Kim Hiang Liow and Qing Ye

Transcription

1 S w i t c h i n g R e g i m e B e t a A n a l y s i s o f G l o b a l F i n a n c i a l C r i s i s : E v i d e n c e f r o m I n t e r n a t i o n a l P u b l i c R e a l E s t a t e M a r k e t s A u t h o r s Kim Hiang Liow and Qing Ye A b s t r a c t We examine whether the recent subprime/global financial crisis caused some significant changes in the excess return distribution and volatility spillover, as well as the link between them and the world market for a select group of international public real estate markets from January 6, 2000 to June 25, Employing univariate and multivariate switching regime beta models, our results suggest that the public real estate markets examined responded significantly to the financial crisis with a significant increase in the volatility parameter compared to normal period. Moreover, the linkages of the public real estate markets with the two world market indices have been altered differently by the financial crisis, and are enhanced in the post-crisis period for the European region. In contrast, the three major Asian public real estate markets display reduced risk spillover effect in the low volatility state from the world market in recent years. Our findings offer important and yet different implications for investors in their pursuit for portfolio diversification and policymakers in contagion management in the Asian and European public real estate and stock markets after a recent major financial crisis. Our main objective is to investigate the regime-dependent returns, volatilities of eight developed public real estate markets, namely, the United States, United Kingdom, France, Germany, Australia, Japan, Hong Kong, and Singapore, as well as their linkages with the world stock and world real estate markets before and after the global financial crisis (GFC) using switching regime beta models (SRBMs), for the January 6, 2000 to June 25, 2015 period. Our SRBM is characterized by two regimes (high volatility state and low volatility state) and two meta-market states (pre-gfc and GFC/ post-gfc). We assess whether the high and low volatility state parameters have been modified/ changed after the GFC by including switches in stochastic return and time-varying volatility characterized by persistence. Our research motivation is derived from the literature suggesting the outbreak of a financial crisis (such as the GFC) may increase the market volatility and J R E R V o l. 3 9 N o

2 1 2 8 L i o w a n d Y e strengthen the risk spillovers across the markets due to the contagion effect. Moreover, according to the asset pricing theory, the GFC may modify the world index volatility and the link of the individual financial markets with the world stock market. Examining the presence of regime-switching time-varying betas across a wide spectrum of national public real estate markets is important as there is equivalent stock market evidence suggesting that the estimated international capital asset pricing model (ICAPM) betas display statistically significant regimeswitching behavior. However, the research results on stock markets may not be automatically extended to public real estate markets. This is where our study, which is about public real estate, intends to contribute. From a broad perspective, a good understanding of the implications of regime switching on the volatility spillover structure and variance-covariance dynamics of international financial markets is important for portfolio diversification and regulatory control. Over the past decades, in addition to economic globalization, monetary integration, and deregulation that are on-going, international financial markets (including public estate markets) have experienced several episodes of economic and financial distresses. During these crises, financial markets interactions and inter-linkages have increased significantly between countries and between their financial markets and the world stock market to the extent of triggering increased and intensive spillover effects that led to extreme market volatility. A good example is the GFC, which was triggered by the U.S. housing markets since Together with the latest European sovereign debt crisis, these events had clear observed increased effects on the volatilities of international financial markets. We focus this regime-change issue on major public real estate markets because it is an under-researched area. In recent years, although much of the real estate research has focused on performance analysis and the inter-relationships between the physical and securitized real estate markets, there is no comparable research work devoted to a comprehensive investigation of the return, volatility, and systematic risk of national public real estate markets in an international setting in a regime-switching environment and that was impacted by the GFC. International public real estate diversification might be more effective than international stock diversification (Eichholtz, 1996; Stevenson, 2000). With impressive growth in the public property industry due to real estate asset securitization and the establishment of real estate investment trusts (REITs) in many countries over the last two decades, the outperformance of public real estate in both their REITs and corporate form, led to increasing investors awareness for this segment of the market. Moreover, with longer time series and high-frequency data available, public real estate market data have often been used to proxy for private property performance in several previous real estate studies. We also extend the analysis using stock market data. This is another important contribution of this paper, as readers want to know in what ways public real estate markets are different from stock markets through differentiating their changes in the regime-dependent parameters due to the GFC, because the underlying risk-

3 S w i t c h i n g R e g i m e B e t a A n a l y s i s return performances of real estate securities are likely to be significantly different from those of stock markets in the short and long run. Many previous studies such as Liow (2008) have reported that real estate securities are much more volatile than stocks especially during crisis times. Moreover, there is strong evidence to suggest that public property has become increasingly less sensitive to common stocks in developed countries (Ling and Naranjo, 2002). So far, except for Billio and Pelizzon (2003) who employed SRBMs to study the implication of the European monetary union on the shock spillovers and variancecovariance of European stock markets and with the world market, to our knowledge there are no other published studies on this topic. One key difference of our study from Billio and Pelizzon (2003) is that we also investigate two-factor SRBMs (both univariate and multivariate) where the global stock market index and an orthogonalized (or residual ) global real estate market index are the factors to see whether they both survive in the same regression, and in particular, whether the orthogonal global real estate factor is still important after controlling the covariance of the global stock market factor in the regression. The results contribute to a better understanding on the relative significance of the global stock and global real estate, as two important risk factors for public real estate markets. The main results indicate that the public real estate markets examined have responded significantly to the GFC with a significant increase in the volatility parameter compared to the normal period. However, the linkages of the public real estate markets with the two world market indices have not been significantly altered by the financial crisis. Additionally, we observe the three Asian public real estate markets display a reduced risk spillover effect in the low volatility state from the world market and have different reactions to the world market betas in both high and low volatility states in recent years. Finally, the residual global real estate factor is important after controlling the influence of the global stock market factor in the regression. This study makes three contributions to the academic real estate literature. First, we contribute to a large literature on regime change that is associated with a significant shift in the fundamental relation between the risk-return trade-off (Liow, Zhu, Ho, and Addae-Dapaah, 2005). There appears to be regime switches in the variance-covariance matrix of different national stock market indices (Longin and Solnik, 2001; Ang and Bekaert, 2002). During high volatility periods, there is a tendency for higher international dependence. Moreover, using Hamilton s volatility regime-switching models (Hamilton, 1990; Hamilton and Susmel, 1994), we can allow discrete shifts in the stochastic volatility model driving the stock markets. Similarly, Liow, Zhu, Ho, and Addae-Dapaah (2005) find that public real estate markets perform differently in different economic environments and this change in investment behavior results in discrete changes in the time series risk-return characteristics of public real estate market indices. Liow and Zhu (2007) find that a regime-switching model outperforms a nonregime dependent model, a world real estate portfolio, and an equally-weighted public property portfolio from the risk-adjusted return performance perspective. J R E R V o l. 3 9 N o

4 1 3 0 L i o w a n d Y e Finally, Lizieri, Satchell, Worzala, and Dacco (1998) explore price movements in the U.S. REITs and U.K. property companies markets using a threshold autoregressive (TAR) model with regimes defined by the real rate of interest. Second, we contribute to the growing literature on financial market integration and contagion. Previous literature has documented that the co-movement between two stock markets is usually extremely high during periods of crises, and is reduced to normal level when the market becomes stable. The high cross-market correlation during the crisis period provides empirical evidence of the international propagation of shocks at this time. As is defined by (Forbes and Rigobon, 2002), the significant increase in cross-market linkages after a shock is called the contagion effect. Ang and Chen (2002) find the correlation between markets is much higher during market downturns, while in the upside market the correlation can be characterized by a normal distribution. Aloui, Aïssa, and Nguyen (2011) find significant extreme dependence between the U.S. and four emerging markets during the GFC. Chudik and Fratzscher (2011) find that during the GFC, the financial conditions in developed markets are sensitive to the U.S. shock, especially in Europe. Finally, Dungey and Gajurel (2013) observe a strong contagion effect from the U.S. stock market to developed and developing markets globally using a CAPM modeling framework. Third, following the methodology of Forbes and Rigobon (2002), Wilson and Zurbruegg (2004) examine the impact of the 1997 Asian financial crisis on the Asia-Pacific public property markets. Their results show the contagion effect is less evident in the public property markets than in the broader equity markets. Other studies on public real estate markets include Gerlach, Wilson, and Zurbruegg (2006) and Liow (2008). Recently, the outbreak of the European financial crisis has drawn researchers attention, such as Hui and Chan (2013). While their Forbes and Rigobon tests fail to show evidence of contagion, their coskewness and cokurtosis tests reveal additional contagion channels across Greece and other major European public real estate markets. Additionally, Case, Guidolin, and Yildirim (2014), as well as Liow and Ye (2014) examine the volatility and correlation changes across different volatility regimes in public real estate markets. They both suggest that a regime-switching model is more successful in identifying the financial crisis and consequential changes of market performance. Given the relative lack of empirical work on the application of the SRBM to public real estate markets, the results from this study should be interesting for global investors, policy makers, and empirical researchers in international finance. The results offer valuable insights into the investment behavior and portfolio implications of public real estate so that investors may still achieve an efficient regime-dependent mean-variance frontier and manage their real estate exposure tactically in todays volatile financial environment. The plan of this paper is as follows. We describe the sample and data requirements, as well as provide a concise explanation of the univariate and multivariate SRBMs.

5 S w i t c h i n g R e g i m e B e t a A n a l y s i s With the relevant empirical results reported and main implications discussed, we close with concluding remarks. D a t a a n d D e s c r i p t i v e S t a t i s t i c s We use a weekly (Thursday Thursday) 1 total return index (measured in local currency) of eight developed public property markets and two world market proxies in excess of the three-month Treasury bill (TB) yield (a proxy for riskfree rate) for the countries examined. The study period is from January 6, 2000 to June 25, 2015, which contains 808 weekly observations for each market. This period includes the collapse of the technology bubble in the U.S. in March 2000, the 9/ 11 terrorist attacks in 2001, the stock market downturn in October 2002, the invasion of Iraq in March 2003, the Chinese stock market decline in February 2007, the subprime and GFC, and the 2010 European sovereign debt crisis, etc., all of which had significant observed effects on the volatilities of international financial markets. The two world market proxies are the global stock market (GST) and global real estate (GRE). Their excess returns are employed as the two world market index proxies, XGST and XGRE. Similar to the beta coefficient of the CAPM for individual property investments, the beta coefficient of the ICAPM for a country s real estate market may be defined as the ratio of the covariance between the expected (excess) returns on the country s real estate market and the expected (excess) returns on the world market portfolio to the variance of the expected (excess) returns on the world market portfolio. Hence the term international beta may be understood as an index of the systematic risk for a country s real estate market with respect to the world market and is one of the three important factors in the ICAPM that considers the global pricing of real estate market risk. The real estate literature is silent as to which proxy is more appropriate to represent the world market, although the Morgan Stanley Capital International (MSCI) world index has been commonly used in international stock (Fama and French, 1998) and international real estate pricing studies (Bond, Karolyi, and Sanders, 2003). The weekly returns are calculated as the natural logarithm of total return index from the Standard & Poor s (S&P) Global Property Market Index and Broader Market Index (BMI). This global property database (S & P), 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. All total return indices and the respective TB rates were downloaded from Datastream. 2 We use excess market return to avoid any structural breaks caused by movement of the broader economy. Weekly data are employed to avoid the non-synchronous trading hours of international markets while still keep the dynamics and structural breaks in the market return series. The selected markets include Australia (AU), Hong Kong (HK), Japan (JP), Singapore (SG), France (FR), Germany (GE), United Kingdom (UK), and United J R E R V o l. 3 9 N o

6 1 3 2 L i o w a n d Y e States (US). These markets are geographically located in three continents and are the most advanced global public real estate markets. As such, the fluctuations in these markets are more likely to be influenced by the movements in global public real estate markets and financial crises. The U.S. has the world s largest real estate market, which is also the most transparent securitized real estate market. Public properties have a long history in Europe with the U.K. as the European s largest public real estate market. Germany has a long history of indirect real estate vehicles, such as open-ended funds, closed-ended funds, and listed property companies. In the Asia-Pacific region, Japan as a major world economy has a long tradition of listed real estate, with some of the world s largest real estate development companies, such as Mitsubishi Estate and Mitsubishi Fudosan. Together with the U.S., Australia is one of the two most mature public real estate markets, with its listed property trusts (LPTs) regarded as a highly successful indirect real estate investment vehicle. Hong Kong and Singapore have a track record of listed real estate companies that have been contributing a relatively important role in the respective local stock market indexes. Finally, REITs have been successfully established in all public real estate markets. The descriptive statistics of the return data for the public real estate markets and stock markets of the eight countries are reported in Exhibit 1. As the numbers indicate, the kurtosis value for all series is highly positive, indicating a peaked distribution from normal distribution. The JB test statistics also strongly reject the normality distribution for all return series. M e t h o d o l o g y The dynamics of the volatility process of the eight public real estate markets are analyzed using a Markov-switching (MS) approach. The Markov regime-switching methodology can be considered as the generalization of the simple dummy variable approach. As such, applying Hamilton s (1990) regime-switching model can allow discrete shifts in the stochastic volatility process driving the public property markets. We focus on the effects of the GFC crisis/post crisis 3 on the link between the public real estate markets examined and the two world market indices, as well as their idiosyncratic volatilities in a MS context. To achieve this objective, we use a SRBM, also applied by Billio and Pelizzon (2003), to estimate volatility and risk spillover in order to link the public real estate markets to the world market indices. The SRBM is a one-factor (world market) model in the APT framework, where the excess return of a public real estate market is characterized by the regime switching of the world market index risk and the regime switching of the public real estate market risk. By doing so, we can assess whether the GFC affected the stochastic volatility and risk spillover process of the world market indices, the link between the selected public real estate markets and the world market proxies, as well as the integration among the public property markets when the volatility increases and whether the level of linkage has a break before and after the GFC. Additionally, we examine a two-factor model where the

7 S w i t c h i n g R e g i m e B e t a A n a l y s i s Exhibit 1 Summary Statistics of Weekly Public Property and Stock Returns (local currency): January 6, 2000 to June 25, 2015 Panel A: Public real estate markets Mean Max. Min. Std. Dev. Skewness Kurtosis JB Test AU HK JP SG FR GE UK US Panel B: Stock markets AU HK JP SG FR GE UK US Global stock market Global real estate Notes: Legends: AU (Australia), HK (Hong Kong), JP (Japan), SG (Singapore), FR (France), GE (Germany), UK (United Kingdom), US (United States). Source: Standard and Poor s (S&P). XGST and a residual ( orthogonalized ) XGRE are the factors to see whether they both survive in the same regression. For this purpose, the univariate (which considers one market at a time) and a multivariate (which consider all eight markets at the same time) versions of the SRBM are employed. 4 U n i v a r i a t e S R B M We consider a univariate SRBM where the excess return of an individual public real estate market is explained by a constant term and the world market index proxy in a regime-switching setting. In each regime, the excess market return is J R E R V o l. 3 9 N o

8 1 3 4 L i o w a n d Y e allowed a different probability distribution. Our objective is to evaluate if there is any structural change in the stochastic process of the individual public real estate market s average excess return, excess market variance, and beta parameters before and after the GFC. Specifically, the presentation of the model is as follows: y u (s ) (s )r (s ), IIN(0,1) (1) i,t i,t t i t w,t i t i,t i,t where s t is a Markov chain governing the volatility regimes of individual excess market return yi,t for market i at time t and rw,t is the world market index. The regime-dependent excess mean of market i is measured by u i,t(s t). The sensitivity of individual market i on r w,t can be measured by the factor loading i (s t ), which takes different values in different market regimes, and measures the ratio of the covariance between market i and the world market index to the variance of the latter. A larger coefficient of i indicates higher sensitivity of the individual market risk with the world market. To test if the degree of such dependence has changed and increased since the GFC, we introduce a dummy variable D t in equation (1), which takes the value of 0 before breakpoint and 1 onward to capture this effect. The date of the breakpoint is determined endogenously by applying Bai and Perron s (2003) structural break test to the two benchmark indices r w,t. 5 Specifically, the model is as follows: y u (s ) (s )D (s )r i,t i,t t i t t 1,i t w,t (s )r D (s ). (2) 2,i t w,t t i t i,t Thus the excess market return before the structural break date (pre-gfc) would be: y u (s ) (s )r (s ) (3) i,t i,t t i t w,t i t i,t and the excess market return after the structural break date (post-gfc) would be: y u (s ) (s ) { (s ) (s )}r (s ). (4) i,t i,t t i t 1,i t 2,i t w,t i t i,t

9 S w i t c h i n g R e g i m e B e t a A n a l y s i s i (s t ) and 2,i (s t ) reflect the change in average excess market return and factor loading of the world market index before and after the outbreak of the GFC, respectively. M u l t i v a r i a t e S R B M We model the excess returns of all eight public real estate markets in a multivariate regime-switching regression framework in order to take into account the correlation between the different public real estate markets. Following Billio and Pelizzon s (2003) multivariate SRBM with specific Markov chains, the excess market returns are assumed to follow the same Markov chain. Specifically, the model is presented as follows (assume a bivariate case, for illustration purposes): y u (s ) (s )r (s ) i,t i,t t i t w,t i t i,t (5) y u (s ) (s )r (s ) j,t j,t t j t w,t j t j,t where yi,t and yj,t are the excess returns of individual market i and j. S t is the Markov chain that governs the regime shifts for both markets. The variancecovariance matrix between the two markets can be written as: (s ) (s ) (s ) (s ) (s ) (s ) i t w t 2 i t 2 i t 2 j t w 2 (s ) (s ) (s ) (s ) (s ) t j t i t w t j t w t j (s t) (i, j) (6) Similarly, the dummy variable D t is added to equation (5) to test whether the dependence of the public property markets with the world market has changed since the GFC: yi,t u i,t(s t) i(s t)dt 1,i(s t)rw,t 2,i(s t)rw,tdt i(s t)i,t y j,t u j,t (s t ) j (s t )D t 1,j (s t )r w,t 2,j (s t )r w,t D t j (s t ) j,t (7) R e s u l t s D e t e r m i n a t i o n o f t h e S t r u c t u r a l B r e a k p o i n t f o r t h e G F C First, we determine the GFC breakpoint endogenously using Bai and Perron s (2003) methodologies on the two world market index proxies. This is to minimize J R E R V o l. 3 9 N o

10 1 3 6 L i o w a n d Y e Exhibit 2 Univariate Switching Regime Models for World Market Index Proxies Excess Global Stock Market Excess Global Real Estate Market Log-likelihood (LR) ratio ,a 0,b 0.209*** 1.331*** 1,a 1,b 1.634*** *** Notes: The subscripts a and b indicate post-crisis (after GFC) and pre-crisis (before GFC), respectively. The subscript 0 indicates low volatility and the subscript 1 indicates high volatility. ***Indicates rejection of the null hypothesis at the 1% level. discretion in the definition of the crisis period. Using their multiple structural break methodology on the full data period, we obtain three breakpoints for XGST: 10/10/2002, 8/7/2008, and 11/20/2008, as well as three breakpoints for XGRE: 8/7/2008, 11/20/2008, and 9/17/2009. In consultation with the occurrence of major economic and financial events, the GFC is separated into four phases (Federal Reserve Board of St. Louis, 2009), Specifically, the estimated breakpoint of 8/ 7/ 2008 falls within the Phase I: Initial financial turmoil period (8/ 1/ /15/2008); the estimated breakpoint of 11/20/2008 falls within the period of Phase 2: Sharp financial market deterioration (9/ 16/ / 31/ 2008). Additionally, Phase 3 defined as macroeconomic deterioration (1/ 1/ /31/2009), while Phase 4 is a phase of stabilization and tentative signs of recovery (4/ 1/ / 4/ 2009). Accordingly the breakpoint at 8/ 7/ 2008 (for both XGST and XGRE) is adopted as the GFC breakpoint for our study, although we recognize the post-2008 is not a single phase. 6 Wo r l d M a r k e t I n d e x P r o x i e s Next, we evaluate whether the two world market risk premia and volatilities did change after 8/7/2008. We use a simple regime switching model (Liow, Zhu, Ho, and Addae-Dapaah, 2005) to analyze any difference in the stochastic process of the world market indices before and after the GFC. In doing so, we assume that the world markets expected excess return and volatility are characterized by two different volatility regimes of low (0) and high (1) states. The transition between the states is governed by a first-order Markov process. Exhibit 2 provides the test results. The log-likelihood (LR) test rejects the null hypothesis of no change in the parameters of the distribution of the excess returns of the two world index proxies (XGST and XGRE) after the GFC. Moreover, there are significant increases on the value of volatility in both the low and high volatility regimes; the volatility parameter is higher in the high state, as well as in the low state of volatility after the GFC for the two world market index proxies. Finally, Exhibit

11 S w i t c h i n g R e g i m e B e t a A n a l y s i s indicates that over the last few years after the GFC, the world market indices have been characterized by the high volatility state, as well as higher volatility in the low volatility state. One implication is that tranquil periods are now characterized by a higher volatility. Accordingly even when the markets are relatively stable, the volatilities could now be higher. U n i v a r i a t e E s t i m a t i o n o n O n e - f a c t o r S R B M Exhibits 4 and 5 report the univariate estimation results between each of the eight developed public property markets and two world market proxies: excess global stock (Exhibit 4) and excess global real estate (Exhibit 5). As the numbers indicate, the significant LR test statistics for all 16 cases indicate the respective dummy models (i.e., two-regime/ two meta-market state SRBMs that include the GFC structural breakpoint) are superior over the corresponding non-dummy models. 7 Second, the changes in mean evaluates whether the difference in the individual markets average excess return is significant after the GFC. The results indicates that, in the low volatility regime, except for JP and SG, there is a significant increase in the average excess return for the remaining six public real estate markets (75%) when using both world market proxies. This means that in recent years, the public real estate markets present a higher excess return than before when the markets are stable. We suspect that this positive effect is more attributable to globalization. In contrast, there is only scattered evidence. In the high volatility regime, only three cases (AU, FR, and UK: with XGST) and two cases (AU and UK: with XGRE) are observed to experience a significant increase in the average excess return. For volatility, we observe a significant increase in the volatility parameter of the high volatility regime for all eight public property markets after the GFC. The means in recent years after the GFC, public real estate markets are characterized with higher excess volatility in the high volatility state. In particular, the excess market variance for GE, UK, US, and AU was much higher for the high volatility regime in recent years, probably contributed partially by the European sovereign debt crisis. In contrast, for JP, SG and to a lesser extent HK and FR, their excess market variance was significantly lower during the post-gfc periods when the markets are in low volatility state. These results are ambiguous since we observe a reduction of volatility in the low volatility regime and an increase in the high one. Other non-asian markets are more volatile after the GFC even though the markets are in stable state, implying that the economic growth and financial development that happened in these advanced economies during normal times may be associated with higher real estate market volatility in recent years after the GFC. Previous studies have documented that betas are higher when the world market index is in the high volatility regime. Our estimated parameters produced mixed evidence. Our results show that there is a structural break in betas for five non- Asian public real estate markets (AU, FR, GE, UK, and US) when the global J R E R V o l. 3 9 N o

12 1 3 8 L i o w a n d Y e Exhibit 3 Smoothed Probability of High Volatility Regime in the Two World Market Indices from Univariate Panel A: Global Stock Market MS Model Panel B: Global Public Real Estate Market stock market is in the low volatility regime and the respective post-crisis betas are significantly higher. These significantly higher post-crisis betas are also estimated for SG, FR, and GE when the global real estate market index is the world market proxy. These results mildly imply during stable periods in recent years that these developed public real estate markets are increasingly linked to the world markets in the wider context of globalization and cross-asset market integration. In contrast, we can only speculate that the decreased or stable beta results observed in the high volatility state for up to 75% of the real estate markets (except the US and to a lesser degree UK) after the GFC period suggest that these

13 Exhibit 4 Univariate SRBM Results for Public Real Estate Markets (World Market Proxy: Global Stock Market) J R E R V o l. 3 9 N o AU HK JP SG FR GE UK US All Parameters 124.4*** 370.3*** 219.3*** 335.8*** 373.8*** 327.2*** 358.6*** 393.6*** Changes in Mean Excess Returns 0,a 0,b 0.355*** 0.783*** *** 0.485*** 0.777*** 0.355*** (0.094) (0.179) (0.261) (0.178) (0.101) (0.146) (0.133) (0.135) 1,a 1,b 1.179* 0.357*** ** ** (0.705) (0.102) (0.424) (0.346) (0.423) (0.621) (0.708) (0.678) Changes in the Linkage with the Global Stock Market 0,a 0,b 0.201*** *** 0.410*** 0.116* 0.340*** (0.058) (0.391) (0.165) (0.134) (0.069) (0.068) (0.068) (0.066) 1,a 1,b ** *** *** 0.556** (0.260) (0.144) (0.155) (0.115) (0.163) (0.200) (0.229) (0.246) S w i t c h i n g R e g i m e B e t a A n a l y s i s 1 3 9

14 Exhibit 4 (continued) Univariate SRBM Results for Public Real Estate Markets (World Market Proxy: Global Stock Market) AU HK JP SG FR GE UK US L i o w a n d Y e Changes in Market Variance 0,a 0,b 0.616*** 1.908*** 0.394*** 3.071*** 0.060*** 0.749*** 0.421*** 1.284*** 1,a 1,b *** 1.215*** 3.922*** 3.587*** 2.819*** *** *** *** Notes: This is a one-factor SRBM model. The table reports the estimation results and test statistics of the following model: y u (s ) (s )D (s )r (s )r D (s ). i,t i,t t i t t 1,i t w,t 2,i t w,t t i t i,t The All Parameters row reports the log-likelihood ratio test statistic. The rejection of test statistic suggests the unrestricted model with dummy variable against the restricted model without dummy variables is statistically significant. The second part reports the estimates of i (s t ), which measures the change of the mean excess returns between post-crisis period 0,a and pre-crisis period 0,b. The subscript 0 indicates low volatility and the subscript 1 indicates high volatility. The third part reports the estimates of 2,i(s t), which is the change in the linkage with the global stock market between post-crisis period 0,a and pre-crisis period 0,b. The final part reports the changes in the market variance between post-crisis period 0,a and pre-crisis period 0,b. *Significant at the 10% level. **Significant at the 5% level. ***Significant at the 1% level.

15 Exhibit 5 Univariate SRBM Results for Public Real Estate Markets (World Market Proxy: Global Real Estate Market) J R E R V o l. 3 9 N o AU HK JP SG FR GE UK US All Parameters 226.7*** 403.0*** 319.4*** 366.4*** 393.9*** 296.8*** 373.9*** 947.2*** Changes in Mean Excess Returns 0,a 0,b 0.466*** 0.684*** *** 0.593*** 0.968*** 0.723*** (0.112) (0.206) (0.291) (0.141) (0.140) (0.159) (0.132) (0.083) 1,a 1,b 1.261* * (0.766) (0.376) (0.430) (0.384) (0.430) (0.544) (0.648) (0.772) Changes in the Linkage with the Global Real Estate Market 0,a 0,b *** 0.438*** 0.342*** (0.064) (0.129) (0.169) (0.108) (0.082) (0.098) (0.075) (0.055) 1,a 1,b *** 0.456*** 0.340*** 0.340*** ** (0.237) (0.117) (0.128) (0.109) (0.117) (0.147) (0.168) (0.205) S w i t c h i n g R e g i m e B e t a A n a l y s i s 1 4 1

16 Exhibit 5 (continued) Univariate SRBM Results for Public Real Estate Markets (World Market Proxy: Global Real Estate Market) AU HK JP SG FR GE UK US L i o w a n d Y e Changes in Market Variance 0,a 0,b 0.558*** 0.403*** 2.774*** 2.971*** 1.133*** 1.348*** 0.753*** 0.283*** 1,a 1,b *** 4.802*** 2.020*** 4.275*** 6.177*** *** *** 8.378*** Notes: This is a one-factor univariate SRBM model. The table reports the estimation results and test statistics of the following model: y u (s ) (s )D (s )r (s )r D (s ). i,t i,t t i t t 1,i t w,t 2,i t w,t t i t i,t The All Parameters row reports the log-likelihood ratio test statistic. The rejection of test statistic suggests the unrestricted model with dummy variable against the restricted model without dummy variables is statistically significant. The second part reports the estimates of i (s t ), which measures the change of the mean excess returns between post-crisis period 0,a and pre-crisis period 0,b. The subscript 0 indicates low volatility and the subscript 1 indicates high volatility. The third part reports the estimates of 2,i(s t), which is the change in the linkage with the global public real market between post-crisis period 0,a and pre-crisis 0,b period. The final part reports the changes in the market variance between post-crisis period 0,a and pre-crisis period 0,b. *Significant at the 10% level. **Significant at the 5% level. ***Significant at the 1% level.

17 S w i t c h i n g R e g i m e B e t a A n a l y s i s markets could be more affected by idiosyncratic factors of the world markets compared to the pre-gfc periods. One implication arising from this different dynamic is that since Asian public real estate markets have been generally perceived as having low exposure to global factors and therefore little integration with the world market and with western economies, incorporating Asian market real estate stocks in an investment portfolio can be seen as part of an attempt to increase returns and reduce risks. On a further note, although recent studies on market integration suggest that national stock markets have become much more correlated than in recent decades, we show that the Asian public real estate sector has instead become negatively correlated with the global real estate market since the GFC. U n i v a r i a t e E s t i m a t i o n o n a Tw o - f a c t o r S R B M In this subsection, we discuss the SRBM analysis of a two-factor model that includes the global stock market factor and a residual (or orthogonolized ) global real estate factor. 8 We examine whether the two factors could both survive in the same regression. In particular, the results for the residual real estate factor could serve to indicate whether global real estate is a significant factor for public real estate after controlling for the global stock market covariance in the SRBM. The results are reported in Exhibit 6. As the numbers indicate, the significant LR test statistics indicate the eight twofactor dummy models are superior over the corresponding eight two-factor nondummy models. With respect to the changes in the average excess returns, we observe there is a significant increase in the low volatility period for after the GFC, possibly due to the impact of globalization. As consistent with the onefactor results, six cases (AU, HK, FR, GE, UK, and US) experienced a significant structural increase in their average risk premia in the low volatility period after the GFC. However, the statistical analysis for the two-factor SRBM could only reject the hypothesis of excess return stability for AU, FR, and UK in the high volatility period. Second, except for the US, JP, and SG in the low volatility state, the volatility parameter of other markets in both the low and high volatility states has statistically increased since January While the volatility results for the US, JP, and SG are less clear because we observe a reduction of volatility in the low volatility state and an increase in the high volatility regime, other volatility spillover results from the two-factor SRBM are more coherent with the theoretical expectation that the remaining markets display a significant volatility increase in both the low and high volatility regimes after the GFC. Finally, we reject the hypothesis of stability of beta in the low volatility state for SG (with a reduction in the link with the residual global real estate benchmark), as well as for JP (with a reduction in the residual global real estate index) in the high volatility period after the GFC. Overall, JP, SG, FR, GE, HK, and the US have experienced significant instability in their links with the global stock market or the residual global real estate benchmarks in at least one volatility state. These results indicate after controlling for the global stock market influence, the residual real estate is J R E R V o l. 3 9 N o

18 Exhibit 6 Univariate SRBM Results for Public Real Estate Markets (World Market Proxies: Global Stock Market & Residual Global Real Estate Market) AU HK JP SG FR GE UK US All Parameters 27.66*** 46.63*** 14.06*** 8.94*** 30.38*** 45.49*** 48.93*** 70.64*** Changes in Mean Excess Returns 0,a 0,b 0.497*** 0.837*** *** 0.513*** 0.882*** 0.723*** (0.114) (0.182) (0.261) (0.196) (0.148) (0.141) (0.125) (0.086) 1,a 1,b 1.473* ** ** (0.820) (0.389) (0.332) (0.342) (0.311) (0.546) (0.505) (0.537) Changes in the Linkage with Global Stock Market 0,a 0,b *** *** 0.389*** (0.075) (0.106) (0.168) (0.168) (0.087) (0.080) (0.065) (0.055) 1,a 1,b *** 0.405*** 0.327*** ** (0.313) (0.136) (0.107) (0.115) (0.275) (0.190) (0.254) (0.235) Changes in the Linkage with the Orthogonalized (Residual) Global Real Estate Market 0,a 0,b ** (0.131) (0.178) (0.241) (0.182) (0.163) (0.133) (0.118) (0.092) 1,a 1,b ** (0.419) (0.239) (0.241) (0.208) (0.242) (0.393) (0.351) (0.326) Changes in Market Variance 0,a 0,b 0.356*** 0.487*** 1.557*** 2.737*** 0.712*** 0.751*** 0.441*** 0.175*** 1,a 1,b 9.125*** 5.327*** 3.555*** 4.269*** 4.590*** *** *** 9.992*** L i o w a n d Y e Notes: This is a two-factor SRBM model. The two factors are (a) the global stock market and (b) the global (orthogonal) real estate market (with the global stock market influence removed). *Significant at the 10% level. **Significant at the 5% level. ***Significant at the 1% level.

19 S w i t c h i n g R e g i m e B e t a A n a l y s i s Exhibit 7 Smoothed Probability of Low Volatility Regime from Two-factor Univariate SRBM for Public Real Estate Markets (World Market Proxies: Global Stock & Orthogonalized Global Real Estate) still an important risk factor for some public real estate markets. However, both world market proxies did not survive for AU and UK in the two-factor regression model. Finally, Exhibit 7 shows the probability of being in the low volatility state (S t 0) from the two-factor univariate analysis for all public real estate markets. We observe that for many markets, the excess returns were characterized by the low volatility regime in the early years before the GFC. However, the HK, JP, SG, and FR markets display strong regime-switching behavior over the sample period in changing quite frequently between the two volatility regimes. Their switches to the high volatility regime were affected mostly by the major crises that happened during the study period, notably the subprime/ GFC happened from J R E R V o l. 3 9 N o

20 1 4 6 L i o w a n d Y e June/ July 2007 and the European debt crisis from January The different reactions from the Asian markets in this regard are significant and should alarm regional investors of the underlying macroeconomic and other domestic uncertainties in influencing their portfolio decision-making, such as sensitivity to economic growth regimes, interest rate regimes, other monetary policy regimes, and major idiosyncratic factors that may affect the globalization process and regime performance of HK, JP, SG, and FR differently from other markets. M u l t i v a r i a t e E s t i m a t i o n o n O n e - f a c t o r S R B M In the univariate analysis, the conditional return for individual markets is described by an independent distribution. Similarly, the high and low volatility regimes for all markets are also independent from each other. However, given the ongoing progress of economic and financial integration, which is further boosted by the GFC, the movements of international public real estate markets cannot be simply isolated from one other. To take into account the potential volatility synchronization across different markets, we estimate a multivariate one-factor SRBM to allow for interaction across markets. We estimate equation (7) where the dependent variable is a vector of all excess market returns. The estimation results are presented in Exhibits 8 and 9. The LR test for the two one-factor SRBMs rejects the null hypothesis of no change in all the regime-dependent parameters after the GFC for all public real estate markets examined. Focusing on the high volatility regime, when the global stock market index is the market index (Exhibit 8), while we observe that the risk premia were significantly negative for four markets (AU, FR, GE, and UK) before the GFC, the risk premia were positive (albeit insignificant) for all markets, implying some public real estate markets (especially the three European markets) are characterized by a higher risk premium in recent years. This moderate structural instability in excess returns is accompanied by a strong increase in the level of volatility for all markets after the GFC. Similarly, there is a significant increase in the volatility parameter in the low volatility state. These results thus indicate that the public real estate markets are more volatile after the GFC even though the markets are in a stable state. For beta, the majority of public real estate markets were significantly linked to the world stock market before the GFC; however, the GFC influenced the behavior of world beta to the extent that none of the markets is linked to the global stock market (low world market beta), although the markets have higher correlations with each other after the outbreak of the GFC. Finally, when the global real estate index is adopted as the market proxy (Exhibit 9), we observe some structural instability in the excess return parameter for the three European and AU markets, as well as a strong increase in volatility spillovers from the world real estate market, results that are in agreement with those from using global stock market proxy. However, we also observe that the three Asian markets (HK, JP, and SG) experienced significant structural changes in their world market betas to the extent that they are now negatively linked to the world real estate market in recent years after the GFC.

21 Exhibit 8 Multivariate SRBM Results for Public Real Estate Markets (World Market Proxy: Global Stock Market) AU HK JP SG FR GE UK US J R E R V o l. 3 9 N o All Parameters 66.01*** Panel A: Regime 0 (low volatility) i (0) 1.024*** 0.445*** 0.410** *** 0.752*** 0.312*** (0.097) (0.134) (0.165) (0.107) (0.121) (0.124) (0.100) (0.112) i (0) ** * 0.776*** 0.368** (0.133) (0.216) (0.292) (0.233) (0.162) (0.176) (0.150) (0.154) 1,i(0) 0.177*** 0.998*** 0.614*** 0.711*** 0.336*** 0.421*** 0.549*** 0.477*** (0.058) (0.076) (0.092) (0.057) (0.069) (0.062) (0.059) (0.063) 2,i(0) 0.200*** 0.329*** * 0.548*** 0.349*** 0.160* (0.077) (0.071) (0.110) (0.158) (0.113) (0.089) (0.081) (0.083) (0.077) i (0) 2.076*** 5.591*** 9.592*** 4.311*** 3.221*** 3.721*** 2.702*** 2.993*** S w i t c h i n g R e g i m e B e t a A n a l y s i s 1 4 7

22 Exhibit 8 (continued) Multivariate SRBM Results for Public Real Estate Markets (World Market Proxy: Global Stock Market) AU HK JP SG FR GE UK US Panel B: Regime 1 (high volatility) L i o w a n d Y e i (1) 2.315** ** 2.310** 2.103* (0.999) (0.670) (0.797) (0.713) (0.584) (1.040) (1.141) (1.065) i (1) (1.258) (0.909) (1.125) (0.942) (0.820) (1.282) (1.388) (1.427) 1,i(1) *** 1.169*** 1.463*** 1.153*** 1.027* (0.599) (0.314) (0.379) (0.317) (0.239) (0.579) (0.574) (0.661) 2,i(1) (0.650) (0.383) (0.449) (0.382) (0.291) (0.619) (0.627) (0.654) i (1) *** *** *** *** 9.502*** *** *** *** yi,t u i,t(s t) i(s t)dt 1,i(s t)rw,t 2,i(s t)rw,tdt i(s t)i,t Notes: y u (s ) (s )D (s )r (s )r D (s ) j,t j,t t j t t 1,j t w,t 2,j t w,t t j t j,t Numbers in parentheses are the standard errors of the coefficient estimates. AU (Australia), HK (Hong Kong), JP (Japan), SG (Singapore), FR (France), GE (Germany), UK (United Kingdom), and US (United States). *Significant at the 10% level. **Significant at the 5% level. ***Significant at the 1% level.

23 Exhibit 9 Multivariate SRBM Results for Public Real Estate Markets (World Market Proxy: Global Real Estate Market) AU HK JP SG FR GE UK US J R E R V o l. 3 9 N o All Parameters *** Panel A: Regime 0 (low volatility) i (0) 1.158*** 0.755*** ** 0.267** 0.420*** 0.890*** 0.683*** (0.097) (0.133) (0.165) (0.113) (0.118) (0.131) (0.101) (0.073) i (0) 0.395*** 0.738*** * 0.423** 0.918*** 0.683*** (0.131) (0.220) (0.287) (0.245) (0.160) (0.182) (0.153) (0.107) 1,i (0) 0.346*** 1.216*** 1.016*** 0.731*** 0.431*** 0.382*** 0.651*** 1.064*** (0.057) (0.078) (0.099) (0.063) (0.066) (0.076) (0.061) (0.045) 2,i (0) *** *** 0.301*** (0.070) (0.113) (0.145) (0.116) (0.080) (0.090) (0.083) (0.055) i (0) 1.888*** 5.397*** 8.845*** 4.334*** 3.018*** 3.805*** 2.581*** 1.359*** S w i t c h i n g R e g i m e B e t a A n a l y s i s 1 4 9

24 Exhibit 9 (continued) Multivariate SRBM Results for Public Real Estate Markets (World Market Proxy: Global Real Estate Market) AU HK JP SG FR GE UK US Panel B: Regime 1 (high volatility) L i o w a n d Y e i (1) 1.895*** ** 2.035*** 1.867** (0.661) (0.553) (0.632) (0.546) (0.474) (0.598) (0.829) (0.695) i (1) (0.856) (0.816) (0.869) (0.796) (0.702) (0.814) (1.079) (0.848) 1,i (1) 0.793*** 1.153*** 1.327*** 1.106*** 0.970*** 0.906*** 0.873** 0.921*** (0.257) (0.202) (0.249) (0.198) (0.162) (0.249) (0.346) (0.275) 2,i (1) * 0.517* 0.381*** (0.274) (0.237) (0.296) (0.198) (0.204) (0.276) (0.380) (0.279) i (1) *** *** *** *** 8.248*** *** *** *** yi,t u i,t(s t) i(s t)dt 1,i(s t)rw,t 2,i(s t)rw,tdt i(s t)i,t Notes: y u (s ) (s )D (s )r (s )r D (s ) j,t j,t t j t t 1,j t w,t 2,j t w,t t j t j,t Numbers in parentheses are the standard errors of the coefficient estimates. AU (Australia), HK (Hong Kong), JP (Japan), SG (Singapore), FR (France), GE (Germany), UK (United Kingdom), and US (United States). *Significant at the 10% level. **Significant at the 5% level. ***Significant at the 1% level.