timeperiods, and unstable between others.
(Table 3 here)
Methodology
The research design adopts a two-step approach. The fist step undertakes the dynamic
conditional correlation (DCC) methodology proposed by Engle (2002) in order to model the
fluctuations of the correlation and volatility between the international real estate security markets
and between the stock markets over time. In the second step, the estimates of the conditional
correlation and volatility are fitted to a multiple regression model in order to investigate the
evolution of the real estate security market correlations.
Modeling the DCC with a GJR DCC MGARCH Model
GARCH models are deployed to explore the stochastic behavior of the financial time
series and, in particular, to explain the behavior of the volatility over time (see Bollerslev et al,
7
1992 for a literature review). The constant conditional correlation (CCC) multivariate GARCH
model, which was proposed by Bollerslev (1990) as an alternative to the computationally
intensive VECH model, is the most widely used MGARCH model in the last decade. Setting all
conditional correlations to be constant, the CCC MGARCH model allows for the conditional
variance equation to take any form of the univariate GARCH process. However, the assumption
that the conditional correlations are constant may appear unrealistic in many empirical
applications. Tse and Tsui (2002) and Engle (2002) generalize the CCC model by making the
conditional correlation matrix time-dependent. While Tse and Tsui (2002) propose a new
MGARCH model with time-varying correlations and a VECH representation based on the
conditional variances and conditional correlations, Engle (2002) proposes a dynamic conditional
correlation (DCC) model that can be estimated with the univariate or two-step methods based on
the likelihood function. Engle (2002) also compares the DCC model with other multivariate
GARCH models and concludes that the DCC models are competitive with the multivariate
specifications, and are superior to moving average methods. In addition, since the conditional
variance is an asymmetric function of past innovations, which increases proportionately more
during market declines, the so-called leverage (asymmetric) effects thus becomes another
important issue in the application of the GARCH family models. Asymmetric GARCH models
include Nelson’s (1991) exponential GARCH model, Glosten et al’s (1993) GJR GARCH model
and Zakoian’s (1994) Threshold GARCH model. In this paper, we resort to the DCC model of
Engle (2002) and the GJR model specification (i.e. the GJR- MGARCH model) in order to
estimate the time-varying conditional correlations in the international real estate security and the
stock markets
Let
Ri ,t be the percentage return at time t for market i , Ω t −1 the all information
available at time t − 1 ,
μ i,t
and hii ,t the conditional mean and the conditional variance
respectively, hij ,t the conditional covariance between the market
i and market j , ε i,t the
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innovation at time t (i.e.,
η i ,t = ε i,t / hii,t
ε i ,t = Ri ,t − μ i ,t
), and
η i,t
the standardized innovation (i.e.,
). The AR (1) model for returns can then be represented as follows:
Ri ,t = β i ,0 + β i ,1 Ri ,t −1 + ε i ,t , ε i ,t Ω t −1 ~ N (0, hii ,t )
(1)
where the conditional mean return for each market is a function of its past own returns,
and the lead/lag relationships are captured by coefficients
β i,1 .
measures the direct effect that a change in return on the market
β i,1
A significant
coefficient
i at time t − 1 would have on
the same market at time t .
The conditional variances follow a univariate GJR-GARCH (1, 1) specification:
(2)
where
α i,1
measures the ARCH effect. The persistence of volatility (i.e. GARCH effect)
is measured by γ i . The unconditional variance is finite if
measures the leverage (asymmetric) effect; I i ,t
and otherwise I i ,t
γ i < 1 . δi
is the coefficient that
= 1 if the innovation in last period is negative
= 0.
The conditional covariance terms are assumed to follow the DCC (1, 1) specification:
hij ,t = ρ ij ,t hii ,t h jj ,t
ρ ij ,t =
(3)
qij ,t
(4)
qii ,t q jj ,t
qij ,t = (1 − a − b) ρ ij + aqij ,t −1 + bη i ,t −1η j ,t −1
where
Equation (1);
(5)
qij ,t is the conditional covariance between the standardized residuals from
ρ ij
is the unconditional correlation between residuals
ε i,t .
The
qij ,t expression
will be mean-reverting when a + b < 1 . This specification reduces the number of parameters to be
estimated and makes the estimation and time-varying correlation more tractable.
Finally, Engle (2002) shows that the log-likelihood of the estimators may be written as:
9
L(θ ) = −
[(
) (
1 T
∑ n log(2π ) + 2 log Dt + ε ′Dt−1 Dt−1ε + log Vt + η t′Vt−1η t − η t′η t
2 t =1
where n is the number of equations;
)] (6)
T is the number of observations; θ is the vector of
parameters to be estimated;
Dt is the diagonal matrix of time varying standard deviations
obtained from Equation (4) and
Vt is the time varying correlation matrix.
Evolution of market correlations and volatility: real estate security and stock markets
To test the relationship between the real estate security and the stock markets with
regard to the evolution of the market correlations and volatilities, we regress the real estate
security market correlation between two countries on the two real estate security market
volatilities, the stock market correlation and the two stock market volatilities. The five independent
variables are moderately to highly correlated, and so disentangling their effects is difficult. For
each country pair, we first conduct the Principal Component Analysis (PCA) to derive a set of
factors that are totally uncorrelated, with the first (dominant) factor accounting for the maximum
variation in the five data series. The most simplistic approach is to retain all components whose
Eigen values exceed unity. These Eigen values measure the contributions of the corresponding
local factors to explain the cross-sectional variation in the five original variables. Once the initial
choice of the factor loading is made, we then interpret the co-movement of the original variables.
The co-movement of the variables would be based on the high factor loadings.
With the dominant factors extracted (maximum five), a regression model is adopted to
analyze the evolution of the real estate security market correlations over time. The multiple
regression model is expressed below:
ρˆ ij = δ 0 + δ 1 (Trend ) + 2 (crash) t + δ 3 (crisis) t + δ 4 F1 + δ 5 F2 + δ 6 F3 + δ 7 F4 + δ 8 F5 + ε t
(7)
Where ρ̂ ij is the conditional correlations for the real estate security market pair (i and j)
predicted from the DCC framework in step 1; F1…..F5 are the possible dominant factors (subject
to the Eigen value criterion) that are derived from PCA on stock market correlation, two real
estate security market volatilities and two stock market volatilities predicted from the DCC
10
framework in step 1; Trend,
Crasht and Crisis t are dummy variables of time trend, stock market
crash period and Asian Financial Crisis period;
estimated and
δ0
to δˆ8 are regression parameters to be
ε t is the model residual.2
Empirical Results
DCC results
Table 4 presents the estimates of the bivariate AR (1) - GJR - DCC (1, 1) models for the
national (Panel A) and the regional (Panel B) real estate security and stock markets. The last two
rows of the table show the estimates of the two DCC (1, 1) parameters. The other rows are the
parameter estimates of the univariate GJR- GARCH (1, 1) models for the individual market
returns. As shown, most of the estimated ARCH, GARCH and the asymmetry parameters are
statistically significant, which implies that the GJR-GARCH (1,1) adequately describes the
monthly return behavior and is able to capture the temporal dependence and the asymmetry of
the stock and the real estate security returns for the 10 national and the six regional markets
under examination.
(Table 4 here)
The estimates of the DCC parameters (a, b) are mostly statistically significant, which
make it reasonably clear that the assumption of the constant conditional correlation is not
supported empirically. Table 5 contains the descriptive statistics for the DCC estimates for all the
country and the regional pairs. The DCCs are in the (0.052, 0.565) range and in the (0.290, 0.792)
range for the real estate security and the stock markets respectively, signifying low to moderately
high interdependence. Similar to the unconditional correlation estimates, the conditional
estimates indicate significantly lower correlations between the national and the regional real
estate security market returns than those between the stock market returns themselves.3 With
few exceptions, the statistics for skewness and kurtosis suggest that many of the series are
significantly skewed and leptokurtic relative to the normal distribution. Finally, the last column of
the table {corr (RE/S)} shows the degree of co-movements between the real estate security
11
market and the stock market correlations. The range is between 0.0027 (AME-EUR) and 0.761
(US-HK) suggesting that movements in the international real estate and the stock market
correlations may well be synchronized. This issue is investigated further below.
(Table 5 here)
Figure 2 shows the average real estate security and the stock market DCCs for four
country-type combinations (all countries, three Asian countries, three developed countries and
the US-other countries). It is clear from the diagrams that significant variations and structural
changes in the correlation structure have occurred within the sample period. Furthermore, the
average correlations do not follow the same patterns for all countries. In addition, the graphs in
Figure 2 show a general, small long-term increase in the correlation for two of the real estate
security market pairs. The largest slope in the period from 1984 to 2006 shows a correlation
increase for all five national real estate security markets. The increase is about 20.54 percent
over the whole period (monthly: 0.07 percent) but it has remained relatively stable or has
decreased slightly during the past years. Similarly, the three Asian real estate security markets
(i.e. JP, HK and SG) also experience an increase in correlation of about 11.27 percent for the
whole period (monthly: 0.04 percent). The increasing conditional correlation (although not
significant) means that the international real estate security markets, in particular, the three Asian
real estate security markets were becoming more closely integrated. This observed trend implies
that there are diminishing benefits from international diversification. Nevertheless, the average
correlations of the three developed real estate security markets (US, UK and JP) and those
between the US and the other four real estate security markets, show a smaller decrease in
correlation of about 1.34 percent for the whole period (monthly: a negative 0.005 percent).
Results for the stock markets are different in that all the average correlations show a smaller
increase in each correlation, ranging between approximately 1.34 percent and 8.34 percent within
the sample period.4
(Figure 2 here)
The link between correlation and volatility
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The conditional volatilities of the paired regional real estate security markets and their
dynamic conditional correlations are plotted in Figures 3(a)–(c). With some exceptions, the
graphs for the three regional pairs show that both the market volatilities tend to move together
and that the correlation tends to move together with the market volatilities.
(Figures 3a to c here)
An econometric estimation of the link between the conditional correlation and the two
market volatilities (represented by their standard deviations) is conducted for all 13 pairs of the
real estate security markets.5 All the estimation results reported in Table 6 were adjusted for
autocorrelation and the White heteroskedasticity-consistent standard errors. The adjusted R2
values range from 26.5% to 90.7%. With minor exceptions, all the positive volatility coefficients
are statistically significant. In such cases, the correlation increases when one market or both
become more volatile, and so the covariance increases more than the market volatilities. For the
US market in conjunction with the other four foreign markets, the major influence is the US
volatility although all the four foreign markets’ volatility coefficients are statistically significant and
yet of smaller magnitude. This is also the case for HK-SG and the two regional market pairs
(AME-ASI and AME-EUR) where both positive volatilities contribute to a larger increase in the
covariance. The investment implication is clear: since global or regime shocks affect the markets’
volatilities and their correlations at the same time, any possible risk diversification benefits of
international real estate investing may well be eliminated owing primarily to the strong and
positive connection between the real estate security market correlation and the conditional
volatilities.
(Table 6 here)
The link between the real estate security and the stock markets
Since the real estate security market is an imperative part of the wider stock market, an
interesting question is whether the movements in the correlation among the national and the
regional real estate security markets and in the correlation among the national and the regional
stock markets are synchronized. For example, the Hong Kong real estate security market may
become increasingly correlated with the Singapore real estate security market at the same time
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that the Hong Kong and Singapore stock markets become increasingly correlated. Hence, we
may expect a positive relationship between the real estate security correlation and the stock
market correlation. The last column of Table 5 provides the supporting evidence.
As the correlation estimates indicate, the co-movements between the international real
estate security and the international stock market correlations are moderately to reasonably high
in some cases, ranging between 0.257 (US-UK) and 0.795 (HK-SG). This means that
approximately between 6.6% and 63.2% of the variations in the international real estate security
market correlations can be accounted by the changes in the international stock market
correlations or vice-versa. On a regional basis, only up to 5.2% of the changes in the international
real estate security market correlations can be explained by the changes in the international stock
market correlations or vice-versa. Although this finding is not new to international investors that
the movements in the international real estate security market correlation follow closely the
movements in the international stock market correlations or vice versa, our contribution is to be
able to estimate the diversification effects that are attributed to the real estate security market comovements.
To test the relationship between the real estate security market correlations, the stock
market correlations and the market volatilities as given in Equation 7, Tables 7 reports the final
multiple regression (MRR) results that include the dominant factor (s) derived from the PCA on
five independent variables (i.e., stock market correlation, two stock market volatilities and two real
estate security market volatilities) that are highly correlated. Table 8 reports the significant factor
loadings (>0.3) that are related to the dominant component (s). Except for one case (AME-ASI)
that has three dominant factors, the remaining 12 market pairs derive two dominant factors that
are linear combinations of the five variables included in the PCA.6
(Tables 7 and 8 here)
There are three key observations. First, for the US real estate security market with four
foreign markets, only one dominant factor (F1) is statistically significant in Equation 7. The factor
loadings results (Table 8) indicate that this factor (F1) is a linear combination of the stock market
correlation, two stock market volatilities and at least one real estate market volatility coefficient.
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Hence, movements in the US market volatilities spread to the four foreign markets and that the
international real estate security market correlations increase during periods of high market
volatilities. Secondly, both dominant factors (F1 and F2) are statistically significant for four market
pairs (UK-HK, UK-SG, HK-SG and JP-HK). With the exception for JP-HK whose volatility
coefficients are of mixed signs (Table 8), the results indicate that the real estate security market
correlations are significantly positively related to the stock market correlation, the two stock
market volatilities and the two real estate security market volatilities. Again, this strong and
positive connection between the conditional correlations and the volatilities is discouraging for
portfolio diversification. Finally, for the three regional real estate security markets, it appears that
there is a strong and positive connection between both the real estate market conditional
volatilities and the correlation. However, the regional real estate security and the stock markets
are not synchronized.
The constant terms ( δ 0 ), denoting the unconditional mean of correlations, are positive
and statistically significant at the one percent level (except for one case whose coefficient is
insignificantly positive). This observation reflects that innovations in one real estate security
market are positively correlated with the other real estate security markets. The correlations are
respectively, between 0.0659 (JP-HK) and 0.4689 (HK-SG) and between 0.3582 (AME-ASI) and
0.5262 (AME-EUR), for the national and the regional real estate security markets. The dummy
variables for the long-term trends in the correlations ( δ 1 ) are mixed. They are slightly positive for
five cases (US-UK, US-HK, JP-SG, AME-EUR, AME-AIS) and at least significantly positive at the
ten percent level for two cases (HK-SG and EUR-ASI), while being slightly negative for five
cases (US-JP, UK-JP, UK-HK, UK-SG and JP-HK) and being significantly negative at the five
percent level for one case (US-SG). The largest slope is 0.00069 for HK-SG. In other words, the
average monthly increase is 0.069%, which means that the HK-SG correlation goes up by an
average of 0.83% a year and a total increase of 20.2% for the whole period. The increasing
conditional correlations imply that there are diminishing benefits from international diversification
that includes these two national real estate security markets. However, the smallest slope is 0.00017 for US-SG that translates into a total decrease in correlation of 4.6% for the whole period.
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The overall conclusion is that the trend toward increased correlation is not similar for all the real
estate security markets, with the average monthly trend coefficients estimated at 0.0044%
(national) and 0.0071% (regional) respectively. These translate into a total increase of only 1.19%
and 1.89% for the whole period for the five national and the three regional real estate security
markets respectively. 7 Thus, despite an increasing interdependence of the international real
estate market (Eicholtz, 1996b); the global average correlation in the international real estate
security markets has remained fairly constant over the past 20 years. The Asian real estate
security markets are on the whole still weakly correlated both with themselves and with the
developed markets. The diversification benefits to be obtained from investing in international real
estate security markets do still exist.
The stock market crash dummies ( δ 2 ) are negative for seven cases and positive for six
cases. Except for one case, the other 12 coefficients are statistically insignificant. From the
investors’ perspective, it implies that none of the countries is a good place to diversify portfolio
risk during the 1987 October stock market crash period although those country pairs with
negative coefficients were slightly safer for the international real estate security investment funds.
The Asian financial crisis dummies ( δ 3 ) are negative and significant for US-SG and
EUR-ASI. For example, the slope is -0.0377 for EUR-ASI, which means that the correlation is on
average lower than the normal level. One possible explanation for the significant negative
coefficient is that the damage due to the crisis was most serious for the Asian countries (ASI); the
European economies (EUR) were relatively safer for portfolio diversification. Finding that the two
regional real estate security markets have become less synchronized, when more contagion did
exist during the Asian economic crisis period, would therefore be good news for the market
participants. Other market pairs such as the US-JP, US-HK, UK-JP, UK-HK, UK-SG and AMEASI also become slightly less correlated during the Asian financial crisis period but the negative
crisis coefficients are all statistically insignificant. On the contrary, the crisis dummies are
(insignificantly) positive for three Asian-pairs (JP-HK, JP-SG and HK-SG) and the markets have
become slightly more synchronized when more contagion did exist during the economic crisis
period. These results would definitely not constitute good news for the market participants.
16
Conclusions
Within the international context, this paper investigates the time-varying correlation
dynamics of the real estate security and the stock markets. Such an investigation is significantly
meaningful to investment portfolio managers as the international correlations appear to fluctuate
widely over time, and to increase over a longer term period particularly in periods of high market
volatility. Consequently, the benefits of portfolio diversification from international investing are
likely to diminish
Subject to the usual empirical limitations that may impact on the results obtained, the
conclusions from this paper can be summarized in the following manner. An explicit and rigorous
modeling of the conditional correlation uniquely indicates that significant variations and structural
changes, in the correlation structure of the international real estate security and the stock markets,
have occurred within the sample period between 1984 and 2006. We find that there is a slight
increase of the international correlation between the five major real estate security markets over
the past 22 years. Nevertheless, some sample markets have not become increasingly correlated
among themselves. We also find that there is a strong and positive connection between the real
estate security market correlation and the conditional volatilities. Furthermore, the real estate
security and the stock market correlations are linked while movements in the international real
estate security market correlations follow closely the movements in the international stock market
correlations or vice versa in some cases. Again, this result may discourage portfolio
diversification. Finally, although the international real estate security market correlations have
generally increased slightly over the long term, they are still significantly lower than those of the
stock markets. The diversification benefit to be obtained from investing in the international real
estate security markets still remains.
Based on the DCC methodology deployed in this paper, future research can focus on the
fundamental determinants of the international correlation across real estate security markets. As
real estate securities form a hybrid of direct properties and stocks, their international correlation is
likely to be affected by the direct real estate market structure and the dynamics of each country
apart from the correlations of the countries’ stock market cycles and the business cycles.
17
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Table 1
Descriptive Statistics of monthly returns: 1/1984 to 3/2006
Mean
USA
UK
Japan
Hong Kong
Singapore
America
Europe
Asia
Table 2
Real estate security market
Stock market
Maximum
Minimum
Std. Dev.
Mean
Maximum
Minimum
Std. Dev.
1.15%
12.33%
-18.91%
4.26%
0.99%
12.47%
-23.85%
4.39%
1.14%
17.57%
-27.66%
5.47%
0.97%
13.72%
-30.02%
4.75%
1.06%
62.41%
-24.54%
9.36%
0.42%
18.27%
-21.80%
5.74%
2.05%
59.79%
-46.99%
11.15%
1.32%
28.66%
-57.06%
8.42%
1.49%
62.43%
-53.70%
11.31%
0.44%
21.28%
-54.23%
7.34%
1.00%
13.43%
-19.79%
4.23%
0.97%
12.36%
-24.04%
4.35%
0.72%
6.94%
-14.91%
2.45%
1.00%
11.23%
-26.61%
4.71%
1.17%
40.69%
-26.17%
7.43%
0.45%
17.20%
-21.42%
5.49%
Unconditional correlations matrices of national and regional real estate
security and stock market returns: 1/1984 to 3/2006
Panel A: national markets
HK
JP
SG
UK
USA
HK
1.0000
0.0494
(2.106)
0.5904
(0.000)
0.3280
(0.000)
0.2908
(0.000)
Real estate security markets
JP
SG
UK
USA
1.0000
0.1041
(0.448)
0.1598
(0.045)
0.1829
(0.014)
1.0000
0.3614
(0.000)
0.4077
(0.000)
1.0000
0.4307
(0.000)
1.0000
HK
1.0000
0.2945
(0.000)
0.6817
(0.000)
0.5763
(0.000)
0.5372
(0.000)
General stock markets
JP
SG
UK
USA
1.0000
0.3421
(0.000)
0.3978
(0.000)
0.3875
(0.000)
1.0000
0.5802
(0.000)
0.5738
(0.000)
1.0000
0.7511
(0.000)
1.0000
Panel B: regional markets
AME
ASI
EUR
Real estate security markets
AME
ASI
EUR
1.0000
0.5314
1.0000
(0.000)
0.3682
0.3824
1.0000
(0.000)
(0.000)
General stock markets
AME
ASI
EUR
1.0000
0.4409 1.0000
(0.000)
0.7828 0.5204 1.0000
(0.000)
(0.000)
Notes:
* The three regional markets are America (AME), Asia (ASI) and Europe (EUR)
* All Bonferroni adjusted p-values (numbers in bracket) for testing the statistical significance of the
correlation coefficients are less than 0.01except JP-HK and JP-SG real estate security market pairs
19
Table 3
Test of the equality of the correlation matrices over time
Panel A: National real estate security markets
test (t-value)
Periods compared
Average correlations
Period1
Period2
Period1
Period2
01/84-05/88
06/88 - 10/92
0.257
0.359
5.08***
06/88-10/92
11/92 - 03/97
0.359
0.254
-4.53***
11/92 - 03/97
04/97 - 08/01
0.254
0.280
0.88
04/97 - 08/01
09/01 - 01/06
0.280
0.322
1.46
01/84-05/88
11/92-03/97
0.257
0.254
01/84-05/88
04/97-08/01
0.257
0.280
01/84-05/88
09/01-01/06
0.257
0.322
06/88- 10/92
04/97-08/01
0.359
0.280
06/88 - 10/92
09/01-01/06
0.359
0.322
11/92 - 03/97
09/01-01/06
0.254
0.322
Panel B: Regional real estate security markets
01/84-05/88
06/88-10/92
11/92 - 03/97
04/97 - 08/01
01/84-05/88
01/84-05/88
01/84-05/88
06/88- 10/92
06/88 - 10/92
11/92 - 03/97
06/88
11/92
04/97
09/01
-
10/92
03/97
08/01
01/06
11/92-03/97
04/97-08/01
09/01-01/06
04/97-08/01
09/01-01/06
09/01-01/06
-0.13
0.57
2.84***
-2.31**
-1.49
3.17***
0.401
0.513
0.416
0.337
0.513
0.416
0.337
0.523
5.44***
-21.28***
-5.60***
9.09***
0.401
0.401
0.401
0.513
0.513
0.416
0.416
0.337
0.523
0.337
0.523
0.523
0.63
-4.05***
3.54***
-18.52***
0.73
8.17***
Note: correlation matrices of monthly national and regional real estate security market returns for five
countries (USA, UK, JP, HK and SG) and three regions (AME, ASI and EUR) are computed over equal
periods of 53 months. We simply calculate the average and standard deviation of the differences in the
correlations in the first period and in the second period and do a t-test to see whether the difference between
the averages is significant. *** - indicates significance at the one percent level.
20
Table 4
GJR-DCC (1, 1) estimates of national and regional markets: 1/1984 to 3/2006
Panel A:
National markets
Real Estate Market
Country1
Country2
β1,0
β 2, 0
β1,1
β 2,1
α1,0
α 2, 0
α1,1
α 2,1
γ1
γ2
a
b
δ1
δ2
US
HK
JP
SG
UK
HK
UK
JP
SG
JP
**0.0104
**0.0109
**0.0112
**0.0108
**0.0097
**0.0104
**0.0098
0.0087
*0.0095
**0.0186
**0.0190
*0.0092
**0.0126
**0.0105
**0.0177
0.0090
**0.0126
**0.0200
**0.0138
**0.0144
0.0832
0.0610
0.0819
0.0674
0.1015
0.0628
0.1030
0.0092
0.0242
0.0263
0.0117
0.0063
**0.1466
0.0418
0.0460
0.0270
**0.1878
-0.0006
**0.2000
**0.1391
**0.0006
**0.0003
**0.0015
**0.0006
0.0010
0.0007
0.0007
0.0008
0.0008
**0.0016
**0.0016
*0.0009
*0.0004
0.0006
**0.0015
0.0009
*0.0003
**0.0018
0.0003
**0.0005
**0.0100
**0.0100
0.0904
**0.0100
*0.1184
*0.1495
*0.1215
*0.1189
0.1179
**0.0808
0.0792
*0.1242
**0.1493
*0.1197
0.0746
*0.1303
**0.1699
0.0742
**0.1680
**0.1280
**0.6100
**0.7700
0.0160
**0.6100
*0.5080
*0.6145
**0.6353
**0.8107
**0.8133
**0.7657
**0.7522
**0.7948
**0.8141
**0.6973
**0.7568
**0.7930
**0.8016
**0.7479
**0.8281
**0.8290
**0.0300
**0.0275
0.0073
**0.0259
0.0133
**0.0300
0.0257
0.0688
0.0146
**0.0883
**0.7556
**0.5963
**0.9550
**0.7136
**0.8846
**0.5100
**0.9167
**0.8169
**0.8959
**0.8378
*0.1087
0.0638
0.1844
0.1008
0.0840
0.0104
0.0099
-0.0203
-0.0284
**0.0516
0.0792
-0.0202
0.0366
-0.0093
0.0947
-0.0234
0.0329
0.0670
-0.0086
0.0016
HK
SG
HK
SG
Stock Market
β1,0
β 2, 0
β1,1
β 2,1
α1,0
α 2, 0
α1,1
α 2,1
γ1
γ2
a
**0.0106
**0.0109
**0.0089
**0.0099
**0.0085
**0.0124
**0.0099
0.0031
0.0030
**0.0095
**0.0134
**0.0035
0.0012
**0.0092
**0.0127
0.0045
0.0049
**0.0097
0.0019
0.0038
-0.0593
-0.0483
-0.0295
-0.0733
0.0169
-0.0868
0.0372
0.0521
0.0661
0.0631
-0.0137
*0.1099
0.1022
-0.0573
0.0107
0.0604
**0.1262
0.0021
**0.1476
0.0622
**0.0006
**0.0007
**0.0005
0.0001
**0.0005
0.0000
0.0000
**0.0009
**0.0010
0.0003
0.0005
**0.0011
**0.0003
0.0001
0.0008
**0.0009
0.0001
0.0011
0.0001
*0.0002
**0.0100
**0.0120
**0.0100
**0.0812
0.0712
**0.2680
**0.2111
**0.0100
**0.0100
**0.1491
**0.2337
**0.0101
**0.2072
**0.1172
*0.1902
**0.0100
**0.3483
*0.1532
**0.2166
**0.2485
**0.6100
**0.4485
**0.6100
**0.8788
**0.6100
**0.8349
**0.8349
**0.6100
**0.6100
**0.8718
**0.8040
**0.5391
**0.7877
**0.8647
**0.7613
**0.6100
**0.7876
**0.7180
**0.8171
**0.8169
0.0509
**0.0306
*0.0528
**0.0469
**0.1166
**0.0320
**0.0535
0.0801
**0.0300
**0.1052
b
**0.7536
**0.6700
**0.8871
**0.9245
**0.7399
**0.4700
**0.9025
**0.6983
**0.8795
**0.7937
δ1
δ2
**0.1578
*0.3126
**0.2244
**0.0001
0.2100
**-0.1493
-0.0715
**0.1679
**0.1728
**-0.1107
**-0.1755
**0.2180
**0.0020
0.0000
-0.0979
**0.1631
**-0.1980
**0.0001
**0.0001
**-0.1253
* denotes 10% significance;** denotes 5% significance
21
Table 4 (Contd)
Panel B:
Market
Region1
Region2
β1,0
β 2, 0
β1,1
β 2,1
α1,0
α 2, 0
α1,1
α 2,1
γ1
γ2
a
b
δ1
δ2
Regional markets
Real Estate Market
AME
EUR
EUR
ASI
ASI
**0.0088
**0.0094
**0.0064
**0.0062
**0.0097
**0.0093
*0.1044
*0.1040
**0.1549
*0.1146
0.0692
*0.1107
**0.0005
**0.0012
**0.0001
**0.0001
**0.0005
**0.0005
**0.0103
**0.0110
**0.2223
**0.1275
**0.1327
**0.1512
**0.6505
**0.1210
**0.6762
**0.7104
**0.6788
**0.6725
**0.0200
**0.0109
**0.0100
**0.8123
**0.7616
**0.8538
*0.0962
**0.3355
-0.1198
0.2359
*0.2851
*0.2924
Stock Market
AME
EUR
ASI
**0.0115
**0.0112
**0.0107
0.0041
*-0.0862
-0.0648
0.0185
**0.1126
**0.0001
**0.0001
**0.0003
**0.0004
**0.1044
**0.1418
0.0518
**0.0112
**0.8773
**0.8467
**0.8253
**0.7942
0.0215
**0.0164
**0.9482
**0.7659
-0.0616
-0.0622
0.0106
**0.1047
EUR
ASI
**0.0096
0.0039
0.0528
0.0754
**0.0003
**0.0004
**0.0102
0.0218
**0.8198
**0.8369
**0.0139
**0.8378
*0.0457
0.0661
* denotes 10% significance;** denotes 5% significance
22
Table 5
US-UK
US-JP
US-HK
US-SG
UK-JP
UK-HK
UK-SG
JP-HK
JP-SG
HK-SG
AME-EUR
AME-ASI
EUR-ASI
Descriptive statistics of monthly conditional correlations for national and
regional real estate security markets (RE) and stock markets (stock): 1/1984
to 3/2006
RE
Stock
RE
Stock
RE
Stock
RE
Stock
RE
Stock
RE
Stock
RE
Stock
RE
Stock
RE
Stock
RE
Stock
RE
Stock
RE
Stock
RE
Stock
Mean
0.429
0.744
0.181
0.388
0.293
0.535
0.408
0.559
0.160
0.397
0.328
0.556
0.361
0.563
0.052
0.290
0.102
0.339
0.565
0.654
0.529
0.792
0.367
0.484
0.382
0.469
Maximum Minimum
0.607
0.331
0.892
0.599
0.356
0.063
0.525
0.305
0.540
0.160
0.841
0.297
0.485
0.363
0.841
0.187
0.264
0.013
0.530
0.279
0.488
0.195
0.942
0.139
0.562
0.099
0.880
0.151
0.309
-0.231
0.609
0.065
0.208
-0.057
0.514
0.099
0.912
0.142
0.949
0.165
0.726
0.445
0.870
0.605
0.529
0.223
0.633
0.278
0.523
0.203
0.693
0.245
Std Dev skewness
0.031
1.381
0.075
0.035
0.032
0.818
0.030
0.606
0.041
1.283
0.061
0.569
0.025
1.124
0.091
-0.890
0.032
-0.625
0.028
0.638
0.035
0.070
0.116
-0.136
0.077
-0.518
0.104
-0.600
0.113
0.117
0.094
0.174
0.042
-0.528
0.064
-0.215
0.160
-0.192
0.129
-0.979
0.031
2.359
0.050
-1.797
0.032
0.272
0.065
-0.421
0.038
-1.200
0.085
-0.078
kurtosis
10.265
1.958
8.851
6.578
10.875
7.944
3.923
6.250
6.805
7.663
8.529
4.102
4.591
5.134
2.545
3.472
5.382
4.724
2.905
5.035
14.939
6.417
11.219
3.583
9.159
3.019
corr(RE/S)*
0.257
0.463
0.761
0.528
0.553
0.495
0.596
0.517
0.684
0.795
0.0027
0.024
0.228
Note: Corr(RE/S) indicates the co-movement (correlation) between the RE an stock correlations which are
predicted from the GJR -DCC model
23
Table 6
Correlation
US/UK
US/JP
US/HK
US/SG
UK/JP
UK/HK
UK/SG
JP/HK
JP/SG
HK/SG
AME-ASI
AME-EUR
EUR-ASI
Link between monthly correlations and market volatility: real estate
security markets: 1/1984 to 3/2006
Constant
Volatility 1
Volatility 2
Adj R2
National real estate securitymarkets
0.239
2.655
1.456
0.629
(4.90***)
(4.90***)
(2.09***)
0.037
2.548
0.392
0.432
(1.44)
(4.53***)
(3.29***)
0.112
3.641
0.263
0.621
(5.51***)
(7.71***)
(1.90*)
0.387
0.216
0.101
0.905
(37.44***)
(4.10***)
(3.08***)
0.177
0.317
-0.368
0.265
(5.32***)
(0.59)
(-1.98**)
0.283
1.021
-0.088
0.844
(8.23***)
(2.78***)
(-0.28)
0.253
2.246
-0.126
0.903
(4.80***)
(2.51**)
(-0.32)
-0.037
-1.457
2.103
0.845
(-1.16)
(-5.20***)
(7.14***)
0.124
-0.579
0.303
0.904
(6.19***)
(-2.46**)
(2.78***)
0.277
1.728
1.018
0.907
(5.18***)
(4.42***)
(2.88***)
Regional real estate security markets
0.258
2.484
0.066
0.427
(8.14***)
(2.90***)
(0.29)
0.359
2.056
3.477
0.682
(14.29***)
(2.32**)
(3.32***)
0.311
3.999
-0.345
0.533
(10.69***)
(3.17***)
(-1.37)
F-stat
DW
113.12
2.001
51.11
2.009
108.69
1.999
626.81
2.000
24.81
1.996
358.37
1.993
615.62
2.002
360.88
2.011
623.76
1.999
646.54
1.992
50.18
1.989
142.61
1.995
76.32
1.995
Notes: All the coefficient estimates are adjusted for auto-correlated and White heteroskedasticity errors; t*** ** *
statistics with robust standard errors are in parenthesis; , , - denotes two tailed significance at the one,
five and ten percent levels respectively.
24
Table 7
δ0
δ1
δ2
δ3
δ4
δ5
δ6
Adjusted R2
F-statistic
DW stat
Multiple regression results of conditional correlation evolution for real estate security markets: 1/1984 to 3/2006
US-UK
0.4179
(30.20***)
0.000087
(1.04)
-0.0228
(-1.27)
0.0017
(0.89)
-0.0195
(-5.72***)
0.00031
(0.05)
NA
US-JP
0.1829
(29.74***)
-0.000002
(-0.04)
0.0283
(1.34)
-0.0248
(-1.30)
-0.0095
(-3.63***)
-0.00017
(-0.03)
NA
US-HK
0.2939
(35.45***)
0.000005
(0.08)
-0.0245
(-1.35)
-0.0125
(-0.88)
-0.0146
(-3.34***)
-0.0141
(-1.48)
NA
US-SG
0.4332
(33.46***)
-0.00017
(-1.98**)
-0.0045
(-0.92)
-0.0059
(-2.29**)
-0.0047
(-2.73***)
0.00051
(0.29)
NA
0.666
76.04
2.023
0.492
37.49
2.018
0.699
88.46
1.998
0.926
473.74
2.004
Notes: Based on equation (7),
δ 0 to δˆ8 are
Correlations between Real Estate Secuirty Markets
UK-JP
UK-HK
UK-SG
JP-HK
JP-SG
0.1674
0.3349
0.3864
0.0659
0.0941
(29.35***) (22.26***) (10.13***)
(1.23)
(3.24***)
-0.000056 -0.000044 -0.00017 -0.000097 0.000047
(-1.49)
(-0.47)
(-0.73)
(-0.29)
(0.29)
0.0319
0.0091
-0.0217
-0.0416
0.0147
(1.77*)
(0.97)
(-1.38)
(-1.51)
(1.80*)
-0.0094
-0.0096
-0.0195
0.0228
0.0042
(-0.99)
(-1.08)
(-1.26)
(0.85)
(1.05)
0.00025
-0.0053
-0.0109
0.0336
0.0013
-0.15
(-7.39***) (-5.86***) (13.50***)
(0.49)
-0.0191
-0.0107
-0.0288
0.0356
-0.0179
(-10.02***) (-7.08***) (-7.24***)
(8.82***)
(-5.66***)
NA
NA
NA
NA
NA
0.471
34.59
2.003
0.871
301.71
1.973
0.923
532.59
2.012
0.891
362.22
2.061
0.935
539.51
1.991
HK-SG
0.4689
(10.04***)
0.00069
(2.37**)
-0.0276
(-1.42)
-0.00044
(-0.03)
-0.0376
(-9.82***)
0.0807
(6.65***)
NA
AME-EUR
0.5262
(84.37***)
0.000019
(0.47)
-0.0357
(-1.42)
0.0016
(0.18)
-0.0011
(-0.85)
0.0207
(6.17***)
NA
0.951
735.15
1.985
0.682
81.93
1.998
AME-ASI
0.3582
(47.46***)
0.000072
(1.46)
0.0441
(1.35)
-0.0209
(-1.27)
-0.0034
(-1.47)
-0.0117
(-2.39**)
0.0004
(0.11)
0.419
24.84
1.976
EUR-ASI
0.3673
(30.64***)
0.00012
(1.82*)
0.0732
(3.37***)
-0.0377
(-2.27**)
0.0004
(0.11)
0.0085
(3.05***)
NA
0.483
42.22
1.989
the regression parameters with constant, time trend, stock market crash dummy, Asian financial crisis
dummy and three significant dominant factors (F1, F2 and F3) that were derived from the Principal Component Analysis (PCA) respectively (see
table 8 for the factor loadings results). All the coefficient estimates are adjusted for auto-correlated and White heteroskedasticity errors; t-statistics with robust
standard errors are in parenthesis; ***, **, * - denotes two tailed significance at the one, five and ten percent levels respectively.
25
Table 8
Results of Principal Component Analysis (PCA): 1/1984 to 3/2006
Correlation
1st mkt
2nd mkt
US
UK
US
JP
US
HK
US
SG
UK
JP
UK
HK
UK
SG
JP
HK
JP
HK
SG
SG
AME
AME
EUR
EUR
ASI
ASI
Factor
-P1
-P1
-P1
-P1
-P1
-P1
-P2
-P1
-P2
P1
P2
-P2
-P1
P2
P2
-P2
P2
Correl (S)
-0.381
-0.378
-0.429
-0.311
-0.742
-0.357
-0.653
0.504
0.929
-
RE-V1
-0.378
-0.439
-0.565
-0.447
-0.443
-0.796
0.537
-0.471
0.705
-0.701
0.571
Factor loadings
RE-V2
ST-V1
-0.416
-0.504
-0.544
-0.546
-0.487
-0.501
-0.483
-0.511
0.406
0.253
-0.459
-0.489
-0.463
-0.499
0.595
0.318
-0.383
-0.479
-0.483
0.699
-0.687
0.682
-
ST-V2
-0.534
-0.491
-0.436
-0.489
-0.434
-0.502
-0.521
0.623
-0.736
-0.491
0.308
Notes: For each real estate security market pair, PCA is conducted on a system that includes five variables
that are moderately to highly correlated; stock market correlation {correl(s)}, two real estate security market
volatilities (RE-V1 and RE-V2) and two stock market volatilities (ST-V1 and ST-V2). The main objective is to
derive at least one dominant factor that represents linear combinations of the five variables. All market pairs
have two dominant factors (except that AME-ASI has three dominant factors); only significant factor(s) from
the multiple regression analysis (see table 7) are included in this table.
Figure 1
Average Unconditional Correlation of real estate security markets
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Dec-86 Dec-87 Dec-88 Dec-89 Dec-90 Dec-91 Dec-92 Dec-93 Dec-94 Dec-95 Dec-96 Dec-97 Dec-98 Dec-99 Dec-00 Dec-01 Dec-02 Dec-03 Dec-04 Dec-05
-0.1
-0.2
-0.3
average correlations (all)
average correlations (3 Asian markets)
average correlations (US with other markets)
Note: This figure reports the (unweighted) average unconditional correlations of (a) all five real estate
security markets (USA, UK, JP, HK and SG), (b) three Asian real estate security markets (JP, HK and SG)
and (c) US with other four real estate security markets. The correlation is computed over sliding windows of
three years, using local currency monthly total returns from 1/1984 to 3/2006.
27
Figure 2
Average conditional correlation: 1/1984-3/2006
Three Asian countries: (b)
All countries: (a)
0.8
0.8
0.7
0.7
Slope: 0.0003
0.6
0.6
0.5
0.5
Slope: 0.0001
0.4
0.4
0.3
0.3
0.2
Slope: 0.0007
0.2
Slope: 0.0004
0.1
0
0.1
84 86 88 90 92 94 96 98 00 02 04 06
Real Estate Market
Stock Market
Trend (Real Estate)
Trend (Stock)
84 86 88 90 92 94 96 98 00 02 04 06
Real Estate Market
Trend (Real Estate)
Stock Market
Trend (Stock)
US with other four countries: (d)
Three developed countries: (c)
0.7
0.9
0.8
0.6
0.7
0.5
Slope: 0.00005
0.4
0.6
Slope: 0.0001
0.5
0.4
0.3
0.3
0.2
Slope: -0.00005
0.1
Slope: -0.00005
0.2
0.1
84 86 88 90 92 94 96 98 00 02 04 06
84 86 88 90 92 94 96 98 00 02 04 06
Real Estate Market
Trend (Real Estate)
Real Estate Market
Trend (Real Estate)
Stock Market
Trend (Stock)
Stock Market
Trend (Stock)
Note: This figure reports the (unweighted) average conditional correlations of real estate security markets
and stock markets of (a) all five countries (US, UK, JP, HK and SG), (b) three Asian countries (JP, HK and
SG), (c) three developed countries (US, UK and JP) and (d) US with other four countries (UK, JP, HK and
SG). The conditional correlation is predicted from the GJR-DCC (1, 1) model. In addition, a simple least
square line (trend) is fitted over the total period for each correlation. The slopes are positive for all stock
market correlations and negative for two of the real estate market pairs (c and d)
28
Figure 3
Regional real estate security markets: conditional correlations and
conditional volatilities: 1/1984 – 3/2006
America vs Asia
0.8
0.6
Correlation
Correlation
America vs Europe
0.7
0.6
0.5
0.4
84
86
88
90
92
94
96
98
00
02
04
0.5
0.4
0.3
0.2
06
84
86
88
Real Estate Market
Volatility
Volatility
0.1
0.06
0.04
0.02
0
86
88
90
92
94
96
American
98
00
92
94
96
98
00
02
04
06
Real Estate Market
0.08
84
90
02
04
06
0.25
0.2
0.15
0.1
0.05
0
84
86
88
90
92
94
American
Europe
96
98
00
02
04
06
Asia
Correlation
Europe vs Asia
0.6
0.5
0.4
0.3
0.2
0.1
84
86
88
90
92
94
96
98
00
02
04
06
Volatility
Real Estate Market
0.25
0.2
0.15
0.1
0.05
0
84
86
88
90
92
94
Europe
96
98
00
02
04
06
Asia
29
Endnotes
1
Each time series has 267 monthly return data. This full sample is divided into five sub-samples that contain
53 monthly return data per time series (ignoring the last two observations). This approach will allow us to
conduct the simple t-test to assess the instability of the correlation matrix between any two sub-periods that
have equal number of monthly observations; that is, a time series that contain 53 monthly observations each
for the five shorter sample periods (53x5 = 275) and ignores the last two observations.
2
It may be difficult to come out with a unanimous agreement on the periods of stock market crash and Asian
financial crisis for all countries. In line with the previous literature and mainly for consistency reasons, the
stock market crash dummy is set from 10/1987 to 12/1987 (3 months) and the Asian financial crisis dummy
is set from 1/1997 to 6/1998 (18 months) to encompass the short time before and after the crisis period.
3
The t-statistics are between -7.04 and -91.49 and are statistically significant at the one percent level.
4
It has to be cautioned a constant linear trend is not consistent with the definition of a correlation coefficient.
Other forms of trend can be modeled, but no theory exists of the exact form of this trend. Also, as with any
time-series study, the starting date can be of importance and render any conclusion somewhat different.
5
All the correlation and volatilities series are stationary as verified by the usual ADF tests. For each market
pair, the two market volatilities have some multicollinearity and disentangling the effects might be difficult.
On the other hand, including only one volatility coefficient reduces the Adjusted R2 significantly.
6
Following the usual procedure, we include those dominant factors that have eigen values greater than or
equal to one.
7
It should be noted that the trends here tend to be lower than those shown in Figure 2 because part of the
overall increase in correlation is explained by an increase in volatility over the sample period.
30