Correlation Dynamics and Determinants in Real Estate Securities Markets A Study of Greater China Economies and their International Linkages

Transcription

1 IRES IRES Working Paper Series Correlation Dynamics and Determinants in Real Estate Securities Markets A Study of Greater China Economies and their International Linkages Liow Kim Hiang Zhou Xiaoxia November 29, 2012

2 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

3 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 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

4 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 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

5 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

6 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

7 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

8 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 , 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 6

9 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

10 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. R We define the daily stock return at market i as R ln( I I ) and market j as ln( I I ) 1 j, t, d j, t, d j, t, d i, t, d i, t, d i, t, d x x 100, where I are the daily real estate stock total return indices. Then the realized variances is given by: Dt t, i ( Ri, t, d ) and t j d 1 Dt 2, ( R j, t, d ) d 1, 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 Dt returns is measured as ( R xr. Finally, the realized correlation ij, t measure between ij, t i, t, d j, t, d ) d 1 the cross-country returns is obtained as ij, t ij, t. Since correlations are bounded between 2 2 i, t x j, t 1 ijt -1 and +1, we use a Fisher-Z transformation: ijt ln( ). 1 ijt (b) 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

11 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, TW- AU, 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 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. 9

12 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 SupF, ( l 1 l) it statistics are evaluated to determine the number of breaks, choosing the SupF, ( l 1 l) statistic that rejects the largest value of l.other it 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. 10

13 (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 correlations 3, 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) 11

14 (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

15 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

16 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: GDP GDP ij 6 12 D 16 0 VAREX 97 1 ijt D 17 CORST i 08 7 Q 18 1 j t DIRECT DIRECT i ijt j t IF 19 2 GST 8 Q 13 2 i IF t Q 20 j t 3 9 RINT 21 3 RINT REGIONREITS i ijt TREND i 22 j t LNRESIZEST LNRESIZEST 10 ijt TS 4 VARRE j t (1) i TS it j t 11 GREV EX 5 VARRE t 15 jt i ijt IS IS j t 14

17 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

18 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

19 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 range between (HK-US) and (Hong Kong/Singapore). Only three economypair (HK-JP, CH-HK and HK-SG) is above 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, HK- US and TW-US; whereas the TW-UK series has an insignificant negative time trend. 17

20 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 (cross-stock) and (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

21 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 (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 (CH-UK) and (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