Mean and Volatility Spillovers across major Real Estate Markets
Zhiwei CHEN* and Kim Hiang LIOW
Department of Real Estate, National University of Singapore
Working paper to be presented at the 22nd ARES Meeting at
Casa Marina Resort, Key West,
Florida, April 19-22, 2006
Abstract
This paper investigates the transmission of returns and volatility among world
stock market and major real estate markets, including Australia, Hong Kong,
Japan, Singapore, United Kingdom, and the United States. A vector
autoregressive multivariate exponential GARCH in mean (VAR-MEGARCH -M)
model is used to identify the source and magnitude of spillovers on a weekly
basis from Jan 1990 to Dec 2005. We find some significant and multidirectional
mean and volatility spillover effects, which indicate these real estate markets are
highly intercorrelated. We also construct total hedged return indices which are
expected to filter out the general stock market impact and the results show that
both mean and volatility correlations have been reduced to a large extent.
Moreover, the volatility spillover effects are found to be more significant within
Asian countries than across the world. That is, the real estate markets seem to
exhibit a continental segmentation in general.
I. Introduction
The size of global real estate investible assets is approximately $6.2 trillion, which equals nearly
15% of the total investible universe (UBS, 2004). The growing globalization of real estate markets
has also been accompanied by a growing body of empirical research attempting to describe and
quantify the ways in which real estate markets within and across countries interact, which is central
to the decision making of investors and portfolio managers.
A large number of empirical evidence show that the conditional variances and covariances of
stock market returns vary over time and exhibit volatility clustering behavior. Volatility clustering is
the tendency of large (small) changes to be followed by large (small) changes of either algebraic
sign. Since investors seek increased diversification across international real estate markets, it is
important to understand the returns volatility and shock persistence of different markets. It is usually
said that increasing equity market integration tends to reduce the benefits of international
diversification. That is why it is important to understand the patterns of market information spillover
and the following volatility spillover.
*
Corresponding author. E-mail address: chenzhiwei@nus.edu.sg
1
II. Literature Review
Most early studies of market interdependencies and contagion effects have generally relied upon
Granger-causality testing of market indices. However, these studies generally failed to capture the
autoregressive second moment of the distribution of stock returns (i.e. the feature that the
conditional variance of stock returns is time varying) which results in inconsistent estimates of the
ordinary least squares estimation of mean spillovers (Gallagher and Twomey, 1998, p. 342).
Accordingly, more recent work has availed itself of the sizeable advances in autoregressive
conditional heteroskedastic (ARCH) and generalized autoregressive conditional heteroskedastic
(GARCH) models to study the conditional volatility of stock markets and ascertain the predictability
of future stock return volatility conditional on past volatilities and return shocks (see Worthington A.
and Higgs H., 2004). The ARCH family models, which formulate conditional variance of returns via
maximum likelihood procedure, have been applied to a wide range of time series analyses, and the
applications in finance have been particularly successful in the last two decades. (see Bollerslev,
Chou and Kroner (1992), Engle (2001), Poon and Granger (2003) for extensive surveys). A few
studies have even extended these to the multivariate case (see, for example, Tse (2000), Tay and Zhu
(2000) and Scheicher (2001)).
With the ARCH family models, numerous studies have investigated the transmission mechanism
of stock price movements across international stock markets. For example, Eun and Shim (1989)
find that innovations in the US stock market are rapidly transmitted to the rest of the world,
although innovations in other national markets do not have much effect on the US market. Von
Furstenberg and Jeon (1989) find that the correlation among the daily stock indices of the US, Japan,
the United Kingdom, and Germany increased significantly after the rash of 1987. Hamao, Masulis,
and Ng (1990) find that daily price volatility spills over from the US to Japan and the UK, and from
UK to Japan. Hamao, Masulis, and Ng (1990), Koutmos and Booth (1995), and Susmel and Engle
(1994) focus on New York, London, and Tokyo. Theodossiou and Lee (1993) examine
interdependencies across the US, Japan, Canada and Germany. Koutmos (1996) investigates the
dynamic interdependence of major European stock markets. Michelfelder (2005) analyzes the
volatility of stock returns of seven emerging markets and compares them with the mature markets of
Japan and US. By using the EGARCH specification with Skewed GED, he finds that US shocks are
rapidly transmitted to the rest of the world.
In addition to the research of volatility spillover effects, some researchers also investigate the
intertemporal relation between expected returns and market risk (i.e. ARCH in mean effect).
Pindyck (1984) claims that much of the decline in US stock prices during 1970s is due to volatility
increases. Bollerslev, Engle, and Wooldridge (1988) similarly find that the conditional volatility of
stock market returns significantly affects their expected value. Conversely, French, Schwert, and
Stambaugh (1987), Baillie and Degennaro (1990), and Theodossiou and Lee (1994) find no relation
between stock market returns and volatility.
In spite of abundant researches of international volatility transmission, the number of reported
2
studies of multivariate GARCH models remains small relative the number of univariate studies (see
Kearney and Patton, 2000, p.34). Furthermore, In et al (2001) have pointed out that relatively few
studies have examined stock market interdependence within the Asian markets. Lam and Li (1997)
have studied volatility in seven Southeast Asian stock markets using an autoregressive random
variance (ARV) model. Interdependence between the US, Japan and four Asian stock markets has
been studied by Liu and Pan (1997). Liu and Pan conclude that the US market is more influential
than the Japanese market in transmitting returns and volatilities to the four Asian markets. Bala and
Premaratne (2003) employed several GARCH models to investigate the volatility co-movement
between Singapore, Hong Kong, Japan, UK and US. Unlike the previous researches which conclude
that spillover effects are significant only from the dominant market to the smaller market, they find
that it is plausible for volatility to spill over from the smaller market to the dominant market.
As for an exclusively real estate market perspective, researches on interlinkages between
international real estate markets turn out to be even more inadequate. Liow, Ooi and Gong (2003)
use an extended EGARCH (1,1) model and find week mean transmission and lack of significant
evidence of cross-volatility spillovers among the Asian and European property stock markets. Liow
and Zhu (2005) take a causality perspective and find that international real estate markets are
generally correlated in returns and volatilities contemporaneously and with lags. The US and UK
markets significantly affect some Asian markets such as Singapore, Hong Kong, Japan and Malaysia
in either mean or return volatility at different lags. Michayluk, Wilson and Zurbruegg (2006)
construct synchronously priced indices of securitized property listed on NYSE and LSE and then
examine dynamic information flows between the two markets. They show that the real estate
markets in these two countries experience significant interaction on a daily basis, and the positive
and negative news impact the markets differently.
This study makes an effort to investigate the mean and volatility transmission across major real
estate markets and the world stock market with the vector autoregressive multivariate exponential
generalized autoregressive conditional heteroskedastic in mean (VAR-MEGARCH-M) model. It
distinguishes itself among other researches in several aspects. First, it provides new evidence for
mean and volatility spillover effects among major real estate markets. Second, as far as the authors
are aware, this is the first study to simultaneously investigate the mean and volatility spillover
effects between stock market and real estate markets. Third, this study should also be the first to
examine the intertemporal relationship between the expected return and risk (i.e. in-mean effect) in
the context of real estate market. Last, it calculates the total hedged returns for each real estate
market, and compares the empirical results with normal indices, which help to find out whether real
estate market interlinkages are actually the result of general stock market spillovers.
The remainder of this paper is organized as follows: The next section presents the specification of
multivariate VAR-EGARCH-M model. The third section describes the data and preliminary
empirical findings. The major findings based on the VAR-EGARCH-M model are presented in
section four. Section five introduces the hedged index technique and the differences in empirical
results compared to the model estimated with normal indices. The final section offers a summary
and concluding remarks.
3
III. Methodology
GARCH models are generally used to explore the stochastic behavior of several financial time
series and, in particular, to explain the behavior of volatility over time (see Bollerslev, Chou and
Kroner (1992) for a literature review). Introduced by Engle, Lilien and Robins (1987), the
GARCH-M model is a more general specification of asset returns that links conditional market
volatility and expected returns. As it is observed that negative news often have greater influence on
volatilities, Nelson’s (1991) exponential GARCH-M (EGARCH-M) model specified the conditional
second moments of the returns to allow for asymmetric effects of market news on the volatility
function. Furthermore, the development of multivariate GARCH (MGARCH) models from the
original univariate specifications represented a major step forward in the modeling of time series.
Modeling the returns simultaneously has several advantages over the univariate approach that has
been used so far. First, it eliminates the two-step procedure, thereby avoiding problems associated
with estimated regressors. Second, it improves the efficiency and the power of the tests for cross
market spillovers. Third, it is methodologically consistent with the notion that spillovers are
essentially manifestations of the impact of global news on any given market. MGARCH-M models
permit time-varying conditional covariances as well as variances; thus allows for possible
interactions within conditional mean and variance of returns of two or more financial series. Here,
the multivariate EGARCH-in-mean (MEGARCH-M) model is adopted to study the transmission
mechanism of returns and disturbances (mean and volatility spillovers) from one national stock
market to others, and to test for market risk premia. The multivariate EGARCH-M model is ideally
suited to test the possibility of asymmetries in the volatility transmission mechanism. In other words,
news generated in one market is evaluated in terms of both size and sign by other markets. This is
appropriate when the conditional variances (volatilities) and covariances of stock return respond
asymmetrically to positive (good) news and negative (bad) news of stock market returns (see Nelson
(1991), inter alia). Note that a negative relationship of the volatility of stocks returns with respect to
market news is usually referred to as the leverage effect (see Black (1976), Christie (1982), Nelson
(1991), among others).
VAR-MEGARCH-M Model
Let Ri ,t be the percentage return at time t for market i where, i = 1,2,…6, (1 = Australia, 2
= Hong Kong, 3 = Japan, 4 = Singapore, 5 = United Kingdom, 6 = United States, 7 = World Stock
Market), Ω t −1 the all information available at time t − 1 ,
and the conditional variance respectively,
and market j ,
innovation
μ i,t and σ i2,t the conditional mean
σ i , j ,t the conditional covariance between the market i
ε i,t the innovation at time t (i.e., ε i ,t = Ri ,t − μ i ,t ), and z i ,t the standardized
(i.e.,
z i ,t = ε i ,t / σ i ,t ).
The
VAR
(q)
multivariate
EGARCH-in-mean
(VAR-MEGARCH-M) model can then be written as follows:
4
q
7
Ri ,t = β i , 0 + ∑∑ β i , j ,k R j ,t −k + ξ iσ i2,t + ε i ,t
for i, j = 1,2,…7,
(1)
σ i2,t = exp⎨α i ,0 + ∑ α i , j f j ( z j ,t −1 ) + γ i ln(σ i2,t −1 )⎬ for i, j = 1,2,…7,
(2)
k =1 j =1
⎧
7
⎫
⎩
j =1
⎭
(
(
)
f j ( z j ,t −1 ) = z j ,t −1 − E z j ,t −1 + δ j z j ,t −1
σ i , j ,t = ρ i , j σ i ,t σ j ,t
)
for i, j = 1,2,…7,
for i, j = 1,2,…7 and i ≠ j .
(3)
(4)
Equation (1) describes the returns of the three markets as a VAR of lag q , where the conditional
mean in each market is a function of past own returns, as well as cross-market past returns
(Koutmos G., 1996). Lead/lag relationships are captured by coefficients
significant
β i, j , for i ≠ j . A
β i, j coefficient measures the direct effect that a change in return to the j th market
would have on the i th market. Volatility feedbacks (i.e., ARCH-M effects) are represented by term
ξ iσ i2 , and ξ i is the coefficient linking conditional market volatility to expected returns.
Equation (2) explains the EGARCH representation of the variance of
ε t . According to the
EGARCH representation, the conditional variance of the returns in each market is an exponential
function of past own, cross-market standardized innovations and past own conditional variance. The
persistence of volatility is measured by
γ i . The unconditional variance is finite if γ i < 1 . If
γ i = 1 , then the unconditional variance does not exist, and the conditional variance follows an
integrated process of order one.
The particular function form of f j ( z j ,t −1 ) is given in Equation (3), which captures the ARCH
(
effect, and is asymmetric function of past standardized innovations. The term z j ,t −1 − E z j ,t −1
)
measures the magnitude effect. If the magnitude of z j ,t −1 is greater than its expected value,
(
)
E z j ,t −1 , the impact of z j ,t −1 on σ i2,t will be greatly positive, providing that α i, j is positive.
The term
δ j z j ,t −1 measures the sign effect. If δ j is negative, stock market declines in market j
will be followed by larger volatility than stock market advances (Koutmos, 1996). In other words,
the parameter
δ j measures the asymmetric volatility transmission mechanism.
5
Equation (4) provides the conditional covariance specification, which captures the
contemporaneous relationship between the returns of the 7 markets. This specification implies that
the covariance of market i and j is proportional to the product of their standard deviations. This
assumption greatly simplifies estimation of the model and it is a plausible one for many applications
(Bollerslev, Chou and Kroner 1992). The coefficient
ρ i, j is the cross-market correlation
coefficient of the standardized residuals between two markets. Statistically, the significant estimates
of
ρ i, j indicates that time-varying volatilities across market i and j are correlated over time.
Assuming normality, the log likelihood for the multivariate VAR-EGARCH-M model can be
written as Equation (5):
(
L(θ ) = −0.5( NT ) ln (2π ) − 0.5∑ ln S t + ε t′S t−1ε t
)
(5)
Where N is the number of equations (four in this case), T is the number of observations, θ is the
parameter vector to be estimated,
ε t′ = [ε 1.t , ε 2,t , ε 3.t , ε 4.t , ε 5.t , ε 6.t , ε 7.t ] is the 1×7 vector of
innovations at time t , S t is the 7×7 time-varying conditional variance-covariance matrix with
diagonal elements given by Equation (2) for i =1,2,…7 and cross diagonal elements given in
Equation (4) for i, j = 1,2,…7 and i ≠ j . The log-likelihood function is highly nonlinear in
θ
and, therefore, numerical maximization techniques are used. The BFGS algorithm is used to
maximize L(θ ) .
IV. Data
The data used in this study include weekly world stock market return and property stock market
returns for Australia, Hong Kong, Japan, Singapore, UK and US from Jan 1990 to Dec 2005. The
proxy indices used are MSCI world return index and the FTSE/EPRA/NAREIT return indices for
real estate market. FTSE/EPRA/NAREIT indices are world-recognized and are used extensively by
investors worldwide for investment analysis, performance measurement, asset allocation, portfolio
hedging and for creating a wide range of index tracking funds. All indices are based on US dollar
currency and are total returns including dividends.
The returns for each market are expressed in percentages computed by multiplying the first
difference of the logarithm of property stock market indices by 100. In terms of data frequency,
weekly data is specified. On the one hand, it has been argued ‘daily return data is preferred to the
lower frequency data such as weekly and monthly returns because longer horizon returns can
6
obscure transient responses to innovations which may last for a few days only’ (Elaysiani et al.,
1998, p. 94). However, Roca (1999, p. 505), among others, has countered ‘……daily data are
deemed to contain “too much noise” and is affected by the day-of-the-week effect while monthly
data are also affected by the month of the year effect’. Ramchand and Susmel (1998), Aggarwal et al.
(1999), Tay and Zhu (2000), and Worthington A. and Higgs H. (2004), are among the large number
of studies that have employed weekly data instead of monthly data in order to provide a sufficient
number of observations required to estimate the GARCH or MGARCH models without the noice of
daily data.
Descriptive Statistics
Table 1 presents descriptive statistics for each return series for the period 1990 to 2005. Sample
means, medians, maximums, minimums, standard deviations, skewness, kurtosis and the
Jarque-Bara statistic, the Ljung-Box statistics for 6 and 12 lags for returns as well as squared returns,
the Kolmogorov-Smirnov (KS) D-statistics, and the ARCH LM test statistics are reported for the
weekly returns. Table 2 is the cross-correlation matrix of the real estate market returns.
Figure 1. Weekly Returns of 6 Real Estate Markets and World Stock Market, Jan
1990 to Dec 2005
Australia (AU)
Hong Kong (HK)
8
Japan (JP)
30
30
20
20
4
10
10
0
0
0
-10
-4
-10
-20
-8
-20
-30
90
92
94
96
98
00
02
04
90
92
Singapore (SG)
94
96
98
00
02
04
90
92
United Kingdom (UK)
40
96
98
00
02
04
02
04
United States (US)
12
8
8
20
94
4
4
0
0
0
-20
-4
-4
-40
-8
-8
-60
-12
-12
90
92
94
96
98
00
02
04
90
92
94
96
98
00
02
04
02
04
90
92
94
96
98
00
World Stock Market
8
4
0
-4
-8
-12
90
92
94
96
98
00
7
The means of returns for all markets range between -0.0014% (Japan) and 0.2887% (US). Except
for Japan, the real estate market returns are all positive on the average level during the sample
period. The standard deviations of returns range between 1.8158% (US) and 5.1600% (Singapore).
From the results of standard deviation, we can roughly conclude that the real estate markets in
traditional Asia area, namely Hong Kong, Japan, and Singapore, are more volatile than those in
Australia, UK, and US. And real estate markets in these Asian countries are also more volatile than
the world general stock market, which is proxied by MSCI world index. The correlations of returns
range from a high of 0.5808 between Singapore and Hong Kong, to a low of 0.0945 between Japan
and US.
Table 1. Summary Statistics of Weekly Returns
AU
HK
JP
SG
UK
US
World
(A). Moments, maximum, and minimum
Mean
0.2593
0.2076
-0.0014
0.0567
0.1494
0.2887
0.0953
Median
0.3247
0.3549
-0.3649
0.1723
0.1292
0.3431
0.2132
Maximum
7.0023
20.3805
23.8109
35.4636
9.9698
7.7988
7.8452
Minimum
-7.3581
-29.0678
-16.6496
-54.2281
-11.7163
-10.3485
-9.9630
Std. Dev.
2.0445
4.4179
4.9311
5.1600
2.4036
1.8158
1.9115
Skewness
-0.2771
-0.4923
0.4428
-0.8559
0.0392
-0.4431
-0.2338
Kurtosis
3.4923
7.3872
4.5736
21.8280
4.6995
6.3877
5.0558
**19.1169
**703.3662
**113.4323
**12435.3300
**100.7001
**426.6230
**154.6431
**0.0777
**0.0463
**0.0637
**0.0493
Jarque-Bera
(B). Kolmogorov-Smirnov test for normality
D
*0.0455
**0.4979
**0.0521
(C). Ljung-Box statistic for up to 6 and 12 lags
Q(6) for R
10.077
**16.773
9.1945
**28.006
*10.895
*12.400
4.5869
Q(12) for R
12.003
**23.688
17.776
**37.466
13.4
*18.969
7.5715
Q(6) for R^2
**48.407
**35.009
**71.997
**111.65
9.2387
**60.910
**74.0400
Q(12) for R^2
**75.037
**97.531
**104.95
**153.22
**21.482
**70.115
**98.9680
(D). ARCH LM test
4 lags
**30.1523
**32.2479
**53.7928
**99.4828
*8.0632
**43.3811
**47.7437
8 lags
**43.0176
**33.9215
**57.8338
**103.0601
*14.2206
**48.9148
**55.7884
12 lags
**45.7820
**84.5006
**71.6488
**121.3447
**21.0601
**50.1298
**59.9967
Note: ** indicate significance at 5% level; * indicate significance at 10% level;
5% critical value for Kolmogorov-Smirnov test is 1.32 / T , where T is number of observation.
The distributional properties of the return series generally appear to be non-normal. All
Kolmogorov-Smirnov test statistics are significant, which leads to a rejection of the assumption of
normality of returns for all markets. From the results of Ljung-Box test, we are able to conclude that
the squared return series are highly auto-correlated, which indicates the ARCH effects may exist. In
the further examination of the ARCH LM test, most of these test statistics are significant at the 5%
level, suggesting the existence of ARCH effects. In other words, the nonlinear dependencies in these
8
return series could be due to the presence of conditional heteroskedasticity, which we are trying to
capture in the next section using the multivariate GARCH model.
Table 2. Cross-Correlation of Real Estate Market Returns and World Stock Market
AU
AU
HK
JP
SG
UK
US
WD
1.0000
0.2868
0.1717
0.2041
0.3029
0.2247
0.3346
HK
0.2868
1.0000
0.2212
0.5808
0.2420
0.2183
0.4536
JP
0.1717
0.2212
1.0000
0.2462
0.2365
0.0945
0.4239
SG
0.2041
0.5808
0.2462
1.0000
0.2293
0.2495
0.4211
UK
0.3029
0.2420
0.2365
0.2293
1.0000
0.2533
0.4225
US
0.2247
0.2183
0.0945
0.2495
0.2533
1.0000
0.4537
WD
0.3346
0.4536
0.4239
0.4211
0.4225
0.4537
1.0000
V. Major Empirical Findings of VAR-MEGARCH-M Model
Before estimation, we use the Akaike Information Criterion (AIC) test to determine the proper
VAR lag order for the model. As the result displayed in Table 3, we adopt a VAR (1) model in the
following estimation.
Table 3. VAR Lag Length Criterion
Lag
0
1
2
3
4
5
6
AIC
33.4249
33.40351*
33.4441
33.4790
33.5293
33.5857
33.6359
Lag
7
8
9
10
11
12
AIC
33.6977
33.7438
33.7834
33.8303
33.8641
33.9260
Note: * indicates lag order selected by criterion
The maximum likelihood estimates of the VAR-MEGARCH-M model are reported in Table 4.
Focusing on the parameters in the conditional mean equation, it can be seen that there are several
significant multidirectional lead/lag relationships in the markets. For example, current returns in
Hong Kong are influenced by past returns in Australia, Japan, US and the world stock market.
Returns in Japan are correlated with past returns in Australia, Hong Kong and itself. Similarly,
current returns in Singapore are influenced by returns of all other countries and the world stock
market in the last period. The return of world stock market is found to have impact upon Asian real
estate market returns in the next period. That is, the real estate markets in Asia are more exposed to
the world general stock market. Among these 6 countries, Australia, Japan and US can be deemed as
the most powerful markets in that their lagged returns influence significantly the conditional means
of other markets. They play major roles as information producers. In general, the multidirectional
nature of these relationships suggests that these 6 real estate markets and the world stock market are
highly correlated in terms of conditional mean spillovers.
9
Table 4. Estimated Coefficients for VAR-MEGARCH-M Model
AU (i=1)
Variable
Coeff.
Std Error
HK (i=2)
Coeff.
Std Error
JP (i=3)
Coeff.
SG (i=4)
Coeff.
Coeff.
Std Error
UK (i=5)
Coeff.
Std Error
US (i=6)
Coeff.
Std Error
World (i=7)
Coeff.
Std Error
β i ,0
**0.4850
0.0169
**0.3523
0.0569
-0.0777
0.0622
**0.0577
0.0209
**0.2332
0.0179
**0.4365
0.0227
**0.0848
0.0224
β i ,1
**-0.0984
0.0115
**0.1375
0.0312
**0.0826
0.0358
**0.0257
0.0112
**0.0223
0.0094
-0.0178
0.0127
**0.0270
0.0135
β i,2
0.0067
0.0067
-0.0097
0.0166
**-0.0930
0.0203
**0.0325
0.0071
**-0.0649
0.0055
-0.0054
0.0065
**-0.0335
0.0066
β i ,3
**-0.0114
0.0055
**-0.0480
0.0147
**-0.1342
0.0169
**-0.0471
0.0059
**-0.0275
0.0044
-0.0083
0.0062
**-0.0418
0.0060
β i,4
**0.0171
0.0064
0.0071
0.0165
0.0265
0.0195
**-0.0482
0.0130
**0.0310
0.0056
**0.0132
0.0067
0.0062
0.0065
β i ,5
**0.0323
0.0094
-0.0003
0.0257
0.0340
0.0297
**0.0870
0.0098
**0.0431
0.0077
0.0162
0.0101
**0.0259
0.0110
β i ,6
**0.0275
0.0132
**0.0858
0.0405
0.0763
0.0432
**0.0510
0.0159
**0.1242
0.0103
**0.0718
0.0123
-0.0020
0.0140
β i ,7
**0.1356
0.0145
**0.1349
0.0405
**0.1462
0.0452
**0.1568
0.0169
0.0188
0.0107
0.0051
0.0139
0.0135
0.0138
ξi
**-0.0714
0.0005
**-0.0206
0.0085
-0.0129
0.0071
**-0.0110
0.0056
**-0.0284
0.0142
**-0.0580
0.0184
-0.0068
0.0107
α i ,0
**0.2381
0.0123
**0.0943
0.0026
**0.1282
0.0025
**0.2288
0.0048
**0.1631
0.0084
**0.1969
0.0134
**0.0132
0.0000
α i ,1
**0.1385
0.0131
**0.0633
0.0050
**0.0416
0.0047
-0.0061
0.0084
**0.0385
0.0057
**0.1223
0.0141
**-0.0511
0.0082
α i ,2
**-0.2071
0.0197
**0.0951
0.0061
**0.0169
0.0065
**0.0613
0.0100
-0.0229
0.0137
-0.0124
0.0178
**-0.0271
0.0041
α i ,3
0.0280
0.0169
**0.0359
0.0074
**0.1457
0.0068
-0.0002
0.0165
**0.0754
0.0093
-0.0050
0.0223
**0.0455
0.0137
α i ,4
**0.2056
0.0145
**0.0627
0.0050
**0.0558
0.0048
**0.1551
0.0147
0.0025
0.0096
**0.1436
0.0129
**0.0511
0.0068
α i ,5
**0.1586
0.0099
**0.1007
0.0031
-0.0028
0.0037
0.0026
0.0067
**0.1741
0.0050
**0.0269
0.0095
**-0.0380
0.0093
α i ,6
**0.0730
0.0169
**-0.028
0.0084
**0.0120
0.0059
0.0116
0.0127
**0.0568
0.0090
**0.1815
0.0139
**0.0214
0.0043
α i ,7
**-0.1021
0.0181
**-0.0588
0.0075
0.0032
0.0062
**0.0513
0.0103
-0.0116
0.0088
**0.1657
0.0133
**-0.0207
0.0055
γi
**0.8245
0.0146
**0.9650
0.0011
**0.9561
0.0014
**0.9137
0.0025
**0.9067
0.0074
**0.8046
0.0152
**0.9869
0.0010
δi
**0.6761
0.0522
**-0.1268
0.0603
**-0.2792
0.0589
**-0.0360
0.0126
**-0.2310
0.0368
-0.0020
0.0536
**-0.367
0.0486
R2
0.0290
0.0151
0.0167
0.0192
0.0164
0.0097
0.0073
Note: ** indicate significance at 5% level.
10
The in-mean effects, which was measured by coefficient
ξ i , are significant except Japan and
the world stock market. Previous researches focusing on general stock markets find no relation
between conditional market volatility and expected returns (see Theodossiou and Lee, 1993). Our
finding is consistent with them in terms of the world general stock market. Considering the real
estate markets, however, we find the contemporaneous variances do have effect on the conditional
means. Furthermore, the sign of such effect appears to be negative for all countries, which means
that an increase in conditional variances will result in a decrease in expected returns.
An important question that arises is to what extent can these relationships in mean returns be
exploited to generate abnormal profits? To answer this question, one need to further take into
consideration the transaction costs as well as foreign exchange risk. In Table 4 we calculated the
uncentered R
2
statistics, which is formulated as R = 1 − (Var (ε i ) / Var ( Ri )) , for i=1,2,…,7.
2
These statistics range from 0.73%, for the world stock market, to 2.90% for Australia. That is, the
percentage of variation in returns that can be explained on the basis of past information is very
small. In other words, if transaction costs and exchange rate risk are taken into account then we
can safely conclude that abnormal profits cannot be obtained merely based on past information
and these markets are weak-form efficient.
Second moment interdependencies (volatility interactions) are measured by the coefficient
α i, j . As shown in Table 4, conditional variance in each market is affected by its own past
innovations. For real estate markets in Australia, Hong Kong and Japan, they receive most
innovations generated in other real estate markets. Specifically, Hong Kong is affected by all past
innovations from other markets. Singapore is affected by its own past innovations, and those of
Hong Kong and world stock market. UK and US are found to have volatility spillover effect to
Asian real estate markets. In terms of volatility interactions, real estate markets in these countries
are highly intercorrelated, which is consistent to what have found in mean spillover analysis. The
world stock market is also found to be highly correlated with real estate markets in that its
volatility spillover effect is significant for four major real estate markets, namely Australia, Hong
Kong, Singapore and US. For both general stock market and major real estate markets,
innovations generated in a market are rapidly transmitted to most of other markets in the next
period.
The degree of volatility persistence (measured by
γ i ) is significant and quite close to 1 for
each market, which indicates a considerable GARCH effect in all real estate markets. Asymmetric
effect, measured by
δ j , is statistically significant for Australia, Hong Kong, Japan, Singapore,
US and the world stock market. Interestingly, the sign of the coefficient δ j for Australia is
positive, which indicates that positive news in Australia will have greater influence upon
conditional variances than negative news. In order to specify the sign and magnitude of volatility
11
spillovers among these markets, we calculate the impact of a ±5% innovation in market i at
time t − 1 on the conditional variance of market j at time t assuming all other innovations
are zero. From equation (2) and (3), such impact can be assessed using the estimated coefficients
α i, j and δ j . The results of this exercise are displayed in Table 5. As expected, the impact of
innovation in market i is mostly felt within the same market. However, the volatility in other
markets is affected substantially. For example, a +5% (-5%) innovation in Hong Kong real estate
market at time t − 1 increases volatility by 0.0738% (0.0953%) in Japan real estate market at
time t . While a +5% (-5%) innovation in the world stock market at time t − 1 decreases
volatility by 0.3224% (0.6956%) in Australia real estate market at time t .
Table 5. Impact of innovations on volatility
%Δ of
%Δ of
%Δ of
%Δ of
%Δ of
%Δ of
%Δ of
volatility in
volatility in
volatility in
volatility in
volatility in
volatility in
volatility in
AU at t
HK at t
JP at t
SG at t
UK at t
US at t
World at t
5%
1.1675
0.5319
0.3492
-0.0511
0.3232
1.0302
-0.4273
-5%
0.2246
0.1026
0.0674
-0.0099
0.0624
0.1983
-0.0827
5%
-0.9001
0.4161
0.0738
0.2680
-0.0999
-0.0541
-0.1182
-5%
-1.1600
0.5372
0.0953
0.3460
-0.1289
-0.0698
-0.1526
5%
0.1010
0.1295
0.5265
-0.0007
0.2721
-0.0180
0.1641
-5%
0.1792
0.2299
0.9363
-0.0013
0.4834
-0.0320
0.2914
5%
0.9958
0.3026
0.2693
0.7503
0.0120
0.6945
0.2466
-5%
1.0708
0.3253
0.2895
0.8067
0.0130
0.7467
0.2651
5%
0.6110
0.3875
-0.0108
0.0100
0.6710
0.1034
-0.1459
-5%
0.9816
0.6221
-0.0172
0.0160
1.0781
0.1658
-0.2338
5%
0.3649
-0.1396
0.0599
0.0579
0.2838
0.9098
0.1068
-5%
0.3664
-0.1402
0.0601
0.0581
0.2850
0.9135
0.1073
5%
-0.3224
-0.1858
0.0101
0.1624
-0.0367
0.5255
-0.0655
-5%
-0.6956
-0.4012
0.0219
0.3514
-0.0793
1.1393
-0.1414
Innovation at
t − 1 from
AU
HK
JP
SG
UK
US
World
In Table 6, residual based diagnostic tests show that the multivariate VAR-MEGARCH-M
model satisfactorily explains the interaction of the six real estate markets and the world stock
market. For the Ljung-Box test for serial correlation, the test results show significant differences
in residuals after applying our model. Specifically, the squared residuals show no evidence of
autocorrelation, which means such effect was successfully captured by our model. Except for
Singapore, the Ljung-Box statistics show little evidence of either linear or nonlinear dependence
in the standardized residuals. From the result of ARCH LM test for the ARCH effect, we can also
conclude that both linear and nonlinear dependencies in the return series have been effectively
filtered. In addition, we assess the validity of the assumption of constant conditional correlations
by testing for serial correlation in the cross product of the standardized residuals. The Ljung-Box
statistics for 6 and 12 lags are reported in Table 7, which shows no evidence of serial correlation
so that the constant correlation specification appears to be a reasonable parameterization of the
variance-covariance structure of the world stock market and 6 real estate markets.
12
Table 6. Diagnostics for VAR-MEGARCH-M Model
AU
HK
JP
SG
UK
US
World
(A). Moments, maximum, and minimum
Mean
0.0256
0.0226
0.0213
0.0221
0.0251
-0.0005
0.0248
Median
0.0516
0.0497
-0.0310
0.0406
0.0102
0.0071
0.0724
Maximum
2.8910
2.8397
3.4512
3.2332
4.4743
3.6137
3.5086
Minimum
-3.6881
-3.1422
-3.0703
-3.4497
-4.1169
-4.6277
-2.8297
Std. Dev.
0.9848
0.9908
0.9830
0.9625
1.0049
1.0133
1.0128
Skewness
-0.1821
-0.0669
0.2155
-0.0337
0.2451
-0.2075
-0.0688
Kurtosis
3.1568
3.0367
3.1373
3.1546
3.9350
4.6917
3.0163
Jarque-Bera
5.0248
0.6154
**6.5397
0.9094
**35.6178
**96.9644
0.6139
0.0429
0.0475
0.0320
(B). Kolmogorov-Smirnov test for normality
D
0.0286
0.0221
0.0312
0.0158
(C). Ljung-Box statistic for up to 6 and 12 lags
Q(6) for z
6.9969
9.0089
1.5991
*12.3680
7.8866
**13.769
3.2625
Q(12) for z
13.8820
Q(6) for z^2
7.8435
**23.0330
4.0757
**23.687
17.972
16.479
6.5451
2.6928
5.5971
4.0279
3.6820
3.4710
Q(12) for z^2
14.7580
2.8779
6.2617
14.3630
5.0016
12.8780
11.9350
3.2900
(D). ARCH LM test
4 lags
2.7485
2.5413
5.2737
2.9034
3.0007
2.6164
2.7997
8 lags
8.7128
2.6926
*13.8776
3.9907
8.4331
5.5765
2.8700
15.1526
5.7303
*20.6380
4.6582
14.0808
11.3076
2.9166
12 lags
Note: ** indicate significance at 5% level; * indicate significance at 10% level;
5% critical value for Kolmogorov-Smirnov test is 1.32 / T , where T is number of observation.
Table 7. Test for Constant Correlation Assumption
Ljung-Box
Statistic
z1, 2
z1,3
z1, 4
z1,5
z1,6
z1,7
z 2,3
Q(6)
2.3876
9.8672
1.5591
1.5463
3.0301
4.7999
4.6391
Q(12)
7.5874
14.628
6.9724
5.8626
11.536
9.3129
7.7704
z 2, 4
z 2 ,5
z 2, 6
z 2, 7
z 3, 4
z 3,5
z 3,6
Q(6)
5.3378
6.139
3.8306
2.6341
7.4716
4.8931
4.6609
Q(12)
8.3767
8.8735
5.3997
9.4244
10.674
13.22
7.995
z 3,7
z 4 ,5
z 4, 6
z 4, 7
z 5, 6
z 5, 7
z 6, 7
Q(6)
4.0626
4.7224
9.3992
2.988
1.7794
2.014
3.6701
Q(12)
16.446
12.158
19.65
5.2311
6.2157
10.93
5.185
Note: ** indicate significance at 5% level.
13
VI. VAR MEGARCH-M Model with Hedged Indices
Real Estate Hedged Index Model
It has been reported that the unadjusted return indices in real estate do not ideally proxy for the
underlying real estate stock market performance for several reasons. For example, the property
stock market is strongly influenced by the general stock market. To circumvent such problem and
to track real estate performance, Giliberto (1993) derives a price-hedged equity REIT return index,
which tracks the performance of commercial real estate much better than the REIT return per se.
Liang et al (1996) further extended Giliberto’s method to compute total hedged indices, which
recognizes the dividend yield as a component in REIT returns. In this paper we follow a model
that is analogous to Liang’s modle to generate real estate hedged indices for each country in
question.
p
s
Rip,t = a + h * Ris,t + ε i ,t
（6）
Rih,t = Rip,t − h * ( Ris,t − R f )
（7）
h
where Ri ,t , Ri ,t , and Ri ,t are the return series of the property stock indices, general stock
indices and the total hedged indices, respectively. R f is the 3 month US Treasury bill rate,
which proxies for the risk-free rate. The coefficient h represents the hedge ratio associated with
general stock indices.
Figure 2. Weekly Hedged Returns of 6 Countries, Jan 1991 to Dec 2005
Australia Hedged Return
Hong Kong Hedged Return
Japan Hedged Return
6
12
15
4
8
10
2
4
5
0
0
0
-2
-4
-5
-4
-8
-10
-6
-12
1992
1994
1996
1998
2000
2002
2004
-15
1992
1994
1996
1998
2000
2002
2004
1992
United Kingdom Hedged Return
Singapore Hedged Return
20
12
1994
1996
1998
2000
2002
2004
United States Hedged Return
10
8
10
5
4
0
0
0
-4
-10
-5
-8
-20
-10
-12
-30
-15
-16
1992
1994
1996
1998
2000
2002
2004
1992
1994
1996
1998
2000
2002
2004
1992
1994
1996
1998
2000
2002
2004
14
The real estate total hedged index is generated following a two-step approach. First, in equation
(6), the weekly total return indices for the property stock market is regressed, on a 1 year window
rolling basis, against the corresponding total return indices for the general stock market. In the
second stage, the hedged ratio enters into the equation (7) to compute the real estate hedged index,
which will be given by the property stock return minus h times the difference between general
stock return and the risk-free rate.
In addition to the return series used in the previous sections, the weekly MSCI price indice for
each country is used here as a proxy for every general stock market. All indices are based on US
dollar currency and include dividends. The returns for general stock market are also calculated in
percentages computed by multiplying the first difference of the logarithm of property stock market
indices by 100. The 3 month US Treasury bill rate is used as risk-free rate. The descriptive
statistics for each hedged return series are presented in Table 8, and Table 9 displays the
cross-correlation matrix. The hedged returns generally exhibit similar properties as normal returns,
with serial autocorrelation, significant ARCH effect, and a large degree of nonnormality.
Table 8. Summary Statistics of Weekly Hedged Returns for 6 Countries
AU
HK
JP
SG
UK
US
(A). Moments, maximum, and minimum
Mean
0.2140
-0.0002
0.3192
-0.0163
0.3023
0.2039
Median
0.2439
-0.0518
0.4437
0.0212
0.5388
0.1909
Maximum
4.3390
11.5495
14.5971
16.6223
10.0363
9.7649
Minimum
-4.6483
-7.8926
-10.0492
-27.9992
-12.1387
-13.3666
Std. Dev.
1.3657
1.7043
3.4684
3.8933
3.1154
2.4825
Skewness
-0.3021
0.3266
0.0712
-0.2760
-0.0982
-0.0616
Kurtosis
3.6184
7.2339
3.6146
8.0865
3.6323
4.8261
**24.3899
**598.7464
**12.9861
**854.0303
**14.3022
**109.2842
**0.0614
*0.0340
**0.0345
Jarque-Bera
(B). Kolmogorov-Smirnov test for normality
D
*0.0421
**0.0516
**0.0369
(C). Ljung-Box statistic for up to 6 and 12 lags
Q(6) for R
*12.616
**17.378
10.324
**30.321
4.4862
**26.722
Q(12) for R
14.937
*20.796
14.332
**37.746
9.1182
**30.714
Q(6) for R^2
**18.585
**102.24
**57.059
**67.267
**26.492
**32.166
Q(12) for R^2
**24.889
**117.36
**129.48
**98.397
**60.989
**55.716
(D). ARCH LM test
4 lags
**13.7583
**79.1472
**32.7929
**51.9009
**11.1182
**20.9372
8 lags
**18.0608
**82.1166
**59.8611
**55.7437
*23.8914
**26.7929
12 lags
**20.2156
**86.6613
**66.8558
**65.1416
*46.0568
**36.1385
Note: ** indicate significance at 5% level; * indicate significance at 10% level;
5% critical value for Kolmogorov-Smirnov test is 1.32 / T , where T is number of observation.
15
Table 9. Cross-Correlation of Hedged Real Estate Market Returns
AU
HK
JP
SG
UK
US
WD
AU
1.0000
0.0637
0.5317
0.0473
0.4573
0.0586
-0.0308
HK
0.0637
1.0000
0.0933
0.6809
0.0843
0.5234
0.0481
JP
0.5317
0.0933
1.0000
0.1079
0.7723
0.0980
-0.0937
SG
0.0473
0.6809
0.1079
1.0000
0.1001
0.7670
0.0354
UK
0.4573
0.0843
0.7723
0.1001
1.0000
0.1539
-0.0807
US
0.0586
0.5234
0.0980
0.7670
0.1539
1.0000
0.0150
WD
-0.0308
0.0481
-0.0937
0.0354
-0.0807
0.0150
1.0000
Results of VAR MEGARCH-M Model with Hedged Indices
Again, we use the AIC test to determine the VAR lag for the model.
Table 10. VAR Lag Length Criterion
Lag
AIC
Lag
AIC
0
1
2
3
4
5
6
29.2851
29.27403*
29.3100
29.3540
29.3965
29.4449
29.5031
7
8
9
10
11
12
29.55429
29.60778
29.64096
29.70317
29.74367
29.79504
Note: * indicates lag order selected by criterion
The estimated coefficients for mean and volatility spillovers of hedged real estate returns are
reported in Table 11. Generally Speaking, the hedge technique has reduced the degree of
interdependences across these 6 real estate markets and the world stock market in both first and
second moment spillovers.
For the mean equation, it can be seen that the past returns in Australia only have influence upon
its own current returns. Similarly, the past returns in Hong Kong show significant impact on the
current returns in Australia and Singapore. The multidirectional mean spillover effects of Japan,
Singapore, UK and US are highly significant in the estimation, which indicates that the real estate
markets of these countries are highly correlated. The world stock market, still have considerable
power in terms of mean spillover effect. Real estate markets in Australia, Japan, UK and US are
2
all under substantial influence of the world stock market. We also calculated uncentered R
statistics, which range from 0.06%, for the United States, to 2.45% for the world stock market.
The results are consistent with previous findings in that the percentage of variation in hedged
returns that can be explained on the basis of past information is also very small.
In terms of the variance equation, the high degree of volatility persistence is also significant for
each market. The volatility transmission mechanism is asymmetric for Australia, Hong Kong,
Singapore and UK. For the volatility spillover, Australia, Singapore and US are found to be the
least influential markets. The innovation generated in these markets generally stay inside of the
home markets. On the other side, Hong Kong and Japan are the most powerful markets in terms of
volatility transmission to other markets. Except for Australia, all real estate markets receive past
innovations from less than two other markets, which suggests that the real estate markets are less
16
Table 11. Estimated Coefficients for VAR-MEGARCH-M Model with Hedged Returns
AU (i=1)
Variable
Coeff.
Std Error
HK (i=2)
Coeff.
Std Error
JP (i=3)
Coeff.
SG (i=4)
Coeff.
Coeff.
Std Error
UK (i=5)
Coeff.
Std Error
US (i=6)
Coeff.
Std Error
World (i=7)
Coeff.
Std Error
β i ,0
**0.559
0.0293
**-0.5998
0.0379
**0.5754
0.0663
-0.0901
0.0881
**0.6234
0.0640
0.0555
0.0755
**0.4322
0.0513
β i ,1
**-0.097
0.0217
0.0275
0.0314
0.0059
0.0542
0.0212
0.0521
0.0613
0.0532
-0.0420
0.0393
0.0320
0.0437
β i,2
**0.0335
0.0160
-0.0327
0.0271
0.0569
0.0455
**0.1347
0.0505
0.0011
0.0451
0.0009
0.0397
-0.0244
0.0403
β i ,3
**-0.0177
0.0082
-0.0150
0.0114
**-0.0976
0.0248
**-0.0727
0.0218
**-0.1213
0.0227
-0.0294
0.0180
0.0161
0.0168
β i,4
-0.0055
0.0076
-0.0063
0.0132
-0.0388
0.0216
**-0.1916
0.0240
**-0.0940
0.0217
**-0.0944
0.0197
**0.0480
0.0180
β i ,5
**0.0198
0.0085
0.0003
0.0125
0.0310
0.0239
**0.0710
0.0243
**0.0675
0.0223
0.0358
0.0194
0.0333
0.0190
β i ,6
**0.0267
0.0124
0.0178
0.0187
**0.0680
0.0304
**0.1022
0.0345
**0.1771
0.0307
**0.1377
0.0273
-0.0274
0.0242
β i ,7
**0.0345
0.0140
-0.0010
0.0230
**-0.1149
0.0441
0.0531
0.0396
**0.0799
0.0364
**0.1366
0.0303
-0.0222
0.0350
ξi
**-0.1613
0.0210
**0.2504
0.0193
**-0.0159
0.0079
0.0052
0.0096
**-0.0305
0.0082
0.0250
0.0145
**-0.109
0.0169
α i ,0
**0.0472
0.0138
**0.0765
0.0015
**0.7714
0.0198
**0.0492
0.0012
**1.1119
0.0320
**0.4056
0.0182
**0.0337
0.0002
α i ,1
**0.0220
0.0084
0.0037
0.0095
0.0105
0.0128
0.0057
0.0055
0.0182
0.0147
0.0102
0.0147
0.0038
0.0033
α i ,2
**0.0843
0.0258
**0.1253
0.0424
**0.2002
0.0439
0.0216
0.0289
**0.1810
0.0541
-0.0789
0.0475
**-0.0439
0.0180
α i ,3
**-0.0584
0.0268
0.0693
0.0375
**0.1457
0.0498
**0.0787
0.0172
**0.1369
0.0452
**0.1945
0.0490
**0.1613
0.0113
α i ,4
**0.0197
0.0083
-0.0011
0.0088
0.0150
0.0144
-0.0021
0.0039
-0.0164
0.0221
-0.0074
0.0176
**-0.0048
0.0004
α i ,5
**0.0981
0.0284
-0.0493
0.0333
0.0647
0.0488
-0.0226
0.0182
0.0736
0.0475
**-0.1486
0.0427
**-0.0225
0.0101
α i ,6
0.0442
0.0263
-0.0198
0.0348
-0.0405
0.0600
-0.0176
0.0212
-0.0290
0.0509
**0.2625
0.0417
-0.0181
0.0150
α i ,7
-0.0201
0.0219
0.0395
0.0280
**0.1255
0.0593
**-0.0440
0.0209
0.0793
0.0589
0.0850
0.0460
**-0.0895
0.0105
γi
**0.9195
0.0235
**0.9150
0.0055
**0.6710
0.0069
**0.9790
0.0009
**0.4795
0.0130
**0.750
0.0112
**0.9639
0.0010
δi
**4.6990
0.2062
**-0.3743
0.1365
0.0513
0.0353
**3.8660
0.1891
**-0.3535
0.1279
0.0477
0.1341
0.0696
0.0748
R2
0.0209
0.0006
0.0120
0.0089
0.0158
0.0062
0.0245
Note: ** indicate significance at 5% level.
17
correlated in the second moment after filtering out the impact from general stock markets using
hedge technique. Moreover, the world stock market only has influence on the real estate markets
in Japan and Singapore. The past innovation generated in the United States has no influence on
other real estate markets, which is significantly contrary to previous result in which it affects 5
other markets in question. One possible reason may lie in that the general stock market in the US
is so powerful that it influences many other markets in the world, but such effect has already been
filtered in the hedged returns so that a significant volatility spillover from US real estate market to
other markets is not observed. This finding reconfirms that the hedged returns do show some
different characteristics when compared to normal return series. The intercorrelations within Asian
markets are significantly higher than those from UK and US, thus suggesting a considerable
degree of continental segmentation in real estate markets.
Table 12. Diagnostics for VAR-MEGARCH-M Model with Hedged Returns
AU
HK
JP
SG
UK
US
World
(A). Moments, maximum, and minimum
Mean
-0.0265
0.0003
-0.0297
0.0021
-0.0365
-0.0037
0.0095
Median
-0.0120
-0.0131
0.0237
-0.0047
0.0182
-0.0149
0.0319
Maximum
3.2155
3.3214
3.4348
3.2644
3.1213
3.5006
2.8860
Minimum
-3.4564
-3.9140
-3.0641
-3.0765
-3.0022
-3.8416
-3.3972
Std. Dev.
0.9976
0.9834
1.0116
1.0061
1.0177
1.0018
1.0293
Skewness
-0.1656
-0.0334
-0.0179
0.0093
0.0001
0.0064
-0.1497
Kurtosis
3.2876
3.7717
3.0617
2.9542
3.1072
3.3604
3.1048
Jarque-Bera
6.1305
19.1226
0.1622
0.0779
0.3663
4.1453
3.2091
0.0318
0.0232
0.0217
(B). Kolmogorov-Smirnov test for normality
D
0.0282
0.0288
0.0269
0.0202
(C). Ljung-Box statistic for up to 6 and 12 lags
Q(6) for z
2.5065
**17.612
2.8505
**15.721
3.9440
**14.784
4.8756
Q(12) for z
5.4454
**21.837
10.2370
**26.197
4.8908
**32.8000
11.4470
Q(6) for z^2
7.3356
4.7008
7.6972
1.6900
7.1670
3.7477
5.2882
Q(12) for z^2
9.8842
8.3220
**43.0230
3.0604
**21.4850
9.1613
11.7940
(D). ARCH LM test
4 lags
6.5187
2.8400
5.9074
1.4941
2.6531
1.1910
5.3043
8 lags
9.3974
5.4175
**22.6411
1.8971
14.3935
4.8272
4.5283
10.0864
7.9604
33.4713
3.2471
19.9522
7.7495
10.8471
12 lags
Note: ** indicate significance at 5% level;
5% critical value for Kolmogorov-Smirnov test is 1.32 / T , where T is number of observation.
The diagnostic test results are presented in Table 12. Similar to the model with normal indices,
the VAR-MEGARCH-M model also shows satisfactory power to explain the interaction of the six
real estate markets and the world stock market in terms of both mean and volatility aspects. The
linear and nonlinear dependences have been well filtered, except that squared residuals of Japan
18
and UK are significant in Ljung-Box test of 12 lags, and Hong Kong still shows some ARCH
effect in the 8 lagged ARCH LM test. Table 13 displays the results of Ljung-Box test for cross
product of standardized residuals, which indicates no rejection of the assumption of constant
correlation between return series.
Table 13. Test for Constant Correlation Assumption
Ljung-Box
Statistic
z1, 2
z1,3
z1, 4
z1,5
z1,6
z1,7
z 2 ,3
Q(6)
3.7141
6.7890
7.1088
2.7856
7.1063
4.1989
2.5000
Q(12)
6.6204
14.1700
8.7515
11.7440
11.8150
14.969
17.0560
z 2, 4
z 2 ,5
z 2, 6
z 2, 7
z 3, 4
z 3,5
z 3,6
Q(6)
5.6722
3.4242
3.2741
4.4922
6.7250
8.1962
5.2914
Q(12)
7.3551
16.6610
9.5154
10.6480
15.258
15.2800
11.5660
z 3,7
z 4 ,5
z 4, 6
z 4, 7
z 5, 6
z 5, 7
z 6, 7
Q(6)
3.9175
5.7988
1.0524
9.2805
2.2360
4.4905
3.0311
Q(12)
14.102
8.8798
5.3342
14.8500
6.4280
15.7790
18.3490
Note: ** indicate significance at 5% level.
VII. Conclusion
In this paper, we analyze the dynamic interdependence of selected major real estate markets and
the world general stock market simultaneously during the period of Jan 1990 to Dec 2005. The
dynamic first and second moment interactions among these markets are investigated using the
VAR MEGARCH-M model. This model allows us to examine mean and volatility spillover effects
among these markets and account for potential asymmetries that may exist in the volatility
transmission mechanism. We also construct hedged return indices for each market and compare
them with normal return indices to see whether the interactions across markets are actually the
result of general stock market spillovers.
The empirical findings can be summarized as: (1) The VAR MEGARCH-M model generally
well captures market interactions among the 6 real estate markets and the world stock market. (2)
In terms of lead-lag relationships, Australia, Japan, and US are found to play major roles in mean
spillovers, while Australia, Singapore and US are the most influential market in the transmission
of volatility to other real estate markets. The world stock market has substantial impact upon
worldwide real estate markets in both mean and volatility spillovers. (3) It is concluded that the
multidirectional nature of both mean and variance spillover effects suggest that the 6 major real
estate markets and the world stock market are highly correlated and each of them plays roles as
information producers as well as receivers. (4) The asymmetric effects are observed for most of
the real estate markets except the US market. Through innovation impact analysis, we are able to
specify the sign and magnitude of volatility spillovers among these markets. (5) Comparing with
normal indices, hedged real estate indices do filter out noises from general stock markets, and thus
lead to different results in both mean and volatility transmission. (6) With hedged indices, the
model shows that the real estate markets are more significantly correlated within Asia countries.
19
Innovations generated in the United States are even found to have no influence upon other markets.
These results suggest a considerable level of continental segmentation among real estate markets.
For the portfolio managers or other investors dealing with securitized real estate stock, these
results provide several important implications. First, there is clear evidence of information flows
across these real estate markets. Due to the immobile nature of the underlying physical assets, the
securitized real estate markets are expected to be less globally integrated than other financial
assets. In our analysis, however, international property stock markets do well interact with one
another. As a result, the benefits to international diversification of investments in real estate stocks
may become less attractive. Second, Australia and the United States seem to exert more influence
over other markets. For the investors who are active in other property markets around the world,
this implies more caution needs to be placed on news arriving from these two real estate markets,
as they may have significant impacts upon local securitized property prices. Third, the
considerable difference between empirical results of the normal and total hedged return series,
together with the evidence of significant mean and volatility spillover effect from the world stock
market, suggest that investors should always keep in mind that in the short run the highly
intercorrelations of the real estate markets may be partially attributed to the highly correlations
between the stock markets. In the long run, if the securitized real estate market will finally reflect
the prices of the underlying realty assets, which are expected to be less correlated, the empirical
results may be different from what have been discussed here. Finally, the observation of
asymmetric effects on volatility also highlights one other important investment consideration.
Investors will be wise to note the benefits of diversification are possibly smaller than what would
normally be expected. As during the bear markets, when a large amount of negative news has been
seen, the correlations tend to actually increase.
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