Volatility Dynamics and Linkages in International
Securitized Real Estate Markets
*Kim Hiang LIOW
Department of Real Estate
National University of Singapore
Tel: (65)65163420
Fax: (65)67748684
Email: rstlkh@nus.edu.sg
David Kim Hin HO
Department of Real Estate
National University of Singapore
Tel: (65)65161152
Fax: (65)67748684
Email: rsthkhd@nus.edu.sg
* Contact author
15 May 2007
Volatility Dynamics and Linkages in International Securitized Real Estate Markets
Kim Hiang LIOW and David Kim Hin HO, Paper presented at the 2007 Twenty-Third American Real
Estate Society Meeting (Session 35), April 10-14, San Francisco, California, USA.1
Abstract
This study contributes to the literature in international securitized real estate market volatility in three
ways. Each market’s conditional volatility is decomposed into a “permanent” or long-run component and
a “transitory” or short-run component via a Component-GARCH model. Even though with the same
numbers of common factors derived from the “permanent” and “transitory” volatility series, their loadings
are not similar and consequently the long-run and short-run volatility linkages for some markets are
different. Finally there are significant volatility co-movements between real estate and stock markets’
“permanent” and “transitory” components suggesting that real estate markets are at least not segmented
from stock markets in international investing.
.
1.
INTRODUCTION
Numerous empirical studies have investigated the inter-temporal properties of asset
volatilities and their dynamic linkages across international stock markets.
To the best of our
knowledge relatively little research has been published on these topics in international real estate
markets. Real estate is a major capital asset that contributes to both investor diversification and wealth
creation. Because the correlation of real estate investment returns with other capital assets is relatively
low, domestic and international portfolio risk reduction can be achieved by investing in real estate. In
recent years, International property fund managers have been seeking real estate investment
opportunities in the emerging real markets including Asia, with industry sources predicting the global
real estate securities’ market capitalization to significantly increase from $500 billion in 2004 to $ 1
trillion by 2010 (Newell et al, 2005). Specifically, listed real estate investment companies have
become an increasingly important property investment vehicle in Asia and internationally, particularly
through the success of REITs in the USA and LPTs in Australia, the recent establishment of
equivalent REIT vehicles in Japan, Korea, Singapore and Hong Kong and the long-established track
record of listed property companies in Asia. Consequently a comprehensive study of time-varying
volatilities and their linkages across international real estate markets such as in the current paper offers
significant insights into dynamic global real estate volatility behavior and portfolio implications of
real estate investing.
1
We are grateful to Ms Teo Lay Kim’s excellent research assistance offered in this study.
1
With two international dataset that covers 14 securitized real estate markets and the
corresponding stock markets over 1984-2006, the specific objectives of this study are:
(a)
To decompose the time-varying real estate return volatilities into two parts, a permanent
component (trend) and a transitory component using Engle and Lee (1993)’s ComponentGARCH (C-GARCH) methodology
(b)
To examine the correlation structure of international real estate markets’ “permanent” and
“transitory” volatilities using factor analysis. Although various national real estate markets
differ with respect to their size, liquidity, trading structure and regulations, factor analysis
considers that the correlation in volatilities is caused by “a few and dominant” factors
common to all volatility series
(c)
To assess the volatility linkages between real estate and stock markets from the “permanent”
and “transitory” perspectives using multiple regression technique.
This study, which is about international securitized real estate markets, thus contributes to the
real estate volatility literature in international real estate investing. This paper distinguishes itself from
previous real estate studies in at least three aspects. First this paper is unique in that it decomposes the
return volatilities into two components: “permanent” (long-run) and “transitory” (short-term). This
approach seeks to recognize the possibility that the conditional variance may include the two
components to describe short-term and long-term movements of volatilities and hence is able to reveal
important information about the long-run and short-term volatility dynamics in international real
estate investing. Second, rather than investigating the correlation structure in real estate returns, we
employ factor analysis to derive “common factors” (or “principal components”) in the “permanent”
and “transitory” volatility series and further compare their factor structures and loadings. The
knowledge of how volatilities across international real estate markets are linked in the long- and shortrun is important in that the second moment or variance is directly linked to information flow as well as
providing insights concerning the characteristics and dynamics of real estate asset prices. Third, by
repeating the estimations for the corresponding stock markets, we are also interested in finding out
whether the common volatility factors of real estate and stock markets are linked. This appraoch hopes
2
to detect significant evidence of the 2nd moment linkage between the real estate and stock markets and
contributes indirectly to the literature on globalization and securitization of real estate markets.
2.
BRIEF LITERATURE REVIEW
This study involves four main streams of empirical literature in international investing and
portfolio diversification. They are briefly reviewed below.
2.1
Correlation of national stock markets
An important question addressed by the literature concerning international diversification has
been whether or not it allows a reduction in risk, relative to domestic diversification. Many researchers
have adopted different statistical tools in search for co-movement of stock indices. The traditional way
is to look at the estimation of pair-wise correlation coefficients between national share prices (Hui and
Farragher, 1985). In most cases, low positive or negative correlations are a sign of potential benefits of
international diversification through a reduction in portfolio systematic risk. Numerous studies are
conducted on the US and matured markets like Europe, Canada and Japan. Levy and Sarnat (1970),
Watson (1978), Meric and Meric (1989), Arshanapalli and Doukas (1993) and DeFusco et al. (1996)
indicate that international investors would perform better by holding a diversified portfolio in
international major equity markets, rather than engaging on a single market. Bailey and Stulz (1990)
find that Asia-Pacific equity markets are not highly correlated, and international diversification is thus
possible.
2.2
International correlation structure
Ripley (1973) employs factor analysis to search for systematic variation patterns among 19
international equity markets over the period 1960 – 1970. There is evidence that countries like USA,
Canada, Switzerland and the Netherlands has a low degree of unique variability, whereas South Africa
and Japan have considerably high level of unique movement. Recent studies have included AsiaPacific where Hui and Kwan (1986) and Hui (2005) investigate the systematic co-variation and intertemporal stability of share prices for Asia-Pacific and US stock prices using factor analysis. Their
results indicate that diversifications into Hong Kong, Taiwan, Japan and the USA are beneficial as the
3
return generating processes are influenced by different factors. Finally, Illueca and Lafuente (2002)
evaluate the nature of stock market integration by analyzing the characteristics of the factor structures
of returns and volatilities. The return volatilities are estimated from univariate GARCH innovations
that allow for asymmetric impact on volatility. Their findings suggest that the causal transmission
among international stock markets is more intense in terms of volatility.
2.3
Dynamics of return volatilities
Mandelbrot (1963) and Fama (1965) have recognized that return volatility is changing over
time and that high periods of volatility tend to cluster and vice versa. Harvey (1991) and Karolyi and
Stulz (1996) point out that the cross-correlation of stock market returns affects the volatility of
international portfolios and risk premium. Hence, the presence of time-varying risk should be
accounted for. In this regard, the autoregressive conditional heteroscedastic (ARCH) model introduced
by Engle (1982) and later extended to Generalized ARCH (GARCH) by Bollerslev (1986) have been
popular in modeling the stylized features of stock market volatility. Nelson (1990) and Pagan and
Schwert (1990), show that volatility is a non-stationary process. The existence of a unit-root in the
volatility process also indicates the presence of two components in the volatility: a stochastic trend
and a transitory component. Engle and Lee (1993) introduce a Component-GARCH (C-GARCH)
model to decompose the conditional variance into a permanent component and a transitory component.
Gallagher (1999) also reveals the existence of temporary and permanent components in stock prices.
Finally, Ane (2006) provides an investigation on the applicability of the C-GARCH model to describe
the volatilities of Hong Kong stock returns. Her study finds that the permanent volatility component
(trend) has a very high level of persistence. The transitory volatility component, on the hand, appears
much less persistent for all stocks and responds strongly to external shocks.
2.4
Real estate studies
While there are extensive studies on the dynamics and linkages of international stock
markets’ conditional volatilities, far less attention has been devoted to such studies in the real estate
4
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 returns and
volatilities. 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 estateonly portfolio context. Other studies include Echholtz (1996), Ling and Naranjo (1999), Mei and Hu
(2000), Kallburg et al, (2002), Liow and Yang (2005), Cotter and Stevenson (2006), Michayluk et al,
(2006) and Liow (2006). 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. Using an asymmetric covariance GARCH model, Michayluk et al, (2006) examine
the daily volatility spillover effects and time-varying correlation dynamics between the US and UK
securitized real estate markets. Their results show significant asymmetric effects on both the volatility
and correlation between the two markets. Finally, Liow (2006) develops a GJR-GARCH-M model to
assess the volatility persistence and asymmetric characteristics underlying the time-varying volatility
process of Asian securitized real estate markets and further compare them to those of the US, the UK
and Europe; a world stock market index and a world real estate index (two global benchmark proxies).
3.
DATA AND PRELIMINARY STATISTICS
Monthly real estate price index for 14 countries was extracted from the Global Real Estate
Securities Database of Global Property Research (GPR) and Datastream for the period January 1984
to July 2006, giving a total of 271 observations. The sample markets include Australia, Canada,
France, Germany, Hong Kong, Italy, Japan, Netherlands, Norway, Singapore, Sweden, Switzerland,
United Kingdom and United States. Figure 1 presents the average market value of the 14 real estate
markets. GPR, a Netherlands-based firm provides a database containing prices, market capitalization,
dividends, and company characteristics of real estate companies listed on the stock exchanges of more
than 30 countries on a monthly basis since 1984. This unique database contains the history of some
600 real estate companies – both currently listed companies and those that have been delisted. The
5
GPR index is constructed to be representative of the movements in the worldwide real estate securities
market.
(Figure 1 here)
In addition, the broader stock market indices represented by MSCI for the 14 countries are
extracted from Datastream. The MSCI indices are the most widely used country and world indices by
international fund managers for asset allocation decisions and performance measurement. They are
also widely used by academic researchers because of their consistency, extensive market coverage,
and historical availability dating back to 1970.
All data are expressed in US dollars; thereby setting the market price of currency risk equal to
zero. Our study is therefore targeted at a US-based international investor, and provides uniformity in
the comparison of one market with another. Returns are calculated by the first difference of the natural
logarithm of the monthly indices.
To provide a general understanding of the nature of each market return series, Table 1
presents summary statistics for the GPR and MSCI over the full study period. Focusing on the real
estate series (GPR), all average returns are positive except for Canada. Hong Kong has the highest
monthly mean (1.41%) and is followed by Norway (1.34%). Judging from the sample standard
deviations, the Asian maturing/developing real estate markets are, as expected, characterized by a
higher unconditional volatility, compared to the developed markets of the UK, the USA and Europe.
In particular, Singapore and Hong Kong are most volatiles (standard deviations are 11.8% and 11%).
All return series display a peaked distribution relative to the normal (i.e. kurtosis value more than 3)
except Switzerland. Finally, with the exceptions of three European markets (France, Germany and
Switzerland), the normal distribution can also be rejected as an appropriate description of remaining
11 series since all Jarque-Bara statistic (JB) greatly exceed 5.99, which is the 95% quantile of the Chisquared distribution with two degrees of freedom.
(Table 1 here)
Table 2 provides a Pearson correlation matrix that shows the degree of co-movement between
each pair of the real estate markets’ conditional volatilities, which are estimated using GARCH (1, 1)
6
methodology. As the numbers indicate, correlations between the conditional volatilities of all real
estate markets vary between low and high ranges. Only 23 pairs of the 91 markets’ pair-wise
correlation coefficients report a volatility correlation coefficient of 0.3 and above, with CanadaSweden, Hong Kong– Singapore, Australia-Singapore and Canada-Norway reports higher correlations
of about 0.798, 0.790, 0.754 and 0.730 respectively. Overall, international real estate markets are not
independent because they are related through their second moments.
(Table 2 here)
4.
RESEARCH METHODOLOGY
4.1
Permanent and transitory volatilities
We first model the 14 real estate markets’ volatilities using the C-GARCH methodology. This
estimation will reveal the proportions of long and short volatilities as well as the respective level of
persistence across the markets. According to Engle and Lee (1993), the C-GARCH model has the
following specifications:
σ 2 t − qt = α (ε 2 t −1 − qt −1 ) + β (σ 2 t −1 − qt −1 ) ----------------------------------(1)
qt = ω + ρ (qt −1 − ω ) + φ (ε 2 t −1 − σ 2 t −1 ) --------------------------------------(2)
The above model allows mean reversion to a varying level q t ;
σ t is the total volatility while
qt (Equation 2) is the time-varying long-run volatility. Equation (1) describes the transitory
component,
σ 2 t − qt which converges to 0 with powers of α + β . Finally ρ is usually between 0.99
and 1 so that q t approaches
4.2
ω very slowly.
Principal component structure of “permanent” and “transitory” volatilities
Principal component analysis (PCA) is the most popular technique of classical multivariate
factor analysis. The objective is to derive a reduced set of uncorrelated variables (“principal
7
components” or “factors”) in terms of linear combinations of the original variables, so as to maximize
the variance of these components.
In the present context, with the 14 permanent and transitory volatility series, respectively,
derived from the C-GARCH methodology, the factor structures of “permanent” and “transitory”
volatilities are separately estimated using the PCA. This process seeks to represent each market’s
volatility as a linear combination of the “components” plus an error term. The extracted “factors” can
be regarded mathematically as the best “indices” that explain the volatility-generating process of the
14 markets. The first “factor” is the combination that accounts for the largest amount of variance in
the sample. The second “factor” accounts for the next largest amount of variance and is uncorrelated
with the first. Successive “factors” explain progressively smaller portions of the total sample variance.
By examining the factor structures of “permanent” and “transitory” volatilities, the results will reveal
whether international real estate volatilities are clearly segmented or whether their volatilities are
spread more globally from the long-term and short-run perspectives. To aid factor interpretation, the
varimax method of orthogonal rotation is employed. The Kaiser criterion is used to decide on the
“factors” that should be retained. As a common rule, those “factors” with an eigenvalue greater than
or equal to one are retained. These eigenvalues measure the contributions of the corresponding factors
to explain the cross-sectional variation of volatilities (permanent and transitory) in international
securitized real estate markets.
4.3
Relationship between factor structures of real estate and stock market volatilities
The strength of relationship between the real estate markets’ “factors” and stock markets’
“factors” derived from the PCA is investigated using multiple regression technique (equation 3). Of
paramount interest here is whether the real estate volatility “components” ( RE1 , RE 2 ......REi ) could
be related significantly to the stock market volatility “components” ( S1 , S 2 .....S j ) at an international
level, thereby indicating whether international real estate markets are clearly or partially segmented
from international stock markets.
8
jt
REit = λ0 + λ j ∑ S jt + ε it ………………….(3)
1t
5.
EMPIRICAL RESULTS
Table 3 contains the estimation results for 14 real estate C-GARCH models. A direct
comparison of the various parameter estimates reveals some differences of magnitude across the 14
securitized real estate markets. Some main observations are made. First, 11 autoregressive parameter
ρ in the trend equation is above 0.9. This indicates that the permanent component of the conditional
variance displays a high degree of persistence. Further test using the Augmented Dickey Fuller (ADF)
technique reject the existence of unit-root in the permanent component. The sum
α + β represents the
volatility persistence level of the transitory component that is found to be much weaker for many
markets. Hence it appears that deviations of the conditional variance from its trend are temporary for
most real estate indices. This conclusion is in general agreement with Engle and Lee’s (1993)’s
findings for stock market indices. The arrival of new information, as represented by the shocks ( ε
2
t −1 )
affects the transitory component ( φ ) in many cases. The absolute values for factor of proportionality
( α / φ ) range from 0.644 for Norway to 11.667 for Japan for an average value of 2.346. Figure 2 plots
the time evolution of the total variance, permanent variance and transitory variance for the 14 real
estate markets. In general, the plots indicate that the permanent components have smooth movements;
however in the cases of France, Hong Kong and Switzerland, some shocks
ε 2 t −1 conveys information
relevant to the long-run level of variance, causing the trend to fluctuate sharply at some dates.
Additionally, the transitory component as represented by the difference between the total variance and
the trend (
σ 2 t − qt ) responds largely to market fluctuations. Finally, Table 4 reports some
specification tests to assess the goodness-of–fit of the C-GARCH models. With some minor
exceptions, the test statistics LB(5), LB(10), LB(20), LB(50) LB2(5), LB2(10), LB2(20), LB2(50),
9
ARCH-M(5) and ARCH-M(10) indicate that the C-GARCH specification performs generally well in
describing the behavior of international securitized real estate returns.
(Table 3, Figure 2 and Table 4 here)
Table 5 presents the varimax rotated loadings concerning the factor solution for real estate
“permanent” volatilities. The solution involves five factors which joint accounts for 79.7 percent of
the sample variance. In accordance with the weight of each country in each factors (with factor
loadings of 0.3 and above), we have:
Factor 1: Canada, Sweden, Norway, Hong Kong, UK and Japan
Factor 2: Australia, Singapore, US and UK
Factor 3: Germany, Japan, UK and Hong Kong
Factor 4: Italy, France and Switzerland
Factor 5: Netherlands and US
The first two factors may be interpreted “global” because they include securitized real estate
markets from the three key regions (Asian, Europe and North America). The first factor, whose
explanatory power reaches 23.7% of the total variance, is affected by the volatilities from six real
estate markets of the three regions. The second factor shows about 17.3 percent of the total explained
volatility and is spread evenly among Australia, Singapore and USA and to a lesser degree, UK.
Further empirical results reveal that Factor 4 may be identified with the “European” economies
because Factor 4 has higher loadings for the European markets of Italy, France and Switzerland only.
Of the 14 markets, the loadings of the UK, US, Japan and Hong Kong are distributed in at least two
factors. One other observation is that Singapore and Hong Kong are not correlated in their permanent
volatilities although they are highly correlated in their total volatilities. Finally, The factors
corresponding to the real estate market returns (not reported) explains about 70 percent of total
variance, while the factors behind the permanent volatility solution reach 80 percent as well as the
loadings are not so clearly distributed in each factor, suggesting that the long-run real estate market
volatility is spread more globally around the world.
10
(Table 5 here)
The factor solution concerning the “transitory” volatilities is presented in Table 6. They are:
Factor 1: Canada, Sweden, Norway, UK and Netherlands
Factor 2: Japan, Germany, UK, France and Switzerland
Factor 3: Singapore, Australia and Hong Kong
Factor 4: Italy, Hong Kong
Factor 5: USA
As the number indicates, the percentages of explained volatility by the five factors are about
19.2, 17.9, 17.0, 9.1 and 9.0 respectively. The five factors jointly accounts for about 72.2 percent of
the explained volatility. However, the pattern is not similar to that underlying permanent volatility.
The empirical results also reveal that two factors can be identified with international geographic areas.
Specifically, factor 3 has higher loadings for the Asia-Pacific economies of Singapore, Australia and
Hong Kong while the USA dominates the fifth factor.
Comparing the factor results of the two volatility analyses, the empirical results indicate that
consistency is observed in the volatility co-movements between Canada, Sweden and Norway;
between Singapore and Australia; between Germany, UK and Japan; and between France and
Switzerland, suggesting that risk diversification strategies may not consider the constituent real estate
markets to be segmented from both the short-term and long-run volatility perspectives. .
(Table 6 here)
Finally, the results of multiple regression analyses are reported in Table 7. This would reveal
whether each of the five real estate “permanent” and “transitory” components (RE-F1 to RE-F5)
extracted from the PCA could be explained by the four derived stock market volatility components (SF1 to S-F4) and the respective significance of the relationships. The numbers indicate that real estate
volatility components are significantly related to the stock market volatility component in all cases
with the adjusted R2 s range from 55.9 to 97.2 percent. Specifically, the variations in the long-run real
estate factor 2 and short-run real estate factor 1 are strongly explained by all the four stock market
volatility factors. Our investigations have thus provided additional evidence that real estate and stock
11
markets are linked in their second “permanent” and “transitory” moments and thus complemented the
existing literature in international investing.
(Table 7 here)
6.
SUMMARY AND CONCLUSION
This paper is a contribution to the literature in international real estate market volatility
dynamics and linkages from an alternative perspective. Our approach is divided into three stages:
(a) a Component-GARCH model is used to decompose the temporal variation of 14 real estate
market volatilities into a long-run (“permanent”) and short-run (“transitory”) components; (b) we
use the factor analysis technique to summarize the “permanent” and “transitory” volatility
dynamics into latent factors. The nature of the factor structure allows us to associate each factor
to a specific regional market if appropriate; (c) we investigate the volatility co-movements
between real estate and stock markets in the short-term and long-run using the latent factors
derived from the factor analysis.
Our empirical results reveal the existence of significant “permanent” and “transitory”
components in the volatility process. The trend is found to have a high level of persistence in
many securitized real estate indices whereas the transitory component responds strongly to
external shocks. Even though with the same numbers of common factors derived from the
“permanent” and “transitory” volatility series, their loadings are not similar and consequently the
long-run and short-run volatility co-movements for some markets are different. For example,
while Hong Kong and Singapore are not correlated in their “permanent” volatilities; they are
strongly correlated in their “transitory” volatilities. Finally there are significant volatility comovements between real estate and stock markets’ “permanent” and “transitory” components
suggesting that real estate markets are at least not segmented from the stock markets in
international investing.
12
Overall, important contributions of this study are the findings of separate “permanent”
and “transitory” volatility components in international real estate markets. These results are
important because knowing that real estate market volatilities exhibit separate long-run and shortterm dynamics can help investors understand the evolution of real estate market volatilities better
and find ways of predicting them. In this respect the results also have practical implications,
because they suggest that international integration models for real estate market volatilities should
include short-run and long-run models with different sets of explanatory variables attached to the
two models of volatilities. The presence of the two volatility components for some real estate
markets further indicates that different portfolio management practices may be appropriate for
global investors. The summary of volatility dynamics allow investors to consider a smaller set of
foreign markets for risk diversification thereby save search time and cost. Selection within factors
allows investors and portfolio managers to suit their own taste and risk preference; selection from
different factors ensures risk diversification. Based on the differential volatility dynamics
investigated in this paper, it is likely the optimal portfolio for the long-term would be different
from that of the short-term. Of course, one other most important consideration relates to the
stability of the factors. Stability over long periods is not obviously likely, but the approach would
probably give portfolio validity in at least with analyzing the short-run (“transitory”) volatility.
These questions merit further research.
13
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14
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15
Table 1: Descriptive statistics of real estate and stock market returns – Jan 84 to Jul 06
Panel A: Securitized real estate returns (GPR)
Australia
Canada
France
Germany
Hong Kong
Italy
Japan
Netherlands
Norway
Singapore
Sweden
Switzerland
United
Kingdom
United States
Mean
Maximum
Minimum
Standard
Deviation
Skewness
Kurtosis
Jarque-Bera
0.0123
-0.0012
0.0115
0.0059
0.0141
0.0094
0.0085
0.0086
0.0134
0.0091
0.0079
0.0071
0.132
0.215
0.126
0.086
0.469
0.307
0.542
0.105
0.449
0.523
0.480
0.113
-0.320
-0.321
-0.154
-0.094
-0.628
-0.190
-0.343
-0.178
-0.246
-0.754
-0.452
-0.105
0.050
0.072
0.048
0.033
0.110
0.071
0.100
0.040
0.081
0.118
0.093
0.037
-1.197
-0.686
-0.138
-0.112
-0.597
0.435
0.575
-0.498
0.716
-0.876
-0.078
0.033
9.565
5.563
3.293
3.103
9.161
4.596
6.095
4.455
6.575
10.988
8.768
2.960
551.394
95.485
1.835
0.690
444.722
37.307
123.125
35.115
167.409
755.198
375.970
0.068
0.0105
0.0107
0.116
0.162
-0.210
-0.266
0.043
0.061
-0.887
-0.412
6.113
4.114
144.958
21.704
Panel B: Stock market returns (MSCI)
Australia
Canada
France
Germany
Hong Kong
Italy
Japan
Netherlands
Norway
Singapore
Sweden
Switzerland
UK
US
Mean
0.0098
0.0086
0.0120
0.0099
0.0131
0.0109
0.0064
0.0120
0.0108
0.0054
0.0122
0.0118
0.0105
0.0097
Maximum
0.165
0.137
0.191
0.213
0.287
0.270
0.217
0.143
0.156
0.230
0.206
0.154
0.148
0.125
Minimum
-0.589
-0.249
-0.203
-0.279
-0.570
-0.206
-0.215
-0.196
-0.326
-0.533
-0.251
-0.194
-0.243
-0.239
Std. Dev.
0.068
0.052
0.059
0.066
0.084
0.069
0.068
0.051
0.072
0.077
0.072
0.051
0.051
0.044
Skewness
-2.695
-1.011
-0.330
-0.639
-1.297
0.140
0.072
-0.902
-0.870
-1.429
-0.498
-0.368
-0.367
-0.996
Kurtosis
24.595
6.773
3.915
5.185
12.135
3.580
3.371
5.359
5.553
12.178
4.036
4.348
4.836
6.833
Jarque-Bera
5593.887
206.908
14.380
72.316
1018.267
4.687
1.784
99.590
107.739
1043.461
23.341
26.616
44.140
210.666
16
Table 2
Austraila
Canada
France
Germany
Hong Kong
Italy
Japan
Netherlands
Norway
Singapore
Sweden
Switzerland
UK
US
Correlations in conditional volatilities: Jan 84 – July 06
Australia
1.0000
Canada
-0.0126
1.0000
France
0.4631
0.0538
1.0000
Germany Hong Kong
0.3029
0.5842
0.0534
0.0047
0.2778
-0.0844
1.0000
0.1439
1.0000
Italy
0.1964
0.0853
0.2763
0.0319
0.2477
1.0000
Japan
0.2598
0.4960
0.2902
0.7521
0.1859
0.1555
1.0000
Netherlands
-0.1805
0.2915
0.1448
0.1312
-0.3194
-0.1550
0.0737
1.0000
Norway
0.1613
0.7298
0.3473
0.1248
0.0712
0.0662
0.4831
0.0574
1.0000
Singapore
0.7543
0.0114
0.1466
0.1334
0.7898
0.3542
0.1525
-0.3016
0.0387
1.0000
Sweden
-0.1546
0.7980
0.0357
-0.1854
-0.1688
0.1255
0.1874
0.2409
0.6520
-0.1481
1.0000
Switzerland
0.2396
0.2402
0.5108
0.3419
-0.1366
0.2782
0.5191
0.1196
0.4002
-0.0228
0.2873
1.0000
UK
0.3225
0.0681
0.1046
0.0661
0.1403
0.0603
0.0248
0.0780
0.0525
0.3043
-0.0228
-0.0803
1.0000
US
-0.1834
-0.0472
-0.0496
-0.0756
-0.0836
-0.0047
-0.0823
-0.0134
-0.0673
-0.1343
-0.0311
-0.0325
-0.3544
1.0000
Notes: The conditional volatilities for the 14 real estate markets are estimated using a GARCH (1, 1) model
17
Table 3: Parameter estimates for the C-GARCH (1, 1) model
Parameter estimate for the component GARCH model with student-t error
a0
Australia
Canada
France
Germany
Hong Kong
Italy
Japan
Netherlands
Norway
Singapore
Sweden
Switzerland
UK
US
a1
Ω
Ρ
Φ
Α
β
-0.174
(-0.291)
-0.049
(-0.050)
1.665
(48.943)*
0.243
(0.336)
0.906
(16.987)*
0.664
(1.400)
0.127
(0.126)
-0.672
(-0.658)
-0.986
(85.038)*
0.383
(1.037)
-0.546
(-1.499)
3.052
(0.096)
-0.101
(-0.145)
-0.652
(-2.577)*
0.014
(5.093)*
0.007
(1.746)*
0.009
(2.741)*
0.006
(5.879)*
0.017
(3.156)*
0.006
(1.598)
0.006
(1.109)
0.008
(3.453)*
0.009
-0.058
(-1.084)
0.148
(2.036)*
0.130
(1.971)*
0.054
(1.108)
0.048
(0.826)
-0.002
(-0.034)
-0.031
(-0.506)
0.105
(1.657)*
0.125
0.003
(2.420)*
0.002
(0.812)
0.003
(3.302)*
0.001
(29.364)*
0.010
(3.438)*
0.005
(4.995)*
-0.018
(-0.055)
0.002
(5.266)*
0.007
0.931
(15.938)*
0.991
(91.887)*
0.960
(69.637)*
0.974
(3176.72)*
0.994
(207.678)*
0.839
(30.693)*
0.999
(76.941)*
0.940
(10.181)*
0.974
0.158
(2.355)*
0.034
(2.059)*
0.693
(16.701)*
-0.050
(-22.468)*
-0.043
(-0.553)
0.217
(1.552)
0.006
(0.524)
0.037
(0.820)
0.059
-0.173
(-2.065)*
0.072
(1.028)
-0.716
(-15.992)*
-0.064
(-2.675)*
0.064
(0.835)
-0.280
(-1.855)*
0.070
(0.850)
0.034
(0.371)
0.038
(2.350)*
0.012
(2.430)*
0.015
(3.632)*
0.006)
(2.556)*
0.012
(4.731)*
0.012
(3.281)*
(2.319)*
0.091
(1.739)*
-0.144
(-2.708)*
0.191
(2.900)*
0.048
(0.688)
0.070
(1.140)
(1.884)*
0.014
(1.869)*
0.007
(2.711)*
0.001
(6.185)*
0.002
(6.625)*
0.003
(1.193)
(38.773)*
0.923
(19.489)*
0.943
(23.868)*
0.728
(3.122)*
0.862
(2.448)*
0.994
(69.311)*
(1.635)
0.217
(4.021)*
0.097
(1.898)*
2.362
(0.075)
0.023
(0.314)
0.029
(1.612)
(2.187)*
-0.234
(-2.789)*
-0.106
(-1.559)
-2.340
(-0.074)
0.117
(0.974)
-0.089
(-1.920)*
Loglikelihood
445.866
351.418
441.395
550.563
248.811
342.928
252.646
495.584
320.639
246.118
314.862
514.459
480.309
385.920
Notes: Parameter estimates for Rt = a0 + a1 Rt-1 + ε t, σ2t = qt + α(ε2t-1- qt-1) + β(σ2t-1- qt-1) and qt = ω + ø (ε2t2
1- σ t-1) + ρ(qt-1). Parentheses are used to indicate z-statistics and * indicates significant at the 5%
confidence level.
18
Table 4: Specification Tests for the Component-GARCH model
Specification Tests for the Component-GARCH model with student-t error
LB(5)
Australia
Canada
France
Germany
Hong Kong
Italy
Japan
Netherlands
Norway
Singapore
Sweden
Switzerland
UK
US
6.310
[0.277]
1.867
[0.867]
2.281
[0.809]
1.908
[0.862]
1.841
[0.871]
5.857
[0.320]
1.681
[0.891]
4.353
[0.500]
5.505
[0.357]
2.964
[0.706]
8.175
[0.147]
1.980
[0.852]
1.669
[0.893]
0.745
[0.980]
LB2(5)
3.103
[0.684]
6.370
[0.272]
1.732
[0.885]
1.783
[0.878]
0.649
[0.986]
2.308
[0.805]
1.036
[0.960]
0.731
[0.981]
2.634
[0.756]
0.509
[0.992]
0.548
[0.990]
1.266
[0.938]
1.099
[0.954]
1.199
[0.945]
LB(10)
10.291
[0.415]
7.881
[0.640]
8.361
[0.594]
9.073
[0.525]
6.779
[0.746]
10.986
[0.359]
9.331
[0.501]
12.037
[0.283]
7.097
[0.716]
4.583
[0.917]
10.564
[0.324]
13.293
[0.111]
3.235
[0.975]
1.847
[0.997]
LB2(10)
4.305
[0.933]
10.293
[0.415]
4.045
[0.945]
5.079
[0.886]
1.141
[1.000]
5.211
[0.877]
12.344
[0.263]
5.558
[0.851]
4.721
[0.909]
0.903
[1.000]
6.910
[0.734]
2.526
[0.990]
8.922
[0.540]
2.690
[0.988]
LB(20)
21.309
[0.379]
14.708
[0.793]
15.205
[0.765]
18.441
[0.558]
22.589
[0.309]
17.936
[0.592]
18.559
[0.551]
23.649
[0.258]
20.343
[0.437]
9.473
[0.977]
44.174
[0.001]*
38.455
[0.008]*
9.340
[0.979]
14.098
[0.825]
LB2(20)
25.957
[0.167]
21.416
[0.373]
17.457
[0.623]
10.882
[0.949]
6.132
[0.999]
16.943
[0.657]
23.144
[0.282]
13.373
[0.861]
24.692
[0.213]
6.464
[0.998]
42.478
[0.002]*
8.246
[0.990]
12.355
[0.903]
8.297
[0.990]
LB(50)
58.498
[0.192]
60.540
[0.146]
47.556
[0.572]
42.984
[0.749]
44.969
[0.675]
45.865
[0.640]
32.134
[0.977]
52.906
[0.363]
59.245
[0.174]
36.990
[0.914]
64.803
[0.078]*
65.633
[0.068]*
24.198
[0.999]
37.472
[0.905]
LB2(50)
41.778
[0.789]
53.218
[0.351]
35.385
[0.941]
34.089
[0.958]
16.596
[1.000]
37.801
[0.898]
48.519
[0.533]
27.854
[0.995]
54.881
[0.295]
12.680
[1.000]
64.591
[0.080]*
40.190
[0.838]
30.604
[0.986]
27.738
[0.996]
ARCHM(5)
0.616
[0.688]
1.131
[0.344]
0.310
[0.907]
0.374
[0.867]
0.121
[0.988]
0.433
[0.825]
0.264
[0.932]
0.127
[0.986]
0.497
[0.779]
0.096
[0.993]
0.103
[0.991]
0.264
[0.933]
0.214
[0.956]
0.213
[0.957]
ARCHM(10)
0.399
[0.946]
0.985
[0.457]
0.365
[0.961]
0.448
[0.921]
0.102
[1.000]
0.423
[0.935]
1.156
[0.321]
0.498
[0.890]
0.390
[0.950]
0.087
[1.000]
0.657
[0.763]
0.218
[0.995]
0.807
[0.622]
0.222
[0.994]
19
Table 5
Securitized real estate markets:
Factor loadings for long run (“permanent”) volatilities: Jan 1984 – July 2006
Country
Australia
Canada
France
Germany
Hong Kong
Italy
Japan
Netherlands
Norway
Singapore
Sweden
Switzerland
UK
US
% of variance explained
Cumulative % of variance
explained
Eigenvalue
Factor 1
Factor 2
-0.027
0.912
-0.174
-0.151
0.561
0.117
0.503
0.158
0.867
-0.042
0.871
0.185
0.518
0.120
23.730
0.848
0.010
0.206
0.057
-0.377
0.082
0.137
-0.075
0.153
0.818
-0.095
0.015
0.410
0.783
17.295
23.730
3.322
41.025
2.421
Weights
Factor 3
Factor 4
Factor 5
0.248
0.119
0.283
0.890
0.482
-0.120
0.788
0.028
0.206
0.026
-0.226
0.247
0.633
-0.022
16.960
0.210
0.030
0.708
0.102
0.156
0.791
0.189
0.101
-0.039
0.205
0.137
0.588
-0.007
-0.106
11.939
-0.128
0.101
0.281
0.009
-0.119
-0.267
0.043
0.913
-0.014
-0.328
0.181
0.267
0.153
0.323
9.765
57.984
2.374
69.923
1.671
79.688
1.367
Note: Figures in bold are the main components of each factor.
20
Table 6
Securitized real estate markets:
Factor loadings for short-run (“transitory”) volatilities (Jan 1984 – July 2006)
Country
Australia
Canada
France
Germany
Hong Kong
Italy
Japan
Netherlands
Norway
Singapore
Sweden
Switzerland
UK
US
% of variance explained
Cumulative % of variance
explained
Eigenvalue
Factor 1
Factor 2
0.038
0.840
0.030
-0.251
0.194
0.056
0.287
0.318
0.790
-0.021
0.870
0.282
0.465
0.081
19.201
0.274
0.120
0.609
0.774
0.230
0.134
0.793
0.161
0.215
0.029
-0.114
0.530
0.611
0.109
17.945
19.201
2.688
37.146
2.512
Weights
Factor 3
Factor 4
Factor 5
0.806
-0.059
0.232
0.071
0.668
0.195
0.062
-0.508
0.140
0.883
-0.137
-0.069
0.323
0.0003
17.041
-0.187
0.208
-0.514
0.155
0.454
0.721
0.152
-0.122
-0.116
-0.147
0.093
0.170
-0.271
-0.048
9.135
-0.049
0.342
-0.087
0.199
0.205
-0.151
0.087
0.259
-0.024
0.080
-0.146
-0.489
-0.083
0.827
9.027
54.187
2.386
63.322
1.279
72.349
1.264
Note: Figures in bold are the main components of each factor.
21
Table 7
Regression results between the real estate market factor scores
(RE-F1 to RE-F5) and stock market factor scores (S-F1 to S-F4) in “permanent” and
“transitory” volatilities: Jan 84 – Jul 06
Dependent
variable
Adj R2
RE-F1
0.971
Panel A: Permanent volatility
DurbinRegression coefficients (t-statistics)
Watson
S-F1
S-F2
S-F3
S-F4
1489.5
2.00
-0.0003
-0.2108
0.0335
0.0215
RE-F2
0.929
700.5
RE-F3
0.972
RE-F4
0.749
RE-F5
0.771
F-value
(2.62***)
1875.9
2.05
1.98
0.2831
1.4093
0.7158
0.1761
(3.53***)
(3.16***)
(7.07***)
(2.78***)
-0.1375
0.1341
-0.0636
-0.0258
(-3.83***)
157.2
1.89
0.4190
(-4.12***)
0.2787
-0.058
0.1814
-0.0858
-0.0314
0.2384
(3.11***)
150.7
2.02
0.3173
(1.98**)
(2.59***)
(1.99**)
Panel B: Transitory volatility
F-value
DurbinRegression coefficients (t-statistics)
Watson
S-F1
S-F2
S-F3
S-F4
296.8
1.95
-0.1076
0.0621
-0.1511
0.0651
Dependent
variable
Adj R2
RE-F1
0.886
(-8.77***)
(2.35**)
(-2.77***)
(3.53***)
RE-F2
RE-F3
0.881
0.805
245.6
184.8
2.05
1.93
0.0237
-0.1416
0.0057
-0.1171
-0.0634
-0.1778
-0.2081
0.2656
RE-F4
0.814
157.3
1.96
-0.0704
RE-F5
0.559
(-2.42***)
-0.1000
(2.82***)
-0.0263
(-3.40***)
57.43
2.05
-0.3770
0.3501
(-8.04***)
(3.51***)
-0.2008
(-4.15***)
-0.0960
-0.2703
(-3.43***)
Notes: Following the same procedure as described for real estate volatilities, the 14 MSCI stock markets’
“permanent” and “transitory” components are first derived. Then, the factor solutions for the two sets of
volatility variables are estimated. Each set derives four “factors” (S-F1 to S-F4). The complete results are
not reported to save space; ***, ** - indicates two-tailed significance at the 1 and 5 percent levels
respectively.
22
Figure 1
US
Japan
Hong Kong
Germany
UK
Australia
France
Netherlands
Singapore
Switzerland
Canada
Sweden
Italy
90000
80000
70000
60000
50000
40000
30000
20000
10000
0
Norway
Average Market value of the sample securitized real estate markets: Jan 1984-July 2006
Source: GPR
23
Figure 2
Time Evolution of the conditional (total) variance and its components (transitory variance and permanent variance): Jan 84 – Jul 06
Variance Decomposition for Australia
0.03
0.016
0.025
0.014
0.02
0.012
0.05
0.045
0.04
0.035
0.03
0.025
0.02
0.015
0.01
0.005
0
0.01
0.015
0.008
0.01
0.006
0.005
0.004
0.002
0
1
19 37 55 73 91 109 127 145 163 181 199 217 235 253
0
1
Total Variance
Variance Decomposition for France
Variance Decomposition for Canada
19 37 55 73 91 109 127 145 163 181 199 217 235 253
Transitory Variance
Total Variance
Permanent Variance
Permanent Variance
Varance Decomposition for Germany
1
0.03
0.0025
0.025
Transitory Variance
Variance Decomposition for Italy
Variance Decomposition for Hong Kong
0.003
19 37 55 73 91 109 127 145 163 181 199 217 235 253
Total Variance
Permanent Variance
Transitory Variance
0.03
0.025
0.02
0.002
0.02
0.015
0.0015
0.015
0.01
0.001
0.01
0.005
0.0005
0
0
1
20 39 58 77 96 115 134 153 172 191 210 229 248 267
-0.005
0.005
1
20 39 58 77 96 115 134 153 172 191 210 229 248 267
0
1
Total Variance
Permanent Variance
Transitory Variance
Total Variance
Permanent Variance
Transitory Variance
20 39 58 77 96 115 134 153 172 191 210 229 248 267
Total Variance
Transitory Variance
Permanent Variance
24
Variance Decomposition for Japan
0.035
0.03
Variance Decomposition for Norway
Variance Decomposition for Netherlands
0.004
0.03
0.0035
0.025
0.003
0.02
0.025
0.0025
0.02
0.002
0.015
0.0015
0.01
0.015
0.001
0.01
0.005
0.0005
0.005
0
0
1
0
1
20 39 58 77 96 115 134 153 172 191 210 229 248 267
20 39 58 77 96 115 134 153 172 191 210 229 248 267
Total Variance
Total Variance
Transitory Variance
Variance Decomposition for Singapore
0.06
0.12
0.05
0.1
0.03
0.025
0.04
0.02
0.03
0.015
0.02
0.04
0.01
0.01
0.02
0
0.005
0
20 39 58 77 96 115 134 153 172 191 210 229 248 267
Permanent Variance
Transitory Variance
Variance Decomposition for Switzerland
0.035
0.08
0.06
Transitory Variance
Permanent Variance
Variance Decomposition for Sweden
0.14
Total Variance
Total Variance
Transitory Variance
Permanent Variance
Permanent Variance
1
1
20 39 58 77 96 115 134 153 172 191 210 229 248 267
0
1
20 39 58 77 96 115 134 153 172 191 210 229 248 267
Total Variance
Permanent Variance
Transitory Variance
1
20 39 58 77 96 115 134 153 172 191 210 229 248 267
Total Variance
Transitory Variance
Permanent Variance
25
Variance Decomposition for United States
Variance Decomposition for United Kingdom
0.009
0.008
0.007
0.014
0.012
0.006
0.005
0.004
0.003
0.01
0.008
0.006
0.002
0.001
0
0.004
0.002
1
0
1
20 39 58 77 96 115 134 153 172 191 210 229 248 267
20 39 58 77 96 115 134 153 172 191 210 229 248 267
Total Variance
Permanent Variance
Transitory Variance
Total Variance
Transitory Variance
Permanent Variance
26