CRES: 2005-001
REAL ESTATE RETURN VOLATILTY AND SYSTEMATIC RISK: EVIDENCE FROM
INTERNATIONAL MARKETS
Kim Hiang LIOW, Department of Real Estate, National University of Singapore
Associate Professor (Dr) Kim Hiang LIOW
Department of Real Estate
National University of Singapore
4 Architecture Drive
Singapore 117566
Tel: (65)68743420
Fax: (65)67748684
Email: rstlkh@nus.edu.sg
24 January 2005
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REAL ESTATE RETURN VOLATILTY AND SYSTEMATIC RISK: EVIDENCE FROM
INTERNATIONAL MARKETS
Abstract
This study empirically examines the dynamics of conditional returns, volatility and systematic risk in ten developing and
developed real estate markets and two world market indexes (i.e. world real estate and world stock). We find
clustering, predictability, strong persistence and asymmetry in country-specific and global market conditional volatility.
Moreover, developing real estate markets display higher conditional volatility and persistence than developed markets.
The world real estate market volatility has a statistically significant positive impact on time-varying real estate market
betas for developing real estate markets of Asia-Pacific, Hong Kong, Singapore and Malaysia, and a statistically
significant negative impact on systematic risk for mature real estate markets of Europe and the UK. Additionally, the
extra country–specific market volatility and global market volatility during the Asian financial crisis period seem to
impose a larger size influence than the volatility during total period in some markets. Based on comparisons of insample forecast errors, our findings appear to favor time-varying real estate betas relative to a world real estate index
over a world stock index. Our findings have significant implications for understanding real estate market integration and
global capital markets.
1.
Introduction
An extensive literature is available on the temporal behavior of returns and volatility on different national
/regional stock markets. On the other hand, far less attention has been given to this issue in the real estate literature
due to the lack of longer and higher frequency (such as monthly or weekly) international time series on performance
measurement in real estate. Consequently international investors possess little knowledge on the dynamics of
conditional returns and volatility of major national real estate markets. Additionally, research results on national stock
markets might not be automatically extended to national real estate markets as the underlying risk-return performance
of real estate is likely to be significantly different from that of stock markets in the short-, medium-, and long-run.1
Moreover, while international stock markets are becoming more and more correlated with each other as the world
economy is increasingly global, international real estate markets are still largely segmented. In recent years, although
much of the property research has focused on performance analysis and the inter-relationships between direct and
listed real estate markets, there is no comparable research work devoted to investigation of conditional returns,
volatility and systematic risk of national real estate markets.
Real estate is the world’s biggest business accounting for approximately 15 percent of global gross domestic
product with assets of US$50 trillion compared with US$30 trillion in equities (Bloomberg, 2004). With this enormous
amount of equity in real estate, there is an increasing need for international investors to further understand the
conditional returns, volatility and systematic risk of real estate, which are essential inputs in their asset allocation
process, especially more so when real estate is treated as an alternative investment class that potentially offers more
attractive returns, together with hedge funds, private equity, commodities and other derivatives, as compared to the
more common types of investments such as equities and bonds (Bloomberg, 2004). Furthermore, listed real estate has
become an increasingly important property investment vehicle in Asia and Internationally (Steinert and Crowe, 2001).
With other recent studies such as Conover et al (2002) that highlight the diversification benefits of including
international listed real estate in a mixed asset portfolio, considerable attention has been given to various aspects of
property company performance in Asia and Europe. Consequently a comprehensive study of time-varying returns,
Another research is at present underway to examine the possibility that real estate returns exhibit certain common
return-volatility characteristics that are usually found in stock markets.
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volatility and systematic risk dynamics of international listed real estate markets such as in the current paper is
expected to offer substantial insights to international investors and global portfolio managers in understanding the
investment behavior and portfolio implications of listed real estate so as to achieve an efficient mean-variance frontier.
Additionally, policy makers and market regulators can benefit from this study as more and more Asian economies are
interested in developing REIT type securitized real estate products.
This paper contributes to the ongoing investigation in international real estate asset pricing. It presents
empirical evidence on the dynamics of conditional returns, volatility and betas for the real estate markets of AsianPacific, Australia, Hong Kong, Japan, Singapore, Malaysia, the Philippines, Europe, the United Kingdom and the
United States, and two world market indexes (i.e. world real estate and world stock). Our empirical work contains two
major components that are of interest to International CAPM (Solnik, 1974): volatility and systematic risk. This is of
great significance as the world’s capital markets are generally becoming more integrated (Bekaert and Harvey, 1995).
First, using an ARMA (1, 1) – GJR – GARCH (1, 1) – M model, we focus on individual real estate markets’ volatility
persistence and asymmetries in the time-varying volatility process and further compare them to those of a world real
estate index and a world stock market index, respectively, which are used as two proxies for a global benchmark. An
array of diagnostic show that the ARMA (1, 1) – GJR – GARCH (1, 1) – M model captures the time-varying dynamics
of real estate return volatility in the markets under investigation reasonably well. Estimating the volatility of stock
returns is essential for measuring the systematic risk of a portfolio. Then, two time-varying betas (i.e. beta relative to
world real estate and beta relative to world stock market) are estimated for all ten real estate markets by utilizing the
method of Schwert and Seguin (1990) (henceforth SS). This empirical work is motivated by studies in international
asset pricing, such as Adler and Dumas (1983), Ling and Naranjo (2002), amongst others. Within the ICAPM
framework, the beta may be understood as an index of the systematic risk for a country’s real estate market with
respect to the world real estate market or world stock market. In addition, the effects of the Asian financial crisis on the
time-varying real estate betas of the countries are investigated. Additional findings suggest that the estimates of
conditional beta relative to the world real estate index are preferred to estimates generated using the world stock
market index. Consequently our international study is significant and provides an opportunity for institutional investors
to understand and compare the temporal behavior of real estate market volatility and systematic risk dynamics of these
major national markets. From the academic perspective, the stochastic properties of conditional returns, volatility
persistence and time-varying betas have important implications for equilibrium asset pricing models such as ICAPM
and APT and pricing of options written on real estate stock indexes.
To provide a background for this study, Section 2 reviews related literature on conditional volatility and beta
in the context of international asset pricing. Section 3 describes the data used in this study and presents key statistical
properties of real estate returns. Section 4 outline an ARMA (1, 1) – GJR – GARCH (1, 1) – M model for investigating
conditional return and volatility, the SS method used to estimate time-varying betas and a dummy regression model to
study the effect of the Asian financial crisis on time-varying real estate betas. Section 5 discusses the empirical results.
Section 6 contains concluding remarks.
2.
Related Literature
3
The theoretical framework for this research is risk-return behavior of international real estate. International
investors’ understanding of the risk-return characteristics of real estate has been greatly enhanced following the
development of modern portfolio theory, CAPM, ICAPM and APT in mainstream finance. With the development of
securitized real estate investment vehicles such as real estate stocks and REITs, empirical studies on their return,
volatility and systematic risk dynamics on national real estate markets are important in global real estate investment
and optimal portfolio allocation
It is well documented that the volatility of stock returns can change over time and that both expected returns
and risks can be time-varying. A substantial and growing body of literature is using conditionally heteroscedastic
models to analyze time-varying volatility in national stock markets. Financial economists have employed ARCH model
(Engle, 1982), GARCH model (Bollerslev, 1986), GARCH-M (Engle et al. 1987) and EGARCH model (Nelson, 1991) to
study the stochastic behavior of returns over time. Ng et al. (1991) and Lee and Ohk (1991) use ARCH-type models to
capture the time-varying volatility of stock returns in Pacific Basin stock markets. The general conclusions from these
stock market studies are that stock return volatility is highly persistent and probably is an integrated process. Thus risk
premia are also highly persistent and volatility shocks can have large effects on price. Furthermore there is some
evidence that the conditional variance of stock returns respond asymmetrically to past information in the developed
and Asian stock markets (Koutmos, 1999). Due to the inability of GARCH model to consider the asymmetric effect
between positive and negative stock returns, the weighted innovation models such as EGARCH (Nelson, 1991),
Threshold Autoregressive GARCH (TGARCH – Zakoian, 1990) and GJR-GARCH (Glosten et al. 1993) have been
advanced. This line of research highlights the time-varying asymmetric effect by demonstrating that a negative shock
to returns will generate more volatility than a positive shock of equal magnitude. In real estate literature, however, there
are very few studies investigating the dynamics of returns and volatility in listed real estate and the extent to which
these dynamics are similar between developing /emerging and developed real estate markets (see for examples:
Stevenson, 2002; Bond et al. 2003 and Liow et al. 2004).
Examining the presence of time-varying beta across a wide spectrum of national real estate markets is also
important as there is equivalent stock market evidence suggesting that estimated betas of the ICAPM display
statistically significant time variation. The evidence of beta instability has strongly influenced international asset pricing
research where beta risk is defined relative to a global market proxy (Bekeart and Harvey, 1995). This is particular so
given the increased interest in international real estate allocation and diversification and continuing globalization of the
world’s capital markets. Since international real estate markets are segmented (Wilson and Okunev, 1996). There are
benefits to be gained from diversification. International real estate stock diversification is more effective than
international stock diversification (Eichholtz, 1996). Furthermore, there is evidence of a worldwide factor in international
direct real estate (Goetzmann and Wachter, 2001) and international indirect real estate (Ling and Naranjo, 2002).
Finally, Bond et al. (2003) also find that global and country-specific market risk factors are important.
Similar to the beta coefficient of the CAPM (or a single index model) for an individual property investment,
the beta coefficient of the ICAPM for a country’s real estate market may defined as the ratio of the covariance between
the expected (excess) returns on the country’s real estate market and the expected (excess) returns on the world
market portfolio to the variance of the expected (excess) returns on the world market portfolio. Hence the beta may be
understood as an index of the systematic risk for a country’s real estate market with respect to the market and is one of
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the three important factors in the ICAPM that considers the global pricing of real estate market risk. The real estate
literature is silent as to which proxy is appropriate to represent the world market although the Morgan Stanley Capital
International (MSCI) world index has been commonly used in international stock pricing (Fama and French, 1998) and
international real estate pricing studies (Bond et al, 2003). One significant implication is that international real estate
investors are concerned about the contribution that a particular country will make to the risk of their global portfolio
benchmark. This task is made even more challenging that the country-specific real estate risks are likely to display
temporal instability.
It is not the intention of this study to debate on which world indexes (i.e. world real estate or world stock) are
a good proxy for international real estate investors since the choice of proxy for the world market portfolio is mainly
dictated by the type (i.e. whether real estate or stock) and level of market integration that are available to investors and
their portfolio objectives. Consequently the answer to this question is not immediately obvious. Furthermore, as
previous evidence has suggested that real estate markets are less integrated with global stock market (although this
issue is beyond the scope of current study), international investors may find it useful to have a global real estate
benchmark in their capital asset pricing, as beta (market risk) estimated relative to a world real estate index may turn
out to be adequate and more relevant for international real estate asset pricing. Instead, we explore time-varying
volatility and systematic risk behavior of several developing and developed real estate markets against a world real
estate index and a world stock index. A range of issues are examined, including volatility persistence and asymmetry
characteristics, unconditional beta and instability, estimation and behavior of time-varying real estate betas during the
Asian financial crisis period and choice of a global benchmark in international real estate asset pricing.
3.
Research Data
As in many previous academic real estate studies, we use returns on real estate stocks to proxy for real
estate performance. This choice is mainly justified by the availability of longer time series data and higher frequency
data (such as monthly and weekly) for real estate stocks. Whilst the adequacy of this proxy has been extensively
debated amongst real estate practitioners and researchers, it remains the only substantive “real estate” series
appropriate for any rigorous statistical analysis.
The data used in this study are the weekly Dow Jones Global real estate stock indexes2 for Asian-Pacific
regions / countries (Asian-Pacific,3 Australia, Hong Kong, Japan, Singapore, Malaysia, the Philippines, Indonesia and
Thailand), Europe,4 the United Kingdom, and the United States. DJGI starts collecting weekly real estate price data in
2 The Dow Jones Global Indexes (DJGI) provides comprehensive world indexes to help international investors in
portfolio management and benchmarking. DJGI calculates indexes on 80% of the investable market capitalization in 34
countries including both developed and developing markets. In addition, the DJGI family includes indexes for each of
the 10 economic sectors, 18 market sectors, 51 industry groups and 89 subgroups defined by the Dow Jones Global
Classification Standard. Real estate index (code: 8730) is one of the industry sector indexes and comprises two subsector indexes (not available from Datastream): (a) code 8733: real estate holding and development; and (b) code
8737: real estate investment trusts (http://djindexes.com)
Countries included in the Asian/Pacific index are Indonesia, Malaysia, the Philippines, Singapore, Taiwan, Thailand,
Australia, New Zealand, Hong Kong, Japan and South Korea.
3
Countries included in the Europe Index are: the United Kingdom, Austria, Belgium, Denmark, Finland, France,
Germany, Greece, Ireland, Italy, Norway, Portugal, Spain, Sweden, Switzerland and Netherlands.
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January 1992. Therefore our weekly data start from January 7, 1992 and cover through Sep 28, 2004 for a total of 664
observations. Real estate is an important asset in Asian-Pacific economies and it also plays a very crucial role in
individuals’ investment portfolio. Among them, Japan is a significantly developed economy in Asia and has a long
history of listed real estate. Other countries like Australia, Hong Kong and Singapore have track records of listed real
estate companies that play a relatively important role in general stock market indexes. Our research interest in AsianPacific listed real estate is further motivated by this great opportunity to understand the conditional returns and volatility
of real estate investment in a market structure that is different from the US, the UK and Europe – i.e. land scarcity, high
population density, lower initial yield and relatively high real estate values. Additionally, real estate stocks in Asia are
generally aggressive with high systematic and idiosyncratic risks. Consequently, the Asian-Pacific economies provide
an interesting setting to examine the dynamics of time-varying real estate risk- return in developing economies that
have experienced a rapid economic growth and deregulation of capital markets in recent years. The USA, the UK and
Europe markets are included to provide a comprehensive study of major world real estate markets. They further permit
us to compare and contrast the differences in the nature and degree of volatility process and systemic risk between
developed and developing/ emerging real estate markets.
Weekly real estate stock returns (R) are obtained by taking the logarithmic difference of the stock index (P)
times 100. That is, R t = 100 * (log P t – log P t – 1). In addition, two alternative proxies are used to represent a world
market portfolio, namely, the weekly Dow Jones World Real Estate Index (DJWRE) and weekly Dow Jones World
Stock Market index (DJWALL). All data are expressed in US dollars.
To provide a general understanding of the nature of each real estate market return, Table 1 presents
summary statistics for the return series of the 12 regions /countries and the two world market portfolios. As can be
seen, the sample means of all return series are statistically insignificant at the conventional probability levels. The UK
has the highest weekly mean (0.13%), followed by Australia (0.12%), while Indonesia has the lowest one (-2.40E-05).
Judging from the sample standard deviations, as expected, developing Asian real estate markets are characterized by
a higher unconditional volatility, compared to developed markets of the UK, the USA and Europe. The Thailand real
estate market appears to be the most volatile (17.28%). When comparing the returns of DJWRE and DJWALL, it was
found that the mean return on DJWALL is slightly higher than that of DJWRE (0.09% and 0.08%, respectively) but the
standard deviation is smaller (2.07% and 2.35%, respectively). Another interesting characteristic of the weekly data is
the significant measures of skewness and kurtosis. With two exceptions, the statistics for skewness and excess
kurtosis suggests all series are significantly skewed and leptokurtic relative to the normal distribution.5 However it is
evident from the table that the index of excess kurtosis is considerably higher in the developing real estate markets.
The implication is that for these markets, big innovations of either signs are more likely to be observed at least
unconditionally. Finally, the DJWRE and DJWALL are both positively skewed (0.802 and 0.398), exhibit moderate
kurtosis (4.820 and 1.887) and fail the test of normality (Jacque Bera values of 714.06 and 116.08, respectively).
(Table 1 here)
The presence of intertemporal dependencies in the returns and squared returns are tested by means of the
Ljung-Box portmanteau test (LB). The LB statistic tests the hypothesis that autocorrelations up to the nth lags are
5
The skewness statistics for the UK and USA markets are statistically insignificant.
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jointly statistically significant. The calculated LB statistics, given by Q(20) and Q2(20) are also reported in Table 1. As
can be seen, except for Indonesia, Thailand, Europe, the UK and the US, the hypothesis of linear independence is
rejected at the 5 percent level for the remaining seven markets and the two world portfolios, implying that the
conditional mean of the distribution of real estate stock returns is a function of either past returns or past residuals. On
the other hand, independence of the squared return series is only accepted at the 5 percent level for Indonesia,
Thailand and Europe only. Furthermore, the LB for the squared returns is several times higher than that of returns
themselves in many markets and the two world indexes. The implication is that higher-moment dependencies are
much more pronounced. The dependencies are comparable with the volatility clustering phenomenon that has been
documented for stock markets. Finally, the results for the augmented Dickey Fuller (ADF) and the Phillips and Peron
(PP) tests presented in Table 1 depict that a unit root is present in the logarithm of all the real estate stock indexes and
the two world market indexes. On the contrary, the hypothesis of a unit root is rejected for each of the return series.
Consequently, further investigation of the short-term dynamics of the real estate markets requires first differencing.
4.
Research Methodology
The principal task in this research is to search for the dynamics of real estate market volatility and systematic
risk in an international context. A fairly extensive formal stock market literature has been developed on various
methodologies in the estimation of conditional volatility and systematic risk. As far as this study is concerned the main
points are as follows.
4.1
Conditional Returns and Volatility
Based on the results of Table 1 that suggests the presence of linear and second-moment dependencies, and
to further incorporate the asymmetric effect on conditional volatility as suggested in the literature, we develop an ARMA
(1, 1) – GJR-GARCH (1, 1) (Glosten, Jagannathan and Runkie, 1993) - in mean [henceforth ARMA (1, 1) – GJRGARCH (1, 1) – M] model with the following specifications 6:
Conditional mean equation:
R jt = µ + c1 * R j ,t −1 + c 2 * ε j ,t −1 + c3 * D97 + γh jt + ε jt
………..(1)
ε jt / Ω t −1 ~ N (0, h jt )
Conditional variance equation:
h jt = ϖ + ϑε 2 j ,t −1 + θh j ,t −1 + ηI t −1ε 2 j ,t −1 …………..(2)
In consistent with the literature on conditional heteroscedasticity of stock returns (Bollerslev et al, 1992), the
dimensions of the ARMA and GJR-GARCH components are all unity in order to achieve parameter parsimony. As
reported by Bollerslev et al. (1992), GARCH (1, 1) model appears to be sufficient to describe the volatility evolution of
stock return series.. Moreover, some other empirical studies have shown that a GARCH (1, 1) model provides a
reasonable fit for stock return data (Baillie and DeGennmaro, 1990; Schwert and Seguin, 1990). Finally, the
dimensions are also tested on the basis of log-likelihood ratio tests.
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In the conditional mean equation, the real estate stock return, R jt is assumed to be linearly related to its
lagged one-period returns and lagged one-period error term (or market innovation), its conditional variance h and a
time dummy D97 which takes a value of one for the period July 1997 – June 1998 and zero otherwise. Our main
intention in including the time dummy is to control for regime swifts in Asian real estate markets following the eruption
of Asian financial crisis in July 1997. There is some evidence of a reduction in real estate returns and an increase in
real estate volatility and correlations with other assets following the Asian financial crisis (Kallburg, Liu and
Pasqquariello, 2002). The relationship between stock return and volatility is captured by the estimated coefficient
γ
and we would expect
γ
to be positive for risk-adverse investors and the term
γ
h represents the market risk
premium for expected volatility. This is consistent with most asset pricing models that postulate a relation between
expected return and some measures of risk.
In the conditional variance equation, the conditional variance h is specified as a function of past conditional
variances ( ht −1 ) and past squared innovations ( ε
2
t −1 ).
In addition, the asymmetric effect on conditional variance is
incorporated by using an indicator variable I t −1 to differentiate between the positive and negative shocks.7
The I t −1 variable takes a value of 1 when the previous shock is negative and 0 otherwise. The GJR (asymmetric)
effect is captured by the hypothesis that
η >0.
Hence a positive
η implies
that a negative innovation increases
conditional volatility. When η =0, the model reduces to a standard GARCH (1, 1) – M specification. The ARMA (1, 1) –
GJR - GARCH (1, 1) – M model is estimated using the Approximate Maximum Likelihood method (Laurent and Peters,
2002) and imposing restrictions that
ϖ ,ϑ ,θ
are all >0 to ensure that the conditional variance is positive. As
skewness and kurtosis are important in our estimations, the errors of the log likelihood functions are best represented
by a skewed student distribution.8
4.2
Time-Varying Betas
Using the ICAPM, each real estate market’s beta can be estimated from using equation (3):
R jt = α j + β jt Rmt + ε jt -------------------------(3)
In the GARCH literature, it has been well documented that good news and bad news might have different impacts on
predicting future volatility. This asymmetric effect on conditional variance has been investigated using the Exponential
GARCH (EGARCH) models (Nelson, 1991), the Threshold GARCH (TGARCH) models (Zakoian, 1994) and the GJRGARCH models (Glosten et al.1993). In their study of daily stock returns in the Japanese market, Engle and Ng (1993)
find that the TAR-GJR-GARCH model (autoregressive form of GJR) performs better than other asymmetric model in
Monte Carlo experiments. Our research is the first piece of work to model asymmetries in volatility in real estate
markets using GJR-GARCH methodology.
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Gaussian GARCH processes are unable to account for the leptokurtosis of most return series, an issue that is very
relevant when using developing real estate market data. Moreover, the other two types of log-likelihood function, the
GED and student-t distributions (non-normal) may also account for fat tails, but they are symmetric. We also repeat the
model estimates with all three types of density functions (i.e. skewed student-t, student-t and GED) and the loglikelihood ratios are higher in almost all cases with a skewed student-t distribution.
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Where R jt is the real estate stock return for market j during week t, Rmt is the returns for the two world
market portfolios (DJWRE and DJWALL, respectively), and
ε jt is an error term. The coefficient β jt is a time-varying
beta and measures systematic risk in market j. Following Koutmos et al. (1994) and SS (1990), an augmented market
model of (4) is developed from (3) to estimate β jt :9
R jt = φ j + θ j Rmt + ψ ( Rmt / hmt ) + ε jt ----------------(4)
Where hmt is the conditional variance of return for the respective world market portfolios.The time-varying
beta ( β jt ) for each real estate market is given by (5):
β jt = β j +
ψj
hmt
………………..(5)
From equation (5), ψ has special meaning. A positiveψ for market j implies that its systematic risk varies
inversely with world market volatility. On the contrary, a negative ψ for market j implies that systematic risk and world
market volatility are positively related.
The following multiple regression (equation 6) is applied to study the effect of the Asian financial crisis on the
time-varying real estate betas. The Asian financial crisis of 1997-1998 has resulted in the rise of observed volatility of
the financial and real estate markets in the region and around the world. In particular several countries in the Far East
experienced a plunge in the external values of currencies, stock and real estate prices and a sudden reversal of private
capital flows from June 1997 onwards. Investors may further perceive a rise in the stock /real estate market volatility as
an increase in the stock / real estate market beta. In the present context, the central question here is whether the
conditional volatility of own market and / or the conditional volatility of global (stock / real estate) market has imposed a
direct effect on the beta of the real estate market during the Asian financial crisis.
β jt = c j + γ j D97 + α 1 (CV jt ) + φ1 (CV jt * D97 ) + α 2 ( MCVt ) + φ 2 ( MCVt * D97 ) + ε jt …….(6)
Where
β jt is market j’s time-varying beta as defined in equation (5), CV jt and MCVt
are the conditional
volatility of the individual markets and world market portfolio respectively. The time dummy (D97) is included to test the
extra influence of the volatility during the Asian financial crisis period. The dummy takes the value of 1 from July 1,
1997 to June, 30, 1998 and it is 0 during other periods. The variables CVD97 and MCVD97 measure the potential
effect of the excess volatility of the individual market and the world market, respectively, during the financial crisis on
the beta. The parameters
α 1 and α 2 measure the effect of the own-market conditional volatility and the world market
volatility on the beta of the real estate market during the total period, respectively. The significance and the sign of the
time dummy coefficients imply a direct effect on the beta of the market. Moreover, if
φ1 and φ 2 are significant and
positive, then own-market volatility and global market volatility during the crisis will lead to an increase in the beta of
Stock market studies utilizing the SS approach include Koutmos et al. (1994) and Episcopos (1996). Besides the SS
technique, two other techniques have been developed in the stock market literature: the M-GARCH and Kalman Filter
approaches. Overall, these three approaches to modeling time-varying betas have performed adequately relative to
traditional time-invariant methods (Brooks et al. 2002).
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the market under study. For each market, we examine the effect of the Asian financial crisis on two measures of timevarying betas: i.e. beta relative to DJWRE and beta relative to DJWALlL.
Finally, a comparison of the forecasts is conducted between the conditional beta estimates relative to
DJWRE and conditional beta estimates generated using DJWALL and the results are discussed in terms of
international real estate market pricing.
5.
Empirical Results
5.1
Returns and volatility
Table 2 presents estimation results from the ARMA (1, 1) – GJR - GARCH (1, 1) – M model.10 We first
consider the mean equation. The results indicate that both the AR (1) and MA (1) components are statistically
significant for Hong Kong, Japan, Singapore, the UK, the US and DJWRE index. Likewise, an AR (1) process is
appropriate for Philippines. On the other hand, the results provide no evidence to support the significance of the AR
and MA components for Asian-Pacific, Australia, Malaysia, Europe and DJWALL index. Consistent with expectation,
we also find a significant and negative Asian financial crisis coefficient (C3) each for Asian-Pacific, Hong Kong, Japan,
Singapore, Malaysia and the Philippines real estate markets. Finally, we are unable to find any significant statistical
relationship between the expected return and conditional volatility ( γ - the price of domestic market risk), with the
exceptions of Asian-Pacific, Hong Kong and the Philippines real estate markets. Hence, these results reject the
hypothesis of full real estate market segmentation over the entire sample.
(Table 2 here)
With respect to the estimates of the conditional variance equation, the results of Table 2 indicate that
conditional heteroskedasticity is present in the real estate return series of all 10 markets and the two world market
portfolios. The log-likelihood ratio (between 1002.22 and 1770.46) implies that GJR – GARCH (1, 1) is able to capture
the temporal dependence of volatility reasonably well. The GARCH parameter estimates ( θ ) are all statistically
significant and are larger than the ARCH coefficient estimates ( ϑ ) implying that the prediction of the volatility is
dominated by the AR component. Volatility persistence, measured by ( ϑ + θ ) is high, but always less than 1 for all
markets. In particular, the Singapore real estate market displays the highest volatility persistence (0.9562), followed by
Japan (0.9497), Philippines (0.9314) and Malaysia (0.9258), while the USA market has the lowest one (0.5866). In
general, volatility persistence is higher for developing Asian-Pacific real estate arkets. Likewise, the two world market
portfolios have volatility persistence values of 0.7514 (DJWRE) and 0.8619 (DJWALL) respectively. With the
exceptions of Australia, Singapore and Malaysia, the hypothesis of no asymmetric effect ( η = 0 ) is statistically
rejected for the remaining seven markets and the two world market portfolios. Furthermore, a positive η implies that a
negative shock increases conditional volatility of these markets. This finding is similar to that of Glosten et al. (1993)
Compared to the initial descriptive statistics section (Section 3), Indonesia and Thailand are excluded from this
investigation as their respective GJR - GARCH models failed to achieve convergence under all log-likelihood function
specifications (i.e. normal, GED, student-t and skewed student-t)
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who find strict asymmetry in monthly US stock returns and that negative (positive) innovations increase (decrease)
volatility.
The results of Table 2 are generally consistent with those of other stock market empirical work on time
varying volatility. However, the similarities between developing and developed real estate markets documented in
Table 2 hide some interesting differences. Specifically, the estimated conditional volatility for most of the developing
Asian-Pacific real estate markets is considerably larger than that of the three developed real estate markets, Europe,
the UK and the USA. Table 3 summarizes the evidence. The average values of the conditional standard deviation
confirm the fact that developing Asian-Pacific real estate markets of Malaysia, the Philippines, Singapore and Hong
Kong are more volatile than developed markets.11 Moreover, the estimated conditional volatility series for the
developing Asian real estate markets show a higher degree of dispersion and suggests that large changes in volatility
are more frequent than in developed real estate markets. Finally, the table also shows that both the maximum and
minimum values of the conditional volatility are considerably larger in the developing Asian Pacific real estate markets.
(Table 3 here)
Finally, we conduct several diagnostic checking on the standardized residuals to assess the adequacy of the
models. Table 4 provides the results. Looking at the LB statistics, denoted by Q (10), Q(20), Q2(10) and Q2(20), the 12
models appear to capture the dynamics of linear and non-linear dependencies of the series reasonably well. The LM
Arch test is not able to detect the presence of ARCH effects in any series. Moreover, the sign bias tests proposed by
Engle and Ng (1993) show that there is no remaining leverage component in the shocks12 and the Nyblom stability test
suggests that the estimated parameters are quite stable during the sample period and that no misspecification of the
model is present. On the basis of the various diagnostics performed, it can be said that the ARMA (1, 1) – GJR –
GARCH (1, 1) model describes first- and second-moment dynamics of the real estate markets quite well
(Table 4 here)
5.2
Unconditional betas and stability test results
The standard market model is estimated for each of the real estate markets, using DJWRE and DJWALL as
the global proxies; i.e. risk is in turn defined relative to the two global market factors and consequently two international
beta estimates are derived for each real estate market. As can be seen from Table 5, the range of international beta is
between 0.3757 (Europe) and 1.7903 (Hong Kong) relative to DJWRE; and between 0.3981 (Europe) and 1.1323
(Hong Kong) relative to DJWALL. Examining the results one can see that using DJWRE in comparison to DJWALL
index generates higher beta risk estimates in all markets except for the US and Europe. For example, Hong Kong has
The only two developed Asian-Pacific real estate markets are Japan and Australia. Japan’s conditional standard
deviation is comparable to that of other developing Asian real estate markets. Australia’ conditional standard deviation
(2.26%) is slightly smaller than that of the UK (2.53%) but larger than that of the USA (1.83%) and Europe (1.82%).
11
Engle and Ng (1993)’ tests are based on the news impact curve implied by the particular ARCH-type model used.
The assumption is that if the volatility process is correctly specified then the squared standardized residuals should not
be predictable on the basis of observed variables. These tests are: (a) the sign bias test; (b) the negative sign bias test;
and (c) the positive sign bias test. The first test examines the impact of positive and negative innovations on volatility
not predicted by the model. The negative sign bias test examines how well the model captures the impact of large and
small native innovations. Finally, the positive sign bias test examines possible biases associated with large and small
positive innovations.
12
11
beta estimates of 1.7903 (relative to DJWRE) and 1.1323 (relative to DJWALL), respectively. Similarly, Singapore real
estate market has beta values of 1.4173 (relative to DJWRE) and 0.9998 (relative to DJWALL), respectively.
Consequently these results suggest various real estate markets are less integrated with world stock market, often
regarded as a global market benchmark used in many previous studies.
One key concern is that these (unconditional) international beta estimates may be unstable over time, in
particular, because of the changing real estate portfolio composition and the levels of gearing of the constituents real
estate companies in the respective countries (Matysiak and Brown, 1997). To test the stability of the beta coefficients
over time, the ARCH effects in unconditional heteroskedasticity (White test) and conditional heteroskedasticity
specifications (LM test) are investigated. Table 5 presents the respective test statistics as well as the p-value in
parenthesis. Examining these results, heteroscedasticity (both conditional and unconditional) is found for Asian-Pacific,
Australia, Hong Kong, Singapore, Malaysia and the USA as all the test statistics (White and LM values) are significant
at the 5% level. The remaining four markets, namely, Japan, the Philippines, Europe and UK has either unconditional
or conditional heteroskedasticity (but not both) at the 5% level. These results hold for both world market indexes.
Hence there is clearly some evidence of unstable international real estate betas. When DJWRE is used as the market
benchmark, the cumulative sum of squares (CUSUMSQ) tests suggests great beta parameter instability for seven
markets. Only in the cases of Australia, Japan and Europe did the recursive residuals not exceed the 5% bound of
significance in most of the time periods. The CUSUMSQ results using DJWALL as the world proxy are qualitatively
similar. Figures 1 and 2 provide a summary of the CUSUMSQ results.
(Table 5 here)
(Figures 1 and 2 here)
In summary, the heteroscedasticity and CUSUMSQ test results suggest that international betas for the
respectively real estate markets are unlikely to remain stable over time. Consequently it is appropriate to analyze timevarying beta risk. We next report the SS conditional beta estimates using the GJR –GARCH (1, 1) results.
5.3
Time-varying real estate betas
Table 6 includes heteroskedasticity consistent estimates of Model 4 by the Newey-West method (1987).
Values for the two world market volatilities hmt are obtained from the ARMA (1, 1) – GJR - GARCH (1, 1) – M model of
Table 2. The sign of ψ determines the effect of market volatility on each portfolio.
(Table 6 here)
When DJWRE is used as the market portfolio, the coefficient ψ is negative and statistically significant for
developing real estate stock markets of Asia-Pacific, Hong Kong, Singapore and Malaysia. Hence an increase in the
variance of DJWRE will lead to an increase in the respective betas. On the contrary, the coefficientψ is positive and
statistically significant for mature markets of Europe and the UK, implying an inverse relationship between world real
estate market volatility and systematic risk. Another observation is that for portfolios with average betas less than one
(Australia, Japan, the US, the UK and Europe)ψ is always positive, while for the remaining portfolios with average
12
betas greater than one (Asia-Pacific, Hong Kong Singapore, Malaysia and Philippines), ψ is always negative.13 This
supports the hypothesis that world real estate market volatility affects defensive and riskier markets differently. When
DJWALL is used as the market portfolio,
ψ
is positive for all ten portfolios that have average betas less than one
(between 0.1402 for Europe and 0.9087 for Hong Kong). However, only theψ s for Asian-Pacific, Japan, Europe and
the UK are statistically significant. Table 6 also provides the mean time-varying betas, maximum and minimum values
and summary measures of an augmented-Dickey (ADF) test for stationarity for both world market portfolios. The mean
conditional betas for Asian-Pacific, Hong Kong, Japan and Singapore are statistically greater than one relative to both
global benchmarks. On the contrary, developed real estate markets of Australia, Europe, the UK and the USA have
mean conditional betas significantly less than one (between 0.4403 and 0.5796) relative to both global proxies.
5.4
Effects of the Asian financial crisis on time-varying betas
Table 7 contains results from the estimation of Equation (6).14 All regressions are corrected for serial
correlation using the Cochrane– Orcutt method. The adjusted coefficient of determination (Adj R2) ranges from 0.493 to
0.533 (for betas relative to DJWRE) and from 0.353 to 0.407 (for betas relative to DJWALL).
(Table 7 here)
Panel A of the table provides estimates for betas relative to DJWRE. The effect of the own-market volatility
( α 1 ) on beta is significant for all real estate markets except Australia, Singapore and Malaysia. The significantly
positive volatility coefficient for Asian-Pacific, Hong Kong, the Philippines and the USA implies that as volatility
increases, beta increases and the size (in absolute value) of the positive coefficients is all larger than unity ( between
3.469 and 12.619) implying a significant size effect of own-market volatility on beta. The world real estate market
volatility ( α 2 ) imposes a significant effect on the beta of all markets. Results show that the effect is positive for Asian
Pacific, Hong Kong, Singapore, Malaysia and the Philippines with the remaining real estate markets having a negative
coefficient. Furthermore, all
α2
are quite large in absolute value (between 75.358 and 657.857) implying that the
world real estate market volatility (compared to own-market volatility) imposes a larger size effect on the time-varying
real estate beta for all markets.
Regarding the effect of the Asian financial crisis, the time dummy coefficient (D97) is significantly positive in
the cases of Hong Kong, Singapore, Malaysia and Asian-Pacific markets implying that the Asian financial crisis has a
significant direct effect on these developing real estate markets’ betas. In all developed markets, the dummy coefficient
is negative and is only significant in the cases of Australia and the USA. Adding the crisis dummy to the own-market
volatility, the coefficient ( φ1 ) is significant in four cases and it is positive four times. In cases of Japan, Australia,
Europe and the UK, the coefficient ( φ1 ) is negative, implying that own-market volatility during the financial crisis period
reduces the beta. Overall, the extra own-market volatility during the crisis period appears to impose a moderate size
influence on the real estate market betas. Next, the world real estate market volatility ( φ 2 ) is significant for all markets
The coefficients ψ for Australia, Japan, the US and the Philippines are statistically insignificant.
variables of equation (6) were first investigated to check for unit roots (s) and were found to be stationary li levels
by means of ADF tests. Stationary in levels implies that variables may be applied in standard OLS regressions.
13
14All
13
and it is surprising negative for developing real estate markets of Asian-Pacific, Hong Kong, Singapore, Malaysia and
the Philippines. The size (in absolute value) of the influence imposed by the world real estate market volatility during
the crisis is greater than unity in all cases and imposes a larger effect on the time-varying betas of the real estate
markets. Overall, the extra own-market volatility and world real estate market volatility during the crisis period have
affected the systematic risk of many real estate markets under study, though the effects are not direct indicating for few
markets that the crisis reduced the beta.
Panel B of the same table repeat the estimates on betas relative to DJWALL. The results provide similar
conclusion on the effect of Asian financial crisis. The crisis dummy (D97) is significantly positive for real estate markets
of Asian-Pacific, Hong Kong, Singapore, Malaysia and the Philippines. However, it is also significantly positive for
Australia, a result that might have not been expected. Adding the crisis dummy, the own-market volatility coefficient of
the crisis period ( φ1 ) is positive in all cases except for the USA and it is significant for Asian-Pacific, Hong Kong,
Japan and Singapore real estate markets. On the contrary, the global stock market volatility coefficient ( φ 2 ) is
significantly negative in all cases. Finally, the size (in absolute value) of the coefficients for total period ( α 1 and α 2 ) is
much smaller than those of the crisis period ( φ1 and φ 2 ). Overall, the extra own-market volatility and global stock
market volatility during the crisis period thus seem to impose a larger size influence than the volatilities during total
period.
5.5
Comparison of conditional betas
Under the ICAPM, the appropriate choice of world market index against which to measure international beta
risk is of great interest. Accordingly, we compare SS estimates of conditional real estate beta generated using a world
real estate market index (i.e. DJWRE) and a world stock market index (i.e. DJWALL). We forecast each market’s return
series in sample and then compare the forecast error produced in terms of the mean square error (MSE) and mean
absolute error (MAE) metrics. Table 8 presents the results.
(Table 8 here)
It is evident from Table 8 that the returns (R jt) based on the world real estate index are more “accurate” in
comparison to the forecasts generated using the world market index. Specifically, the average MSE for the conditional
betas relative to DJWRE was lower (0.0300) compared to the average MSE for the conditional betas relative to
DJWALL (0.0352). In addition, the lower average MAE results with DJWRE (0.0220 for DJWRE and 0.0256 for
DJWALL) reinforce the conclusion. The individual market’s forecast results are consistent except for Japan where a
marginally lower MAE is obtained for its DJWALL counterpart.
Our in sample forecast results thus favor conditional betas relative to the world real estate, which has
significant implications for understanding global capital markets. First, the impact of time-varying betas on forecasting
real estate returns in the world market has to be understood for making better portfolio decisions and pricing national
real estate markets. Second, if international real estate markets are segmented, the risk premia attaches to the world
real estate beta and it is the relevant risk measure. However with integrated property of modern capital markets that
includes real estate, the risk premia relate to the world stock market beta and become the relevant risk measure. In
both cases, the price of market risk is the coefficients that links expected returns to the conditional covariance with the
14
international benchmark portfolio (i.e. world real estate or world stock). Additionally, international investors and global
fund managers that are interested in hedging might consider world real estate index that has a higher correlation with
many real estate markets. Of course, these issues are not the focus of the current paper.
Finally, it is further noted that the choice of proxy for the world market portfolio is largely dictated by the type
(i.e. whether real estate or stock) and level of market integration that are available to investors and their portfolio
objectives. Hence the answer to this question is not immediately obvious. Furthermore, as previous evidence has
suggested that real estate markets are less integrated with global stock market (although the issue is beyond the
scope of current study), international investors may find it useful to have a global real estate benchmark in their capital
asset pricing (although a world stock index such as MSCI is commonly used), as beta (market risk) estimated relative
to a world real estate index may turn out to be adequate and more relevant for international real estate asset pricing.
6.
Conclusion
With bullish sentiment about real estate investment opportunities in Asia, our study reinforces the increased
potential importance of Asian listed real estate in investment portfolios for both local and institutional investors. In the
context of real estate market integration and continuing globalization of world’s capital markets, this paper presents
empirical evidence on the dynamics of conditional returns, volatility and betas for listed real estate of Asian-Pacific,
Australia, Hong Kong, Japan, Singapore, Malaysia, Philippines, Europe, the United Kingdom and the United States,
and two world market indexes (i.e. DJWRE and DJWALL).
The conclusions obtained from this study may be summarized as follows. For all national real estate markets
and two world market portfolios included in our sample, we find evidence of time-varying volatility which displays
clustering, high persistence and predictability. The level of volatility and volatility persistence in developing real estate
markets of Asian-Pacific are considerably higher than those of more developed markets, both at the unconditional and
conditional levels. We further find little evidence of a relation between expected returns and country-specific volatility.
The relationship of volatility to past innovations is asymmetric in seven real estate markets and two world market
portfolios, meaning that negative shocks increases volatility more than positive ones. A series of diagnostics performed
on the standardized residuals from the ARMA (1,1)-GJR-GARCH(1,1) models shows little evidence of misspecification.
In almost all cases, International real estate market betas are time-varying. The world real estate market volatility has a
statistically significant positive impact on systematic risk for the developing real estate markets of Asian-Pacific, Hong
Kong, Singapore and Malaysia, and a statistically significant negative impact on systematic risk for mature real estate
markets of Europe and the UK. Additionally, the time-varying betas of mostly developing Asian-Pacific markets have
been affected by the Asian financial crisis. Moreover, the extra country–specific market volatility and global market
volatility during the crisis period seem to impose a larger size influence than the volatility during total period in some
markets. Finally, based on comparisons of in-sample forecast errors, our findings appear to favor time-varying real
estate betas relative to a world real estate index over a world stock index. Consequently, our findings have significant
implications for understanding real estate market integration and global capital markets.
15
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17
Table 1
Descriptive Statistics for Weekly Return Series
Index
Asia-Pacific
Australia
Hong Kong
Japan
Singapore
Malaysia
Philippines
Indonesia
Thailand
Europe
UK
USA
DJW Stock
DJW RE
mean return std deviation
0.0005
0.0365
0.0012
0.0232
0.001
0.0185
-0.001
0.0464
0.0005
0.0505
-0.001
0.0586
-0.0011
0.0597
-2.40E-05
0.1538
-0.0003
0.1728
0.001
0.0185
0.0013
0.0261
0.0011
0.0196
0.0009
0.0207
0.0008
0.0235
skewness
(0.660***)
(0.190**)
(0.655***)
0.482***
(0.172*)
0.634***
0.391***
15.806***
20.210***
(0.223**)
-0.126
-0.129
(0.398***)
(0.802***)
ex kurtosis
6.950***
1.331***
5.917***
1.915***
5.465***
7.738***
2.658***
352.86***
475.97***
0.746***
1.185***
6.115***
1.887***
4.820***
Jarque-Bera
1384.6***
52.99***
1016.2***
127.26***
829.53***
1701.3***
212.36***
3.46e+006***
6.31e+006***
20.91***
40.62***
1036.4***
116.08***
714.06***
Q(20)
36.72***
39.89***
35.13**
32.29**
37.48**
31.72**
30.85*
8.06
2.85
18.45
18.56
28.28
35.89***
35.29**
Q2(20)
272.26***
98.01***
177.91***
27.98*
506.51***
241.64***
129.43***
0.004
0.047
23.59
51.45***
125.10***
284.33***
177.66***
ADF(lnPt)
0.336
0.907
0.102
0.119
0.396
0.741
0.733
0.701
0.666
0.991
0.913
0.681
0.606
0.489
ADF(Rt)
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
PP(lnPt)
0.298
0.925
0.071
0.129
0.290
0.706
0.683
0.640
0.634
0.968
0.878
0.695
0.622
0.402
PP(Rt)
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
Notes: Weekly returns are from January 7, 1992 to Sep 26, 2004 (664 weeks). Q (20) and Q2 (20) are the Ljung-Box test statistics for serial correlations in the returns and squared
returns, respectively. ADF and PP are, respectively, the augmented Dickey-Fuller and Phillips-Perron test probabilities for unit roots. ***, **, * indicates two-tailed significance at the 1, 5
and 10 percent levels respectively.
18
Table 2
Estimates of ARMA (1,1) - GJR - GARCH (1,1) - M Model
Index
Asia-Pacific
µ
γ
ϖ
ϑ
θ
η
-0.0026
C1
0.2406
C2
-0.1805
C3
-0.0178
4.3087
1.1165
0.1153
0.7108
(-2.51**)
(+1.97**)
(+3.03***)
(+2.40**)
(+12.14***)
(+1.80*)
Australia
0.0005
-0.5152
0.4267
0.0019
0.9707
0.0491
0.1006
1591.82
Hong Kong
-0.0065
0.1189
1138.39
(+1.79*)
Japan
Singapore
Malaysia
Philippines
Europe
UK
USA
-0.0034
0.0009
-0.0018
0.6171
-0.5409
-0.0229
4.4521
0.0739
0.7824
(+9.08***)
0.7733
(+3.00***)
(-2.51**)
(-2.15**)
(+2.02**)
(+2.59***)
(+2.09**)
(+13.93***)
0.5181
-0.5401
-0.0115
1.8898
0.2761
0.0145
(+1.85*)
(-1.93*)
(-1.75*)
0.6772
-0.6231
-0.0274
(+1.89*)
(-1.70*)
(-2.03**)
-0.1371
0.2631
-0.0446
(-3.79***)
-0.0324
1.6207
(-3.32***)
(1.77*)
-0.0023
-22.3226
-0.4135
(-1.91*)
(-1.73*)
0.0087
-0.2938
0.002
DJ World Real Estate
-0.002
DJ World Stock Market
0.0006
0.3383
0.3288
-0.4796
0.5131
(-2.43**)
(+2.63***)
-0.8457
0.8779
(-9.04***)
(+10.01***)
0.6181
-0.5175
-0.0046
1.3754
2.9768
-3.2077
-0.0013
-0.6691
-0.0099
7.7361
(+3.00***)
(-2.55**)
(-2.39**)
0.1486
-0.1843
0.0012
0.4957
0.0878
(+2.64***)
0.0874
0.8688
0.0483
1189.71
(+2.17**)
(+18.22***)
0.064
1099.75
1002.22
1.712
0.1578
0.768
(+2.80***)
(11.56***)
1.0611
0.0439
0.6081
0.8208
(+2.88***)
0.6805
0.0134
0.0047
0.0402
0.0712
(+3.63***)
0.8239
0.1936
R jt = µ + c1 * R j ,t −1 + c 2 * ε j ,t −1 + c3 * D97 + γh jt + ε jt
;
Log L
1381.66
0.9352
(+2.15**)
0.639
0.1442
(+29.92***)
0.0099
(+1.75*)
***,
β
0.6005
(+1.70*)
2.0211
-0.0091
0.004
ω
0.8875
0.079
(+17.42***)
(+2.15**)
0.7551
0.0748
(+5.48***)
(+1.67*)
0.843
0.1159
(+8.46***)
(+2.21**)
0.5464
(+4.99***)
0.6802
0.3889
(+2.83***)
0.204
(+11.74***)
(+2.63***)
0.852
0.1638
(+15.26***)
(+2.61***)
1138.74
1726.38
1511.68
1770.46
1643.11
1717.89
h jt = ϖ + ϑε 2 j ,t −1 + θh j ,t −1 + ηI t −1ε 2 j ,t −1
**, * - indicates two-tailed significance at the 1, 5 and 10 percent levels respectively; only significant t-statistics are reported.
19
Table 3 Summary Statistics for Conditional Standard Deviation
Index
Mean
S.D.
Maximum Minimum
Asia-Pacific
0.0327
0.0138
0.1404
0.0207
Australia
0.0226
0.0044
0.0529
0.0174
Hong Kong
0.0462
0.0155
0.1604
0.0316
Japan
0.0458
0.0095
0.0712
0.0269
Singapore
0.0453
0.0209
0.1437
0.0234
Malaysia
0.0525
0.0241
0.1871
0.0295
Philippines
0.0565
0.0144
0.1049
0.0353
Europe
0.0182
0.0016
0.0289
0.0162
UK
0.0253
0.0044
0.0534
0.0201
USA
0.0183
0.0071
0.0701
0.0135
DJWRE
0.0216
0.0077
0.0919
0.0152
DJWALL
0.0195
0.0068
0.0509
0.0124
Notes:
The summary statistics are based on the estimated time series for the conditional volatility obtained from the
benchmark ARMA (1,1)-GJR-GARCH(1,1) model (Table 2)
20
Table 4 ARMA(1,1)-GJR-GARCH (1,1) models - Diagnostic Tests on Standardised Residuals
Index
Asia-Pacific
Australia
Q(10)
7.24
9.73
Q(20)
16.88
23.78
Q2(10)
12.69
16.26**
Q2(20)
23.88
24.87
Sign bias
0.95
0.15
Negative
1.35
0.59
Positive
0.76
0.69
Joint
2.44
2.56
LM ARCH
1.19
1.48
Chi-sq
59.25
60.52
Nyblom
1.48
1.90
RED(10)
11.84
14.93
Hong Kong
Japan
Singapore
Malaysia
Philippines
Europe
UK
USA
DJW RE
DJW Stock
5.71
16.41**
9.20
2.47
7.53
5.14
6.58
3.54
10.71
7.02
16.24
25.62
21.78
11.01
18.88
13.79
16.13
20.22
22.25
23.95
4.74
6.71
6.02
5.45
3.63
9.62
8.22
14.74*
14.71*
3.79
15.97
13.14
12.30
8.68
11.36
15.92
10.71
20.86
20.18
7.36
0.54
0.19
0.26
1.43
0.55
0.53
0.13
0.25
1.34
0.19
1.43
1.29
2.21**
0.55
0.99
0.10
0.27
0.21
0.78
0.05
0.89
0.39
0.40
1.32
0.23
0.47
0.35
1.06
0.80
1.35
3.76
3.07
7.02*
2.65
1.07
0.52
0.26
1.48
1.85
3.73
0.46
0.67
0.53
0.51
0.40
0.87
0.81
1.42
1.51
0.37
52.93
52.38
50.76
64.67*
34.49
47.69
58.53
61.60*
40.82
40.27
1.81
2.41
1.62
1.23
1.72
1.98
1.58
2.37
1.85
2.29
4.67
6.75
5.47
5.18
4.05
6.45
8.18
14.17
13.44
3.70
Notes:
(1)
(2)
(3)
(4)
(5)
Q(10), Q(20), Q2(10) and Q2(20): Ljung-Box statistics for the standardized residuals and their squared values.
The Sign Bias Test (SBT) of Engle and Ng (1993) examines the impact of positive and negative return shocks on volatility not predicted by the model. The negative
(positive) Size Bias test focuses on the different effects that large and small negative (positive) return shocks have on volatility, which is not predicted by the GJR
model. Finally, a joint test for these three tests is also provided.
The LM ARCH test is conducted to test the presence of ARCH effects in the series.
The Chi-square statistic under the adjusted Pearson goodness-of-fit test compares the empirical distribution of the innovations with the theoretical one.
The Nyblom test checks the constancy of parameters over time
**, * indicates two-tailed significance at the 5 and 10 percent levels respectively.
Source: Laurent and Peters (2002)
21
Table 5 Unconditional Beta Stability Test Results
LM(DJWRE)
White(DJWRE)
Unconditional beta (DJWRE)
LM(DJWALL)
White (DJWALL)
Unconditional beta (DJWALL)
Asia-Pacific
40.283
Australia
8.013
Hong Kong
9.939
Japan
0.587
Singapore
19.987
Malaysia
18.246
Phillipines
1.028
Europe
0.841
UK
5.436
USA
60.742
(0.000***)
(0.005***)
14.946
4.529
(0.002***)
(+0.444)
(0.000***)
(0.000***)
(+0.311)
(+0.360)
(0.020**)
(0.000***)
17.084
13.656
18.243
9.478
9.824
2.448
1.375
(0.000***)
9.838
(0.011**)
(0.000***)
(0.000***)
(0.000***)
(0.000***)
(0.000***)
(0.087*)
(+0.254)
(0.000***)
1.4344
42.903
0.4840
18.215
1.7903
22.791
0.9744
1.327
1.4173
45.222
1.1399
25.687
1.1071
1.196
0.3757
0.0343
0.4576
3.188
0.4208
24.395
(0.000***)
(0.000***)
(0.000***)
(+0.250)
(0.000***)
(0.000***)
(+0.274)
(+0.853)
(0.075*)
(0.000***)
27.969
5.392
17.768
26.039
9.432
3.835
7.173
5.851
2.009
31.475
(0.000***)
(0.005***)
(0.000***)
(0.000***)
(0.000***)
(0.022**)
(0.001***)
(0.003***)
(+0.135)
(0.000***)
0.9892
0.4811
1.1323
0.9554
0.9998
0.7808
0.8039
0.3981
0.4528
0.4626
Notes: The ARCH LM test and White heteroscedasticity test are presented as evidence of possible non-stationarity of the unconditional beta to augment the CUSUMSQ tests
presented in Figs 1 and 2. The test results are presented for both proxies of world portfolio (i.e. DJWRE - Real Estate and DJWALL- Stock). ***, **, * indicates two-tailed significance at
the 1, 5 and 10 percent levels respectively.
22
Table 6 Schwert and Seguin (SS) Time-Varying Beta Estimation
Panel A:
Reference portfolio (DJWRE: Real Estate)
Parameter
α
β
χ
Adj R2
Time-varying beta
Mean
Maximum
Minimum
Panel B:
Asia-Pacific Australia
-0.0005
0.0008
Hong Kong
-0.0003
Japan
-0.0012
Singapore
-0.0003
Malaysia
-0.0016
Philippines
-0.0019
Europe
0.0006
UK
0.0008
USA
0.0008
(+1.25)
(-1.05)
(+1.15)
(-0.24)
(-0.78)
(-0.23)
(-0.72)
(-0.89)
(+0.97)
(+0.93)
1.5987
0.4577
2.0172
0.8682
1.9106
1.7006
1.2872
0.1779
0.1645
0.3617
(16.28***)
(4.19***)
(15.92***)
(4.69***)
(7.12***)
(4.72***)
(4.44***)
(3.03***)
(2.10**)
(4.05***)
-0.00009
0.00001
-0.00012
0.00006
-0.00026
-0.00030
-0.00010
0.00011
0.00016
0.00003
(-2.58**)
(+0.35)
(-2.49**)
(+0.77)
(-2.86***)
(-2.30**)
(-0.89)
(4.24***)
(4.51***)
(+0.99)
0.853
0.237
0.716
0.241
0.451
0.224
0.189
0.247
0.192
0.254
1.4441
1.5917
1.3417
0.4944
0.5187
0.4594
1.7028
2.003
1.4945
1.0149
1.1121
0.8748
1.2269
1.8797
0.7738
0.9252
1.6656
0.4114
1.1301
1.2801
1.0259
0.4503
0.6309
0.1902
0.5705
0.8396
0.1828
0.4429
0.4967
0.3653
Japan
-0.0015
Singapore
-0.0005
Malaysia
-0.0017
Philippines
-0.0019
Europe
0.0006
UK
0.0008
USA
0.0007
Reference portfolio (DJWALL: Stock)
Parameter
α
Asia-Pacific Australia
-0.0006
0.0007
Hong Kong
-0.0001
β
(-0.46)
(+1.01)
(-0.08)
(-0.96)
(-0.26)
(-0.71)
(-0.81)
(+0.81)
(+0.82)
(+1.03)
0.6508
0.3888
0.9087
0.3517
0.8128
0.5623
0.7642
0.1402
0.1581
0.5171
χ
(3.07***)
(4.18***)
(3.34***)
(1.66*)
(2.62***)
(2.28**)
(2.25**)
(2.00**)
(1.83*)
(4.10***)
0.00015
0.00005
0.00006
0.00030
0.00008
0.00009
0.00002
0.00011
0.00013
-0.00002
(2.05**)
(+1.18)
(+0.97)
(4.19***)
(+0.89)
(+1.24)
(+0.17)
(5.41***)
(4.63***)
(-0.65)
0.329
0.184
0.224
0.219
0.168
0.076
0.075
0.232
0.151
0.239
Adj R2
Time-varying beta
Mean
Maximum
Minimum
1.1359
1.5971
0.7069
0.5226
0.6498
0.4043
1.2281
1.5334
0.944
1.2181
2.0418
0.4518
1.0804
1.3349
0.8437
0.8767
1.1757
0.5986
0.8211
0.8752
0.7708
Notes: Time-varying betas for real estate market j is R jt = φ j + θ j Rmt + ψ ( Rmt / hmt ) + ε jt and is given by
0.5116
0.8646
0.1832
β jt = β j +
ψj
hmt
0.5796
0.9803
0.2068
0.4403
0.5082
0.367
; two betas are estimated for each market (i.e.
beta relative to DJW Real Estate and beta relative to DJW Stock). T- values are included in parenthesis. Standard error for the estimates is corrected for heteroscedasticity using the
Newey – West method. ***, **, * indicates two-tailed significance at the 1, 5 and 10 percent levels respectively.
23
Table 7 Asian Financial Crisis and Time-varying Betas
Panel A: Betas Releative to Global Real Estate (DJWRE)
c
1.376
Asia-Pacific
(307.74***)
Australia
γ
0.090
α1
12.619
(7.71***)
(3.94***)
-0.019
0.2258
φ1
-0.559
-4.311
(-5.29***)
Hong Kong
Japan
Singapore
Malaysia
Philippines
Japan
Malaysia
Philippines
Europe
-10.512
-20.993
-119.242
111.824
(-3.47***)
(-2.97***)
(-23.56***)
(19.51***)
9.543
24.035
574.116
-553.226
(2.75**)
(23.99***)
(-20.09***)
10.331
657.857
-595.864
(2.18**)
(24.83***)
(-20.05***)
11.209
132.807
-125.543
0.924
0.225
(44.65***)
(3.57***)
0.599
0.381
(26.91***)
(6.22***)
1.054
0.028
3.349
(2.26**)
(3.48**)
(24.92**)
(-20.57***)
-0.040
-130.929
-389.662
-218.884
0.673
204.796
(-22.92***)
(17.26***)
-333.39
302.778
(-23.77***)
(18.61***)
0.766
(-3.42***)
-0.181
-49.128
-106.915
(-2.66**)
0.477
-0.055
(208.01***)
(-8.78***)
γ
α
5.751
1
21.913
φ
1
(3.66***)
φ1
64.275
(15.90***)
α
2
α2
φ
2
φ2
0.116
-39.291
51.952
-229.015
-585.489
(34.04***)
(2.56**)
(-6.10***)
(6.33***)
(-12.37***)
(-6.58***)
0.556
0.035
-2.378
22.838
-71.358
-134.928
(53.24***)
(2.75***)
(-13.19***)
(-5.02***)
1.319
0.090
-8.724
13.604
-163.415
-333.599
(53.54***)
(3.01***)
(-2.96***)
(3.56***)
(-13.10***)
(-6.12***)
1.695
-0.051
-129.277
109.318
-437.091
-667.243
(-7.34***)
(2.85***)
(-13.74***)
(-6.45***)
-140.218
-208.898
1.158
0.047
-6.802
7.426
(58.34***)
(1.97**)
(-2.59***)
(2.29**)
(-13.76***)
(-6.62***)
0.958
0.090
-1.907
1.278
-168.995
-228.496
(40.35***)
(3.19***)
(-14.26***)
(-6.95***)
0.837
0.014
(182.99***)
(2.11**)
0.672
-0.041
0.727
-0.728
-240.684
0.743
538.721
(-5.76***)
-0.024
(21.86***)
USA
α1
-75.358
(-23.03***)
1.282
(21.45***)
UK
(-11.73***)
-0.015
(26.18***)
Singapore
-237.629
(18.34***)
1.095
c
Hong Kong
246.498
9.813
Panel B: Betas Releative to Global Stock Market (DJWALL)
Australia
28.891
(16.71***)
(2.39**)
(47.01***)
Asia-Pacific
-30.898
(-23.86***)
0.188
(42.57***)
USA
(-10.06***)
(7.62***)
0.601
UK
(15.62***)
1.562
(183.54***)
Europe
φ2
-128.422
(155.88***)
(151.81***)
-4.095
α2
111.593
-74.885
280.277
(-4.56***)
0.419
-0.021
-5.542
(77.04***)
(-3.14***)
(-4.39***)
-0.333
-30.358
-41.803
(-14.07***)
(-6.53***)
-179.549
-319.527
(-12.72***)
(-6.23***)
-213.167
-345.273
(-13.36***)
(-6.99***)
51.406
53.517
(14.16***)
(3.01***)
Adj R2
0.514
DW
2.11
0.493
2.15
0.503
2.12
0.515
2.15
0.524
2.13
0.507
2.14
0.533
2.11
0.501
2.13
0.498
2.15
0.517
2.12
Adj R2
0.391
DW
2.08
0.354
2.11
0.363
2.08
0.403
2.09
0.359
2.10
0.355
2.09
0.353
2.10
0.382
2.07
0.372
2.09
0.371
2.10
Notes:
β jt = c j + γ j D97 + α 1 (CV jt ) + φ1 (CV jt * D97 ) + α 2 ( MCVt ) + φ 2 ( MCVt * D97 ) + ε jt ;
D97: time
dummy for Asian financial crisis; CV- own market volatility; MCV – world market (real estate / stock) volatility;
- indicates two tailed significance at the 1- and 5 percent levels respectively; only significant t-statistics are
reported
***, **
24
Table 8
Index
Asia-Pacific
Australia
Hong Kong
Japan
Singapore
Malaysia
Philippines
Europe
UK
USA
Average
Mean Square Error (MSE) and Mean Absolute Error (MAE) Forecast Results
MSE
DJWRE
0.0140
0.0203
0.0264
0.0404
0.0373
0.0515
0.0536
0.0160
0.0234
0.0169
0.0300
DJWALL
0.0299
0.0209
0.0438
0.0412
0.0459
0.0562
0.0573
0.0162
0.0240
0.0170
0.0352
MAE
DJWRE
0.0089
0.0157
0.0192
0.0308
0.0274
0.0361
0.0393
0.0125
0.0175
0.0121
0.0220
DJWALL
0.0213
0.0164
0.0322
0.0305
0.0318
0.0387
0.0417
0.0126
0.0181
0.0122
0.0256
Notes: This table reports the MSE and MAE between then observed real estate stock return series and the forecast
real estate stock return series. The forecasts are generated using the SS approach to estimating conditional betas with
DJWRE (Real Estate) and DJWALL (Stock) as proxies for a world portfolio.
25
Figure 1(a)
Cumulative sum of squares from the recursive residuals for Singapore (relative to DJWRE)
1.2
1.0
0.8
0.6
0.4
0.2
0.0
-0.2
92
93
94
95
96
97
98
CUSUM of Squares
99
00
01
02
03
04
5% Significance
Note: The results (parameter instability) for Singapore was also found for Asian-Pacific, Hong Kong, Malaysia, the
Philippines, UK and the USA real estate markets
Figure 1(b)
Cumulative sum of squares from the recursive residuals for Europe (relative to DJWRE)
1.2
1.0
0.8
0.6
0.4
0.2
0.0
-0.2
92
93
94
95
96
97 98 99 00 01
CUSUM of Squares
02
03
04
5% Significance
Note: The recursive residuals do not exceed 5% bound of significance for most of the time periods, suggesting some
parameter stability. The result for Europe was also found for Australia and Japan
26
Figure 2(a)
Cumulative sum of squares from the recursive residuals for Malaysia (relative to DJWALL)
1.2
1.0
0.8
0.6
0.4
0.2
0.0
-0.2
92
93 94 95 96 97 98 99 00 01 02 03 04
CUSUM of Squares
5% Significance
Note: The results (parameter instability) for Malaysia was also found for Asian-Pacific, Hong Kong, Japan, Singapore,
the Philippines, UK and the USA real estate markets
Figure 2(b)
Cumulative sum of squares from the recursive residuals for Australia (relative to DJWALL)
1.2
1.0
0.8
0.6
0.4
0.2
0.0
-0.2
92
93 94 95 96 97 98 99 00 01 02 03 04
CUSUM of Squares
5% Significance
Note: The recursive residuals do not exceed 5% bound of significance for most of the time periods, suggesting some
parameter stability. The result for Australia was also found for Europe.
27