Correlation Dynamics and Determinants in Real Estate Securities
Markets – A Study of Greater China Economies and their International
Linkages
Professor Liow Kim Hiang (rstlkh@nus.edu.sg) and Miss Zhou Xiaoxia
(Isabella.zxx@gmail.com), Department of Real Estate, National University of Singapore
This Draft
November 29, 2012
Correlation Dynamics and Determinants in Real Estate Securities
Markets – A Study of Greater China Economies and their International
Linkages
Abstract
We study the quarterly realized correlation behavior in the three Greater China (GC) real estate securities
markets and their selected regional/ international partners over the period 1995-2011. We trace out how the
pattern of international co-movements of the real estate securities markets changed over time. Using
correlation spillover methodology, we find that the correlation movements among the real estate securities
markets and among the stock markets are synchronized. There is also some extent of correlation
dependence (spillover) across the real estate securities markets. In addition, the realized correlations are
subject to regime switching with one or two structural breaks detected. Finally, the general results that
emerge from estimating pooled cross-sectional time series models and time-series regression models is that
international correlations of real estate securities market returns are significantly linked to four main factors
including stock market correlations, global real estate market volatility, direct property market return
differential and global stock market returns. Given the plentitude of variables available to international
investors, it thus becomes important for them to consider only those factors that are particularly useful for
modeling the changes in the international co-movements of real estate securities markets returns over time.
Our GC results are indicative in this direction.
1.
INTRODUCTION
Similar to stock markets, the international co-movement of real estate securities returns is of key
importance for global investors who seek to invest in a well-diversified real estate investment portfolio.
The co-movement of international stock/real estate securities markets is generally estimated by crossmarket return correlation coefficient. The return correlations are likely to increase over time as a result of
rising economic interdependence through international trade and investment flow, as well as growth and
development in international financial markets, increasing stock market synchronization and increasing
level of real estate securitization activities. Specifically, as a consequence of this globalization and
internationalization of real estate investments, it is expected that real estate securities markets will have
become increasing integrated, and that this integration will lead to increased co-movement of prices among
public real estate markets globally. Since this correlation structure reflects the nature and extent of global
real estate securities market integration, as well as the risk-return and diversification performance of
international real estate securities portfolios, a better understanding of dynamic movements in the real
estate securities markets’ correlation structure and the forces behind market integration is important for
1
international investors to realize the potential risks and rewards of global real estate diversification. To our
knowledge, these twin aspects have not been adequately studied in the real estate literature.
In this study, we systematically analyze the dynamic movements and driving forces behind real
estate securities markets’ time-varying integration within the three Greater China (GC) economies
(Mainland China, Hong Kong and Taiwan), as well as their international linkages with the US, the UK,
Australia, Japan and Singapore. Our empirical indicator of the degree of integration of the real estate
securities markets is the realized correlation of returns among the eight markets. There are some main
reasons for this growing research interest: the growing presence of China in the world economy, the rapidly
growing size and influence of the Chinese stock markets and the emergence of the GC region as one of the
most dynamic regions in the world since the last decade. Liow and Newell (2012) find that the three GC
real estate securities markets are integrated among themselves because they are linked together by their
geographical proximity, close economic relationships and political similarities. In addition, with the real
estate assets sharing the same trend, the multilateral economic activities could have contributed a great deal
to the correlation linkages among the three GC markets and their regional /international economic partners
in other parts of Asia, Europe and North America. Moreover, the economic globalization between the
mainland China and Hong Kong has been greatly enhanced since Hong Kong’s sovereignty returned to
China in 1997. As of 2011 third quarter, the total exports and imports among the three economies have
reached 350 billion USD, while the total trade of Mainland China with the US, the UK, Japan and
Singapore has reached 750 billion USD. The accession of China to the World Trade Organization (WTO)
in November 2001 further marks a distinctive change in China’s economic relation with the world.
Moreover, its real estate market is further supported with continuing strong economic growth, massive
urbanization and the growth of private real estate ownership (Liow and Newell, 2012). Against this
background, it is thus timely to understand, model and forecast the dynamic movements in the correlation
structure of the GC real estate securities portfolios. Results from this study could provide a better grasp of
the functioning of the GC real estate securities markets, as well as allow investors and policy makers
understand better the driving forces that influence the co-movements of real estate securities markets within
and across the GC areas, which could be different from the corresponding stock markets. Our twin research
strategy is the following:
2

We estimate realized correlations among the three GC markets, as well as between each of the
three GC markets and their selected regional/international partners to understand how the
pattern of the international co-movement of real estate securities returns has changed over
time. Our estimates reveal a tendency of the sample real estate securities market correlations
to increase over time. Moreover, there exists correlation dependence (in term of correlation
spillover) between real estate securities and stock markets, as well as across the real estate
securities markets. Finally, the realized correlations are subject to regime switching as
reflected in the detection of structural breaks. These time series characteristics will be
incorporated in modeling the correlation structure over time, and thus the evolution in real
estate securities market integration.

We undertake a regression-based analysis to assess whether macroeconomic variables and
real estate factors (securitized and unsecuritized) help explain changes in real estate securities
market correlations within and across the GC areas. Results are generally robust against the
pooled cross-section time series regression models with random effects, feasible generalized
least squares (FGLS) and a dynamic generalized method of moment (GMM) techniques,
individual regressions using seemingly unrelated regression (SUR) method, as well as out-ofsample correlation forecasting
Our contribution to the research field is thus not to provide a new methodology to study
international correlation structure, but rather to draw on earlier research studies conducted for stock
markets such as Karolyi and Stulz, (1976); Bodurtha et al. (1989); Campbell and Hamao (1992); Bracker
and Koch (1999); Bracker et al (1999) and Pretorius (2002). However we depart from the existing literature
in several aspects which we hope to contribute.
First, previous stock market studies mainly focused on countries in the US, Europe and other
developed countries. In contrast, no published study on international real estate securities markets,
particularly within and across the GC areas can be found. Our study using a GC and international real estate
securities dataset is thus different from a larger body of literature, and thereby contribute specifically to the
real estate market integration literature in the GC context on an extended period.
3
Second, instead of relying on parametric procedures (e.g. GARCH) to estimate variance and
correlation as in Liow and Newell (2012), we appeal to the realized correlation methodology to estimate expost realized correlations across the real estate securities markets studied. In consistent to Anderson et al.
(2001), correlations so constructed are model free and contain little measurement error as the sampling
frequency of the returns approaches infinity. These econometric merits motivate our use of this approach
which has received less formal attention in the real estate literature. In addition, the realized correlation
framework allows us combine with recent developments in time series econometrics to study real estate
securities correlation behavior from a spillover and regime-switching perspectives.
Third, we cast a wider net in term of state variables. In addition to the economic state variables,
we consider stock market correlations and a global stock return factor; securitized real estate market factors
which include relative real estate market size (i.e. real estate market capitalization /stock market
capitalization), real estate securities market volatility, global real estate volatility and a REIT dummy, as
well as a direct real estate market return factor for each economy studied. The use of the four securitized
real estate specific variables and one direct real estate factor further distinguishes our work from other
stock market studies. They will be explained in the “methodology” section below.
Fourth, the set of 18 pairwise realized correlation equations is estimated as a pooled crosssectional time series model, explicitly controlled for unobserved heterogeneity both in the cross-section and
the time series dimension; as well as controlled for cross-sectional dependence using panel random effects
and feasible GLS estimators. We also use Dynamic GMM as a robust check. This pooled analysis is
conducted on a quarterly dataset dominated both in the US dollars and in the home currency. Additional
robustness check on the pooled sample involves the use of unconditional returns and real returns to
estimate the pairwise correlations. Additionally, we estimate a system of seemingly unrelated regression
(SUR) that includes potential determinants of individual pairwise realized correlations. Finally, our
correlation model is employed to generate out-of-sample forecasts of the realized correlation structure. The
outcomes from these empirical implementations should strengthen support to the validity of the model in
explaining and forecasting the realized correlation structure for our dataset and is an evidence of our
modest methodological contribution in international real estate research.
4
Finally, the findings from this study will not only be specific to within and across GC areas, but
will also have significant and wider implications on international diversification in real estate securities
markets and indicate that modeling the correlation structure with economic factors, securitized real estate
factors, direct real estate market factors and stock market factors is useful in assisting portfolio managers to
exploit international investment opportunities in real estate securities.
The paper proceeds at follows. Section 2 reviews the relevant stock market and real estate
literature. Section 3 presents the sample real estate securities markets. This is followed by Section 4 where
the realized correlation, correlation spillover and correlation regime estimation methodologies are first
explained, and are then followed by a discussion of a theoretical model that includes various determinants
of real estate securities correlation structure. Section 5 reports the correlation behavior and significant
factors. The forecasting performance of the correlation model with respect to alternative forecasting
techniques is also evaluated. Section 6 concludes the paper.
2.
LITERATURE REVIEW
A review of literature indicates that there are generally two categories of explanations as to why
there is co-movement between different national stock markets. The first group of explanation is attributed
to “contagion” effect, which is defined as that part of the market correlations that cannot be explained by
economic fundamentals; but instead is due likely to crisis. For example, the average level of stock market
correlation was generally much higher during the recent global financial crisis (GFC) compare to the precrisis period. In contrast, the second group of explanation, “economic integration” suggests that the more
the economies of two countries are integrated, the more interdependent their financial and stock markets
will be. Moreover, economic integration includes not only trade relationships, but also co-movement in the
economic indicators that influence financial asset returns, including interest rates, money supply, inflation
and foreign direct investment. Since securitized real estate is a component part of stock market in many
countries, the underlying stock market co-movement will also influence the correlation between the two
corresponding securitized real estate markets (Liow et al, 2009). From the convergence perspective,
economic theory suggests since key macroeconomic variables such as industrial production, interest rate,
inflation and term structure premium can influence real estate market performance. Therefore whether the
5
two real estate markets will converge (diverge) over time might also depend on the extent to which these
macroeconomic variables in the two countries have converged (diverged).
In so far as our work is related to stock market studies, Chan and Zhang (1997) find that stock
market co-movement is correlated positively with the extent of trade with the explanatory power of trade
range between 5% and 40% of the variation in the correlation, depending on the measure of correlation
used. Bracker and Koch (1999) find that the degree of stock market interdependence as measured by the
magnitude of correlation is a positive function of market volatility and a trend, as well as a negative
function of exchange rate volatility, term structure differentials, real interest rate differentials and the return
on the world market index. In another study, Bracker et al. (1999) specify a set of macroeconomic variables
that characterize and influence the degree of co-movement for each pair of stock markets (US and eight
other developed country stock markets) using a pooled time series regression model. Their significant
factors include bilateral trade dependence, real interest rate differential, market size differential and a time
trend. Other related studies include Pretorius (2002), Johnson and Soenen (2002), Tavares (2009), Beine
and Candelon (2010) and Walti (2011).
While the academic real estate literature has explored into the inter-relationship between and
among real estate market returns across national boundaries (e.g. Guerts and Jaffe, 1996; Ling and Naranjo,
2002; Hoesli et al. 2004); as well as the time-varying correlation and volatility dynamics of securitized real
estate markets (e.g. Michayluk et al, 2006; Cotter and Stevenson, 2006; Liow et al, 2009; Case et al. 2011),
there is inadequate research examining the main determinants of real estate returns/correlations from the
macroeconomic/international economic perspective; with some notable exceptions by McCue and Kling
(1994), Brooks and Tscolacos (1999) and Bardhan et al. (2008). Using a dataset of 946 firms from 16
countries from 1995-2002, Bardhan et al. (2008) examine whether globalization and increasing economic
and financial integration have affected the rate of return of their sample of global public real estate firms
over the study period. Their economic variables include GDP growth, exchange rate change, exchange rate
forward, interest rate differential and economic openness. In contrast, none of real estate papers has
assessed the impact of increasing globalization of financial/economic activities on international real estate
market correlation structure; although Liow and Newell (2012) have found that the average conditional
correlations between the three GC real estate securities markets have outweighed their average conditional
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correlations with the US securitized real estate market, thereby supporting closer integration between the
GC markets due to geographical proximity and closer economic links. However, a formal investigation of
the correlation determinants did not appear in their study.
3
RESEARCH SAMPLE AND DATA
We include Standard & Poor’s daily closing real estate stock indexes for three GC {China (CH),
Hong Kong (HK), Taiwan (TW)} and five non-GC real estate securities markets {Australia (AU), Japan
(JP), Singapore (SG), the US and the UK}, as well as the daily bilateral exchange rates between the US
dollar and the other seven currencies, from 1995Q1 through 2011Q4 (68 quarters).1 This global property
database, the latest international public real estate database in the market, is designed to reflect components
of the broad universe of investable international real estate stocks reflecting their risk and return
characteristics. The US, UK, JP and AU have well-developed financial markets and open capital accounts.
In particular, the US and JP are the main investors and trading partners with the GC economies. SG, due to
its geographical proximity and cultural similarity, has had close economic ties with the three GC economies.
As many of the macroeconomic variables are only available quarterly, we employ daily returns to construct
a quarterly realized time series of the correlation matrix and conduct the analysis quarterly in home
currency, as well as in the US dollar term (explained in the next section). Figure 1 plots the time series
trend of these eight real estate securities market total return indices from 1995Q1 to 2011Q4.
(Figure 1 here)
4.
METHODOLOGY
This study takes a two-step approach. We first examine how realized correlations within and
across the GC areas vary over time, as well as their two important time series characteristics, correlation
dependence and correlation regime over the entire study period. Second, we explore why the correlational
interdependence varies in intensity over time. This two-step procedure offers a comprehensive investigation
of correlation dynamics and determinants in the context of real estate securities market integration within
and across the GC areas. The relevant methodologies are briefly explained below.
1
Since most of our explanatory factors are only available on a quarterly basis (2 nd part), we have to use quarterly
variables to match with the data frequency.
7
4.1
Realized correlation estimates and time-series behavior
(a)
Realized correlation estimation
As mentioned above, this paper computes a time-varying measure of cross-real estate securities
market correlations by appealing to the concept of realized moments (/correlation). This approach
represents an alternative to the use of parametric models such as the multivariate GARCH models or DCC
models in estimating time-varying conditional correlations. According to Anderson et al. (2001), the
estimation of covariance through the realized moments increases the precision of correlation estimates. In
the present context, we use daily return data of the eight national real estate securities markets in order to
compute a quarterly estimate each of the cross-market correlation.
We define the daily stock return at market i as
Ri ,t ,d  ln( I i ,t ,d I i ,t ,d 1 ) x100 and market j as
R j ,t ,d  ln( I j ,t ,d I j ,t ,d 1 ) x 100, where I are the daily real estate stock total return indices. Then the
realized variances is given by:
Dt
Dt
d 1
d 1
 t2,i   ( Ri ,t ,d ) 2 and  t2, j   ( R j ,t ,d ) 2
, where (d= 1,….D), D t is
the total business day in the quarter t. Then, the realized covariance between cross-country real estate stock
returns is measured as  ij ,t
Dt
  ( Ri ,t ,d xR j ,t ,d ) . Finally, the realized correlation  ij,t measure between
d 1
the cross-country returns is obtained as
 ij ,t 
-1 and +1, we use a Fisher-Z transformation:
(b)
 ij ,t
 i2,t x 2j ,t
1   ijt
 ijt  ln(
. Since correlations are bounded between
1   ijt
).
Correlation dependence
One issue which has great implication for correlation modeling is whether there is any significant
link between cross-asset correlations and within-asset correlations over time. Specifically, we hope to
answer two related questions. The first is whether the movements in correlations among the real estate
securities markets and among the stock markets (i.e. cross-asset correlations) are synchronized. For
example, the China real estate securities market may become increasingly correlated with the Hong Kong
8
real estate securities market at the same time the China and Hong Kong stock markets become increasingly
correlated. Consequently, a positive relationship between the real estate market correlations and stock
market correlations might be expected.2 Second, investors might also expect a positive relationship among
the international real estate securities market correlations due to the influence of some common factors. To
measure the degree of correlation dependence, we motivate the generalized volatility spillover index
methodology of Diebold and Yilmaz (2012) to estimate a “correlation spillover index” in order to ascertain
whether there is a connection among the real estate securities market correlations within the and across the
GC areas (CH-HK, CH-TW and HK-TW as a VAR system; CH-JP, CH-SG, CH-AU, CH-US and CH-HK
as a VAR system; HK-JP, HK-SG, HK-AU, HK-US and HK-UK as a VAR system; TW-JP, TW-SG, TWAU, TW-US and TW-UK as a VAR system); as well as the extent of interdependence between each pair of
real estate securities and stock market correlations. The correlation spillover index methodology is based on
decomposition of correlation forecast error variances obtained from a vector auto-regression (VAR). We
first model the respective VAR systems and then conduct a variance decomposition analysis to 12-quarter
(three years) long rolling windows of the correlation structure. For each factor i we add the shares of its
correlation forecast error variance due to shocks come from other correlations j. Then we sum across all i to
obtain the correlation spillover index. In other words, the “correlation spillover index”, as we wish to label,
is the sum of all non- diagonal in the correlation forecast error variance matrix. Our correlation spillover
analysis covers two aspects; (a) an aggregate correlation spillover index which measures what proportion of
the correlation forecast error variance comes from spillovers; and (b) correlation spillover plots which are
constructed from the rolling-samples of the spillover indices to assess the extent and nature of the
correlation spillover (dependence) variations over time.
(c)
Correlation regimes
Using Bai and Perron (BP) (2003)’s multiple structural break approach, we recognize the possible
presence of a multiple-regime time-varying realized correlations in some securitized real estate markets by
testing for multiple structural breaks in the mean level of realized correlation series, as well as identifying
2
Liow et al (2009) finds that the co-movements between international real estate securities and stock market
correlations range between 0.257 and 0.795, implying that between 6.6% and 63.2% of the variations in international
real estate securities market correlations can be accounted by the changes in international stock market correlations or
vice-versa.
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statistically the dates of these mean correlation shifts. Our motivation is derived from the empirical
literature that measures “contagion” as a significant increase in the correlations between financial markets
(Forbes and Rigobon, 2002). This requires the search for at least a structural break in a correlation series
between financial markets, thereby implying that the time-varying nature of correlations has to be
distinguished from a structural change in correlations due to a crisis. Methodologically, BP consider
infrequent multiple structural changes in a linear model estimated by least squares and derive the rate of
convergence and the limiting distributions of the estimated break points. The BP procedure starts with
examining the double maximum statistics to determine whether any structural breaks are present. If the
double maximum statistics are significant, then the
the number of breaks, choosing the
SupFi ,T (l  1| l ) statistics are evaluated to determine
SupFi ,T (l  1| l ) statistic that rejects the largest value of l .Other
procedure to select the number of breaks includes the use of the Bayesian Information Criterion (BIC) and
a modified Schwarz criterion (LWZ) (BP, 2003). Finally, the trimming parameter of at least 0.15 (M=5) is
recommended when heteroskedasticity and series correlation and allowed in the time series.
4.2
Determinants of correlation structure
We include four key considerations governing the selection of the correlation factors and their
proxies; (a) changes over time in the economic factors that determine stock/real estate securities market
returns are also the potential determinants of changes in asset market correlations over time; (b) real estate
securities market and direct property market characteristics that could possibly influence the extent of
market interdependence; (c) availability of relevant time series proxies from 1995Q1 to 2011 Q4 (68
quarters), and (d) development of parsimonious models in order to reduce potential multicollinearity among
the various selected factors. Further, we are guided by economic theory that provides a priori information
about some relevant variables and their signs of the coefficients. For the purpose of this study, all variables
are categorized into “macroeconomic”, “securitized real estate market”, “direct real estate”, “world market”,
“Institutional development”, “crisis”, “time dummies” and “others”. Table 3 provides the list of selected 22
factors, their measurement proxy and expected signs of coefficients. A brief discussion on their economic
justification follows.
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(a)
Macroeconomic factors
Prior studies have considered possible fundamental economic factors which could influence
expected returns in a national real estate market (Chen et al, 1986; McCue and Kling, 1994; Brooks and
Tsolacos, 1999). These studies suggest the following popular economic factors as potential determinants of
national real estate returns in each time period. They include nominal gross domestic product growth
(GDP), actual Inflation (IF), real interest rates (RINT) and term structure premium (TS). These variables
represent different aspects of a country‘s macroeconomic performance which are able to affect expected
cash flow and/or discount rates in that national market and thus have a significant bearing on the market’s
expected returns (Bracker and Koch, 1999). Over time, if there is greater divergence in the macroeconomic
behavior across countries, then the absolute value of the macroeconomic performance differential is
expected to be negatively with the extent of their stock /real estate stock market correlations. Accordingly,
in this first step we hypothesize that the pairwise real estate securities markets’ realized correlation as a
function of the absolute divergence of the four macroeconomic factors stated above. Our expectation is
that smaller divergence in the macroeconomic behavior across economies should lead to greater correlation
across stock/real estate stock markets; thereby implying negative coefficients for the four macroeconomic
differential factors.
In addition, we include three additional macroeconomic factors that may directly influence
international stock/ real estate equity correlations. First, bilateral exchange rate returns (EXCH) may
influence bilateral trade/investment conditions and thus national equity and real estate equity returns. A
potential negative influence on the correlation is expected. Second, the variance of bilateral exchange rate
(VAREX) is a possible source of volatility which may dampen economic and stock market integration.
Third, when two countries have a strong trade relationship, their economies and stock markets are likely to
be more interdependent. From our earlier evidence that indicates the real estate securities markets’
correlations are significantly and positively linked to the stock markets’ correlations3, we include the stock
market correlation (CORST ijt) factor to proxy for stock market integration (which also reflects the strength
of the bilateral trade/investment relationship).
3
See also Liow et al (2009)
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(b)
A world market factor
Due to the asymmetric behavior of the correlation structure in times of rising versus falling
markets worldwide, the return on a world market portfolio (represented by the global stock return: GST)
may display a negative relationship with the real estate stock correlation structure over time.
(c)
Securitized real estate market factors
Apart from the economic variables discussed in the previous section, we include four securitized
specific variables that can potentially influence the extent of real estate securities market correlations.
These factors are global real estate securities market volatility, relative real estate securities market size,
real estate securities market volatility and REIT influence.
First, world market volatility is an important determinant of correlations across national markets
(Longin and Solnik, 1995). In our context, higher volatility of global real estate securities portfolio (GREV)
may force international investors to demand higher rates of returns that could result in higher correlations
across different pairs of national real estate securities markets. Second, the size of a national real estate
securities market relative to its stock market (LNRESIZEST) may indicate its growth, maturity and
importance of real estate securities market in the national economy. In our case, real estate securities
market accounts for an average of 6.29% (China), 9.98% (Hong Kong) and 1.02% (Taiwan) of local stock
market capitalization between 2005 and 2009 (Bloomberg). In addition, the relative size of a national real
estate equity market could affect its return performance due to differential information, transaction costs
and trading liquidity. Hence two national real estate securities markets with a small disparity in relative real
estate securities market size may imply smaller differences in market microstructure and may thus be more
correlated, thereby implying a negative coefficient for the LNRESIZEST variable. Third, market volatility
influences positively its return. In addition, Liow et al. (2009) find that correlation increases when one
market or both markets become more volatile. We thus allow the real estate securities market volatility
factor in both economies to enter the regression model independently (VARRE i and VARRE j), rather than
in the form of an absolute differential. Finally, we test a REIT dummy factor in the study. This refers to the
existence of a REIT market structure in many economies after the Asian Financial Crisis (AFC).
Specifically, we hypothesize two real estate securities markets may be more interdependent caused by the
12
establishment of a REIT market structure in the two economies. For our sample, while there is absence of a
REIT structure in the Chinese economy to-date, other seven markets introduced a REIT-like structure at
different points in time during the study period. We further hypothesize that the correlation between two
real estate securities markets that are in the same region (Asia, Europe and North Americas) may be higher
than that of two real estate securities in different regions. Combining the REIT factor nand regional effects,
our null hypothesis is the correlation between two real estate securities markets that are in the same region
and have a REIT structure established during quarter t may be higher than that of two markets that behave
otherwise. We use “REGIONREIT” to indicate dummy equals 1 if two same-region economies have a
REIT market each during period t; 0 otherwise. We have to confess that since the establishment of REITlike structure in many economies is a relatively new phenomenon, its impact on the public real estate
market integration is still not clear. Therefore the inclusion of this REIT dummy factor in this study is
considered purely exploratory.
(d)
A direct real estate market factor
Since real estate securities are hybrid of direct properties and stocks, their correlations are likely to
be affected by the domestic real estate market’s performance. We therefore include a direct real estate
factor (DIRECT) that proxies for the real estate market performance in each economy. Because there is
lack of a reliable direct real estate performance benchmark in many economies, we use an orthogonalized
real estate securities return factor to proxy for “DIRECT”. Specifically, by regressing each economy’s real
estate securities returns against the stock market’s returns, we derive an “unsecuritized” or “direct” real
estate return factor which is statistically independent of the underlying stock market performance. This
orthogonal approach was also used by McCue and Kling (1994). Moreover, the absolute value of the direct
real estate market return performance differential between the two economies should be negatively
correlated with their real estate securities market correlations.
(e)
An institutional development factor
Since the development of the economies, stock and real estate securities markets in these countries
(e.g. China vs. Japan vs. Singapore vs. the US are in different stages), it is necessary for us to account for
the different stages of market development, variations in market transparency and institutional differences
13
among the sample markets before their real estate securities market correlations can be addressed. Towards
this end, we use the World Bank Governance indicators which cover six aspects of institutional quality (IS)
- voice and accountability; political instability and violence; government effectiveness; regulatory quality;
rule of law and control of corruption. We compute a simple average of these six indices as a proxy for
aggregate institutional quality. The absolute value of the average (IS) differential between two economies
could have a negative relationship with the correlation of their real estate securities markets. The
underlying argument is that two real estate securities markets could be potentially correlated if minimal
institutional obstacles to cross-border real estate capital flows are present.
(f)
Crisis dummies
We use two crisis dummies - Asian financial crisis of 1997 (D97) and Global financial crisis of
2008 (D08). These two dummy variables are used to test the effect of the 1997 AFC and 2008 GFC on the
correlations; i.e. whether the average level of correlation was higher during the two crisis periods.
(g)
Time Dummies
Similar to stock markets, real estate securities market correlations are expected to be higher over
time due to increasing globalization and securitization, increasing stock market correlation and ongoing
relaxation of foreign exchange control policies. The coefficient of a simple linear time trend (TREND)
should hence have positive sign. In addition, three quarterly dummy variables (Q1, Q2 and Q3) are used to
test whether the real estate securities market correlations have a quarterly component. Finally, we also
include a one-quarter lagged correlation variable (Corr t-1) as a covariate in the model.
4.3
Final empirical model
Combining all 22 variables, the final empirical regression model (1) is specified below:
 ij  0  1 GDPi  GDPj t  2 IFi  IF j t  3 RINT i RINT j t  4 TSi  TS j t  5 EX ijt
 6VAREX ijt  7 CORSTijt  8GSTt  9 REGIONREITS ijt  10VARRE it  11VARRE jt
 12 DIRECTi  DIRECT j  13 LNRESIZESTi  LNRESIZEST j  14GREVt  15 IS i  IS j
t
t
 16 D97  17 D08  18Q1  19Q2  20Q3  21TREND  22  ijt 1 ............(1)
14
t
4.4
Empirical implementation
(a)
For 18 pairs of real estate securities markets, 4 we compute the realized correlations over each
quarter (  ijt ) between 1995Q1 and 2011Q4 from the time series of daily returns. The resulting
time series of 68 quarterly observations on the correlation matrix reveals the nature and changes in
the correlation structure over time. Their time series behaviors are examined from the correlation
dependence and correlation regime perspectives; both have significant implications for modeling
the correlation structure.
(b)
The variables are first tested for their stationary property using three panel unit root tests; the
Harris-Tzavalis (1999), Breitung (2000) and Im-Pesaran-Shin (2003) tests. These three tests have
as the null hypothesis that all 18 panels contain a unit root.
(c)
Equation 1 is specified for the 18 pairwise correlations. The regression series are estimated in
three different ways, for both local dollar and US dollar returns. First, all 18 equations will be
estimated as a pooled cross-sectional model to minimize unobserved panel-level effects, thereby
constraining all regression coefficients, except the intercepts, to be identical across all 18
equations. As the Hausman test indicates the GLS random effect estimator is better than a within
estimator for fixed effect models, we first estimate Models 1 (local dollar returns) and 4 (US dollar
returns) with a GLS estimator for random effects model.5 Second, we estimate Models 2 (local
dollar returns) and 5 (US dollar returns) by using feasible generalized least square (FGLS) to
account for cross-sectional correlation dependence and possible heteroskedasticity across panels
(i.e. the variance for each of the panels differs). Finally, we use a consistent generalized method of
moment (GMM) estimator (Arellano and Bond, 1991) for the parameters of Models 3 (local
4
This refers to the correlations between CH-HK, CH-TW, HK-TW, CH-JP, CH-SG, CH-AU, CH-US, CH-UK, HK-JP,
HK-SG, HK-AU, HK-US, HK-UK, TW-JP, TW-SG, TW-AU, TW-US and TW-UK
5
The pooled OLS solution is not practical for our case since it might be overly restrictive and can have a complicated
error process (such as heteroskedasticity across panel units and serial correlation within panel units). In contrast the
fixed-effects (FE) and random-effects (RE) models allow for heterogeneity across units but confine the heterogeneity to
the intercept terms of the relationship. Please consult the standard econometric texts for the differences between FE and
RE models. Further, a Hausman test is conducted to confirm whether the regressors are uncorrelated with the individual
level effect (then the RE estimator is consistent and efficient) or if the regressors are correlated with the individuallevel effect (then the FE estimator is preferred).
15
dollars returns) and 6 (US dollar returns). This dynamic panel GMM model is implemented to
render the unobserved panel effects orthogonal to the one-quarter lagged correlation variable, as
well serves a robustness check on the pooled sample specification.
(e)
We test whether using an unconditional correlation measure, as well as expressing returns in real
terms producing different results. In addition, we estimate the 18 equations as a system of
seemingly unrelated regressions (SURs) that incorporate potential contemporaneous correlation
across the regression error terms while allow the individual parameter estimates to vary across
different pairs of markets.
(f)
Following Bracker and Koch (1999), we compare the out-of sample forecasting ability of the
realized correlation models (for both local dollar and US dollar returns) with four other alternative
forecasting models (no change model; historical average model, ARIMA model and Baynes
model).6 The performance of these five models is evaluated on the basis of achieving minimum
root mean square error (RMSE) and a Theil decomposition of the MSE into bias, variance and
covariance proportions (Pindyck and Rubinfield, 1998).
5.
RESULTS
5.1
Time series correlation dynamics
Table 1 provides descriptive statistics for the cross-market realized correlation estimates (in local
dollar returns) for the 18 real estate securities market pairs and four group averages (i.e. averages of GC,
China and international, Hong Kong and international, Taiwan and international) 7 over the entire study
6
Following Bracker and Koch (1999), the “no change” model employs the one-step forecast correlation from the
previous quarter. The “historical average” specification uses the average one-step forecast correlation over the previous
eight quarters. The third model develops an individual ARIMA specification to forecast one-step ahead. The Bayne
approach regresses each bilateral correlation toward the overall mean across all correlations of the previous quarter.
Finally, the fitted values from the correlation model (equation 1) are used to forecast one-step ahead.
7
In this study, all the five non-GC real estate securities markets (AU, JP, SG, US and UK) are considered
“international”. In addition to the 18 market-pair, the following four group averages are constructed: (a) within GC
(average realized correlations of CH-HK, CH-TW and HK-TW); (b) China and international (CH-INT) (average
realized correlations of CH-JP, CH-SG, CH-AU, CH-US and CH-UK); (c) Hong Kong and international (HK-INT)
(average realized correlations of HK-JP, HK-SG, HK-AU, HK-US and HK-UK); and (d) Taiwan and international
(TW-INT)(average realized correlations of TW-JP, TW-SG, TW-AU, TW-US and TW-UK). Henceforth, these four
group averages will be followed consistently in subsequent analyses, where applicable.
16
period, as well as the mean and standard deviation during the global financial crisis (GFC) period.
Additionally, Figure 2 compares the average time series variations of cross-real estate and cross stock
market correlations over the entire study period for the four groups.
(Table 1and Figure 2 here)
As the numbers in Table 1 indicates, average quarterly real estate market securities correlations
for 1995-2011 range between -0.018 (HK-US) and 0.555 (Hong Kong/Singapore). Only three economypair (HK-JP, CH-HK and HK-SG) is above 0.30. The average correlation among the three GC economies is
0.256, which is, respectively, about 88.2%, 9.4% and 118.9%, higher than the averages between Chinainternational (0.136), between Hong Kong-international (0.234) and between Taiwan-international (0.117).
Therefore the average realized correlations among the three GC real estate securities markets have
outweighed their average realized correlations with the US/UK/AU/JP/SG real estate securities markets,
reflecting closer integration among the three GC real estate securities markets due possibly to geographical
proximity and closer economic links. These findings are thus in general agreement with the work of Liow
and Newell (2012). Over the entire study period, the time trend analyses reveal that after controlling for the
effects of AFC and GFC, the estimated realized correlations have experienced a significant increase of
2.97% (GC), 1.43% (CH-INT), 0.88% (HK-INT) and 1.14% (TW-INT) per annum, implying there is an
increasing trend of real estate market integration within and across the GC areas. In contrast, the
insignificant increase of correlation coefficients of the three GC markets with the US and UK markets
provide some degree of portfolio diversification motivation to attract US/UK investors to invest in the GC
real estate securities markets. 8 Finally, a (much) higher level of correlation for many market-pairs is
observed during the GFC period. Specifically, the realized correlations during the GFC period report an
increase (relative to the full period) of about 110.5% (CH-HK), 46.5% (TW-HK), 125.2% (CH-TW),
110.8% (CH-INT), 36.6% (HK-INT) and 26.4% (TW-INT), implying some realized correlation series may
be subject to regime switching. The Bai and Perron (2003)’ structural break analysis will be followed to
ascertain the existence of correlation regimes in all realized correlation series.
8
There is an insignificant positive time trend each in the realized correlation series of CH-UK, CH-US, HK-UK, HKUS and TW-US; whereas the TW-UK series has an insignificant negative time trend.
17
The graphs in Figure 2 support a trend toward greater integration within and across the GC
stock/real estate securities markets. Moreover, Figure 2 indicates the corresponding cross-stock correlations
are consistently higher than the cross-real estate securities market correlations. Within the GC areas, the
average realized correlations are 0.4902 (cross-stock) and 0.2564 (cross-real estate). Additionally, the
cross-stock realized correlations are 83.1% (CH-INT), 37.3% (HK-INT) and 90.4% (TW-INT) higher than
the respective cross-real estate securities market correlations. The results are thus in agreement with Liow
et al. (2009) that indicates (significantly) lower cross-real estate securities market correlation, and thus
implies lower market integration than the corresponding stock markets in international developed countries.
5.2
Correlation dependence
To detect whether there is a significant link between cross-real estate correlations in the four
regions of interest (GC, CH-INT, HK-INT and TW-INT), Table 2 presents four real estate securities
correlation spillover tables for the entire study period. Following Diebold and Yilmaz (2012), each table is
constructed using the row normalization method with the sum of the correlation forecast error variances in
a row equals 100%.9. The i th entry is the estimated contribution to the forecast correlation variance of factor
i, resulting from innovations to factor j. The sum of the correlation forecast error variance in a row,
excluding the diagonal returns, indicates the impact on the correlation forecast error variance of other
factors in the VAR system. The aggregate “correlation spillover index” is computed as the sum of all
correlation forecast error variances in the square matrix minus the sum of the diagonal correlation forecast
error variances. We rely on a 12-quarter (3-year)-ahead correlation forecast as the quarterly time-series data
are not sufficiently long. Panel (a) of Table 2 reports a 3 x 3 correlation spillover table within the GC areas.
Over the full period, about 34.3% of the correlation forecast error variance comes from correlation spillover
among the three real estate securities market correlation series (i.e. CH-HK, CH-TW and HK-TW). The
remaining 65.7% of the total forecast error variance is explained by own correlation shocks rather than
spillover of shocks across the foreign correlation series. Additionally, the correlation spillover indices are,
respectively, 43.5% (CH-INT: Panel b), 31% (HK-INT: Panel c), and 35.1% (TW-INT: Panel c). Based on
these results, we are inclined to conclude that the extent of correlation dependence (in terms of correlation
9
Alternatively, the column normalization method makes the sum of the forecast error variance in each column equals
to 100%.
18
spillover) in real estate securities markets is moderate. Compared with the other three groups, the CH-INT
has the highest aggregate correlation spillover index, and thus highest correlation dependence. We interpret
this result to reflect as China opens her doors since 2000’s, her international economic and capital market
linkages have grown in tandem with its open economic policies. Consequently, her real estate securities
market correlation interacts significantly with various major international markets in line with increasing
globalization and integration of world financial markets
(Table 2 here)
Given that the aggregate correlation spillover index can only provide an indication of the
“average” correlation dependence behavior over the entire study period, we estimate correlation spillover
indices over rolling 12-quarter sub-sample windows (i.e. rolling correlation dependence). Figure 3 presents
a spillover plot each for the four groups. With some exceptions of correlation spillover between HK-INT
and TW-INT, the four correlation spillover plots display somewhat different fluctuating patterns over
various sub-sample windows, implying that the time-varying correlation dependence among the four
groups might not share a common trend. Finally, we have observed while the correlation spillover index
reveals a trend of increased dependence across the three GC groups, there is some evidence of declining
real estate securities market correlation dependence among the CH-INT group members following the
Lehman Brother’s bankruptcy in September 2008.
(Figure 3 here)
The average degree of dependence between real estate securities and stock market correlations is
indicated in Table 3. First, the co-movements between real estate securities and stock markets correlations
are between 0.330 (CH-UK) and 0.888 (HK-SG), with 14 correlation coefficients has a value each of more
than 0.5 (Column 2). Thus about between 10.9% and 78.9% of the variations in real estate securities market
correlations can be attributed to the changes in the corresponding stock market correlations or vice-versa.
In addition, column 3 of Table 3 quantities the dependence between the two cross-asset correlations from
the spillover perspective, with the estimated aggregate correlation spillover index ranges from a low of
11.3% (TW-UK), 11.5% (CH-UK) to a high of 40.9% (CH-SG) and 44.5% (HK-SG). Finally, column 4
indicates that on average, 10 real estate securities market pairs are at the giving end of the net correlation
19
transmission over the entire period. Similarly, another seven cross-stock market correlations are a net
transmitter of correlation with differing magnitudes of net spillover.10 Taking the results as a whole, we are
inclined to conclude, for our dataset, the international correlation structure of real estate securities and the
broader stock markets are linked to each other from the co-movement and correlation spillover perspectives.
Furthermore, greater co-movements are accompanied by stronger magnitudes of correlation spillover
between the cross-real estate and cross-stock market correlations. This knowledge about the time-varying
correlation dependence from the co-movement and spillover perspectives will thus help investors in
estimating better the changing diversification effects in their cross-asset decisions in international mixed
portfolios.
(Table 3 here)
5.3
Correlation regimes in real estate securities markets
The first issue to be considered is the determination of the number of breaks for each of the 18
realized correlation series. The BP (2003)’s sequential procedure (using 5% significance level) reveals
with the exceptions of four correlation series (CH-UK, HK-US, TW-US and TW-UK), all other 14 cases of
F(1/0) statistic have at least one structural break (two regimes). Additionally, two F (2/1) statistics are
statistically significant, indicating two structural breaks (three regimes) characterize the HK-AU and TWSG realized correlation series.
Table 4 reports the dates for the identified structural breaks in the mean level for the 14 realized
correlation series. The break dates correspond to the end of each regime. One observation is that many of
the correlations’ structural changes obtained coincide with the official periods of GFC and are common to
some markets (2006Q1, 2006Q4, 2007Q2, 2008Q2, 2008Q3 and 2009Q1). In addition, there are other
instances of market-specific breaks, such as 1999 Q1 (HK-AU), 2002Q2 (TW-SG) and 2005Q1 (CH-HK).
Finally, Table 4 provides the mean of the 14 realized correlation series under different regimes.
With a minor exception, all contiguous regimes’ correlation non parametric (median t-test) are at least
10
In addition to the total spillovers (from/to each market I, to/from all other markets, added across i) Diebold and
Yilmaz (2012) introduce the concept of net direction spillovers (the difference between to/from a particular market).
20
significant at the 5% level implying that the break points identified are robust. Based on these results, we
are inclined to conclude that real estate securities market correlations for our dataset are subject to regime
changes similar to asset volatility. Failure to consider changing behavior in cross-market correlations and
covariance forecasting due to regime changes might thus result in inaccurate or sub-optimal portfolio
diversification benefit estimates in global real estate investing.
(Table 4 here)
5.4
Correlation determinants
5.4.1
Panel unit root tests
All time series variables are first tested for their stationary property using panel unit root tests.
With one exception, all three panel unit root processes (Harris-Tsavallis test, Im-Pesaran-Shin test and
Breitung test) have consistently rejected the null of a unit root in the respective variables (Table 6). Since
all variables in the regression are stationary, the assumptions of classic regression analysis are fulfilled.
Consequently, we proceed to the regression analysis.
(Table 6 here)
5.4.2
Pooled cross-section time-series models
Table 7 reports the results (in both local currency and US dollar returns) of estimating Equation 1
as a pooled cross-sectional and time series regression using (a) a generalized least square (GLS) estimator
for random effect model; (b) feasible GLS method; and (c) dynamic GMM estimation (Models 1-6). The
dependent variable is the transformed realized correlation coefficient since the raw realized correlation
coefficients are not normally distributed.
Overall, the chosen independent factors offer substantial
explanatory power on the time series movement in the realized correlation structure (Adjusted R2 is
between 0.704 and 0.715). Significant explanatory variables (p<0.10) for both local currency and US dollar
returns include stock market correlation (CORST), relative real estate securities size differential
(LNRESIZEST), direct real estate market return performance differential (DIRECT), global real estate
securities market volatility (GREV) and one-quarter real estate securities market correlation {Correlation(1)}. For local currency denominated returns, significant independent variables for both random effects
21
model and dynamic panel-GMM estimation include actual inflation differential (INF), institutional
development differential (IS) and a quarterly dummy (Q2). Alternatively, for US dollar returns, additional
significant variables for both random effects model and dynamic GMM estimation include actual inflation
differential (INF) and a quarterly dummy (Q2). Moreover, the influence of all the significant variables is
consistent to the requirements of the economic theory. Additionally, we observe the influence of the REIT
factor (REGIONREITS) is statistically insignificant at the 10% level. Finally, among the key
macroeconomic variables, only inflation differential is found to be negatively impact the realized
correlations estimated in both local currency and US dollar returns. Other macroeconomic variables are
statistically insignificant at the 10% level.
(Table 7 here)
Table 8 presents the random effect model estimation results using (a) traditional unconditional
correlations estimated between the pairs of the daily (nominal) returns over the quarters; (b) transformed
realized correlations estimated using real returns; and (c) unconditional correlations estimated using real
returns. These three alternative measures of real estate securities market co-movements provide tests for the
robustness of the pooled sample results reported in Table 7. A total of six models are estimated. Again, the
selected independent variables offer reasonably strong explanatory power on the time series movements in
the correlation structure (Adjusted R2 is between 0.549 and 0.866). Similar to the nominal realized
correlation estimate, stock market correlation (CORST) is found to increase significantly the co-movements
of real estate securities market returns. The same applies to global real estate securities market volatility
(GREV) and one-period lagged correlations (Correlation
t-1).
In contrast, direct property market return
differential (DIRECT) and global stock market returns (GST) are found to decrease the co-movements of
real estate securities market returns. Finally, to a lesser extent, the relative real estate securities market size
differential (LNRESIZEST) and institutional quality differential (IS) are significantly related to the
nominal and real unconditional correlations, estimated for both US dollar and home currency returns.
(Table 8 here)
5.4.3
Results of the seemingly unrelated regressions (SUR) model
22
Table 9 reports the SUR results by presenting the frequency that each independent regression
coefficients takes on a (significant) positive or negative value across all 18 equations for the transformed
nominal realized correlations, estimated for US dollar denominated and for local dollar returns, respectively.
(Table 9 here)
Whilst the SUR results indicate some additional factors that might potentially influence realized
correlations, they nevertheless reinforce the pooled sample results. We briefly explain the individual
influence of the key regression variables on the correlation structure below.
One dominant factor from the SUR analysis is stock market correlation (CORST), which is
significant positive in all 18 equations (local dollar returns) and 16 equations (US dollar returns). Given
that greater stock market correlations are likely to increase real estate securities market correlations due to
their strong dependence (Table 3), their relationship is now firmly established. Second, global real estate
market volatility (GREV) reveals a positive influence on the realized correlation structure. For the US
dollar returns, the coefficient for this variable is positive in 13 of 18 equations, and is statistically
significant in five equations. In home currency return, this coefficient is only positive in eight equations but
significant in six equations. Third, the direct property markets’ return differential (DIRECT) displays a
tendency for a negative relationship with the realized correlation structure. In Table 9, this coefficient is
negative 13 times and with three significant coefficients (local dollar returns), as well as 12 times (with
four significant – US dollar returns) These results are reinforced in the pooled results of Table 7, suggesting
a negative link between the direct property market return differential and the realized correlation structure.
Fourth, the global stock market return (GST) appears to influence negatively the real estate securities
markets’ realized correlation structure. This negative coefficient is negative between 11 and 13 times, and
is significant between three and four times. This negative coefficient is consistent with the pooled sample
results, implying greater co-movements across the sample real estate securities markets when the world
stock market is declining. Fifth, while the SUR results indicate some tendency for the relative real estate
securities market size differential (LNRESIZEST) to influence positively the realized correlation structure
(the coefficient is positive between 7 and 11 times, and between two and four coefficients are significant).
In contrast, the pooled regression results of Table 7 indicate a significantly negative relationship between
23
the LNRESIZEST variable and the correlation structure. Therefore, whether two real estate securities
markets that are more disparate (or similar) in LNRESIZEST should have lower correlations is arguable.
Additionally, the SUR analysis reveals some other factors that appear to influence the correlation
structure to different degrees. Notably, the trend is positive in 10 equations, and significant in five, on a
local dollar basis. Similar results (11 positive with 5 significant) are obtained for US dollar returns. This
outcome generally supports a trend towards greater integration across the real estate securities markets over
time. Other potential factors include: real estate securities market volatility and institutional quality
differential (for both local and US dollar returns); as well as term structure premium differential and real
interest rate differential (for local dollar returns).
Based on the pooled regression and SUR models, we are inclined to conclude that stock market
correlations, global real estate market volatility, direct property market return differential and global stock
market returns are four main determinants of real estate securities market correlation structure for our
dataset. Additionally, some other potential factors are one-period lagged correlation, relative real estate
securities market size, institutional quality differential, inflation differential, real interest rate differential
and term structure premium differential. These factors are combined to explain a substantial proportion of
correlation structure within and across the GC areas.
5.4.4
Forecasting the correlation structure
Table 10 compares the one-step-ahead forecasting ability of the correlation model (equation 1)
with that of other four models (see 4.4f). First the performance of the five models is evaluated on the basis
of minimizing the Root Mean Squared Error (RMSE) across the set of 18 forecasts every quarter from
2009Q1 to 2011Q4 (12 quarters). As the numbers in Table 10 indicates, the strongest forecast performance
in terms of RMSE is given by the correlation model (equation 1) for the years 2009, 2010, 2011 and
average of 2009-2011 (for local dollar returns), as well as for the years 2009, 2010 and average of 20092011 (for US dollar returns). The only exception is that the historical model outperforms all other models
for US dollar returns for the year 2011.
(Table 10 here)
24
We then follow the standard procedures to partition the Theil decomposition (U) of the MSE into
three components: bias (U b), variance (U v) and covariance (U c))11. For local dollar returns, results in
Table 10 indicate the correlation model outperforms other four models in offering desirable forecast
characteristics in terms of their Theil decomposition. However, the performance of the correlation model
drops for US dollar returns. As the numbers indicate, except for the “no change” model, the remaining four
models are the outperformers in different sub-periods in terms of Theil decomposition.
6.
CONCLUSION
.
In this study, we employ daily data on national real estate securities market returns from 19952001 to generate a quarterly realized correlation series for eight markets within and across the GC areas.
Our estimates reveal a tendency of international real estate securities market correlations to increase over
time. Moreover, there exists correlation dependence (in term of correlation spillover) between real estate
securities and stock markets, as well as across the real estate securities markets. Finally, the realized
correlations are subject to regime switching as reflected in the detection of structural breaks. These time
series characteristics are incorporated in modeling the correlation structure over time, and thus the
evolution in real estate securities market integration.
A theoretical correlation model that includes potential macroeconomic factors, securitized /direct
real estate market factors, world market factor, institutional development factor, crisis dummies and time
dummies is specified, using both local dollar returns and US dollar denominated returns. We undertake a
regression-based analysis to determine the significant correlation factors. Results are generally robust
against the pooled cross-section time series regression models with random effects, feasible generalized
least squares (FGLS) and dynamic panel GMM techniques, individual regressions using seemingly
unrelated regression (SUR) method, as well as out-of-sample correlation forecasting.
Based on the results generated, we are inclined to conclude that stock market correlations, global
real estate market volatility, direct property market return differential and global stock market return are
11
According to Pindyck and Rubinfield (1998), the three components should sum to 1. Moreover, the optimal foresting
model should ideally yield values of U b and U v should be small so that most of the bias is concentrated on the
covariance proportions.
25
four main determinants of real estate securities market correlation structure for our dataset. Additionally,
some other potential factors are one-period lagged correlation, relative real estate securities market size,
institutional quality differential, inflation differential, real interest rate differential and term structure
premium differential. These factors are combined to explain a substantial proportion of correlation structure
within and across the GC areas. Finally, given the plentitude of variables available to international investors,
it thus becomes important for them to consider only those factors that are particularly useful for modeling
the changes in the international co-movements of real estate securities markets returns. Our GC results are
thus indicative in this direction.
Some of the above findings motivate further research. First, it would be useful to replicate the
study to include all national real estate securities markets classified by regions (Asian, Europe and
Americas) and stage of development (developed and emerging) to confirm whether the findings from this
study could be generalizable. Second, the simultaneous relationships between stock markets and real estate
securities markets can be explored by including each national stock market (instead of global stock market)
in the correlation model. In this manner, it is hoped that that any findings on the economic influence could
be more accurately attributed to the securitized real estate market per se. Third, we believe the REIT factor
distinguishes between stock and real estate securities markets. As such, its significance in our correlation
model deserves a closer examination to investigate whether the correlation between two real estate
securities markets (within the same region) that have a REIT market structure during quarter t could be
higher than that of two markets that behave otherwise. With longer time series available, future research
can test for the significance of this REGIONREIT factor across other international real estate securities
markets.
26
References
Anderson, T.G., Bollerslev, T., Diebold, F. and Eberns, H. (2001), “The distribution of realized stock return
volatility” Journal of Financial Economics 61(1): 43-76
Arellano, M. and Bond, S.R. (1991), “Some tests of specification in panel data: Monte Carlo evidence and
an application to employment equations” Review of Economic Studies 58: 277-297
Bai, J. and Perron, P. (2003), “Computation and analysis of multiple structural change models” Journal of
Applied Econometrics 18:1-22
Bardhan, A. Edelstein, R. and Tsang, D. (2008), “Global financial integration and real estate security
returns” Real Estate Economics 36(2): 285-311
Baum, C. (2006), An introduction to modern econometrics using Stata, StataCorp LP.
Beine, M and Candelon, B. (2011), “Liberalization and stock market co-movement between emerging
economies” Quantitative Finance 11(2): 299-312
Bodurtha, J.N., Cho, D.C. and Senbet, L.W. (1989), “Economic forces and stock market: an international
perspective” Global Finance Journal 1: 221-46
Bracker, K. and Koch, P.D. (1999), “Economic determinants of the correlation structure across
international equity markets” Journal of Economic and Business 51, 443-471
Bracker, K., Docking, D.S. and Koch, P.D. (1999), “Economic determinants of evolution in international
stock market integration” Journal of Empirical Finance 6, 1-7
Brooks, C. and Tscolacos, S. (1999), “The impact of economic and financial factors on UK property
performance” Journal of Property Research 16(2), 139-152
Campbell, J. and Hamao, Y. (1992), “Predictable stock returns in the United States and Japan: a study of
long-term capital market integration” Journal of Finance 47: 43-66
Case, B. Yang, Y. and Yildirim, Y. (2011), “Dynamic correlations among assert classes: REIT and stock
returns” Journal of Real Estate and Finance (forthcoming)
Chen, N., Roll, R. and Ross, S. (1986), “Economic forces and the stock market” Journal of Business, July,
383-403
Chen, N. and Zhang, F. (1997), “Correlations, trade and stock returns of the Pacific-Basin markets”
Pacific-Basin Finance J. 5, 559-577
Cotter, J. and Stevenson, S. (2006), “Multivariate modeling of daily REIT volatility” Journal of Real Estate
Finance and Economics 32: 302-325
Diebold, F. and Yilmaz, K. (2012), “Better to give than to receive: predictive directional measurement of
volatility spillovers” International Journal of Forecasting 28, 57-66.
Erb, C.S., Harvey, C.R., and Viskanta, T.E. (1994), “Forecasting international equity correlations”
Financial Analysts Journal 50, 32-45
Guerts, T.G. and Jaffe, A.J. (1996), “Risk and real estate investment: an international perspective” Journal
of Real Estate Research 11(2): 117-130
Hoesli, M., Lekander, J. and Witkiewiez, W. (2004) “International evidence on real estate as a portfolio
diversifier” Journal of Real Estate Research 26(2): 161-206
Johnson, R. and Soenen, L. (2002), “Asian economic integration and stock market co-movement” The
Journal of Financial Research 25(1): 141-157
27
Ling, D. and Naranjo, A. (2002), “Commercial real estate return performance: a cross-country analysis”
Journal of Real Estate Finance and Economics 24(1): 119-142
Liow, K.H., Ho, David K.H., Faishal, M.F. and Chen, Z. (2009), “Correlation and volatility dynamics in
international real estate securities markets” Journal of Real Estate Finance and Economics 39(2): 202-223
Liow, K.H. and Newell G. (2012), “Investment dynamics of the Greater China securitized real estate
markets and international linkages” Journal of Real Estate Research (forthcoming)
Lizieri, C. and Satchell, S (1997), “Interactions between property and equity markets: an investigation of
linkages in the United Kingdom 1972-1992” Journal of Real Estate Finance and Economics 15(1), 11-26
McCue, T.E. and Kling, J.L (1994), “Real estate return and the macroeconomy: some empirical evidence
from real estate investment trust data: 1972-1991” The Journal of Real Estate Research 9(3). 277-287
Michayluk, D. Wilson, P. and Zurbruegg, R. (2006), “Asymmetric volatility, correlation and return
dynamics between the US and UK securitized real estate markets” Real Estate Economics 34(1): 109-131
Pindyck, R. and Rubinfield (1998), Econometric models and economic forecast, McGraw-Hill Book Co
Tavares, J. (2009), “Economic integration and the co-movement of stock returns” Economic Letters 103,
65-67.
Walti, S. (2011), “Stock market synchronization and monetary integration” Journal of International Money
and Finance 30, 96-110
Yang, J., Zhou, Y.Y. and Wang, Z. (2009), “The stock-bond correlation and macroeconomic conditions:
one and a half centuries of evidence” Journal of Banking and Finance 33, 670-689
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Table 1
Realized Correlations in real estate securities markets
Notes: This table reports the average value, standard deviation, maximum value, minimum value and
quarterly trend of real estate securities markets’ realized correlations(RC)(in local dollars) for the full
period (1995Q1-2011Q4, 68 quarters), as well as the average value and standard deviation of the RC
series during the global financial crisis (GFC) period (2007Q3-2009Q4, 10 quarters). The quarterly trend
is estimated via the following equation: RCt  f ( RCt 1. , AFC t , GFCt , trend t , const ) (AFC: Asian
financial crisis period: 1997Q3-1999Q4, 10 quarters) with Newey-West HAC Standard errors and
covariance adjustment. ***, **, * - indicates that the estimated quarterly time trend is statistically
significant at the 1%, 5% and 10% level respectively.
Full period
CH-HK
CH-TW
HK-TW
Mean
0.3617
0.1771
0.2304
Std dev
0.3017
0.2160
0.1949
Max
Min
0.8567 -0.1711
0.6933 -0.3587
0.7057 -0.3064
GC average
CH-JP
CH-SG
CH-AU
CH-US
CH-UK
0.2564
0.1765
0.2875
0.1588
0.0174
0.0382
0.2065
0.2271
0.2652
0.2116
0.1308
0.1337
0.7319
0.7008
0.7130
0.6294
0.3231
0.3508
CH-INT(average)
HK-JP
HK-SG
HK-AU
HK-US
HK-UK
0.1357
0.3255
0.5553
0.2979
-0.0176
0.0111
0.1296
0.1894
0.1673
0.1822
0.1516
0.1717
HK-INT(average)
TW-JP
TW-SG
TW-AU
TW-US
TW-UK
0.2344
0.1962
0.2150
0.1324
0.0131
0.0267
TW-INT(average)
0.1167
GFC
Trend (%)
0.800***
0.700***
0.534***
Mean
0.7614
0.3988
0.3376
Std dev
0.0486
0.1891
0.2200
-0.1044
-0.2173
-0.1621
-0.2314
-0.3227
-0.2613
0.742***
0.650***
0.679***
0.368***
0.077
0.046
0.4992
0.4781
0.6025
0.3723
-0.0413
0.0186
0.1274
0.1065
0.0903
0.1693
0.1672
0.1500
0.4064
0.6336
0.8122
0.6540
0.2784
0.3949
-0.0795
-0.1871
0.0498
-0.0547
-0.3830
-0.4044
0.357***
0.448***
0.396***
0.172***
0.023
0.017
0.2860
0.5530
0.7111
0.4588
-0.0929
-0.0289
0.0528
0.0469
0.0662
0.1253
0.1706
0.2019
0.0978
0.1898
0.2031
0.1825
0.1317
0.1277
0.4433
0.6030
0.6043
0.5783
0.2737
0.3167
0.0278
-0.1988
-0.2986
-0.2430
-0.3532
-0.2085
0.219***
0.571***
0.620***
0.352***
0.060
-0.082
0.3202
0.3204
0.3574
0.2426
-0.0718
-0.0071
0.0457
0.1946
0.1843
0.2021
0.1151
0.1359
0.0992
0.3626
-0.0867
0.286***
0.1683
0.0923
29
Table 2
Correlation spillover in real estate securities markets: 1995-2011
(a) Within Greater China areas (correlation VAR: CH-HK, CH-TW and HK-TW)
CH-HK
CH-TW
HK-TW
Contribution to others
Contribution including
owns
CH-HK
85.4
40.6
22.7
63
149
CH-TW
10.7
47.2
12.9
24
71
HK-TW
3.9
12.1
64.4
16
80
From others
15
53
36
103
Correlation spillover
index: 34.30%
(b) Across China and international (correlation VAR: CH-JP, CH-SG, CH-AU, CH-US and
CH-UK)
CH-JP
CH-SG
CH-AU
CH-US
CH-UK
Contribution to others
CH-JP
40.7
21.6
21.7
0.6
0.0
44
85
CH-SG
39.9
54.3
31.4
1.5
2.9
76
130
CH-AU
16.2
19.1
37.9
3.1
8.9
47
85
CH-US
2.2
2.7
4.1
77.6
16.5
25
103
CH-UK
1.1
2,3
4.9
17.3
71.8
26
97
Contribution including
owns
From others
59
46
62
22
28
218
Correlation
spillover
index:
43.50%
(c) Across Hong Kong and international (correlation VAR: HK-JP, HK-SG, HK-AU, HK-US
and HK-UK)
HK-JP
HK-SG
HK-AU
HK-US
HK-UK
Contribution to others
HK-JP
64.1
22
23.4
0.1
4.8
50
114
HK-SG
17.7
62.5
15.2
0.5
3.6
37
99
HK-AU
14.7
12.5
57
4.8
1.9
34
91
HK-US
2.4
1.1
3
82.7
11
18
100
HK-UK
1
1.8
1.4
12
78.7
16
95
Contribution including
owns
From others
36
37
43
17
21
155
Correlation
spillover
index:
31.00%
(d) Across Taiwan and international (correlation VAR: TW-JP, TW-SG, TW-AU, TW-US and
TW-UK)
TW-JP
TW-SG
TW-AU
TW-US
TW-UK
Contribution to others
Contribution including
owns
TW-JP
60.1
25.6
13.1
0.6
0.6
40
100
TW-SG
28.5
63.2
21.8
0.1
1.5
52
115
TW-AU
10.6
10.2
55.2
6.5
8
35
91
TW-US
0.4
0.2
4.3
74.5
18.5
23
98
TW-UK
0.4
0.9
5.6
18.3
71.4
25
97
From others
40
37
45
25
29
Correlation
spillover
index:
35.10%
Notes: The estimates are based on the realized correlations (in local dollars).The underlying variance decomposition is
based upon a monthly VAR of order 1, identified using a generalized VAR spillover framework proposed by Diebold
and Yilmaz (2012) (forecast error variance decompositions are invariant to variable ordering). The (i, j)th value is the
estimated contribution to the variance of the 12-quarter ahead correlation forecast error variance of series i coming
from innovations to the correlation of series j
30
Table 3
Relationship between real estate securities market correlations and
stock market correlations: 1995Q1-2011Q4
Economy pair
Correlation coefficient
(t-stat) 1
Correlation spillover
index (%) 2
Net directional spillover
(%) (real estate /stock) 3
China-Hong Kong
0.8210*** (11.68)
39.0
6 (real estate)
China - Taiwan
0.7025*** (8.02)
31.2
13 (stock)
Hong Kong-Taiwan
0.7410*** (8.97)
33.4
9 (stock)
China-Japan
0.7442*** (9.05)
35.7
9 (real estate)
China-Singapore
0.8248*** (11.85)
40.9
10 (real estate)
China-Australia
0.3824*** (3.36)
11.3
5 (real estate)
China – US
0.4415***(4.00)
17.6
1(real estate)
China – UK
0.3259***(2.81)
11.5
1 (stock)
Hong Kong – Japan
0.6725*** (7.38)
29.8
6 (real estate)
0.8878*** (15.67)
44.5
1(stock)
0.6824*** (7.58)
31.5
3 (real estate)
Hong Kong – US
0.6401***(6.77)
30.0
0
Hong Kong - UK
0.6444***(6.84)
30.3
1 (real estate)
Taiwan – Japan
0.6983*** (7.93)
29.7
15 (stock)
Taiwan – Singapore
0.7453***(9.08)
34.2
16 (stock)
Taiwan – Australia
0.6774*** (7.48)
28.0
18 (stock)
Taiwan – US
0.5183***(4.92)
22.4
1 (real estate)
Taiwan – UK
0.3843***(3.38)
11.3
1 (real estate)
Hong Kong –
Singapore
Hong Kong –
Australia
Notes:
1
This is the Pearson correlation coefficient between real estate securities market and stock market
correlations across two economies. *** - indicates two-tailed significance at the 1% level.
2
This is the average correlation spillover index between real estate securities correlation and stock market
correlation
3
Following Diebold and Yilmaz (2012)’s methodology that measures the directional spillovers in a
generalized VAR framework, for each real estate correlation series, we define net directional correlation
spillover as the difference between (a) the directional correlation spillovers transmitted by the real estate
correlation to the corresponding stock market correlation; and (b) the directional correlation spillovers
received by the real estate correlation from the corresponding stock market correlation
31
Table 4
Correlation regimes in real estate securities markets:
1995Q1 – 2011Q4
Notes: Based on the Bai-Perron break point analysis, the break dates are: CHHK (2005Q3), CHTW (2007Q2),
HKTW (2002Q2), CHJP (2006Q1), CHSG (2006Q1), CHUS (2009Q1), HKJP (2006Q1), HKSG (2006Q1), HKUK
(2008Q3), TWJP (2007Q2), TWAU (2006Q4), CHAU (2006Q1), HKAU (1999Q1, 2005Q4), and TWSG (2002Q2,
2008Q2). The independent-samples median test statistic is the non-parametric test of the null hypothesis that the
average (realized) correlations of every two contiguous regimes are equal. ***, **, * - indicates statistical
significance at the 1%, 5% and 10% level. Of the 10 realized correlation series, only 14 pairs are reported as the
remaining 4 pairs (CH-UK, HK-US, TW-US and TW-UK) have no structural break detected. (Source: derived
from SPSS Statistics 20)
Correlation
(realized, LCL)
CH-HK
Correlation test
Regime 1
Regime 2
Regime 3
Mean correlation
0.1650
0.7001
Median t-test
-
36.435***(0.000)
Mean correlation
0.0938
0.4084
Median t-test
-
14.809***(0.000)
Mean correlation
0.1273
0.3119
Median t-test
-
2.419 (0.120)
Mean correlation
0.0545
0.4154
Median t-test
-
26.280***(0.000)
Mean correlation
0.1284
0.5986
Median t-test
-
37.799***(0.000)
Mean correlation
0.0036
0.0888
Median t-test
-
3.904**(0.048)
Mean correlation
0.2349
0.5208
Median t-test
-
21.287***(0.000)
Mean correlation
0.4850
0.6929
Median t-test
-
21.287***(0.000)
Mean correlation
-0.0085
0.0940
Median t-test
-
3.424* (0.064)
Mean correlation
0.1308
0.3779
Median test
-
9.142***(0.002)
Mean correlation
0.0763
0.2672
Median test
-
8.571***(0.003)
Mean correlation
0.0450
0.3815
Median test
-
21.287***(0.000)
Mean correlation
0.3431
0.1416
0.4417
Median test
-
7.765**(0.016)
26.861***(0.000)
Mean correlation
0.0935
0.2439
0.4259
4.909** (0.027)
10.268***(0.001)
CH-TW
HK-TW
CH-JP
CH-SG
CH-US
HK-JP
HK-SG
HK-UK
TW-JP
TW-AU
CH-AU
HK-AU
TW-SG
Median test
32
Table 5
Explanatory Variables used in this Study
Group
Factor
Represented
by
Measured by
Expected
sign of
association
with
correlation
Macroeconomic
Growth
differential in
gross domestic
product
NGDP ijt
Absolute nominal gross domestic product (GDP)
growth differential between the two economies
during quarter t.
Negative
Inflation
INF ijt
Absolute INF differential between the two
economies during period t; INF is estimated from
consumer price index during quarter t
Negative
Real interest
rates
RINT ijt
Absolute real interest (RINT) differential between
the two economies during period t; RINT = (Oneyear deposit rate – inflation) during quarter t.
Negative
Term structure
premium
TS ijt
Absolute term structure premium (TS) between the
two economies during period t. The TS is defined
as the difference between long-term and short-term
government bond rates in a country during quarter t
Negative
% change in the
bilateral
exchange rate
EX ijt
Change in bilateral exchange rate during quarter t
Negative
Variability in
exchange rate
VAREX ijt
Variance in daily exchange rate during quarter t
Negative
Stock market
integration
CORST ijt
Correlations (realized /unconditional) between the
two corresponding stock markets during quarter t
Positive
Existence of a
REIT market
structure
REGIONREITS ijt
Dummy equals 1 if both stock markets have a
REIT structure and are in the same region (Asia,
Europe and North America) during quarter t; 0
otherwise.
Positive
Market
volatility
VARRE it
VARRE jt
Variance (realized /unconditional) of real estate
securities market i and market j during quarter t
Positive
Relative size of
real estate
securities
markets
LNRESIZEST ijt
Absolute LNRESIZEST differential between the
two economies’ real estate securities markets
during quarter t. LNRESIZEST is calculated as:
LN{(MCAP)real estate /(MCAP)stock}
Negative
Direct real
estate market
performance
DIRECT ijt
Absolute DIRECT differential between the two
economies’ orthogonalized real estate securities
markets during quarter t. For each economy,
Negative
Securitized
real estate
DIRECT is calculated as the residuals (  t ) from
the regression:
(Re turn) re,t     (return) stock,t   t
Global real
estate securities
market
volatility
GREV t
Unconditional variance of daily global real estate
securities market index (extracted from S&P
Global Property) return during quarter t
33
Positive
World
market
Global stock
market returns
GST t
Percent change in global stock market (proxied by
S&P BMI) index during quarter t
Negative
Institutional
development
Institutional
quality
IS ijt
Absolute IS differential between the two economies
during quarter t. IS covers six aspects: voice and
accountability; political instability and governance;
government effectiveness; regulatory quality; rule
of law and control of corruption (World Bank
Governance Indicators – WBGI). Represented by a
simple average of the six indices as a a proxy for
aggregate institutional quality
Negative
Crisis
dummies
Asian financial
crisis (AFC)
D97
Dummy equal to 1 for AFC periods, 0 otherwise
Positive
Global financial
crisis (GFC)
D08
Dummy variable equal to 1 for GFC, 0 otherwise
Positive
Seasonal
dummy
Q1, Q2 , Q3
Seasonal dummy variables for the first three
quarters
Positive
/negative
Linear trend
TREND
Quarterly linear time trend
Positive
Lagged
correlation
Correlation (-1)
One-quarter lagged correlation during quarter t
Positive
Time
dummies
Others
34
Table 6
Panel Unit Root Test Results: 1995Q1 – 2011Q4
Variable
Harris-Tsavallis (HT)
test
Im-Pesaran-Shin
(IPS) test
Breitung (BT) test
RC(LCL)
0.3377***
-17.6953***
-14.2423***
RC(USD)
0.3429***
-17.3081***
-13.7442***
RCST(LCL)
0.3784***
-17.1884***
-13.0133***
RCST(USD)
0.3826***
-17.4742***
-12.5399***
GDP (differential)
0.6756***
-12.5950***
-9.3305***
INF (differential)
0.0397***
-20.9518***
-18.9104***
RINT (differential)
0.1306***
-19.2163***
-12.1403***
TS (differential)
0.4019***
-16.0086***
-12.0978***
EXCH
0.0726***
-20.8406***
-20.0768***
VAREX
0.1000***
-21.8518***
-21.4918***
GST
-0.1032***
-23.4621***
-20.9554***
GREV
0.1612***
-19.3854***
-21.30-47***
IS (differential)
0.7539***
-4.1039***
-5.2560***
LNRESIZEST
(differential)
0.5357***
-11.5957***
-6.8675***
RVARREUSD1
0.1504***
-20.0056***
-21.3081***
RVARREUSD2
0.1344***
-19.3553***
-19.5021***
RVARRELCL1
0.1756***
-19.5254***
-20.8766***
RVARRELCL2
0.1309***
-18.9030***
-19.3655***
VARREUSD1
-2.1893***
-3.0366***
-10.0635***
VARREUSD2
-0.6400***
-1.1686
-6.9567***
VARRELCL1
0.1765***
-19.4853***
-21.3211***
VARRELCL2
0.1321***
-18.8689***
-19.5261***
DIRECT (differential)
(LCL)
-0.0464***
-22.2594***
-19.2222***
DIRECT (differential)
(USD)
0.0269***
-21.2868***
-19.8059***
Notes: (a) Harris-Tsavalis (HT) test – Ho: panels contain unit root; Ha: panels are stationary (b) Im-Pesaran Shin
(IPS) test – Ho: panels contain unit root; Ha: some panels are stationary (c) Breitung (BT) test – Ho: panels
contain unit root; Ha: panels are stationary. *** - indicate that Ha is statistically significant at the 1% level.
Please refer to Table 1 for variable description (Source: Extracted from Stata 12.0).
35
Table 7
Results of pooled time series and cross-sectional regression analysis: 1995Q1-2010Q4 (Dependent variable: realized
correlations)
Based on equation 1, the dependent variable is the bilateral realized correlations (RC) between real estate securities market i and j (18 pairs), estimated from daily returns over each quarter from
1995 to 2011. This table presents results (local currency and US-dollar) of estimating the equation as a pooled time series and cross-sectional regression using three different estimation methods.
Models 1and 4 are fitted with a generalized least squares (GLS) estimator for random effect models. Models 2 and 5 are fitted using feasible GLS which allows the error terms of panels to be
correlated in addition to having different scale variances (heteroskedasticity across panels). Models 3 and 6 are fitted with using dynamic panel-data GMM ***, **, * - indicates statistical
significance at least at the 1%, 5% and 10% level respectively. Figures in parenthesis are the z-statistics associated with the significant coefficients (Source: extracted from Stata 12.0).
Local dollar returns
Variable
US dollar return
Model 1
Random effect GLS
Model 2
Feasible GLS
Model 3
Dynamic GMM
Model 4
Random effect GLS
Model 5
Feasible GLS
Model 6
Dynamic GMM
Coefficient
Coefficient
Coefficient
Coefficient
Coefficient
Coefficient
0.034
-1.479***
(-2.93)
-0.178
0.121
-0.030
-0.449
0.185
-1.331***
(-2.89)
-0.025
0.299
0.654
0.253
0.519
0.123
-1.6436***
(-2.84)
-0.231
-0.001
0.107
-2.183***
(-4.90)
-0.058
-1.476
1.065
-1.012
0.834
0.199
0.707
-1.939***
(-2.79)
0.749
VARRE it
-11.586
0.458***
(11.52)
0.594
-14.032
0.538***
(18.84)
0.471
-12.228
0.461***
(26.67)
0.551
15.747
0.476***
(27.76)
0.297
VARRE jt
-0.641
10.358
0.436***
(5.86)
0.902*
(1.74)
-0.735
0.032
0.027
-0.919***
(-2.61)
0.022
-0.421
REGIONREITS ijt
LNSIZEST ijt (differential)
-1.434**
(-2.31)
-0.023
20.386
0.496***
(9.74)
1.310**
(2.38)
-0.871
0.015
-0.008
-0.037*
(-1.86)
-19.144***
(-3.24)
-0.039**
(-2.00)
-24.902***
(-4.04)
-0.027**
(-2.19)
-18.807***
(-3.29)
-0.022***
(-2.79)
-14.787***
(-3.00)
-0.013*
(-1.89)
-12.760***
(-2.61)
-0.038***
(-3.07)
-26.739***
(-5.60)
GDP ijt (differential)
INF ijt (differential)
RINF ijt (differential)
TS ijt (differential)
EX ijt
VAREX ijt
CORST ijt
DIRECT ijt (differential)
0.257
-0.488
36
GREV t
GST t
IS ijt (differential)
D97
D08
Q1
Q2
Q3
TREND
Correlation(-1)
Constant
326.267***
(3.10)
-6.948
-0.069*
(-1.80)
0.033
208.610***
(2.72)
-14.560**
(-2.40)
-0.040
430.910***
(3.93)
-4.809
-0.063*
(-1.72)
0.061*
(1.69)
0.005
-
0.025
275.034***
(3.52)
-13.945**
(-2.49)
-0.037**
(-2.06)
0.038
161.247*
(1.78)
-21.518***
(-3.09)
-0.017
223.430**
(2.03)
-15.714***
(-3.58)
-0.041
0.017
0.070
-0.024
0.009
-0.026
0.019
0.019
-
0.046**
(2.03)
0.018
0.044
0.039*
(1.91)
0.024
0.010
0.007
0.019
0.005
0.052***
(3.41)
0.023
0.039
0.033
0.047***
(3.50)
0.016
0.0008
0.0016
0.0005
0.00002
0.0007
0.217***
(4.51)
0.067
0.246***
(5.65)
-0.017
0.076**
(2.46)
0.064
0.171***
(7.54)
0.083***
(2.62)
0.189***
(8.49)
0.011
37
0.028
0.0033*
(1.74)
0.137***
(4.85)
0.044
Table 8
Results of pooled time series and cross-sectional regression analysis: 1995Q1-2010Q4, using different measures of
correlations
Based on equation 1, we use three alternative measures of correlations (nominal unconditional correlations, real realized correlations and real unconditional correlations). This table presents
results (local currency and US-dollar) of estimating the equation as a pooled time series and cross-sectional regression using a generalized least squares (GLS) estimator for random effect
models. ***, **, * - indicates statistical significance at least at the 1%, 5% and 10% level respectively. Figures in parenthesis are the z-statistics associated with the significant coefficients
(Source: extracted from Stata 12.0).
Variable
Unconditional correlations (nominal)
Realized correlations (real)
Unconditional correlations (nominal)
Model 7
Local dollar returns
Coefficient
Model 8
US dollar returns
Coefficient
Model 9
Local dollar returns
Coefficient
Model 10
US dollar returns
Coefficient
Model 11
Local dollar returns
Coefficient
Model 12
US dollar returns
Coefficient
0.302**
(2.12)
-1.134*
(-1.84)
0.245
0.606
0.231
-25.962
0.403***
(3.28)
-0.856
-0.108
0.289
0.173
-0.715
-0.364
-0.892
0.319***
(3.31)
-0.801
0.306
0.077
0.294
14.472
0.193
-0.086
-0.041
-33.907
-0.284
1.361
0.328
15.017
0.099
0.767
0.105
-31.307
0.197
0.446
0.092
10.011
VARRE it
0.494***
(11.97)
10.065
0.521***
(10.48)
0.491
0.563***
(14.20)
1.587
-5.671
0.004
0.195
0.023
26.020
0.0018
14.176
0.021
LNSIZEST ijt (differential)
-0.035**
(-2.34)
-18.215***
(-3.75)
228.529***
(2.89)
-0.039**
(-2.33)
-22.216***
(-4.85)
191.352***
(3.02)
0.069**
(2.49)
2.019***
(4.72)
0.108
0.177**
(2.27)
-0.014
0.522***
(12.76)
-12.324
VARRE jt
REGIONREITS ijt
0.734***
(23.50)
0.304*
(1.83)
-0.076
-0.014
-0.028*
(-1.90)
-21.472***
(-7.24)
293.678***
(3.07)
-0.035**
(-2.42)
-21.358***
(-5.23)
234.216***
(4.48)
GDP ijt (differential)
INF ijt (differential)
RINF ijt (differential)
TS ijt (differential)
EX ijt
VAREX ijt
CORST ijt
DIRECT ijt (differential)
GREV t
-0.017
-17.443***
(-3.67)
206.865***
(3.06)
38
-31.740***
(-4.73)
113.975
-17.382***
(-3.04)
-0.090***
(-2.79)
0.015
-16.787**
(-2.47)
-0.085***
(-2.75)
0.001
-16.220***
(-5.69)
-0.0004
-7.166*
(-1.93)
0.023
0.052
0.036
0.047
-0.038
0.029
-0.010
-0.073
-0.026
-0.055
-0.019
Q2
0.028
Q3
0.015
TREND
0.0001
0.054**
(2.43)
0.059***
(2.66)
0.0005
0.047***
(2.81)
-0.059**
(-2.59)
0.0006
Correlation(-1)
Constant
0.226***
(5.33)
0.007
0.200***
(5.01)
-0.024
Adjusted R2
0.698
0.713
GST t
IS ijt (differential)
D97
D08
Q1
-18.145***
(-4.00)
-0.056*
(-1.84)
0.018
-18.898***
(-7.28)
-0.064**
(-2.30)
-0.007
0.009
0.019
-0.065**
(-2.64)
0.006
-0.017
-0.078**
(-2.60)
0.016
0.033
-0.019
0.008
0.0014
0.0018
0.096***
(2.76)
-0.071
0.0036**
(2.16)
0.555***
(7.15)
-0.083
0.145***
(2.74)
-0.062
0.339***
(3.33)
-0.095
0.886
0.549
0.653
0.688
39
Table 9
Summary results of Seemingly Unrelated Regression (SUR analysis): 1995-2001
Based on equation 1, the dependent variable is the bilateral nominal realized correlations (RC) between real estate securities market i and j (18 pairs), estimated from daily returns over each
quarter from 1995 to 2011. This table presents results (local currency and US-dollar) of estimating the equation for each of the 18 pairs as a SUR model. We report the frequency that the
parameter estimate for each independent variable takes a (significant) positive or negative value, across all 18 equations. *- only seven REGIONREIT coefficients could be estimated. (Source:
extracted from Stata 12.0).
Variable
Local dollar returns
US dollar returns
No. of
positive
coefficients
No of significant
positive
coefficients at the
10% level
No. of
negative
coefficients
No of significant
negative
coefficients at the
10% level
No. of
positive
coefficients
No of significant
positive
coefficients at the
10% level
No. of
negative
coefficients
No of significant
negative
coefficients at the
10% level
GDP ijt (differential)
INF ijt (differential)
RINF ijt (differential)
TS ijt (differential)
11
4
9
6
2
0
1
1
7
14
9
12
0
2
4
5
11
6
9
9
2
0
4
2
7
12
9
9
0
3
3
3
EX ijt
15
1
3
0
14
1
4
1
VAREX ijt
9
1
9
0
12
2
6
0
CORST ijt
18
18
0
0
17
16
1
1
VARRE it
9
3
9
0
12
6
6
1
VARRE jt
10
1
8
2
9
1
9
4
4
0
3
0
3
0
4
0
*REGIONREITS
11
4
7
1
7
2
11
2
DIRECT ijt (differential)
5
1
13
3
6
2
12
4
GREV t
9
6
9
1
13
5
5
2
GST t
IS ijt (differential)
7
1
11
3
5
1
13
4
4
0
14
3
6
9
12
2
D97
D08
Q1
8
1
10
1
7
2
11
1
6
7
2
2
12
11
2
2
7
7
2
2
11
11
2
2
Q2
14
1
4
0
12
2
6
1
LNSIZEST ijt
ijt
(differential)
Q3
12
0
6
1
11
2
7
2
TREND
10
5
8
1
11
5
7
0
Correlation(-1)
8
3
10
2
10
3
8
0
40
Table 10
Evaluation of forecasting results
Following Bracker and Koch (1999), we employer five models to generate forecasts of the realized correlations (nominal) for the next quarter: (a) no change model use the correlation from the
previous quarter as the forecast; (b) historical average model uses the average correlation over the previous eight quarters; (c) An ARIMA model is used to forecast one-quarter ahead; (d)
Baynes approach regresses each bilateral correlation toward the overall mean across all correlations of the previous quarters; and (e) our model uses the fitted value to forecast one-quarter
ahead. Where applicable, the estimation period is 1995-2008; the holdout forecast period is 2009-2011. As such, we generate a set of 12 one-quarter-ahead forecasts of realized correlations for
each model. This table presents the root mean squared errors (RMSE) and Theil decomposition of forecast MSE (U) for each forecasting model ( U b - bias proportion;
and
U v - variance proportion
U c - covariance proportion) for average of 2009, average of 2010, average of 2011 and average of 2009-2011 (12 quarters). Numbers in bold indicate the best forecasts.
Evaluation
criteria
Period
No change
RMSE
0.3280
0.2777
Bayes
approach
0.6104
Our model
0.2382
Historical
average
0.3128
ARIMA
0.3123
Bayes
approach
0.6159
Our model
0.3392
Historical
average
0.3315
ARIMA
2009
2010
0.4558
0.3500
0.4182
0.5494
0.3116
0.4312
0.3553
0.4040
0.5626
0.3139
2011
0.4603
0.3069
0.4262
0.7613
0.2726
0.4468
0.2943
0.3884
0.7737
0.3516
2009-2011
0.4184
0.3295
0.3856
0.6422
0.2740
0.4020
0.3208
0.3567
0.6488
0.2974
2009
0.2100
0.1695
0.1701
0.4218
0.1380
0.1887
0.1505
0.1420
0.3803
0.1230
2010
0.2868
0.1980
0.2449
0.3743
0.2005
0.2493
0.1875
0.2190
0.3519
0.1834
2011
0.2597
0.1544
0.2276
0.4626
0.1394
0.2395
0.1385
0.1940
0.4490
0.1816
2009-2011
0.2521
0.1740
0.2142
0.4196
0.1593
0.2258
0.1588
0.1850
0.3937
0.1627
2009
0.059
0.1221
0.0470
0.0413
0.0476
0.1315
0.1730
0.0560
0.0439
0.0872
2010
0.1600
0.1167
0.1758
0.0557
0.0963
0.1917
0.1764
0.1575
0.0586
0.1523
2011
0.2387
0.2383
0.2527
0.1752
0.0989
0.2506
0.3405
0.2969
0.2544
0.2196
2009-2011
0.1527
0.1590
0.1585
0.0907
0.0810
0.1913
0.2300
0.1701
0.1180
0.1531
2009
0.3125
0.1403
0.0176
0.9587
0.1537
0.4072
0.0826
0.0326
0.9561
0.1589
2010
0.2891
0.2333
0.1656
0.9443
0.1502
0.2368
0.1921
0.1541
0.9414
0.1276
2011
0.3680
0.2383
0.2667
0.8248
0.2141
0.3833
0.1775
0.2469
0.7456
0.2398
2009-2011
0.3232
0.2040
0.1500
0.9093
0.1727
0.3424
0.1507
0.1445
0.8810
0.1754
2009
0.6281
0.7377
0.9354
0
0.7986
0.4614
0.7444
0.9114
0
0.7538
2010
0.5508
0.6500
0.6586
0
0.7533
0.5715
0.6315
0.6884
0
0.7200
2011
0.3932
0.5234
0.4806
0
0.6871
0.3660
0.4820
0.4562
0
0.5409
2009-2011
0.5240
0.6370
0.6916
0
0.7463
0.4662
0.6193
0.6854
0
0.6715
U
Ub
Uv
Uc
Local dollar returns
No change
US dollar returns
41
0.2266
Figure 1
Real estate securities market daily total return indices (in local dollars)
7
6.4
5.0
Taiwan
Hong Kong
China
6.0
4.5
5.6
4.0
5.2
3.5
4.8
3.0
4.4
2.5
6
5
4
3
4.0
1996
1998
2000
2002
2004
2006
2008
2010
6.0
2.0
1996
1998
2000
2002
2004
2006
2008
2010
6.5
1996
5.6
5.2
5.5
5.2
4.8
5.0
4.8
4.4
4.5
4.4
4.0
2000
2002
2004
2006
2008
2010
6.5
2004
2006
2008
2010
2006
2008
2010
Australia
6.0
4.0
2002
6.0
5.6
1998
2000
Singapore
Japan
1996
1998
4.0
1996
1998
6.0
2000
2002
2004
2006
2008
2010
1996
1998
2000
2002
2004
United States
United Kingdom
5.6
6.0
Real estate securities market daily total
return indices (LCL)
Source: S & P
5.2
5.5
4.8
5.0
4.4
4.5
4.0
1996
1998
2000
2002
2004
2006
2008
2010
1996
1998
2000
2002
42
2004
2006
2008
2010
Figure 2
Average realized correlations (in local dollars): real estate securities and stock markets
1.0
.5
Within Greater China areas (GC)
Across China and international
.4
0.8
Stock markets
(av erage = 0.2485)
Stock markets (av erage = 0.4902)
.3
0.6
.2
0.4
.1
0.2
.0
RE securities markets (av erage = 0.1357)
RE securities markets (av erage = 0.2564)
0.0
-.1
-0.2
-.2
95
96
97
.6
98
99
00
01
02
03
04
05
06
07
08
09
10
11
95
96
97
.5
Across Hong Kong and international
98
99
00
01
02
03
04
05
06
07
08
09
10
11
Across Taiw an and international
.4
.5
Stock markets (av erage = 0.3218)
Stock markets
(av erage = 0.2222)
.3
.4
.2
.3
.1
.2
.0
RE securities markets (av erage = 0.1167)
.1
-.1
RE securities markets (av erage = 0.2344)
.0
-.2
95
96
97
98
99
00
01
02
03
04
05
06
07
08
09
10
11
95
96
97
98
99
00
01
02
03
04
05
06
07
08
09
10
11
Notes: The various realized correlation series are: within Greater China (average of China-HK, China-Taiwan and HK-Taiwan); China & international (average of China-Japan, ChinaSingapore, China-Australia, China-US and China-UK); average of Hong Kong & international (HK-Japan, HK-Singapore, HK-Australia, HK-US and HK-UK); Taiwan & international
(average of Taiwan-Japan, Taiwan-Singapore, Taiwan-Australia, Taiwan-US and Taiwan-UK)
43
Figure 3
Rolling correlation spillover in real estate securities markets
70
80
Within Greater China (GC)
China and international
75
60
70
50
65
40
60
30
55
20
50
10
45
1998
2000
80
2002
2004
2006
2008
2010
1998
2000
80
Hong Kong and international
70
70
60
60
50
50
40
40
30
2002
2004
2006
2008
2010
Taiwan and international
30
1998
2000
2002
2004
2006
2008
2010
1998
2000
2002
2004
2006
2008
2010
Notes: The realized correlation (in local dollars) spillover plots are based on12-quarter windows and 12-quarter forecast horizon. The correlation groups are: Within Greater China (ChinaHK, China-Taiwan and HK-Taiwan); China & international (China-Japan, China-Singapore, China-Australia, China-US and China-UK); Hong Kong & international (HK-Japan, HKSingapore, HK-Australia, HK-US and HK-UK); Taiwan & international (Taiwan-Japan, Taiwan-Singapore, Taiwan-Australia, Taiwan-US and Taiwan-UK)
44