Kim Hiang LIOW *
Department of Real Estate
National University of Singapore
4 Architecture Drive
Singapore 117566
Tel: (65)65161152
Fax: (65)67748684
Email : rstlkh@nus.edu.sg
Department of Real Estate
National University of Singapore
4 Architecture Drive
Singapore 117566

With a sample of 14 developed real estate securities markets during the study period 1993-2008, the main objective of this paper is to investigate market integration using the concepts of risk-return convergence and beta convergence. We find that international developed real estate securities markets have been moving toward greater integration in terms of increasing correlation and faster speed of convergence in returns and volatilities. However, the finding of an insignificant risk-return convergence trend also implies that the risk and return characteristics of the real estate securities markets have not become less different from each other over the study period, supporting the view that the idiosyncratic “real estate factor” and “country factor” of individual markets might have become more important over time.
This paper investigates market convergence among 14 developed securitized real estate markets from three continents during the study period 1993-2008. In the context of financial market integration, we consider real estate securities market integration to indicate convergence of returns and risks of securitized real estate markets in different national economies.
1 We analyze the dynamics of securitized real estate market integration using beta-convergence (measuring the speed of convergence) and risk-return convergence (measuring the extent of convergence). Securitized real estate is a hybrid of stock, bond and real estate. As securitized real estate markets continue to expand in size, they represent an increasingly significant but not yet well-understood segment of the financial systems in the global economy.
2 This study is thus motivated to contribute to the historical evolution of the risk-return characteristics as well as the convergence dynamics across the 14 international developed real estate securities markets during the study period 1993-2008.
1 Integration of financial markets is broadly classified into domestic financial market integration (e.g. among money, credit, bond, stock and real estate markets) and international financial market integration
(e.g. across national or regional stock markets, across national or regional bond markets, and across national or regional securitized real estate markets etc.). Financial markets are integrated when the law of one price holds (Ayuso and Blanco, 2000). This indicates convergence of returns on assets that are issued in different countries and generate identical cash flows (Baele et al. 2004).
2 Accordingly to Dhar and Goetzmann (2006), due to the strong growth and remarkable risk-adjusted performance over time, the securitized real estate sector has now been recognized as an “essential:” asset class in mixed-asset portfolios, with industry sources predicting the global real estate securities market capitalization to increase significantly from $500 billion in 2004 to 1 trillion by 2010 (Newell et. 2005).
However, very little is known regarding the degree of interlinkages among international real estate securities markets compared to those of world equity markets and bond markets (Yunus, 2009).
1

Even though the concept of convergence 3 and the respective techniques have been employed in various economic growth (e.g. Barro and Sala–I-Martin, 1992) and financial market integration (e.g.
Babetskii et al. 2007) studies to our knowledge, this is one of the first study in the real estate arena that utilizes both risk-return and beta convergence indicators to the global world of finance to jointly investigate the extent and evolution of integration in international developed securitized real estate markets. Our specific contributions are two fold. First, we examine whether there is a significant risk-return convergence
(or divergence) among our sample markets by detecting the presence (or absence) of a significant trend in the risk-return distance measures. The risk-return distance is measured based on the Euclidean distance (see
Section 4 below). We consider this risk-return convergence concept to be an extension of the

convergence concept appeared in the economic growth literature because sigma-convergence is unable to simultaneously consider the risk and return attributes of the data.
4 Second, Babetskii et al. (2007) point out since the sigma-convergence (or risk-return convergence) only indicates to what extent the markets are integrated, we estimate another convergence indicator (

-convergence) to assess the speed of integration.
5
These two complimentary indicators, which appear for the first time in a stock /real estate study, 6 will provide a clearer picture regarding the degree, evolution and current level of real estate securities market integration in the developed countries. Finally, we also assess the empirical relationship between international correlation change and risk–return convergence. This is because, as pointed out by Eun and
Lee (2010), knowledge in both correlation structure and risk-return characteristics is needed to provide a
3 In general term, convergence denotes an approach toward a definite value, a definite point, a common view or opinion, or toward a fixed or equilibrium state in the long-term or short- run.
4 In the economic growth literature,

-convergence happens when the cross-sectional standard deviation of per capita income among regions diminishes over time. In applying this concept to detect financial market integration, diminishing cross-sectional standard deviation for standard deviations of returns can be interpreted as evidence of risk-convergence or return-convergence. Solnik and Roulet (2000) use this concept of dispersion as cross-sectional correlation to estimate the global correlation level of stock markets.
5 According to the economic growth literature, there is beta-convergence when the partial correlation between growth in income and its initial level is negative (Young et al. 2008). Babetskii et al. (2007) point out that the two convergence indicators have different informational content in that beta convergence does not imply sigma convergence. Furceri (2005) points out that these two concepts measure two different phenomena of the convergence process. Moreover, no mathematical relation is able to establish a clear causality between the two types of convergence
6 As discussed in Section 2 (literature review) below, although Eun and Lee (2010) adopted the meanvariance convergence approach in analyzing international stock market integration, they did not conduct the beta-convergence examination.
2

fuller picture of financial market integration, as increasing correlation does not necessarily imply riskreturn convergence.
Our analysis has important implications for international diversification and policy formulation. If international developed securitized real estate markets’ risk-return characteristics are found to converge significantly toward each other over time, then these markets have become more similar from each other in terms of risk and return performances. Accordingly, they have relatively high degree of integration among themselves. Moreover, if the risk-return convergence is accompanied by
 convergence, it would imply that the securitized real estate markets are moving faster towards integration and consequently there is little or even no long-run diversification opportunity in international real estate investing. This knowledge on market convergence and its evolution, together with common trends analysis and short-term dynamic correlation will provide a more complete picture of the dynamic relationships (both long-term and short run) across the securitized real estate markets concerned. In contrast, if the developed securitized real estate markets are found to have diverging risk-return characteristics over time and in addition accompanied with lower speed of convergence, then the gains from international real estate securities portfolio diversification should still remain attractive. From the policy makers’ perspective, our results also indicate that global market conditions, such as the global financial crisis which started in mid-2007 (and has not ended) can influence significantly the risk-return convergence dynamics. This additional knowledge on market convergence dynamics will be useful in their policy formulation regarding cross-border real estate investment, especially in periods of market turmoil, to achieve stability in domestic and international financial markets. This is where our study intends to contribute and complement the integration literature involving international real estate securities markets.
The paper is organized as follows. Section 2 focuses on the latest literature in securitized real estate market integration. This is followed by Section 3 which explains the research sample and data characteristics. Section 4 provides a brief discussion of the risk-return convergence and

-convergence approaches and relevant empirical tests. The empirical results are provided in Section 5 and Section 6 concludes the research.
3

As an important subject, traditional research in stock market integration evolves mainly around the themes of correlation, causality, co-integration and cycle synchronization. Yu et al. (2010) provides a survey of these indicators to assess the degree of stock market integration in Asia. Another empirical dimension of stock market integration which has been given less formal attention is the application of two convergence indicators; i.e.

- and

- convergence to measure, respectively, the speed and state of similarity among the markets examined. These two measures are based on the law of one price. Babeskii et al. 2007 consider these two indicators in analyzing the dynamics of stock market integration of Czech
Republic, Hungary, Poland and Slovakia relative to the Euro currency union. More recently, Eun and Lee
(2010) extend the concept of sigma convergence to risk-return convergence. Essentially, this involves developing a combined risk-return (rather than two separate measures: risk or return) distance measure to evaluate how similar a stock market is to the rest of sample markets in terms of risk-return performances.
Consequently this will provide a clearer indication as to whether international stock market integration is driven by changing risk-return characteristics, in addition to changing correlation structure over time
(Longin and Solnik, 1995).
In so far as the correlation issue is concerned, several studies have detected the time-varying nature of correlations across international real estate securities markets. Using the DCC methodology of
Engle (2002), Liow et al (2009) examine the time-varying correlation and volatility links of several national /regional securitized real estate and stock markets. They find that real estate securities markets’ conditional volatilities and stock markets’ volatilities are synchronous over time. Moreover, the international correlation structure of real estate securities and the broader stock market are linked to each either. In another study, Liow (forthcoming) finds that international correlations have been increasing over time among some major securitized real estate markets as well as between the real estate securities markets and the global stock market; although this integration process has been much slower than that among the corresponding local stock markets as well as from the global stock market. Regarding the risk-return performances of securitized real estate markets, although prior studies such as Hamelink and Hoesli (2005),
Bond et al (2003) and Ling and Naranjo (2002) have investigated the main determinants of international real estate securities returns using different datasets over different study periods, none of the studies
4

examined the issue of changing risk-return characteristics of the real estate securities markets over time.
The third strand of literature employs multivariate co-integration technique to investigate the nature and extent of long-term equilibrium relationships among international real estate securities markets (e.g.
Eichholtz et al, 1998; Kleiman et al. 2002; Yang et al. 2005; Liow, 2008 and Yunus, 2009). Yunus (2009) investigates the dynamic interdependence among the securitized real estate markets of Australia, France,
Hong Kong, Japan, Netherlands, UK, and US for the period 1990-2007. Using co-integration test and common trends analysis, she finds that international securitized real estate markets are becoming increasing integrated which would be indicative of increasing convergence over time. In addition, the US and
Japanese markets are the sources of the common stochastic trends that drive the co-integrated markets toward long-run equilibrium relationships.
Our sample of 14 developed real estate securities markets came from three continents and was gathered from the S&P Global Property database, 7 including Australia, Hong Kong, Japan, Singapore
(Asia-Pacific), Canada, the USA (North America), Belgium, France, Germany, Netherlands, Spain, Sweden,
Switzerland and the UK (Europe). Although these real estate securities markets are considered relative developed and homogenous, they are nevertheless different with regard to their respective national economies, economic growth rates as well states of stock markets and direct real estate markets. In addition, these real estate securities markets have different market capitalizations, institutional and regulatory frameworks, market transparencies, trading systems and transaction costs. The sample period is from
January 1993 through December 2008 in order to include Germany in the study.
8 For the global financial markets, 2008 was a year that the global markets were engulfed in the sub-prime mortgage crisis, triggered by a dramatic rise in mortgage delinquencies and foreclosures in the U.S., which gave rise to major and
7 This S&P global property database, the latest international public real estate database in the market, is designed to reflect components of the broad universe of investable international real estate stocks reflecting their risk and return characteristics. In total, the database has indices (both capitalization weighted and float adjusted) comprised of over 500 companies from more than 35 developed and emerging markets with a minimum market value of $100 million (Serrano and Hoesli, 2009).
8 Except for Germany which was listed in the S&P Global Property database since June 1992, the other 13 markets were listed since August 1989.
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adverse consequences for banks and financial markets around the globe. As the economic turmoil accelerated, real estate securities continued their sharp decline. The S&P global property index fell an astounding 48.9% in 2008, while the S&P developed property index dropped by an equally dismal 47.6%.
Similarly, the emerging property dropped 60.4% over 2008.
Moreover, the total market capitalization for
S&P Property fell to approximately US$684 billion as of end 2008, compared to previous year’s market capitalization of US$1409 billion, an all time high for the industry.
We employ weekly real estate securities market returns, which are computed as natural logarithmic of the total return indexes relative, I in successive weeks; i.e. t
Ln
(
I t
I t
 1
) , in our analysis.
Using weekly data hopes to avoid the problem of non-synchronous trading and short-term correlations due to noise. Further, all analyses are conducted in US dollars as well as in local currency terms. Table 1 provides the usual summary statistics of weekly returns over the full study period of 16 years. As the numbers indicate, the real estate securities markets derive different risk-return performances over this full period. Moreover, the distribution of return for all 14 real estate stock indexes is non-normal, characterized by higher peakedness and fat tails relative to a normal distribution.
(Table 1 here)
Figure 1 provides scatter plots of the risk-return characteristics for the 14 sample markets “relative to” to the cross-market average in four separate years, i.e. 1993, 2000, 2007 and 2008. The cross-market average weekly return performances are: 0.074% (1993), 0.056% (2000), -0.16% (2007) and -1.28% (2008); and the corresponding cross-market average weekly standard deviation performances are: 1.39% (1993),
1.47% (2000), 2.57% (2007) and 5.72% (2008). In Figure 1, the y-axis measures the difference of each market’s average return from the cross-market average; the x-axis measures the degree of the each market’s standard deviation (“risk”) from the cross market average of standard deviations. It appears from Figure 1 that the ellipse linking all the 14 observations for each year till 2007 becomes successively smaller over time. However, the ellipse expands in 2008, suggesting that the risk-return characteristics of the sample markets might have first converged toward each other till 2007; and thereafter diverged from each other in
2008.
(Figure 1 here)
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This is an expanded approach to the so-called

(sigma) -convergence concept which appears in the economic growth literature. In our case,

-convergence of the securitized real estate markets is said to happen when the cross-sectional standard deviation (risk) of weekly returns among markets diminishes over time (Solnik and Roulet, 2000). However,

-convergence is unable to consider simultaneously the risk and return attributes of the each time series observation Following Eun and Lee (2010) which is the only published study that investigated risk-return convergence in international stock markets, we first estimate the “risk-return distance” as a mean to quantify the degree to which a securitized real estate market differs from the rest of sample markets. Then we compute the Euclidean distance (similar in cluster analysis) to measure the degree of risk-return differences among the markets. With the Euclidean risk – return distance measured, statistically significant (or otherwise) time trends in the cross-market average distance as well as individual distances are then investigated. The risk-return distance methodology is briefly explained as follows:
(a) Mathematically, the Euclidean distance between two observations (in two dimensional x and y planes), d is computed as: xy
The greater the Euclidean distance between the observations, the more dissimilar they are in terms of their characteristics. In our study, each real estate securities market corresponds to an observation that is represented by two-dimensional characteristics, i.e., risk and return.
(b) The risk-return distance (RRD) is first computed for a particular market as the Euclidean distance between a pair of mean return and standard deviation for a market, and a pair of the cross-market average of mean returns and the cross-market average of standard deviations for N markets.
Let X be the particular market:
7

X = ( x return
, x riski
) = ( x
1
, x
2
), or
Let Y be the Cross-Market(Country) Average:
Y = ( y return
, y risk
) = ( y
1
, y
2
) , or
(c) The return distance (RED) of a market is derived from the cross-market average for N markets based on the absolute difference between the mean return for the market and the cross-market average return. Specifically, the return distance for market x during the period t ( RED ) is xt computed as follows: where

is the mean return for market x during the period t. xt
(d) Similarly, the risk distance (RID) of a market is derived from the cross-market average for N markets based on the absolute difference between the standard deviation for the market and the cross-market average standard deviation. Specifically, the risk distance for market x during the period t ( RID ) is computed as follows: xt where
 xt
is the standard deviation for market x during the period t.
8

(e) To compute the normalized RRD, the proportion of a variable to the sum of the two variables is used as its weight . To be compatible with the Euclidean distance measure, the weight for each variable is determined as follows:
(f) where W(RED) is the weight for the return distance variable and W(RID) is the weight for the risk distance variable.
Finally, The RRD is computed with each variable being normalized by its own weight:
(g) where RRD xt is the risk-return distance for market x during the period t.
With the estimates of the risk-return distance for each market, we next compute the cross-market average of the risk-return distance for the 14 sample markets for each period. The convergence hypothesis is then tested for any significant time-trend in the cross-market average risk-return measure. There is some evidence that the risk-return characteristics of international securitized real estate markets have converged if the risk-return distance displays a significant downward time trend.

Originated in the economic growth literature, this concept is used to assess the speed of convergence of returns of the underlying securitized real estate market. Specifically, we estimate the
9

following time-series regression between market j ( R j
) and the cross-market average (proxy for real estate benchmark R ) : m
 (
R jt

R mt
)   j
  j
(
R j , t
 1

R m , t
 1
)  l
4

 1
 l
 (
R j , t
 l

R m , t
 l
)   jt
In the above equation,
 is the first difference operator;
 j is the market-specific intercept and
 is the white-noise error term; the maximum lag length is 4 because we are using weekly data. We focus on the magnitude of

which measures the speed of return convergence across the developed securitized real estate markets. Empirically, we assess the time-varying

dynamics by converting the above equation into state-space form, i.e. the estimates of
 j
could be directly obtained via the Kalman filter technique
(while keeping
 j time-invariant). The use of state-space representation (Bekaert and Harvey, 1995) is to allow the speed of return convergence (

) to change over time; thereby takes into consideration possible structural changes over the study period. In addition, we repeat the estimations by investigating the speed of beta convergence in volatility across the sample markets. While return-based

-convergence measures the speed of return convergence, volatility-based

-convergence measures the speed of risk convergence.
For each quarter during January 1993 –December 2008, the cross-market average of the riskreturn distance (RRD) measures for the 14 sample markets are reported in Table 2. Included in the same table is also the average cross-market average risk distance (RID) and return distance (RED) measures. All the three distance measures are computed based on the weekly real estate securities returns in US dollar term. Over the full study period, the absolute difference between the average return (standard deviation) for a market and the cross-market average return (standard deviation) is 0.378% (0.496%) per quarter.
Using the Euclidean method, the cross-market average of the quarterly risk-return distance is about 0.985% during the sample period. The maximum and minimum distances are, respectively, 2.591% (2008 Q4) and
10

0.536% (2004Q4). The convergence ratio (maximum/minimum) of the risk-return distance is thus 4.83
9 .
The cross-market averages of the three distance measures in local currency terms (not reported for the sake of brevity) are: 0.975% (RRD), 0.353% (RED) and 0.511% (RID) per quarter.
(Table 2 here)
At the end of the sample period (i.e. 2008 Q4), the average risk-return distance is 2.591% and is
206% of the average risk-return distance at the start of the sample period (1993 Q1 - 1.255%), indicating the sample markets might have become much more different from each other in term of risk-return performances. At the same time, the average return (risk) distance at the end of the sample period is about
99% (156%) greater than the average return (risk) distance at the start of the sample period. Hence, the markets’ risk-return divergence as at end 2008 was contributed by the dual divergences in the return as well as risk dimensions. As mentioned above, global financial markets were greatly affected by the worst economic crisis since the Great Depression. Many real estate securities markets during this crisis period
(starting from summer 2007) experienced a sharp decline in their return performance as well as a significant increase in their return volatility. The widespread of the global financial crisis in 2008 has thus contributed significantly to the securitized real estate markets’ risk-return divergence. In contrast, the average risk-return distance of our sample markets was decreased by about 35% over the period from 1993
Q1 to 2007 Q2 (the average risk-return distance as of end Q2 2007 is 0.815%) indicating the risk-return distance measure fluctuates substantially over this period due to the global financial crisis.
10
(Table 2 here)
Figure 2 plots the cross-market average risk-return, return as well as risk distance measures over time in both US dollar (Panel A) and local currency (Panel B) terms. As can be seen, there is a slight (and insignificant) downward trend in the cross-market average risk-return distance measure during the sample period 1993-2008. This is associated with a similar and insignificant downward trend each in both the return and risk distance measures. In addition, the three distance measure appears to fluctuate substantially about the average time trend and is probably a function of market condition. Further observations of Figure
9 The convergence ratio for 17 developed stock markets in Eun and Lee (2010)’s study is worked out to be
4.64 (mean).
11

2 indicates the risk-return distance measures for the sample markets have become significantly diverged during the two market crisis period; the first phase covers the mid 1997- end 1998 period which coincides with the Asian Financial crisis (AFC); the second phase is linked to the global financial crisis (GFC) which reflects the dual divergences in the return as well as risk dimensions. Comparatively, our risk-return distance measures indicate that the GFC has caused greater market divergence than the AFC; the calculated risk-return distance for 2008 Q4 records its highest of 2.95% in the 16-year history; similarly, both the return distance (0.95%) and risk distance (1.39%) also reflect the greatest dual divergences. These three measures are much higher than those of 1988 Q1 that reports a second highest in its risk-return distance
(1.82%), return distance (0.64%) and risk distance (1%) respectively. Finally, the above conclusions are qualitatively similar, regardless of whether the distances are measured in US dollar or local currency terms.
(Figure 2 here)
We then estimate the following regression to formally test if there is a significant time trend (

) in the cross-market average of risk-return, risk and return distance measures for the 14 sample markets:
Dis tan ce t
    * Time
  t
(Time= 1,…………64).
The standard ADF test is used to check if the error term from the regression is stationary (with constant and no time trend). If that is the case, we can rely on the Newey-West heteroskedastic autocorrelation consistent standard errors and covariance t-statistic to interpret

. The results are reported in Table 3, with Panel A reporting the US dollar results (6 regressions), whereas the results with local currency returns (6 regressions) are reported in Panel B. Since the ADF unit root test rejects the null hypothesis that errors have a unit root at least at the 5% significance level for all 12 regressions (three USD average distance measures, three USD median distance measures, three local currency average distance measures and three local currency median distance measures), the standard test is likely to be reliable. As the numbers indicate, 10 out of 12

coefficients are negative; however none of them is statistically significant at the conventional levels of probability. Based on these test results, we have to conclude that the risk-return distance characteristics for the 14 developed securitized real estate markets have failed to
12

converge significantly towards each other during the sample period caused by insignificant dual convergences in return and risk measures. Over the last 16 years, international risk-return convergence for the 14 developed real estate securities markets remains fairly stable despite its intermittent fluctuations over some periods. Since our results also indicate again the exchange rate variable has no effect on the riskreturn convergence of the sample markets, henceforth we will focus the convergence issues with the US dollar returns.
(Table 3 here)
Table 4 reports the convergence results for the individual markets. As the numbers indicate, we can only reject the null hypothesis that there is no risk-return distance convergence at the 5% level for 5 out of 14 markets. These five markets are: Belgium, Hong Kong, Singapore, Sweden (all three distance measures are significantly converged) as well as the Netherlands (with insignificant return distance measure). Three markets, i.e. Canada, France and Japan, display a tendency toward risk-return convergence, albeit statistically insignificant. Other four markets, Spain, Germany, Switzerland and the UK are found to diverge from the rest of sample markets in their risk-return characteristics, although the divergence trend is only significant for Spain at the 10% level. Finally, the risk-return distance results for the US and Australia are not reliable as their respective unit root tests for residuals are statistically insignificant. Additionally, there are six cases of return distance convergence and seven cases of risk distance convergence among the
14 sample markets. Overall, our test results indicate that only less than 50% of the individual markets are expected to converge toward the international risk-return average. Other markets are either characterized by insignificant degree of risk-return convergence or with some degree of risk-return divergence.
11 These results are in broad agreement with the cross-market average results (Table 3) and imply that the developed real estate securities markets might have some long way to go before a full risk-return convergence would be reached. As such, real estate securities markets in these developed economies can continue to be an effective vehicle for international diversification. One final observation is that it appears that the initial
11 Bearing in mind the effect of the GFC (started in mid 2007) on financial market integration, we also run similar convergence tests for the cross-market average and for individual markets over the period 1993-
2007. In agreement with Table 1, the results are different with both convergences exhibited at the market average level as well as for 11 out of 14 markets. These contrasting results (not reported in order to conserve space) highlight the significant influence that changing global market condition, such as the GFC that peaked in 2008, plays a key role in affecting the risk-return characteristics and thus financial market
(including securitized real estate market) integration.
13

distance (or intercept

) and the slope coefficient (

) are inversely related to each other across the markets. For example, Spain has a low slope coefficient (0.0000042) and low

-intercept (0.0085). In contrast, markets with a higher absolute slope, such as Hong Kong and Singapore, have an intercept coefficient each of more than 0.015. Figure 3 indicates formally an inverse relationship between
 and

, which indicates that partial correlation between change in risk-return (toward the international average or focal point) and its initial level is negative. Hence there is some preliminary evidence of
 convergence from this analysis.
(Table 4 and Figure 3 here)
Finally, we examine whether if there is an asymmetry in the risk-return distance convergence, similar to that of international correlation 12 , using the following regression:
Dis tan ce t
   
1
*
Time
 
2
*
SD t
(
Global
)  
3
*
Down t
 
4
*
SD t
(
Global
) *
Down t
  t where: SD t
(
Global
) is the standard deviation of the global stock market returns; “Down” is a dummy variable that takes the value of 1 if the average value of weekly global stock market returns is negative, and zero otherwise; the last explanatory term in the regression is an interaction term between the standard deviation of the global market returns and the dummy variable. As can be seen from the crossmarket average results reported in Table 5, after taking into account possible asymmetry in the distance measures and global stock market volatility, the risk-return, risk and return characteristics have converged significantly at the 1% level during the study period. The standard deviation of the weekly global stock market returns, SD t
(
Global
) , is found to be significantly positive at the 1% level, implying that the riskreturn distance (risk distance/return distance) of the sample markets become greater when the world stock market is more volatile There is, however, no evidence of asymmetry in the three distance measures across bullish and bearish global stock market conditions as the “down” dummy variable is statistically insignificant in all three cases. Finally, the interaction term turns out to be significantly positive for risk-
12 Liow et al. (2009) reported there is an asymmetry in the correlation of international securitized real estate markets under different market conditions: the correlation is higher under “crisis” (bearish) market conditions than under “non-crisis” (or bullish conditions).
14

return and return characteristics at least at the 10% level implying the effect of the global stock market volatility is asymmetric under the bullish versus bearish stock market conditions.
(Table 5 here)

` Our above risk-return convergence analysis detects some presence of beta-convergence. To formally test this issue, results of the

-convergence (in return and volatility) tests for the full study period as well as for 1993-2000 and 2001-2008 are reported in Table 6. Since all the values in the table are negative, there is convergence of real estate securities market returns and volatilities. Regarding the betaconvergence in returns, the absolute values of the

coefficient are close to one for four markets
(Germany, Hong Kong, Singapore and the UK) indicating that the narrowing of return differentials between the individual markets and the international average is relatively fast.; the shock’s half - life for these four markets is much less than a week for the beta-values reported.
13 As such, these four real estate securities markets are said to be characterized by high degree of monotonic convergence. In contrast, other
10 markets have absolute beta convergence values range from 1.018 to 1.235, implying convergence happens with oscillations for these markets. Additionally, a comparison for the two shorter periods 1993-
2000 and 2001-2008 reveals that the pace of beta-convergence for most markets has been fairly stable, the differences between earlier and later periods are mostly statistically insignificant. With regard to the beta convergence values in volatility, they are all lower than the respective return estimates and none of the absolute volatility beta-convergence values is above 0.9 (the highest value is 0.865 for Hong Kong). The three lowest absolute volatility beta-convergence values are, respectively, 0.409 (Canada), 0.562 (Germany) and 0.644 (Belgium), indicating that these three markets are characterized by relatively lower degree of beta-convergence in volatility compared to other markets. Finally, 11 out of the 14 markets record a decrease in their absolute volatility beta-convergence values in the second sample periods, with markets such as Canada (from 0.949 to 0.317), Germany (from 0.918 to 0.514), Singapore (from 0.886 to 0.619),
Belgium (from 0.819 to 0.558), Netherlands (from 0.917 to 0.689) and Sweden (from 0.901 to 0.687) observed a more than 20 percent decrease in the volatility beta–convergence over the later years.
13 The half-life is calculated as: ln( 0 .
5 ) ln(   1 )
15

(Table 6 here)
Figure 4 displays the time-varying estimates of beta-convergence in returns and volatilities for the real estate securities indices grouped by three regions. Summary statistics of these time-varying betaconvergence values are provided in Table 7. In general, there is fast beta-convergence of returns for seven markets (US, Hong Kong, Singapore, France, Germany, Netherlands and Sweden) because all their average beta-convergence values are negative and close to one. Although the average beta values for other seven markets are negative, their respective convergences oscillate wildly as the market condition changes. In so far as the beta convergence in volatility is concerned, again all beta values are negative; with only three markets (Australia, UK and the US) characterized by oscillatory beta-convergence; the other 11 markets are indicated by the existence of different degree of beta-convergence in volatility (range between 0.751
(Belgium) and 0.991 (France)). It further appears that except for the North America (with the US and
Canada markets) region, real estate securities markets from other two regions (Asia and Europe) share a broadly similar beta-convergence trend each based on return and volatility estimations. These observations imply there could be a common factor driving the beta-convergences in return and volatility towards regional securitized real estate market integration. Future research could explore this “common trend” issue in beta-convergence and detect the underlying driving forces.
(Figure 4 and Table 7 here)
We investigate the relationship between correlation change and risk-return convergence to check whether they are positively linked for our sample markets. Eun and Lee (2010) has shown mathematically increasing correlation may not always associate with the risk-return convergence.
Table 8 show the pair-wise average monthly correlations among the 14 developed securitized real estate markets during the full study period. The cross-market average correlation is about 0.30; and individual correlations range between 0.09 (Switzerland and the US) and 0.61 (France-Netherlands).
Overall, international correlations among the real estate securities markets are on the low ends with 50 correlation coefficients (out of total 91) scoring below 0.30.
(Table 8 here)
16

The time trends between the cross-market average monthly correlations and cross-market average monthly risk-return distance measures for our sample of developed real estate securities market during the study period 1993-2008 are compared in Figure 5. As can be seen, the monthly time trend coefficient in correlation is 0.22%, implying that the international developed real estate securities market correlation has increased by an annual average 2.67% over the study period. This increasing correlation among the markets is only accompanied by a negligible reduction of average monthly risk-return distance over the same study period (see also Figure 2). Our results are thus in agreement with Eun and Lee (2010) that the increasing stock market correlation and risk-return convergence may be related but are distinct phenomena.
(Figure 5 here)
In this paper, we have discussed three aspects of real estate securities market integration in 14 developed countries. Our measures of market integration are constructed upon two complementary concepts of convergence; namely, risk-return convergence and

-convergence as well correlation change during the study period 1993 to 2008.
Our results can be summarized as follows, (a) the risk-return distance measures fluctuate greatly over 1993-2008, the range is between 0.536% and 2.591%. At the market average level, we are unable to detect a significant risk-return convergence among our sample of 14 developed real estate securities markets during the period 1993-2008. This insignificant risk-return convergence is accompanied by insignificant dual convergences in return as well as risk dimensions. Similarly, only five individual markets are found to converge toward the international risk-return average, implying the international developed real estate securities markets might have some long way to go before a full risk-return convergence would be reached. As such, real estate securities markets in these developed economies can continue to be an effective vehicle for international diversification; (b) the risk-return distance measures for the developed real estate securities markets have become significantly diverged during two market crisis period (Asian financial crisis: AFC and global financial crisis: GFC) which reflects the dual divergences in the return as well as risk dimensions. Furthermore, the GFC appears to have caused greater market divergence than the
AFC based on risk-return distance measures; (c) there is existence of beta-convergences in return and
17

volatility for many of the sample markets; with some markets display monotonic convergence but other markets’ convergence oscillates wildly during different periods. Furthermore, the estimated speeds and dynamics of beta-convergences (in return and volatility) analyzed at the three regional levels suggest possible presence of a “common convergence factor” among the securitized real estate markets of the three regions; (d) increasing correlation among the real estate securities markets is only accompanied by negligible reduction of risk-return distance over 1993-2008. As such, increasing stock market correlation and risk-return convergence may be related but are distinct phenomena.
In conclusion, our study has attempted to assess three major indicators of international real estate securities market integration. During the study period 1993-2008, international developed real estate securities markets have been moving toward greater integration in terms of increasing correlation and faster speed of convergence in returns and volatilities. However, the finding of an insignificant risk-return convergence trend also implies that the risk and return characteristics of the real estate securities markets have not become less different from each other over the study period, supporting the view that the idiosyncratic “real estate factor” and “country factor” of individual markets might have become more important over time.
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19

Panel A: U.S. Dollar Returns, Jan 1993 - Dec 2008
Australia
Belgium
Canada
France
Germany
Hong Kong
Japan
Netherlands
Singapore
Spain
Sweden
Switzerland
United
Kingdom
Mean Median Max Min Std Dev Skewness Kurtosis Jarque-Bera
-0.0003 0.00005 0.097 -0.182 0.015 -3.699 52.104 85792.0 ***
0.0004 0.00024 0.065 -0.080 0.012
0.0005 0.00046 0.097 -0.048 0.011
-0.099
0.787
9.608
12.419
1520.7 ***
3172.7 ***
0.0011 0.00105 0.071 -0.074 0.011
0.0014 0.00113 0.071 -0.106 0.014
0.0010 0.00005 0.131 -0.103 0.018
-0.392
-0.910
0.454
9.611
13.723
9.102
1542.2 ***
4115.7 ***
1324.3 ***
-0.0001
0.0008
0.0007
0.0012
0.0019
0.0009
-0.00060 0.108 -0.101
0.00039
0.00059
0.00096
0.00172
0.00031
0.060 -0.077
0.101 -0.103
0.068 -0.090
0.076 -0.080
0.072 -0.052
0.021
0.010
0.019
0.014
0.015
0.010
0.0006 0.00036 0.084 -0.091 0.012
United States 0.0011 0.00016 0.131 -0.118 0.013
0.162 5.967 310.0 ***
-0.461 11.817 2734.6 ***
-0.178
-0.585
8.344
7.877
997.9 ***
875.0 ***
0.013
0.510
6.972
7.388
549.0 ***
706.1 ***
-0.440
1.584
12.621
34.115
3247.2 ***
34033.3 ***
Panel B: Local Currency Returns, Jan 1993 - Dec 2008
Australia
Belgium
Canada
France
Germany
Hong Kong
Japan
Netherlands
Singapore
Spain
Sweden
Switzerland
United
Kingdom
Mean Median Max Min Std Dev Skewness Kurtosis Jarque-Bera
-0.0004 0.00000 0.064 -0.103 0.011 -2.051 27.700 21812.2 ***
0.0003 0.00000 0.061 -0.069 0.011
0.0004 0.00000 0.102 -0.047 0.010
-0.057
1.229
12.905
17.807
3413.5 ***
7837.8 ***
0.0010 0.00106 0.068 -0.063 0.009
0.0013 0.00018 0.070 -0.095 0.013
-0.428 12.899 3435.0 ***
-0.821 14.196 4454.8 ***
0.0010
-0.0001
0.0007
0.0007
0.0012
0.0015
0.0007
0.00000
0.00000
0.00043
0.00014
0.00065
0.00076
0.00000
0.131 -0.103
0.110 -0.097
0.070 -0.065
0.108 -0.107
0.058 -0.099
0.074 -0.075
0.066 -0.045
0.018
0.020
0.008
0.018
0.013
0.013
0.008
0.0006 0.00053 0.077 -0.067 0.011
United States 0.0011 0.00016 0.131 -0.118 0.013
0.457
0.036
9.120
6.313
1332.1 ***
382.0 ***
-0.046 19.825 9849.1 ***
-0.077 8.923 1221.2 ***
-0.599
0.032
0.683
9.182
7.507
1379.6 ***
707.0 ***
12.724 3354.6 ***
-0.110
1.584
11.393
34.115
2452.6 ***
34033.3 ***
Note : *** - indicates statistical significance at the 1% level
20

Year
1993
Quarter
Return
Distance
(%)
Risk
Distance
(%)
Risk-
Return
Distance
(%)
Year
1 0.477% 0.631% 1.255%
2 0.395% 0.594% 1.090%
3 0.402% 0.562% 1.101%
2001
Quarter
Return
Distance
(%)
Risk
Distance
(%)
Risk-
Return
Distance
(%)
1 0.420% 0.497% 1.041%
2 0.301% 0.390% 0.781%
3 0.393% 0.482% 0.984%
1994
1995
1996
1997
1998
1999
2000
1 0.444% 0.720% 1.285%
2 0.386% 0.632% 1.123%
3 0.358% 0.487% 0.962%
2002
1 0.416% 0.608% 1.139%
2 0.374% 0.380% 0.871%
3 0.335% 0.382% 0.831%
2003
1 0.330% 0.424% 0.855%
2 0.304% 0.346% 0.740%
3 0.229% 0.255% 0.555%
2004
1 0.364% 0.432% 0.914%
2 0.343% 0.455% 0.897%
3 0.356% 0.486% 0.961%
2005
1 0.643% 0.995% 1.818%
2 0.551% 0.711% 1.415%
3 0.531% 0.861% 1.531%
2006
1 0.459% 0.582% 1.180%
2 0.372% 0.505% 0.997%
3 0.386% 0.566% 1.056%
2007
1 0.452% 0.599% 1.174%
2 0.418% 0.571% 1.108%
3 0.418% 0.439% 0.981%
2008
1 0.299% 0.436% 0.810%
2 0.324% 0.402% 0.826%
3 0.363% 0.421% 0.888%
1 0.319% 0.359% 0.772%
2 0.304% 0.355% 0.749%
3 0.330% 0.364% 0.795%
1 0.284% 0.338% 0.701%
2 0.318% 0.434% 0.846%
3 0.248% 0.286% 0.611%
1 0.257% 0.252% 0.585%
2 0.228% 0.271% 0.572%
3 0.286% 0.342% 0.708%
1 0.341% 0.417% 0.855%
2 0.326% 0.476% 0.902%
3 0.274% 0.339% 0.693%
1 0.323% 0.404% 0.819%
2 0.331% 0.376% 0.815%
3 0.416% 0.464% 1.008%
1 0.526% 0.619% 1.317%
2 0.396% 0.481% 0.982%
3 0.440% 0.698% 1.300%
Average Distance : 0.378% 0.496% 0.985%
Notes :
The cross-market average distance measures are quarterly and in U.S. dollar terms. The return (risk) distance for a market is computed as the absolute difference between the mean of weekly returns (standard deviation) for the market and the cross market average of mean weekly returns (standard deviation) for 14 developed real estate securities markets. Before the risk-return distance is computed, the return (risk) distance is normalized to make similar the impact of each distance. The Euclidean distance is used to measure the risk-return distance.
21

.
Cross-Market
Average
Cross-Market
Median
Panel A: U.S. dollar returns
Dependent Variable
Risk-Return Distance
Intercept
( α ) time (

) T
HAC
0.010523 -0.0000016 -1.010
Return Distance
Risk Distance
Risk-Return Distance
Return Distance
Risk Distance
0.003963 -0.0000004 -0.807
0.005391 -0.0000010 -1.103
0.008708 -0.0000008 -0.572
0.002977 0.0000001 0.084
0.004462 -0.0000009 -1.162
Panel B: Local currency returns
R
2
0.008
0.003
ADF Unit
Root Test for Residuals
-6.102 ***
-5.071 ***
Cross-Market
Average
Dependent Var0iable
Risk-Return Distance
Return Distance
Risk Distance
Risk-Return Distance
(
Intercept
 ) time (

) T
HAC
0.010310 -0.0000014 -0.876
0.003612 -0.0000002 -0.366
0.005576 -0.0000011 -1.240
0.008380 -0.0000004 -0.284
Cross-Market
Median
Return Distance
Risk Distance
0.002617 0.0000002 0.505
0.004782 -0.0000012 -1.577
Notes : The test is implemented by running the regression: Dis tan ce t
 
R 2
0.006
0.001
ADF Unit
Root Test for Residuals
-5.881 ***
-3.923 **
  * Time
  t
(Time=
1,…………64. T is the Newey-West heteroskedastic autocorrelation consistent t-statistic. The ADF unit root test is
HAC applied to test the null hypothesis that the errors have a unit root (with a constant and no time-trend). ***, **- indicates statistical significance at the 1% and 5% level
22

Country
Australia
Belgium
Canada
France
Germany
Hong Kong
Japan
Netherlands
Singapore
Spain
Sweden
Switzerland
United
Kingdom
United States
Measure (
Intercept
α ) (
Period
β )
THAC
[Period]
Risk-Return Distance 0.005755 0.0000047 1.963 **
Return Distance
Risk Distance
0.002295
0.002822
0.0000017
0.0000024
1.719 *
1.733 *
R-
Square
0.031
0.017
0.022
Risk-Return Distance 0.011010 -0.0000059 -2.990 *** 0.044
Return Distance 0.003695 -0.0000016 -2.389 ** 0.022
Risk Distance 0.006044 -0.0000034 -2.488 ** 0.025
ADF Unit
Root Test for residuals
-0.781
-10.563 ***
-6.634 ***
-5.128 ***
-22.678 ***
-9.213 ***
Risk-Return Distance 0.009774 -0.0000025 -1.529
Return Distance 0.004440 -0.0000025 -3.000 ***
0.011
0.032
Risk Distance 0.003916 0.0000009 1.215
Risk-Return Distance 0.007606 -0.0000010 -1.042 0.003
Return Distance
Risk Distance
Risk-Return Distance
Return Distance
0.002369 0.0000006 1.606
0.004661 -0.0000022 -3.046 *** 0.027
0.008966
0.003684
0.0000008 0.363
0.0000004 0.368
0.001
Risk Distance 0.004052 0.0000005 0.452
Risk-Return Distance 0.015700 -0.0000065 -2.762 *** 0.020
Return Distance
Risk Distance
0.006337
0.007538
-0.0000022
-0.0000040
-2.487 **
-2.699 ***
0.012
0.016
Risk-Return Distance 0.015831 -0.0000012 -0.500
Return Distance 0.006113 -0.0000003 -0.265
0.001
Risk Distance 0.008135 -0.0000011 -0.745
Risk-Return Distance 0.008253 -0.0000027 -2.666 *** 0.023
-15.029 ***
-16.016 ***
-9.522 ***
-7.147 ***
-10.206 ***
-9.044 ***
-13.139 ***
-9.590 ***
-13.764 ***
-5.470 ***
Return Distance
Risk Distance
0.002576 -0.0000003 -0.829
0.005016 -0.0000025 -3.311 *** 0.035
Risk-Return Distance 0.017064 -0.0000081 -2.961 *** 0.020
Return Distance 0.006628 -0.0000029 -2.862 *** 0.014
Risk Distance 0.008543 -0.0000044 -2.710 *** 0.014
Risk-Return Distance 0.008519 0.0000042 1.801 * 0.014
Return Distance
Risk Distance
0.003712
0.003427
0.0000014 1.558
0.0000029 1.990 ** 0.017
Risk-Return Distance 0.015016 -0.0000112 -5.048 *** 0.089
Return Distance
Risk Distance
Risk-Return Distance
Return Distance
0.005949 -0.0000043 -4.876 *** 0.060
0.007400 -0.0000059 -4.122 *** 0.063
0.007131
0.003181
0.0000029 1.280
-0.0000003 -0.501
0.013
Risk Distance
Risk-Return Distance
Return Distance
Risk Distance
0.002795
0.007851
0.002716
0.004496
0.0000040
0.0000005
2.482 **
0.355
0.0000007 1.111
-0.0000007 -0.943
0.049
0.000
-7.259 ***
-7.021 ***
-7.351 ***
-7.882 ***
-8.526 ***
-12.004 ***
-23.663 ***
-26.083 ***
-10.554 ***
-9.476 ***
-7.404 ***
-8.185 ***
Risk-Return Distance 0.008847 0.0000035 0.844
Return Distance 0.001787 0.0000033 3.163 ***
0.008
0.057
Risk Distance 0.006631 -0.0000011 -0.362
1.317
-9.201 ***
0.002 2.856
Notes : The test is implemented by running the regression: Dis tan ce t
    * Time
  t
(Time=
1,…………64. T is the Newey-West heteroskedastic autocorrelation consistent t-statistic. The ADF unit root test is
HAC applied to test the null hypothesis that the errors have a unit root (with a constant and no time-trend). ***, **, * - indicates statistical significance at the 1%, 5% and 10% level
23

Cross-
Market
Average
Risk-Return
Distance
Intercept
( α )
Period
( β ) Global_SD Down
Global_SD
* Down R 2
ADF Unit Root
Test for residuals
(13.13)*** (-3.01)*** (7.16)*** (-1.36) (1.67)*
Return
Distance (13.92)*** (-2.67)*** (5.77)*** (-1.18) (2.55)**
Risk
Distance (10.01)*** (-3.01)*** (6.65)*** (-1.12) (0.20)
Note :
This table reports the test results of the convergence hypothesis for 14 developed markets under varying market conditions. Global_SD is the standard deviation of weekly global market stock returns. Down is a dummy variable which takes on the value of one if the mean of weekly global market returns is negative, and zero if otherwise. The following regression is used for each dependent variable: Dependent variable t
β
3
*Down + β
4
* Global_SD*Down + ε t
. T
HAC
= α + β
1
* Period + β
2
* Global_SD +
is the Newey-West heteroskedastic autocorrelation consistent (HAC) tstatistic. The ADF unit root test is applied to test the null hypothesis that the errors have a unit root (with a constant and no time-trend).***, **, * - indicates statistical significance at the 1%, 5% and 10% level.

Notes
Australia
Japan
Hong Kong
Singapore
Belgium
France
Germany
Netherlands
Sweden
Spain
Switzerland
UK
Canada
US
Return-based Risk-based
1993-2008 1993-2000 2001-2008 1993-2008 1993-2000
-1.235
-1.167
-1.264
-0.847
-1.001
-1.144
-0.950
-0.983
-1.038
-1.040
-0.916
-1.081
-1.018
-1.047
-1.022
-0.994
-1.094
-1.096
-1.167
-0.878
-0.960
-1.048
-0.919
-0.875
-0.997
-1.006
-0.998
-1.037
-0.975
-1.006
-0.930
-1.117
-1.086
-1.040
-1.032
-1.158
-0.971
-1.209
-1.048
-1.079
-1.006
-1.020
-1.237
1.165
-0.823
-0.865
-0.861
-0.644
-0.799
-0.562
-0.734
-0.836
-0.832
-0.735
-0.817
-0.409
-0.711
-0.752
-0.881
-0.886
-0.819
-0.953
-0.918
-0.917
-0.901
-0.908
-0.879
-0.988
-0.949
-0.964
2001-2008
-0.849
-0.982
-0.919
-0.619
-0.558
-0.796
-0.514
-0.689
-0.687
-0.816
-0.731
-0.801
-0.317
-0.705
Based on:
 (
R jt

R mt
)   j
  j
(
R j , t
 1

R m , t
 1
)  l
4

 1
 l
 (
R j , t
 l

R m , t
 l
)   jt
. All estimates are statistically significant at the 1% level.
24

Australia
Japan
Hong Kong
Singapore
Belgium
France
Germany
Netherlands
Sweden
Spain
Switzerland
UK
Canada
US
Notes
Australia
Japan
Hong Kong
Singapore
Belgium
France
Germany
Netherlands
Sweden
Spain
Switzerland
UK
Canada
US
Mean
-1.134
-1.128
-0.902
-0.961
-1.045
-0.919
-0.903
-0.979
-0.987
-1.031
-1.044
-1.028
-1.018
-0.948
-1.117
-0.822
-0.906
-0.993
-0.751
-0.991
-0.981
-0.886
-0.858
-0.858
-0.814
-1.001
-0.913
-1.003
-0.784
-0.852
-0.867
-0.759
-0.982
-0.905
-0.899
-0.875
-0.863
-0.801
-1.005
-0.928
-0.944
Median Std dev
Panel A: return-based
-1.154
-1.120
-0.914
-0.975
0.060
0.071
0.041
0.048
-1.039
-0.917
-0.919
-0.994
-0.996
-1.035
-1.032
-0.990
-1.013
-0.948
0.029
0.072
Panel B:risk-based
-1.091
0.101
0.041
0.090
0.068
0.083
0.027
0.092
0.037
0.083
0.382
0.103
0.222
0.033
0.104
0.121
0.038
0.039
0.059
0.071
0.025
0.062
0.099
Maximum
-0.606
-0.605
-0.546
-0.601
-0.702
-0.917
-0.567
-0.583
-0.842
-0.300
-0.798
-0.958
-0.793
-0.631
-0.841
-0.579
-0.829
-0.406
-0.429
-0.793
-0.256
-0.725
-0.726
-0.549
-0.331
-0.811
-0.208
-0.669
Based on:
 ( R jt

R mt
)   j
  j
( R j , t
 1

R m , t
 1
)  l
4

 1
 l
 ( R j , t
 l

R m , t
 l
)   jt
.
Minimum
-1.258
-2.559
-0.981
-1.225
-1.161
-0.624
-0.990
-1.079
-1.016
-1.194
-1.183
-1.408
-1.170
-1.139
-1.493
-11.536
-1.357
-2.224
-0.804
-2.119
-1.204
-0.933
-0.902
-1.425
-1.063
-1.144
-0.963
-2.141
25

BE CA FR GE HK JP NE SG SP SW SZ UK US
AU 0.27 0.33 0.31 0.26 0.37 0.22 0.33 0.29 0.28 0.37 0.27 0.40 0.24
BE 0.18 0.55 0.41 0.14 0.14 0.53 0.21 0.32 0.36 0.52 0.36 0.10
CA
FR
0.25 0.21 0.27 0.21 0.27 0.27 0.20 0.33 0.14 0.35 0.47
0.44 0.22 0.17 0.61 0.24 0.46 0.44 0.48 0.43 0.19
GE
HK
JP
0.22 0.19 0.43 0.23 0.31 0.30 0.34 0.38 0.23
0.22 0.23 0.58 0.23 0.27 0.13 0.32 0.25
0.23 0.29 0.12 0.13 0.19 0.24 0.12
NE
SG
SP
SZ
SW
UK
0.29 0.40 0.44 0.49 0.43 0.18
0.25 0.23 0.13 0.32 0.24
0.38 0.31 0.37 0.14
0.33 0.37 0.26
0.31 0.09
0.31
Notes : ‘AU’ is Australia, ‘BE’ is Belgium, ‘CA’ is Canada, ‘FR’ is France, ‘GE’ is Germany, ‘HK’ is Hong Kong, ‘JP’ is Japan, ‘NE’ is Netherlands, ‘SG’ is Singapore, ‘SP’ is Spain, ‘SW’ is Sweden, ‘SZ’ is Switzerland, ‘UK’ is the
United Kingdom, and ‘US’ is the United States
26

Notes :
This figure indicates how much the risk-return characteristics of the 14 developed real estate securities markets differ from each other in four separate years, 1993, 2000, 2007 and 2008. The origin is the cross-market average of returns
(standard deviations) for 14 markets. Weekly US dollar returns are used to compute the return distance (y-axis) and risk distance (x-axis) of each market from the cross market average. For each year, an ellipse is drawn to encompass all 14 observations for the year
27

Panel A: US Dollar returns
0.030
0.025
0.020
0.015
0.010
0.005
y   =  ‐ 0.00002x
+   0.01053
0.000
19
93
19
94
19
95
19
96
19
97
19
98
19
99
20
00
20
01
20
02
20
03
20
04
20
05
20
06
200
7
200
8
Cross ‐ Market   Average   RRD   (per   quarterly)
Linear   (Cross ‐ Market   Average   RRD   (per   quarterly))
0.010
0.008
0.006
0.004
0.002
y   =  ‐ 0.00001x
+   0.00396
0.000
19
93
19
94
19
95
19
96
19
97
19
98
19
99
20
00
20
01
20
02
20
03
20
04
20
05
20
06
20
07
20
08
Cross ‐ Market   Average   RED   (per   quarterly)
Linear   (Cross ‐ Market   Average   RED   (per   quarterly))
0.016
0.014
0.012
0.010
0.008
0.006
0.004
0.002
0.000
199
3
19
94
199
5
19
96
19
97
19
98
19
99 y   =  ‐ 0.00001x
+   0.00540
20
00
20
01
20
02
200
3
20
04
200
5
200
6
20
07
20
08
Cross ‐ Market   Average   RID   (per   quarterly)
Linear   (Cross ‐ Market   Average   RID   (per   quarterly))
28

Panel B: local currency returns
0.030
0.025
0.020
0.015
0.010
0.005
y   =  ‐ 0.00002x
+   0.01032
0.000
199
3
199
4
19
95
199
6
199
7
19
98
199
9
200
0
20
01
20
02
200
3
20
04
200
5
20
06
200
7
20
08
Cross ‐ Market   Average   RRD   (per   quarterly)
Linear   (Cross ‐ Market   Average   RRD   (per   quarterly))
0.010
0.009
0.008
0.007
0.006
0.005
0.004
0.003
0.002
0.001
0.000
y   =  ‐ 0.00000x
+   0.00361
19
93
19
94
19
95
19
96
19
97
19
98
19
99
20
00
200
1
20
02
20
03
20
04
20
05
20
06
20
07
20
08
Cross ‐ Market   Average   RED   (per   quarterly)
Linear   (Cross ‐ Market   Average   RED   (per   quarterly))
0.016
0.014
0.012
0.010
0.008
0.006
0.004
0.002
0.000
y   =  ‐ 0.00001x
+   0.00559
19
93
19
94
19
95
19
96
19
97
19
98
19
99
20
00
20
01
20
02
20
03
20
04
20
05
20
06
20
07
20
08
Cross ‐ Market   Average   RID   (per   quarterly)
Linear   (Cross ‐ Market   Average   RID   (per   quarterly))
29


Note : the intercept (

) and slope (

) coefficients based on the regression
( Risk
 return ) t
    * Time
  t
30

-0.6
-0.7
-0.8
-0.9
-1.0
-1.1
-1.2
Beta-convergence (return)
Canada
US
94 96 98 00 02 04 06 08
0.0
-0.5
-1.0
-1.5
-2.0
-2.5
Beta-convergence (volatility)
Canada
US
94 96 98 00 02 04 06 08
-0.5
0
Beta-convergence(return)
-1.0
Beta-convergence (volatility)
-4
-1.5
-2.0
-2.5
Australia
Hong Kong
Japan
Singapore
-8
Australia
Hong Kong
Japan
Singapore
-3.0
-12
94 96 98 00 02 04 06 08 94 96 98 00 02 04 06 08
0.0
0.0
Beta-convergence (volatility)
Beta-convergence (return)
-0.5
-0.4
-1.0
-0.8
-1.5
-1.2
-2.0
-1.6
94 96 98 00 02 04 06 08
Belgium
Netherlands
Switzerland
France
Spain
UK
Germany
Sweden
-2.5
94 96
* Note : based on Kalman filter estimates of the beta-convergence regression
98
Belgium
Netherlands
Switzerland
00 02
France
Spain
UK
04 06 08
Germany
Sweden
31

0.7
0.03
0.6
0.025
0.5
0.02
0.4
0.3
y = 0.0022x + 0.0934
0.015
y = -5E-06x + 0.0102
0.01
0.2
0.1
0.005
0
1993 1994 1995 1995 1996 1997 1997 1998 1999 1999 2000 2001 2001 2002 2003 2003 2004 2005 2005 2006 2007 2007 2008 month
0
Cross-mkt average correlation Cross-mkt average risk-retun distance
Linear (Cross-mkt average risk-retun distance) Linear (Cross-mkt average correlation)
Note s: This figure compares the time trend between the cross-market monthly average risk-return distance measure and the cross-market average monthly correlation distance measure, from the period 1993 to 2008.
32