Correlation and Volatility Dynamics in International Real Estate Securities Markets

Transcription

1 IRES IRES Working Paper Series Correlation and Volatility Dynamics in International Real Estate Securities Markets Kim Hiang LIOW Kim Hin David HO Muhammad Faishal IBRAHIM Ziwei CHEN Department of Real Estate National University of Singapore

2 J Real Estate Finan Econ (2009) 39: DOI /s Correlation and Volatility Dynamics in International Real Estate Securities Markets Kim Hiang Liow & Kim Hin David Ho & Muhammad Faishal Ibrahim & Ziwei Chen Published online: 29 January 2008 # Springer Science + Business Media, LLC 2008 Abstract We study international correlation and volatility dynamics of publicly traded real estate securities using monthly returns from 1984 and We also examine, for comparison, the correlations among the corresponding stock markets. A multivariate dynamic conditional correlation model captures the time-varying correlation within the full period. We confirm lower correlations between all real estate securities market returns than those between the stock market returns themselves. Some significant variations and structural changes in the correlation structure happened within the sample period. We detect a strong and positive connection between real estate securities market correlations and their conditional volatilities. We also find the international correlation structure of real estate securities and the broader stock market are linked to each other. Our results have economic motivations regarding the potential integration of international real estate securities markets and the possibility of including information on changing correlations and volatilities to design more optimal portfolios for international real estate securities. Keywords Time-varying correlation. Volatility. Dynamic conditional correlation model. Real estate securities markets. Stock markets Introduction There is extensive evidence to show that diversifying across national stock markets, given the low correlation of returns between them, would enable investors to reduce their total portfolio risk without sacrificing return. Moreover, the correlations among international stock markets are time-varying, with the correlations rising in periods of high volatility (Longin and Solnik 1995). This paper addresses several important K. H. Liow (*) : K. H. D. Ho : M. F. Ibrahim : Z. Chen Department of Real Estate, National University of Singapore, 4 Architecture Drive, Singapore , Singapore rstlkh@nus.edu.sg

3 Correlation and Volatility Dynamics in International Real Estate Securities Markets 203 issues with respect to the international correlation and volatility dynamics of publicly traded real estate securities in five national markets of the USA, UK, Japan, Hong Kong and Singapore as well as three regional markets of Americas, Europe and Asia between January 1984 and March The five countries have well-developed and mature real estate investment markets that have public listed companies or funds owning property. This enables them to offer investors an alternative indirect approach to investing in real estate. The analysis uses conditional monthly returns adopting an Autoregressive (AR) model in which the conditional volatilities are modeled in a Generalized Autoregressive Conditional Heteroskedasticity (GARCH) framework and the conditional correlations are estimated in a Dynamic Conditional Correlation (DCC) model. Throughout the analysis, the findings for real estate are compared with the corresponding results for the broader stock market indexes. The international correlation and volatility structure of public real estate markets is important to investors seeking to capture the portfolio benefits from international real estate investing. To the best of our knowledge, this topic has not been adequately studied. An added contribution of this paper is that the connection among the conditional real estate securities market correlations, the conditional stock market correlations and their market volatilities is investigated through the DCC model. Although a great deal of attention has been paid to the relationship between real estate returns and stock market returns, what have not been studied sufficiently are the relationships between the conditional volatility of the two asset markets as well as between the international correlation structure of these two markets. A closely related underlying economic motivation is whether or not international diversification would be significantly discouraged owing primarily to the diminishing benefits of such diversification. This could be attributed to the rising correlation and volatility between the two asset markets. Two specific issues emerge as a consequence. First, we investigate whether or not the international correlation structure of real estate securities markets and the broader stock markets are linked to each other. For example, could the UK real estate securities market become more increasingly correlated with the US real estate securities market at the same time that the UK and the US stock markets are increasingly synchronized? Second, we examine whether or not the correlation of returns of the real estate securities markets between two countries does increase when the volatility in one or the other country increases, particularly in those periods that involve stock market crashes, and during the 1997 Asian financial crisis. Accordingly, the objectives of this study comprise the following: (a) To investigate whether or not the conditional volatilities of real estate securities market returns change over time (b) To compare the conditional correlations of real estate securities market returns between countries with the conditional correlations of the broader stock markets of these countries (c) To assess the nature and extent of the time-varying conditional correlations of the real estate securities market return between countries over time (d) To assess the relationship between international real estate securities correlations and the corresponding changes in conditional volatility over time

4 204 K.H. Liow et al. (e) To investigate whether or not the international correlation structure of the real estate securities market and the broader stock market are linked to each other (f) To examine whether or not real estate securities market conditional volatility and stock market volatility are synchronous over time The study is organized as follows: a selective literature review is provided in Related Literature. This is followed by an explanation of the research sample and methodology in Data and Methodology respectively. A discussion of the results and investment implications are provided in Empirical Results. The final section concludes this paper together with a summary of the main results. Related Literature Similar to common stocks, the benefits of international diversification of real estate stems from the low correlation between national real estate markets. Eichholtz (1996a) has favorably reported even significantly lower correlations between national real estate returns than those between common stock or bond returns, as real estate markets are more often affected by local factors. Nevertheless, there is evidence that real estate markets are becoming more open and interdependent due to rapidly increasing international capital flows that involves global funds such as the Asian real estate investment trusts (REITs). Longin and Solnik (1995) and Solnik et al. (1996) reiterate the evidence that international stock market correlation is evolving through time. Further, a general increase in the market correlations can erode the benefit of international risk diversification in the long run. The general level of international stock market correlation can increase when global factors dominate domestic ones, and can affect all financial markets (Longin and Solnik 1995). Since real estate securities market is a part of the wider stock market, the increase in correlation among the national stock markets and national real estate securities markets may well be synchronized. Solnik et al. (1996) have found that the movements in international stock market correlations do not follow closely the movements in international bond market correlations or vice versa. However, no formal attention has been given on the possible co-movement between international real estate securities correlations and stock market correlations. The stochastic properties of stock market correlation measures have been investigated by Kaplanis (1988), who fits time-series models to the rolling correlation measures of the public market equities in 15 national markets. Her tests reject the hypothesis that the correlation between these public equity markets is constant. Longin and Solnik (1995) estimate a multivariate GARCH model and test the null hypothesis that the correlation between equity markets is constant. They reject the model and conclude that international stock market correlation is not constant. Their conditional correlation results further indicate an average increase of the international stock market correlation over the past thirty years. In addition, international correlation rises in periods of high market volatility. In their study of the correlations of six foreign stock markets with the US stock market, Solnik et al.

5 Correlation and Volatility Dynamics in International Real Estate Securities Markets 205 (1996) also show that international stock market correlations vary over time and across countries They find that although the correlation of the individual foreign stock markets with the US stock market has increased slightly over the past 37 years, it has not increased over the past 10 years. Finally, they also find that international correlation increases in periods of high market volatility. Consequently, increased international stock market correlations would result in diminishing portfolio diversification benefits in an investment environment when international portfolio risk reduction and the diversification benefits are most needed by domestic investors. Yang (2005) examines international stock market correlations between Japan and four other Asian stock markets using Engle s (2002) DCC analysis in the period between 1990 and Yang s results support the findings of earlier stock market studies that it is necessary to consider the market condition when conducting international asset allocation. While there are extensive studies on the dynamics of international stock market conditional correlations and portfolio diversification, far less attention has been devoted to such studies in the real estate literature. This is mainly due to the lack of longer and high frequency time series for real estate return data. Consequently, many real estate studies focus on the unconditional real estate/reit correlation with the broader stock market. Worzala and Sirmans (2003) provide an excellent review of international real estate stock literature, focusing on the diversification benefits in a mixed-asset portfolio context or a real estate-only portfolio context. Other studies include Echholtz (1996a, b), Okunuv and Wilson (1997), Ling and Naranjo (1999), Mei and Hu (2000), Okunev et al. (2000), Kallberg et al. (2002), Clayton and Mackinnon (2003), Wilson and Zurbruegg (2004), Liow and Yang (2005), Cotter and Stevenson (2006) and Michayluk et al. (2006). Some evidence regarding the instability of international correlation and covariance structure of property equity returns is reported by Eichholtz (1996b). Lu and Mei (1999) and Hu and Mei (1999) find some diversification benefits through investing in emerging market property indexes. However there is an unfavorable asymmetry in the unconditional correlations between these indexes and the US index, i.e. the unconditional correlations are higher during highly volatile periods. Gordon and Canter (1999) find that the unconditional correlation coefficients between real estate stock indexes and the wider public equity indexes in his sample of 424 securities from 14 countries have not been stable over time. Utilizing the Australian Property Trust (LPT) data in the period between 1980 and 2000, Newell and Acheampong (2001) find that the unconditional correlations between LPTs and common-stocks vary considerably, with an increased correlation between the LPTs and shares that is linked to the increased volatility of the LPT and stock markets. Liow and Sim (2006) detect some evidence of instability in the unconditional correlations between the US and the Asian real estate securities markets over Cotter and Stevenson (2006) deploy the multivariate VAR-GARCH technique to examine the time-varying conditional volatilities and correlations in the daily US REIT and equity series. Finally, using an asymmetric covariance GARCH model, Michayluk et al. (2006) examine the daily volatility spillover effects and time-varying correlation dynamics between the USA and UK securitized real estate markets. Their results show significant asymmetric effects on both the volatility and correlation between the two markets.

6 206 K.H. Liow et al. Data Our monthly real estate securities return data are obtained from the Global Property Research (GPR) database on five national markets, namely, the United States (USA), the United Kingdom (UK), Japan (JP), Hong Kong (HK) and Singapore (SG); and for three regional markets, namely, America (AME) 1, Europe (EUR) and the Asia/ Far East (ASI). The USA market, being the world s largest, most mature and most transparent securitized real estate market is an apparent choice. The UK is a major world economy and is Europe s largest property market. Japan is also a major world economy and has a long history of listed real estate. The remaining two Asian markets of Hong Kong and Singapore have each enjoyed remarkable rapid economic growth in the past decade and both have established track record of securitized real estate investment and development companies in their capital markets. As of 1st April 2006, the GPR General database includes 33 country indices, five regional indices and two world indices ( In order for a country to be eligible to be included in the GPR index, it must have listed property investment companies of sufficient size. A firm must have had a market capitalization of more than USD 50 million as well as a minimum of 75% of all revenues must come from equity real estate investment. Our sample includes monthly data from 1984:1 to 2006:03, the longest time series data that are available for all sample countries. Monthly real estate securities returns (R) are obtained by taking the natural logarithmic difference of the index times 100. The respective stock market indices are compiled by the Morgan Stanley Capital Index (MSCI) and are obtained from Datastream on-line information system. The MSCI stock market indices are widely used by international fund managers for asset allocation decisions and performance measurement as well as by researchers for academic studies. Finally, all returns are expressed in local currency (currency hedged) returns. This avoids the incorporation of currency movements into the analysis, and for the concerned investor, it should make the findings more generalizable to all investors under the assumption that they have perfect hedging ability. Table 1 provides the mean and standard deviation for all return series. The mean real estate securities returns per month vary from 0.72% (Europe) to 2.05% (Hong Kong). The monthly standard deviations range from 2.45% for Europe to 11.31% for Singapore. Tables 2 and 3 report the unconditional correlations for the national and the regional real estate securities market returns estimated from 1984 to Similar numbers for the stock markets are produced. The Bonferroni adjusted p values are used to assess the statistical significance of the correlation coefficients. As the numbers indicate, the coefficients for the real estate securities markets are significantly positive at the least at the 5% level (except for JP-SG and JP-HK), indicating that real estate securities returns move in the same direction in the same month. The highest coefficient is (HK and SG) and the lowest is (JP and HK) while the average coefficient is around With one exception (AME and 1 The America (AME) regional index has two constituents: the USA and Canada country indices.

7 Correlation and Volatility Dynamics in International Real Estate Securities Markets 207 Table 1 Descriptive Statistics of monthly returns: 1/1984 to 3/2006 Real estate securities market Stock market Mean (%) Maximum (%) Minimum (%) Std. dev. (%) Mean (%) Maximum (%) Minimum (%) Std. dev. (%) USA UK Japan Hongkong Singapore America Europe Asia This table gives the mean, standard deviation and range (maximum and minimum) of monthly returns (expressed in percentage term) for five national and three regional real estate securities markets. EUR), each real estate securities market correlation is lower than its corresponding stock market correlation. The real estate securities market correlations vary from to while the stock market correlations vary between and These findings are in agreement with Eichholtz (1996a) who finds that national real estate return correlations are significantly lower than national common-stock return correlations. The fairly low to moderate levels of the international real estate securities market correlations suggest that national factors strongly affect the local real estate securities prices; probably reflects in part the existence of country-specific factors related to latent country-related macroeconomic state variables and institutional structure that can vary significantly across countries/regions. Table 2 Unconditional correlations matrices of national real estate securities and stock market returns: 1/ 1984 to 3/2006 Real estate securities markets General stock markets HK JP SG UK USA HK JP SG UK USA HK JP (2.106) (0.000) SG (0.000) (0.448) (0.000) (0.000) UK (0.000) (0.045) (0.000) (0.000) (0.000) (0.000) USA (0.000) (0.014) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) This table gives the unconditional correlation matrices of national real estate securities returns. The five national real estate markets are: United States (US), United Kingdom (UK), Hong Kong (HK), Japan (JP), Singapore (SG). All Bonferroni adjusted p values (numbers in bracket) for testing the statistical significance of the correlation coefficients are less than 0.01except JP-HK and JP-SG real estate security market pairs.

8 208 K.H. Liow et al. Table 3 Unconditional correlations matrices of regional real estate securities and stock market returns: 1/ 1984 to 3/2006 Real estate securities markets General stock markets AME ASI EUR AME ASI EUR AME ASI (0.000) (0.000) EUR (0.000) (0.000) (0.000) (0.000) This table gives the unconditional correlation matrices of national and regional real estate securities returns. The three regional markets are America (AME), Asia (ASI) and Europe (EUR). All Bonferroni adjusted p values (numbers in bracket) for testing the statistical significance of the correlation coefficients are less than The average unconditional correlations between (a) all five national real estate securities markets; (b) between the US and the other four markets and (c) between the three Asian markets; are plotted in Fig. 1. The unconditional correlations are estimated over a sliding window of 36 months (3 years). Although the unconditional correlations do not follow the same pattern for all the three averages, they fluctuate over time. This provides a good visual support of the instability of international real estate securities unconditional correlations across national markets and regions. Fig. 1 Average Unconditional Correlation of real estate securities markets. This figure reports the (unweighted) average unconditional correlations of a all five real estate securities markets (USA, UK, JP, HK and SG), b three Asian real estate securities markets (JP, HK and SG) and c US with other four real estate securities markets. The correlation is computed over sliding windows of three years, using local currency monthly total returns from 1/1984 to 3/2006. The main objective is to provide a visual support of the instability of international real estate securities market correlations across national and regional markets

9 Correlation and Volatility Dynamics in International Real Estate Securities Markets 209 Table 4 Test of the equality of the unconditional correlation matrices over time Periods compared Average correlations Test (t-value) Period 1 Period 2 Period 1 Period 2 National real estate securities markets 01/84 05/88 06/88 10/ ** 06/88 10/92 11/92 03/ ** 11/92 03/97 04/97 08/ /97 08/01 09/01 01/ /84 05/88 11/92 03/ /84 05/88 04/97 08/ /84 05/88 09/01 01/ ** 06/88 10/92 04/97 08/ * 06/88 10/92 09/01 01/ /92 03/97 09/01 01/ ** Regional real estate securities markets 01/84 05/88 06/88 10/ ** 06/88 10/92 11/92 03/ ** 11/92 03/97 04/97 08/ ** 04/97 08/01 09/01 01/ ** 01/84 05/88 11/92 03/ /84 05/88 04/97 08/ ** 01/84 05/88 09/01 01/ ** 06/88 10/92 04/97 08/ ** 06/88 10/92 09/01 01/ /92 03/97 09/01 01/ ** Correlation matrices of monthly national and regional real estate securities market returns for five countries (USA, UK, JP, HK and SG) and three regions (AME, ASI and EUR) are computed over equal periods of 53 months. We calculate the average and standard deviation of the differences in the correlations in the first period and in the second period and do a t-test to see whether the difference between the averages is significant. *Indicates significance at the 5% level **Indicates significance at the 1% level Finally, we estimate the unconditional correlation matrix for the national and the regional real estate securities markets over five adjacent periods of 53 months. In doing so, we test for the equality of the correlation matrices over adjacent subperiods as well as over non-adjacent sub-periods by the usual t-test, to see whether the difference between the averages is statistically significant. 2 Table 4 reports the results. As the numbers indicate, the null hypothesis of a constant correlation matrix is rejected at the 5% confidence level in five out of the ten national market comparisons and in eight out of the ten regional market comparisons. These results are broadly similar to the findings by Eichholtz (1996b) who finds that international property share correlations are stable between some time-periods, and unstable between others. 2 Each time series has 267 monthly return data. This full sample is divided into five sub-samples that contain 53 monthly return data per time series (ignoring the last two observations). This approach will allow us to conduct the simple t-test to assess the instability of correlation matrix between any two subperiods that have equal number of monthly observations; that is, a time series that contain 53 monthly observations each for the five shorter sample periods (53 5 = 275); and ignores the last two observations. An alternative method is to use Jenrich test.

10 210 K.H. Liow et al. Methodology The research design adopts a two-step approach. The first step undertakes the DCC methodology proposed by Engle (2002) to model the fluctuations of the correlation and volatility between international real estate securities markets and between stock markets over time. In the second step, the estimates of the conditional correlation and volatility are fitted to two multiple regression models in order to investigate the evolution of the real estate securities market correlations over time. Modeling the Conditional Correlations with DCC-GJR-GARCH Specification GARCH models are deployed to explore the stochastic behavior of financial time series and, in particular, to explain the behavior of the return volatility over time (Bollerslev et al. 1992). The constant conditional correlation (CCC) multivariate- GARCH (MGARCH) model, which was proposed by Bollerslev (1990) as an alternative to the computationally intensive VECH model, is the most widely used MGARCH model in the last decade. Setting all conditional correlations to be constant, the CCC-MGARCH model allows for the conditional variance equation to take any form of the univariate GARCH process. However, the assumption that the conditional correlations are constant may appear unrealistic in many empirical applications. Tse and Tsui (2002) and Engle (2002) generalize the CCC model by making the conditional correlation matrix time-dependent. While Tse and Tsui (2002) propose a new MGARCH model with time-varying correlations and a VECH representation based on the conditional variances and conditional correlations, Engle (2002) proposes a DCC model that can be estimated with the univariate or two-step methods based on the likelihood function. Engle (2002) also compares the DCC model with other MGARCH models and concludes that the DCC models are competitive with the multivariate specifications as well as superior to moving average methods. Further, since the conditional variance is an asymmetric function of past innovations, which increases proportionately more during market declines, the so-called leverage (asymmetric) effects thus becomes another important issue in the application of the GARCH family models. Asymmetric GARCH models include Nelson s (1991) exponential GARCH model, Glosten et al. (1993) s GJR-GARCH model and Zakoian s (1994) Threshold-GARCH model. In this paper, we resort to the DCC model of Engle (2002) and the GJR-GARCH model specification (i.e. GJR- DCC-GARCH) to estimate the time-varying conditional correlations in international real estate securities and stock markets. The model is briefly explained below. Let R i,t be the percentage return at time t for market i, Ω t 1 all information available at time t 1, μ i,t and h i,t the conditional mean and variance respectively, h ij,t the conditional covariance between the market i and market j, ɛ i,t the innovation p ffiffiffiffiffiffiat time t (i.e., ɛ i,t =R i,t μ i,t ), and η i,t the standardized innovation (i.e., η i;t ¼ " i;t h ii;t). The AR (1) model for returns can then be represented as follows: R i;t ¼ b i;0 þ b i;1 R i;t 1 þ " i;t ; " i;t Ω t 1 N 0; h ii;t ð1þ where the conditional mean return for each market is a function of its past own returns, and the lead/lag relationships are captured by coefficients β i,1. A significant

11 Correlation and Volatility Dynamics in International Real Estate Securities Markets 211 β i,1 coefficient measures the direct effect that a change in return on market i at time t 1 would have on the same market at time t. The conditional variances follow a univariate GJR-GARCH (1, 1) specification: h ii;t ¼ a i;0 þ a i;1 " 2 i;t 1 þ g ih ii;t 1 þ d i I i;t " 2 i;t 1 ð2þ where α i,1 measures the ARCH effect. The persistence of volatility (i.e. GARCH effect) is measured by γ i. The unconditional variance is finite if γ i <1. δ i is the coefficient that measures the leverage (asymmetric) effect; I i,t =1 if the innovation in last period is negative and otherwise I i,t =0. The conditional covariance terms are assumed to follow the DCC (1, 1) specification: pffiffiffiffiffiffipffiffiffiffiffiffi h ij;t ¼ r ij;t h ii;t h jj;t ð3þ q ij;t q ii;t q jj;t r ij;t ¼ pffiffiffiffiffiffipffiffiffiffiffiffi ð4þ q ij;t ¼ ð1 a bþr ij þ ah i;t 1 h j;t 1 þ bq ij;t 1 ð5þ where q ij,t is the conditional covariance between the standardized residuals from Eq. 1; ρ ij is the unconditional correlation between residuals ɛ i,t. Equation 5 is the DCC model in which a and b are scalar parameters to capture the effects of previous (first lagged realization) standardized shocks and dynamic conditional correlations on current dynamic conditional correlations, respectively. The q ij,t expression will be mean-reverting when a+b<1. This specification reduces the number of parameters to be estimated and makes the estimation of time-varying correlation more tractable. Finally, Engle (2002) shows that the log-likelihood of the estimators may be written as: LðÞ¼ θ 1 X T 2 t¼1 n logð2πþþ2 logjd t jþ" 0 D 1 t D 1 t " þ log j Vt jþη 0 t V 1 t η t η 0 t η t ð6þ where n is the number of equations; T is the number of observations; θ is the vector of parameters to be estimated; D t is the diagonal matrix of time varying standard deviations obtained from Eq. 4 and V t is the time varying correlation matrix. Evolution of Market Correlations and Volatilities: Real Estate Securities and Stock Markets To test the relationship between the sample real estate securities and stock markets with regard to the evolution of market correlations and volatilities, we regress the real estate securities market correlation between two countries on the two real estate securities market volatilities, the stock market correlation and the two stock market volatilities. The five independent variables are moderately to highly correlated, thus disentangling their effects is difficult.

12 212 K.H. Liow et al. For each country pair, we first conduct the Principal Component Analysis (PCA) to derive a set of factors that are totally uncorrelated, with the first (dominant) factor accounting for the maximum variation in the five variables. The most simplistic approach is to retain all components whose eigenvalues exceed unity. These eigenvalues measure the contributions of the corresponding local factors to explain the cross-sectional variation in the five original variables. Once the initial choice of the factor loading is made, we then interpret the co-movement of the original variables. The co-movement of the variables would be based on high factor loadings. With the dominant factors extracted (maximum five), a regression model is run to analyze the evolution of the real estate securities market correlations over time. The multiple regression model is formulated below: ^ρ ij ¼ δ 0 þ δ 1 ðtrend Þþδ 2 ðcrashþ t þδ 3 ðcrisisþ t þδ 4 F 1 þ δ 5 F 2 þ δ 6 F 3 þ δ 7 F 4 þ δ 8 F 5 þ " t ð7þ Where ^ρ ij is the conditional correlation for the real estate securities market pair (i and j) predicted from the DCC framework in step 1; F 1..F 5 are the possible dominant factors that are derived from the PCA on stock market correlation, two real estate securities market volatilities and two stock market volatilities predicted from the DCC framework in step 1; Trend, Crash t and Crisis t are dummy variables of time trend, stock market crash period and Asian financial crisis period; δ 0 to δ 8 are regression parameters to be estimated and ɛ t is the model residual. 3 The effects of the stock market crash have well been documented in the literature. Immediately following the Asian crisis, real estate prices in many Asian economies plunged. A research study by Kallberg et al. (2002) finds that there were reduction in real estate return and an increase in real estate market volatilities and correlations following the Asian financial crisis. Empirical Results DCC Results Tables 5 and 6 present the estimates of the bivariate AR (1)-DCC (1, 1)-GJR- GARCH (1, 1) models for the national (National markets) and the regional (Regional markets) real estate securities and stock markets. The last two rows of the table show the estimates of the two DCC (1, 1) parameters (i.e. a and b in Eq. 5). The other rows are the parameter estimates for the univariate GJR- GARCH (1, 1) models for the individual markets. As shown, most of the estimated ARCH, GARCH and the 3 It may be difficult to come out with a unanimous agreement on the periods of stock market crash and Asian financial crisis for all countries. Following previous literature, the stock market crash dummy is set from 10/1987 to 12/1987 (3months) and the Asian financial crisis dummy is set from 1/1997 to 6/1998 (18months) to encompass the short time before and after the crisis period.

13 Correlation and Volatility Dynamics in International Real Estate Securities Markets 213 Table 5 DCC (1, 1) -GJR- GARCH (1, 1) estimates of national markets: 1/84 3/06 Real estate securities markets Country1 US UK JP HK Country2 HK JP SG UK HK JP SG HK SG SG β1, ** ** ** ** ** ** ** ** * ** β2, ** * ** ** ** ** ** ** ** β1, β 2, ** ** ** ** α 1, ** ** ** ** ** α2, ** * * ** * ** ** α1, ** ** ** * * * * ** α 2, * * * * ** ** ** γ ** ** ** * * ** ** ** ** γ ** ** ** ** ** ** ** ** ** ** δ * ** δ a ** ** ** ** ** b ** ** ** ** ** ** ** ** ** ** Stock markets β1, ** ** ** ** ** ** ** ** β 2, ** ** ** ** ** β 1, β2, * ** ** α1, ** ** ** ** ** ** α 2, ** ** ** * α 1, ** ** ** ** ** ** ** ** ** α 2, ** ** ** ** * ** ** * ** ** γ ** ** ** ** ** ** ** ** ** ** γ ** ** ** ** ** ** ** ** ** ** δ ** * ** ** ** ** ** ** δ ** ** ** ** ** ** ** ** a ** * ** ** ** ** ** ** b ** ** ** ** ** ** ** ** ** ** The DCC (1, 1)-GJR-GARCH (1, 1) equations are: Ri;t ¼ b i;0 þ b i;1 Ri;t 1 þ "i;t (mean equation); hii;t ¼ ai;0 þ ai;1" 2 i;t 1 þ g ihii;t 1 þ diii;t" 2 i;t 1 (variance equation) and q ij;t ¼ ð1 a b Þ^ρ ij þ aη i;t 1 η j;t 1 þ bqij;t 1 (DCC equation). Mean intercepts (β1,0 and β2,0), 1-month lagged coefficients (β1,1 and β2,1), variance intercepts (α1,0 and α2,0), ARCH coefficients (α1,1 and α2,1), GARCH coefficients (γ1 and γ2), leverage coefficients (δ1 and δ2), and DCC parameters (a, b); a and b are scalar parameters that capture the effects of previous (first lagged realization) standardized shocks and dynamic conditional correlations on current dynamic conditional correlations, respectively. The t-statistics attached to all coefficients (not reported) are estimated with robust standard errors. US United States, UK United Kingdom, HK Hong Kong, JP Japan, SG Singapore *Denotes 10% significance **Denotes 5% significance

14 214 K.H. Liow et al. Table 6 DCC (1, 1) -GJR- GARCH (1, 1) estimates of regional markets: 1/84 3/06 Real estate securities market Stock market Region1 AME EUR AME EUR Region2 EUR ASI ASI EUR ASI ASI β 1, ** ** ** ** ** ** β 2, ** ** ** ** β 1, * * ** * β 2, * * ** α 1, ** ** ** ** ** ** α 2, ** ** ** ** ** ** α 1, ** ** ** ** ** ** α 2, ** ** ** ** γ ** ** ** ** ** ** γ ** ** ** ** ** ** δ * ** * δ * * ** a ** ** ** ** ** b ** ** ** ** ** ** The DCC (1, 1)-GJR-GARCH (1, 1) equations are: R i;t ¼ b i;0 þ b i;1 R i;t 1 þ " i;t (mean equation); h ii;t ¼ α i;0 þ α i;1 " 2 i;t 1 þ γ ih ii;t 1 þ δ i I i;t " 2 i;t 1 (variance equation) and q ij;t ¼ ð1 a bþ^ρ ij þ aη i;t 1 η j;t 1 þ bq ij;t 1 (DCC equation). Mean intercepts (β 1,0 and β 2,0 ), 1-month lagged coefficients (β 1,1 and β 2,1 ), variance intercepts (α 1,0 and α 2,0 ), ARCH coefficients (α 1,1 and α 2,1 ), GARCH coefficients (γ 1 and γ 2 ), leverage coefficients (δ 1 and δ 2 ), and DCC parameters (a, b); a and b are scalar parameters that capture the effects of previous (first lagged realization) standardized shocks and dynamic conditional correlations on current dynamic conditional correlations, respectively. The t-statistics attached to all coefficients (not reported) are estimated with robust standard errors. AME America, EUR Europe and ASI Asia/Far East *Denotes 10% significance **Denotes 5% significance asymmetry parameters are statistically significant, which implies that the GJR- GARCH (1, 1) describes the monthly return behavior adequately. In addition, they are able to capture the temporal dependence and asymmetry of the stock and real estate securities returns for the ten national and the six regional markets under examination. The estimates of the DCC (1,1) parameters (a, b) are mostly statistically significant. Therefore, the assumption of constant conditional correlation is not supported empirically. Table 7 contains the descriptive statistics for the DCC estimates for all the country and the regional pairs. The conditional correlations are in the (0.052, 0.565) range and in the (0.290, 0.792) range, respectively, for the sample real estate securities and stock markets, signifying no to moderate interdependence. Another observation is that similar to the unconditional correlation estimates, the results indicate significantly lower conditional correlations between the national and regional real estate securities market returns than those between the stock market returns. With few exceptions, the statistics for skewness and kurtosis suggest that many of the correlation series are significantly skewed and leptokurtic relative to the normal distribution. Finally, the last column of the table [Corr (RE/S)] shows the degree of comovement between the real estate securities correlations and stock market correlations.

15 Correlation and Volatility Dynamics in International Real Estate Securities Markets 215 Table 7 Descriptive statistics of monthly conditional correlations for national and regional real estate security markets (RE) and stock markets (stock): 1/1984 to 3/2006 Mean Maximum Minimum Std Dev Skewness Kurtosis Corr(RE/S) US-UK RE Stock US-JP RE Stock US-HK RE Stock US-SG RE Stock UK-JP RE Stock UK-HK RE Stock UK-SG RE Stock JP-HK RE Stock JP-SG RE Stock HK-SG RE Stock AME-EUR RE Stock AME-ASI RE Stock EUR-ASI RE Stock Column 1 shows the countries/regions: United States (US), United Kingdom (UK), Japan (JP), Hong Kong (HK), Singapore (SG, America (AME), Europe (EUR) and Asia/Far East (ASI). The conditional correlations for the real estate markets and stock markets are derived from the DCC (1, 1)-GJR-GARCH (1, 1) estimates. Corr(RE/S) indicates the co-movement between RE (real estate securities market) correlation and S (stock market) correlation. The range is between (AME-EUR) and (US-HK) suggesting that movements in international real estate securities market and stock market correlations are correlated. This issue is further investigated below. Figure 2 shows the average real estate securities and stock market conditional correlations for four country-type combinations (all countries, three Asian countries, three developed countries and the US other countries). We observe that there are some significant variations and structural changes in the correlation structure occurred within the sample period. The correlations do not follow the same patterns for all countries. For the case of real estate, reference to Fig. 2 shows four graphs of correlation trend. In two cases, the slope is small positive, and in two cases it is small negative. The absence of a significant positive trend in real estate correlations is also evidenced later in the trend coefficients in Table 9 (reported below). Overall, the international real estate average correlation has remained fairly constant although the conditional correlation structure between countries changes over time. Results for the stock markets are similar in that all the four averages show an insignificant

16 216 K.H. Liow et al. Fig. 2 Average conditional correlation: 1/1984 3/2006. This figure reports the (unweighted) average conditional correlations of real estate securities markets and stock markets for a all five countries (US, UK, JP, HK and SG), b three Asian countries (JP, HK and SG), c three developed countries (US, UK and JP) and d US with other four countries (UK, JP, HK and SG). The conditional correlation is predicted from the GJR-DCC (1, 1) model. In addition, a simple least square line (trend) is fitted over the total period for each correlation series. The slopes are positive for all stock market correlations and negative for two of the real estate securities market pairs (c and d) increase in correlation, ranging between approximately 1.34% and 8.34% within the sample period. 4 The Link between Correlation and Volatility in Real Estate Securities Markets The conditional volatilities of the paired regional real estate securities markets and their dynamic conditional correlations are plotted in Fig. 3. In general, the graphs 4 It has to be cautioned that a constant linear trend is not consistent with the definition of a correlation coefficient. Other forms of trend can be modeled, but no theory exists of the exact form of this trend. Also, as with any time-series study, the starting date can be of importance and render any conclusion somewhat different.

17 Correlation and Volatility Dynamics in International Real Estate Securities Markets 217 Fig. 3 Conditional correlations and volatilities of regional real estate securities markets: 1/1984 3/2006. The conditional monthly volatilities of three paired regional real estate securities markets (America, Europe and Asia) and their monthly time-varying correlations over the study period are plotted show that both market volatilities tend to move together and that the correlation tends to move together with the market volatilities. An econometric estimation of the link between the conditional correlation and the two market volatilities (represented by their standard deviations) is conducted for all 13 pairs of real estate securities markets. 5 All the regression results reported in Table 8 are adjusted for autocorrelation and White heteroskedasticity-consistent standard errors. The adjusted R 2 values range from 26.5% to 90.7%. With minor exceptions, all positive volatility coefficients are statistically significant. In such cases, the correlation increases when one market or both become more volatile, and the covariance increases more than the market volatilities. For the US market in conjunction with the four foreign markets, the major influence is the US volatility although all the four foreign 5 All the correlation and volatilities series are stationary as verified by the usual ADF tests. For each market pair, the two market volatilities have some multicollinearity and disentangling the effects might be difficult. On the other hand, including only one volatility coefficient reduces the Adjusted R 2 significantly.

18 218 K.H. Liow et al. Table 8 Multiple Regression of the link between correlations and volatilities in real estate securities markets: 1/1984 3/2006 Correlation Constant Volatility 1 Volatility 2 Adj R2 F-stat DW National real estate securities markets US/UK (4.90***) (4.90***) (2.09***) US/JP (1.44) (4.53***) (3.29***) US/HK (5.51***) (7.71***) (1.90*) US/SG (37.44***) (4.10***) (3.08***) UK/JP (5.32***) (0.59) ( 1.98**) UK/HK (8.23***) (2.78***) ( 0.28) UK/SG (4.80***) (2.51**) ( 0.32) JP/HK ( 1.16) ( 5.20***) (7.14***) JP/SG (6.19***) ( 2.46**) (2.78***) HK/SG (5.18***) (4.42***) (2.88***) Regional real estate securities markets AME-ASI (8.14***) (2.90***) (0.29) AME-EUR (14.29***) (2.32**) (3.32***) EUR-ASI (10.69***) (3.17***) ( 1.37) Column 1 shows the countries/regions: United States (US), United Kingdom (UK), Japan (JP), Hong Kong (HK), Singapore (SG, America (AME), Europe (EUR) and Asia/Far East (ASI). For each country pair, volatility 1 refers to the real estate securities market 1 s conditional volatility; volatility 2 refers to market 2 s conditional volatility. All conditional volatility estimates were derived from the DCC (1, 1)- GJR-GARCH (1, 1) estimates. All coefficient estimates are adjusted for auto-correlated and White heteroskedasticity errors; t-statistics with robust standard errors are in parentheses. DW is the Durbin Watson test statistic; N=267 monthly observations. *Denotes two tailed significance at the 1% level **Denotes two tailed significance at the 5% level ***Denotes two tailed significance at the 10% level markets volatility coefficients are statistically significant and yet of smaller magnitude. This is also the case for HK-SG and the two regional market pairs (AME-ASI and AME-EUR) where both positive volatilities contribute to a larger increase in the covariance. The investment implication is clear: since global or regime shocks affect the markets volatilities and their correlations at the same time, any possible risk diversification benefits of international real estate investing may be significantly reduced as a result of the strong positive connection between the real estate securities market correlations and their conditional volatilities. Finally, it is noted that the above finding does not apply to the case of Japan where we observe a significantly negative relationship between the variables in two out of three cases. The Link between Real Estate Securities and Stock Markets Since real estate securities market is an imperative part of the wider stock market, an interesting question is whether the movements in correlations among the real estate securities markets and among the stock markets are synchronized. For example, the Hong Kong real estate securities market may become increasingly correlated with the Singapore real estate securities market at the same time the Hong Kong and Singapore stock markets become increasingly correlated. Consequently, a positive relationship between the real estate securities market correlations and stock market correlations might be expected. The last column of Table 7 provides the supporting evidence.

19 Correlation and Volatility Dynamics in International Real Estate Securities Markets 219 Table 9 Multiple regression results of conditional correlation evolution for real estate securities markets: 1/1984 to 3/2006 Correlations between Real Estate Securities Markets US-UK US-JP US-HK US-SG UK-JP UK-HK UK-SG JP-HK JP-SG HK-SG AME-EUR AME-ASI EUR-ASI δ (30.20***) δ (1.04) δ ( 1.27) δ (0.89) δ ( 5.72***) δ (0.05) (29.74***) ( 0.04) (1.34) ( 1.30) ( 3.63***) ( 0.03) (35.45***) (0.08) ( 1.35) ( 0.88) ( 3.34***) ( 1.48) (33.46***) ( 1.98**) ( 0.92) ( 2.29**) ( 2.73***) (0.29) (29.35***) ( 1.49) (1.77*) ( 0.99) ( 7.39***) ( 10.02***) (22.26***) ( 0.47) (0.97) ( 1.08) ( 5.86***) ( 7.08***) (10.13***) ( 0.73) ( 1.38) ( 1.26) (13.50***) ( 7.24***) (1.23) ( 0.29) ( 1.51) (0.85) (0.49) (8.82***) (3.24***) (0.29) (1.80*) (1.05) ( 9.82***) ( 5.66***) (10.04***) (2.37**) ( 1.42) ( 0.03) ( 0.85) (6.65***) (84.37***) (0.47) ( 1.42) (0.18) ( 1.47) (6.17***) δ6 NA NA NA NA NA NA NA NA NA NA NA (0.11) (47.46***) (1.46) (1.35) ( 1.27) (0.11) ( 2.39**) Adjusted R 2 F statistic DW stat (30.64***) (1.82*) (3.37***) ( 2.27**) (3.05***) NA Row 2 shows the countries/regions: United States (US), United Kingdom (UK), Japan (JP), Hong Kong (HK), Singapore (SG, America(AME), Europe(EUR) and Asia/Far East (ASI). (b) Based on Eq. 7: ^ρ ij ¼ δ0 þ δ1 ðtrend Þþ δ2 ðcrash Þ t þδ3 ðcrisis Þ t þδ4f1 þ δ5f2 þ δ6f3 þ δ7f4 þ δ8f5 þ "t; δ0 to ^δ8 are the regression parameters with constant, time trend, stock market crash dummy, Asian financial crisis dummy and three dominant factors (F1, F2 and F3) that were derived from the Principal Component Analysis (PCA). The conditional correlations ( ^ρ ij ) are derived from the DCC-GJR-GARCH estimates. All the coefficient estimates are adjusted for auto-correlated and White heteroskedasticity errors; t-statistics with robust standard errors are in parentheses. DW is the Durbin Watson test statistic; N=267 monthly observations. *Denotes two tailed significance at the 1% level **Denotes two tailed significance at the 5% level ***Denotes two tailed significance at the 10% level