AN ASSESSMENT OF THE RISK AND RETURN RELATIONS IN THE ASIAN-PACIFIC REAL
ESTATE MARKETS
Kim Hiang LIOW, Department of Real Estate, National University of Singapore
Corresponding Author
Dr. Kim Hiang LIOW
Associate Professor
Department of Real Estate
National University of Singapore
4 Architecture Drive
Singapore 117566
Tel: (65)65163420
Fax: (65)67748684
Email: rstlkh@nus.edu.sg
4 APRIL 2006
1
AN ASSESSMENT OF THE RISK AND RETURN RELATIONS IN THE ASIAN-PACIFIC REAL
ESTATE MARKETS
Abstract
This paper examines the risk-return relations in five Asian-Pacific real estate stock markets of Australia,
Japan, Hong Kong, Malaysia and Singapore for the period September 1992 to August 2004. These five
markets have a significant real estate market each in their respective economies. Although beta is useful in
an unconditional situation, testing the CAPM by separating up and down markets obtains a higher
significance for beta in explaining the return-generating process of Asian-Pacific real estate stocks.
Moreover, whilst beta squared and kurtosis appear to play a significant role in explaining returns in up
market, beta squared, unsystematic risk and skewness seem to be relevant in real estate stock pricing. It
further appears that the model beta and beta squared has the greatest explanatory power to the crosssectional variations in the Asian Pacific real estate stock returns across different regression models.
Finally, the average monthly excess returns for the five Asian Pacific real estate stock markets is positive
and yet statistically insignificant. The symmetry of the risk-return relation in up and down markets is only
weak to moderate. Overall, our results imply that beta is a useful risk measure for portfolio managers in
making optimal investment decisions and other risk factors are also useful in explaining cross-sectional
variations in Asian-Pacific real estate stock returns in up or down markets. Our empirical analyses
therefore advance investors’ understanding about the return-generating process of real estate stocks in an
international context.
1.
INTRODUCTION
Previous research studies have extensively debated whether systematic risk (beta) in the
Capital Asset Pricing Model (CAPM) (Sharpe, 1964; Lintner, 1965) is significantly related to returns
of common stocks; and furthermore, whether some other factors such as size, book-to-market value
ratio, financial leverage, earnings/price ratio, cash flow /price ratio, past sales growth and other
statistical risk measures like unsystematic risk, skewness and kurtosis are relevant in the risk-return
generating process of common stocks. This debate comes about mainly due to the way in which the
betas and other variables were tested in the CAPM framework. Earlier empirical studies using an
unconditional framework of the CAPM mostly find that beta and returns were not related empirically,
whether in domestic or in international stock markets. On the contrary, some other empirical studies
adopting a conditional framework of the CAPM based on up and down markets (e.g. Pettengill et al,
1995) find a significant conditional relation between beta and returns in national stock markets and
support for positive risk-return tradeoff. Moreover, other variables (mentioned above) can add
explanatory power to the conditional CAPM model depending on market condition. This is greatly a
relief and re-affirms the usefulness of the CAPM in financial asset pricing.
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With increasing globalization of the world capital and real estate markets since the 90’s,
several recent studies have highlighted the portfolio diversification benefits of including international
listed real estate in a mixed portfolio in Asia and internationally (e.g. Worzala and Sirmans, 2003).
Although much of this real estate company research has focused on performance analysis in specific
Asian markets and the inter-relationship between the respective indirect and direct property markets,
none of them has specifically empirically investigated the role of beta in explaining the return
generating process of real estate stocks. Consequently, the findings from this study are especially of
the great interest to institutional investors in public real estate markets as many of them rely on the
CAPM in making their investment decisions. Moreover, this study that includes other statistical risk
measures in addition to the beta will suggest whether a multi-factor CAPM specification is a more
useful approximation to the real estate stock return-generating process. Finally, in an international
context, an interesting question is whether there are significant variations in the relative importance of
betas and other risk factors in explaining international real estate stock returns. The results will
provide useful guidance in investing in International real estate markets. Our present study on Asian
real estate stock markets represents the first attempt.
Accordingly, we extend the previous stock market research and investigate the risk-return
relations in five Asian-Pacific public real estate markets of Australia, Japan, Hong Kong, Malaysia
and Singapore for the period September 1992 to August 2004 as prior studies such as Liu and Mei
(1992) find that the return characteristics of stocks are not necessarily similar to real estate returns.
These five countries have an established listed real estate market each in their respective economies
and deserve a study. Using disaggregate real estate firm return data, we employ the traditional version
of CAPM and a conditional CAPM model based on up and down markets (Pettengill et al. 1995) to
evaluate whether beta is an important determinant of equilibrium pricing in the Asian-Pacific real
estate markets under the different specifications. Since the Asian-Pacific real estate stock returns are
non-normally distributed with significant skewness and kurtosis (Liow and Chan, 2005), we also
include four other risk factors (beta squared, unsystematic risk, skewness and kurtosis) in the returngenerating process. With the increased significance of international securitized property as a real
3
estate investment vehicle for institutional investors to gain worldwide real estate exposure, this study
is significant in helping researchers and investors understand better the risk-return relation in major
Asian-Pacific real estate markets particularly with respect to the significance (or otherwise) of beta in
pricing real estate stocks and whether other stock risk factors are also important in predicting real
estate stock portfolio returns. The empirical analyses therefore advance our understanding about the
return-generating process of public real estate in an international context. The specific objectives of
this study are thus:
(a)
To examine the risk-return relations of real estate stocks under the unconditional CAPM
model
(b)
To explore the risk-return relations of real estate stocks under the conditional framework
developed by Pettengill et al. (1995)
(c)
To determine whether four other risk factors (i.e. beta squared, unsystematic risk, skewness
and kurtosis) are significant determinants of equilibrium pricing in the Asian-Pacific real
estate stock markets
(d)
To compare the significance and magnitude of the risk factors on real estate stock returns
across the five Asian-Pacific real estate markets
This study therefore contributes to the international real estate literature, in particular real
estate stock pricing, in at least three ways. We extend our empirical investigation to cover five major
Asian-Pacific real estate markets and over an extended period of 12 years. This period covers the
boom and bust phases of the most recent real estate market cycle in Asia. The wider coverage of the
Asian-Pacific markets and longer time period is in line with the growing importance of Asian listed
real estate markets in the global context in the coming years. Second, we explore the return-generating
process of real estate stocks from a multi-factor perspective that includes several risk factors, of which
beta is one of them. This is also in line with the conventional wisdom that real estate returns are likely
to be related to more than one factor. Third, we compare unconditional and conditional risk-return
models. This will allow us to confirm whether market condition (i.e. up and down markets) is relevant
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in pricing real estate stock returns. Furthermore, the conditional model will allow us to see if a long
run risk-return tradeoff exists. The remainder of the study is structured as follows: Section 2 provides
a literature review. Data and methodologies employed are described in Sections 3 and 4 respectively.
Section 5 discusses the empirical results while Section 6 concludes the paper.
2.
RELATED LITERATURE
There is considerable empirical literature investigating the applicability of the CAPM to stock
market. For the purpose of this paper, the relevant literature is classified into two categories:
unconditional and conditional CAPMs.
In the earlier literature where the unconditional CAPM model was extensively studied, Fama
and MacBeth (1973) tested the validity of the CAPM with the US stock return data from 1935 to 1968
based on two regressions. Contemporaneous betas were first estimated using rolling time series
regressions of excess stock returns. Then estimated betas were used to predict the one-step-ahead
cross-sections of stock returns by regressing portfolio returns to estimate market risk premia. They
found a positive trade-off between risk and return. In addition, beta was the only measure of risk that
systematically affected the average returns. They concluded that the results supported the CAPM in
the US stock market. Other research studies that supported the CAPM also include Hawawini and
Michel (1982) on the Brussels stock market and Hawawini et al. (1983) on the French stock market
On the other hand, some other studies on the unconditional CAPM have also found that the
applicability of the CAPM appear weak in that beta alone does not provide an adequate explanatory
power for the risk-return relations observed in domestic and international markets; other factors such
as size, book-to-market equity ratios and debt-equity ratio also help explain stock returns. Lakonishok
and Shapiro (1986) found that beta and residual standard deviation were not able to explain the crosssectional variation in NYSE stock returns; only size could significantly explain returns. Fama and
French (1992) found an insignificant relation between beta and average monthly returns of NYSE
stocks. Instead, they discovered that size (proxied by market capitalization) and book-to-market value
ratio (BV/MV) had significant explanatory power in portfolio returns. Fama and French (1992)
5
described the factors size and BV/MV as proxies for different dimensions of risk, explaining that risk
is multidimensional and size and BV./MV are good proxies for this risk. Heston et al. (1999)
documented the cross-sectional relation between beta, size and average returns of 2100 stocks in 12
European countries between 1978 and 1995. They found that the average returns were related crosssectionally related to both beta and size. Specifically on beta, high beta countries outperformed low
beta countries. Within countries the relation between average return and beta was weaker. Chui and
Wei (1998) investigated the risk-return relation on five Pacific-Basin emerging markets: Hong Kong,
Korea, Malaysia, Taiwan and Thailand. They found a flat relation between average returns and market
beta. However, stock returns were more related to size effect and BV/MV.
Second, the conditional CAPM literature includes studies regarding the ability of beta in
explaining average stock returns based on up and down markets, as betas are time-varying. The main
feature is that in the conditional CAPM, a dual-beta model replaces the traditional all-in beta model.
In their study, Bhardwaj and Brooks (BB) (1993) classified months as either bull or bear markets
according to whether the monthly market return was higher or lower than the median market return for
the sample period. Adopting this classification, they found significant differences between systematic
risks in the bull and bear markets. Using an all-in beta model, Howton and Peterson (HP) (1998)
found similar results with Fama and French (1992) in that beta was not significant while BV/MV is a
significant factor explaining stock returns. However, when cross-sectional regressions were estimated
with the bull-market and beta-market betas following BB’s methodology, HP found that the
coefficients on bull-market betas were always significantly positive and, with the exception of some
January models, bear–market betas were significantly negatively related to returns. They also found
that the relationships between returns and other variables, like size and BV/MV, changed with market
condition.
Pettengill et al. (1995) formalised the “dual-beta” approach in assessing the reliability of beta
in measuring risk. They pointed out that when the realized market returns exceeded the risk-free rate
(i.e. up market), the relationship between beta and realized returns should be positive. Similarly, when
the realized markets returns were below the risk-free rate (i.e. down market), there should be a
6
negative relation between beta and realized returns. By augmenting the cross-sectional regression to
control for the sign of the realized market premium, they found that there was strong support for beta
under this conditional framework on the US stock market. Hence the claim that beta is an insignificant
determinant of equilibrium pricing should be re-examined. Following Pettengill et al. (1995), Fletcher
(2000) examined the conditional relationship between beta and returns in 18 international stock
markets between January 1970 and July 1998. He discovered a significantly positive relationship
between beta and returns in periods when the world market excess returns were positive and a
significant negative relationship in periods when the world market excess returns were negative.
Additionally, this relationship was symmetric and there was a positive mean excess return on the
world index on the average. Chiao et al. (2003) tested a four-moment conditional CAPM in up- and
down-market conditions on the Taiwan stock market. Although they found that the unconditional
four-moment CAPM models performed badly, covariance, co-skewness and co-kurtosis risks were
significant in explaining stock returns over the up-market sub-periods. Tang and Shum (2003)
investigated a conditional CAPM model on 13 national stock markets using both monthly and weekly
returns. Using an ICAPM, they found a significantly positive relationship between beta and returns in
up markets, but a significantly negative relationship in down markets, for both monthly and weekly
returns and for two different proxies of the world market portfolios. In another study, Tang and Shum
(2004) found that the explanatory power of his conditional CAPM model based on Pettengill et al
(1995)’s methodology increased tremendously and there was a significant positive (negative) relation
between beta and returns when the market excess returns were positive (negative). Their results also
indicate that other risk factors such as unsystematic risk, total risk and kurtosis in addition to beta are
important in pricing stock returns in the Singapore stock market. Finally, in an investigation of the UK
stock markets using Pettengill et al. (2005)’s methodology, Hung et al. (2004) discovered that beta
was very significant in their conditional CAPM models. Additionally, whilst co-skewness and cokurtosis were not significant explanatory variables, Fama and French factors (i.e. size and BV/MV)
were significant in the conditional framework of the UK stock returns.
7
To the best of our knowledge, only two real estate studies have specifically investigated the
significance of betas across market conditions. Glascock (1991) developed a dummy variable
procedure to test for excess returns and change in risk behaviour across market conditions in his
sample of the US real estate firms from 1965-1986. Specifically, he tested five different definitions of
up / down markets and found mixed results for beta under the different model specifications. Conover
et al. (2000) employed a dual-beta model, similar to that of HP, to examine the cross-section of returns
of their equity real estate investment trust (EREIT) sample over bull and bear markets. They found no
significant relationship between the EREIT returns and a constant beta. However, when betas were
allowed to vary over bull and bear markets, beta alone was significant in explaining the EREIT returns
during bull market months. On the contrary, there was no significant relationship between beta and
returns during bear market months. Finally, size and BV/MV were negatively related to returns during
bear markets. Finally, Liow and Chan (2005) investigated the pricing of international real estate stocks
with covariance, coskewness and cokurtosis using a four-moment CAPM model in a time-varying
context.
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.
Finally, for most countries, the real estate stock index returns display a fairly strong tendency to move
with the underlying real estate returns (Kallberg et al, 2002).
We include five major Asian-Pacific real estate markets (Australia, Japan, Hong Kong,
Singapore and Malaysia) in this study. The choice of this Asian-Pacific sample is expected to be of
significant interest to the US and other international investors due to the significance of the respective
private real estate markets in the economies and that these public real estate markets have been
8
investigated less thoroughly in the past. The study period is from September 1990 to August 2004
that covers the boom and bust phases of the most recent real estate market cycle in Asia. Japan is a
significantly developed economy in Asia and also a world industrialized economy. There has been a
long history of Japanese real estate companies. Australian securitized real estate sector is a leading
player in global real estate, mainly through its successful listed property trust (LPT) vehicles. Other
markets like Hong Kong, Malaysia and Singapore are major economic forces in the region.
Additionally, Hong Kong and Singapore have track record of listed real estate companies that play a
relative important role in the general stock indexes. Table 1 provides additional information on the
key macroeconomic and stock market indicators for the five economies. It is noticed that there are
variations across the national samples, mainly distinguished by their economic development status (i.e.
developed versus maturing economies) and some stock market characteristics. Finally, REITs have
been successfully introduced in Japan and Singapore; HK and Malaysia will likely to have their first
REIT introduced end 2005. 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 international investors.
(Table 1 here)
We obtain 186 real estate companies that have the full period return index data (i.e. 144
observations) from the Datastream International. All return data are adjusted for dividends and
expressed in US $. Hence, all empirical results are presented from an American investor’s point of
view. Table 2 provides the breakdowns of the companies by country and the numbers of portfolios
formed (see section on research methodology). The market indexes and risk-free rates extracted from
the Datastream are: ASX 300 and inter-bank 3-month rates (Australia), Hang Seng Index and
interbank 3-month rates (Hong Kong), Tokyo SE Topix index and 3-months Euro Yen rates (Japan),
Kuala Lumpur SE Composite Index and 3-month Treasury Bill rates (Malaysia), and Singapore AllEquities Index and 3-month Treasury Bill rates (Singapore). For each firm, monthly real estate stock
9
returns (R) are obtained by taking the logarithmic difference of the return index (RI) times 100. That
is R t = 100 * (Log RI t – Log RI t-1).
(Table 2 here)
4.
RESEARCH METHODOLOGY
As in Tung and Shim (2004), the 12-year full sampling period (September 1992 – August
2004) is divided into three consecutive sub-periods: the portfolio formation period (September 1992 –
August 1995), the parameter estimation period (September 1995 – August 1998) and the model testing
period (September 1998 – August 2004). In the first sub-period, individual real estate stocks’ betas are
estimated by regressing individual stock excess returns on the market excess returns. For each
country, the estimated betas are ranking in ascending order and equally weighted portfolios (with
roughly equal portfolio sizes) are then formed. Consequently, the breakdowns of 21 equally weighted
portfolios are: 2 (Australia), 8 (Hong Kong), 4 (Japan), 5 (Malaysia) and 2 (Singapore). In the
estimation period, betas and other real estate stock risk characteristics (beta squared, unsystematic
risk, skewness and kurtosis) of each portfolio formed in the construction period are estimated. In the
final stage, real estate stock returns of the 21 portfolios from the first month of the testing period
(September 1998) are matched with the corresponding portfolios’ risk measures obtained from the
estimation period. The process is repeated by dropping the first month’s observation in the estimation
period (September 1995) and adding the second month’s observation in the testing period (October
1998). This procedure is continued for the third and the following months up to the last month of the
testing period (August 2004). Once the entire matching process is completed, the monthly returns of
the 21 portfolios in the whole testing period are then regressed on their corresponding estimated
parameters and the respective statistical significances are then assessed
Following the two-step stochastic process proposed by Fama and Macbeth (1973), Equation
(1) represents the equilibrium relationship:
~
R jt = α~0t + α~1t β j + α~2t β 2 j + α~3t SR j + α~4t SKW j + α~5t KUR j + ε~ jt ...............(1)
10
Where R jt is portfolio j ‘ s excess returns at time t;
β j is portfolio j’ s systematic risk; SR j is
portfolio j’ s specific risk (unsystematic risk); SKW j is portfolio j’s relative skewness coefficient;
KUR j is portfolio j’ s relative kurtosis coefficient and ε jt is the usual error term. In addition, a
dummy variable,
ϕ is added to Equation (1) to test the conditional effect; i.e. where ϕ =1 if the
~
monthly excess market return, Rmt >0; and
~
ϕ =0 when Rmt <0. This is to allow us to test the
conditional relationship between beta and returns as well as other variables. Consequently, the
unconditional and conditional regressions used in this study are as follow:
Unconditional regression:
~
R jt = α~0t + α~1t β j + α~2t (var iable j ) + ε jt ……..(2)
Conditional regression:
~
R jt = α~0t + α~1ut β j + α~2ut (var iable j ) + α~1dt β j (1 − ϕ ) + α~2 dt (var iable j )(1 − ϕ ) + ε jt ……(3)
(Where the variables is either beta squared, unsystematic risk, relative skewness coefficient or relative
kurtosis coefficient)
Based on equations (2) and (3), we test seven hypotheses. First, H1-H5 are tested for both the
unconditional and conditional framework. H1 tests whether the intercept is 0 and if beta is priced; H2
tests if the coefficient of beta squared is zero, or the return-beta relationship is non-linear; H3 tests if
unsystematic risk explains the return-generating process of real estate stocks; H4 and H5 test for the
presence or absence of relative skewness (defined as skewness minus risk free return) and relative
kurtosis (defined as kurtosis risk free return). Second, H6 and H7 follow from Pettengil et al. (1995)’s
conditional arguments that if a symmetrical conditional relation between beta and risk exists, then and
the risk premium (slope coefficient) in up and down markets is symmetrical (H6) and the average
market excess returns is positive (H7). Table 3 provides the seven hypotheses and the expected
outcomes
(Table 3 here)
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5.
EMPRIRICAL RESULTS
5.1
Real Estate Portfolio Characteristics
Table 4 provides some key risk characteristics of the 21 portfolios for the estimation period.
They are average excess returns, average beta, average skewness, average kurtosis and average
unsystematic risk. As the numbers indicate, 15 portfolios have a beta each of more than 1 that is
typical of the systematic risk characteristics of Asian real estate stocks. In addition, 12 portfolios’
excess returns are positively skewed although the skewness values are small. The kurtosis of all
portfolios except one exceeds three. It ranges from 2.899 to 7.967. The distribution of the excess
returns thus has fail tails compared with a normal distribution. Finally, the specific risk of all real
estate stock portfolios ranges between 1% and 11.1%.
(Table 4 here)
5.2
Results from the Unconditional CAPM
Table 5 presents the results of the unconditional relation between beta and returns for the
respective real estate stock markets. It is noted that the value of
α 0 is not statistically different from
zero at the 5% level for Australia, Malaysia and Singapore, providing some evidence consistent with
the Sharp-Lintner hypothesis. The value of
α 1 (between -0.050 for Japan and 0.004 for Singapore) is
statistically insignificant too, except for Japan. Hence, our real estate stock results are consistent with
stock market results (e.g. Tang and Shum, 2004) that the positive relation between beta and returns is
very weak under the unconditional situation.
(Table 5 here)
Additionally, Table 5 also presents the unconditional empirical results on beta when one other
risk measure is added. As the results indicate, when unsystematic risk and skewness are added
separately in the equation, beta for the Singapore real estate stocks become positive and statistically
significant at the 5% level. Additionally, beta-squared, unsystematic risk, skewness and kurtosis play a
significant role in pricing the Japan, Hong Kong and Singapore, Singapore and Malaysia real estate
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stocks respectively. It is further noted that the signs of regression coefficients for betas of Japanese
real estate stocks are negative from what we expect from the finance theory. Finally, all the Adjusted
R2 values are negative or low implying that the unconditional CAPM models are far from adequate in
pricing real estate stocks for Asian-Pacific countries.
5.3
Results from the Conditional CAPM
Tables 6 and 7 report the results of the conditional relation between beta and returns in up and
down markets respectively. The value of
α 0 is statistically significant at least at the 5% level in all
up- and down-market cases and is inconsistent with the Sharpe-Lintner hypothesis. As observed, there
is a systematic but conditional relation between beta and realized returns in some markets. When the
excess market return is positive (up market), the
α 1u values for Singapore (0.074), Malaysia (0.186)
and Hong Kong (0.052) are statistically significant at the 1% level suggesting high-beta portfolios
receive a larger positive risk premium than low-beta portfolios in up-market in the three countries. In
down-market, the two statistically significant (at the 1% level)
α 1d values are -0.080 (Singapore) and -
0.131 (Malaysia) indicating that high-beta portfolios incur higher losses than low-beta portfolios in
down market for the real estate stocks of these two countries.
(Tables 6 and 7 here)
Furthermore, the beta results do not change significantly when other risk factors are added to
the conditional equations. The relation between real estate returns and beta is non-linear for Australia
and Hong Kong in up-market condition; and Australia and Japan in down-market condition; as the
respective beta-squared values are statistically significant at least at the 5% level. There is also some
evidence that unsystematic risk plays a role in pricing the real estate stock returns. Specifically, the
conditional results presented in Table 7 show that the unsystematic risk in down market is
significantly negatively related to the real estate stock returns of Hong Kong, Japan and Malaysia.
Furthermore, the slope coefficient (for Hong Kong and Malaysia) is considerably larger than that of
beta coefficient, indicating that unsystematic risk (specific risk) plays an even more significant role in
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pricing the Hong Kong and Malaysian real estate stock returns in down market. The implication is that
the real estate stock market not only compensates the systematic risk, but also the specific risk. Hence,
investors in the Hong Kong, Malaysia and (to a lesser degree) Japanese real estate stock markets do
not hold diversified portfolios and accordingly they need compensation for bearing unsystematic risk
in the real estate market, particularly when the market excess returns are negative. Our results also
lend some support to the conventional wisdom that idiosyncratic volatility is able to affect real estate
stock returns.
In up market, rational investors may be willing to accept smaller returns for positive
skewness. Table 6 shows that in up-market, the slope coefficients of skewness for Hong Kong and
Singapore have the expected negative sign and are statistically significant at least at the 5% level.
Similarly, when the market excess returns are negative (down-market), the slope coefficient of
skewness for Japan has the expected positive sign and is statistically significant at the 5% level. Our
results hence suggest that skewness plays a role in pricing some Asian real estate stocks. Finally,
Tables 6 and 7 also indicate that there is a significantly positive (negative) relation between returns
and kurtosis in up-market for Malaysia and (down) market for Japan and Malaysia at the 1% level.
Again, this indicates that kurtosis is an additional risk factor that should be considered in pricing some
Asian-Pacific real estate stocks.
By comparing the adjusted coefficient of determination (R2) of each regression model, the
country model that has the greatest explanatory power to realized returns in up and down markets is
also identified. In up market, the country models selected are: beta and beta squared (Australia), beta
and beta squared (Hong Kong), beta and unsystematic risk (Japan), beta and Kurtosis (Malaysia), and
beta and skewness (Singapore); whereas in down markets, the respective models are: beta and beta
squared (Australia), beta and unsystematic risk (Hong Kong), beta and beta squared (Japan), beta and
skewness (Malaysia), and beta (Singapore). One possible explanation for these cross-sectional
differences is that the tax, legal and political structures of the five countries could have significant
effects on the degree of correlation between the average return and the various risk factors observed
(Liow and Webb, 2005). This issue is of course beyond the scope of the current paper.
14
In relation to Hypothesis 6, Table 8 reveals that the hypothesis of the symmetrical risk
premiums for beta in up and down markets is rejected for Hong Kong, Malaysia and Singapore as the
respective F-statistics are statistically significant at least at the 10% level. When beta squared is added
to the conditional relation between beta and returns, the slope coefficients (i.e. risk premiums) of beta
during up and down markets are statistically different at least at the 10% level for Australia, Hong
Kong and Japan. Similarly, the slope coefficients of beta squared during up and down markets are
statistically different at least at the 10% level for Hong Kong and Japan. For the case of beta and
unsystematic risk during up and down markets, the slope coefficients of beta and unsystematic risk
are, respectively, statistically different at least at the 10% level for Hong Kong, Japan and Malaysia
and Australia and Japan. When skewness is introduced, the risk premiums of beta during up and down
markets are not statistically different for Australia and Singapore while the slope coefficients of
skewness are found to be statistically significant at the 1% level for Malaysia only. For the case of
kurtosis and beta during up and down markets, the same result is found for kurtosis and the slope
coefficients of beta are not statistically different for Australia and Malaysia. Overall, the results imply
that investors in the respective real estate stock markets react differently to the risk factors during up
and down markets. Again, these findings reinforce the existence and importance of country specific
factors in influencing real estate stock returns.
(Table 8 here)
Finally, Table 9 reports that the average annualized excess returns are, respectively, 16.83%
(Malaysia), 11% (Singapore), 9.55% (Hong Kong), 7.17% (Australia) and 0.39% (Japan), in the
testing period, which fail to reject the null hypothesis of zero excess market return at the 5% level.
Hence the reward for bearing risk in the respective markets, although is positive, is nevertheless weak.
Accordingly, Hypothesis 7 is accepted.
(Table 9 here)
5.4
Pooled regression results
The above country results suggest that the responses and statistical significance of all risk
factors to real estate stock returns are not uniform and depend upon the individual real estate markets.
15
Furthermore investors in the different real estate markets react differently to the risk factors during up
and down markets. In this section, we report the results from estimating a pooled sample that
comprises all 21 Asian-Pacific real estate stock portfolios for both the unconditional and conditional
models. The overall results will complement the individual market analyses and provide international
investors and portfolio mangers with an aggregate perspective regarding the risk-return relation when
investing in the Asian-Pacific real estate stock markets.
Table 10 presents the results of the unconditional relation between beta and returns for the
entire Asian-Pacific real estate stock market. In addition, the empirical results on the unconditional
beta when other risk factors are added are also presented. Overall, beta is a useful measure of risk. It is
linearly related to the average returns and is statistically significant at the 1% level. However beta
alone is only able to explain about 5% of the cross-sectional variation in real estate stock returns.
Additional results show that beta is always significantly and positively related to returns when other
risk factors (except beta squared) are added to the unconditional model. Of the four risk factors added,
beta squared (p<0.05) and kurtosis (p<0.01) emerge as additional significant risk factors that explain
real estate stock returns. Nevertheless, the highest adjusted R2 is only 5.6% for the unconditional
CAPM model that includes beta and kurtosis as explanatory variables of returns.
(Table 10 here)
When the risk-return relation is investigated under Pettengill et al. (1995)’s conditional
framework, Table 11 reveals that the Adjusted R2 of the conditional beta model improve significantly
from about 5% to a high of about 17%. The increased explanatory power of the conditional beta to the
cross-sectional variations in real estate stocks is thus obvious. Except for beta-squared, the
significance of other risk factors differs in up and down market conditions. Specifically, the
conditional relation between real estate returns and beta is nonlinear regardless of market conditions.
Furthermore, whilst kurtosis appears to play an important role in pricing Asian-Pacific real estate
stocks in up-market, unsystematic risk and skewness are significant in pricing Asian-Pacific stock
returns in down market. Consequently, beta, beta-squared, and to a lesser degree, unsystematic risk,
16
skewness and kurtosis can help explain significantly the return-generating process of Asian-Pacific
real estate stocks.
(Table 11 here)
Further evidence regarding the importance of the respective factors can be confirmed by the
adjusted R2. In up market, when the factors are added separately to the conditional relation between
beta and returns, adjusted R2 remain the same for the addition of unsystematic risk and skewness,
indicating that these two factors are not priced. On the contrary, adjusted R2 increases for the addition
of beta squared and kurtosis. Similar observations can be made with regard to the importance (or
otherwise) of the respective factors in down market. Specifically, beta squared, unsystematic risk and
skewness appear to be priced as their addition into the condition models results in an increase in the
adjusted R2. Finally, the conditional model that includes beta and beta squared has the greatest
explanatory power to the cross-sectional variations in the Asian Pacific real estate stock returns across
the different regression models - the adjusted R2 values are respectively, 0.2018 (up-market) and
0.2123 (down market).
The average annualized excess return for the pooled Asian-Pacific Sample is about 10.99% (t
=0.62). Moreover, the null hypothesis of zero monthly excess market returns cannot be rejected at the
conventional significance levels. Table 12 also shows an F-statistic of 5.20 rejects the null hypothesis
of symmetrical risk premiums for beta in up and down markets. Specifically, when beta-squared is
added to the conditional relation between beta and returns, the risk premiums of beta and beta squared
during up and down markets are statistically different at the 1% level. For the case of beta and
unsystematic risk during up and down markets, the same result is found although the significance of
the risk premiums for beta is reduced to the 10% level. When skewness is introduced, the risk
premiums of beta during up and down markets are found to be statistically different at the 5% level
whilst the slope coefficients of skewness are not statistically different. For the case of kurtosis during
up and down markets, the same result is found. Overall, the pooled results indicate that the slope
coefficients of beta squared and unsystematic risk are not symmetrical in the Asian-Pacific real estate
17
stock markets. There are two important implications arising from these results. The first is that the
relation between real estate stock returns and beta is non-linear. Consequently, other possible
properties of Asian-Pacific real estate stock returns like mean-reversion, long memory and regimeswitching needs to be explored in future research. Second, it is likely that investors do not hold
diversified portfolios in the Asian-Pacific real estate stock markets since idiosyncratic volatility still
affects real estate stock returns.
(Table 12 here)
6.
CONCLUSION
In this study, the return-generating process of five Asian-Pacific public real estate markets
individually and as a whole is investigated using both the unconditional and conditional CAPM
models over a period of 12 years. With the increased significance and re-emergence of Asian real
estate stocks as property investment opportunities for international investors, this study is timely and
provide investors with additional knowledge with regard to the risk-return relations and pricing in the
regional Asian-Pacific real estate stock markets. To the best of our knowledge, this is one of very few
empirical studies that comprehensively investigate the significance of beta and other risk factors in up
and down markets for real estate investment in an international context.
Although the unconditional relation between beta and returns is found to be significantly
positive for the Asian-Pacific real estate stock market as a whole, the explanatory power is very low.
Furthermore, there is some evidence of nonlinear risk-return relation. Kurtosis also plays a significant
role in pricing the Asian-Pacific real estate stocks. However, the incremental explanatory power to
real estate stock returns is still very limited.
A significantly positive relation in up market and a significantly negative relation in down
market between beta and returns are detected when the conditional CAPM model based on Pettengill
(1995)’s methodology is investigated. The increased explanatory power of the conditional beta to the
cross-sectional variations in real estate stocks is obvious. Except for beta-squared, the significance of
other risk factors differs in up and down market conditions. More specifically, the conditional relation
18
between real estate returns and beta is nonlinear regardless of market conditions. Whilst beta squared
and kurtosis appear to play a significant role in explaining returns in up market, beta squared,
unsystematic risk and skewness seem to be relevant in real estate stock pricing. Furthermore the
model beta and beta squared has the greatest explanatory power to the cross-sectional variations in the
Asian Pacific real estate stock returns across the different regression models. Finally, the average
monthly excess returns for the five Asian Pacific real estate stock markets is positive and yet
statistically insignificant. The symmetry of the risk-return relation in up and down markets is only
weak to moderate. Overall, in consistent with previous stock market findings, our results imply that
beta is a good tool in explaining the cross-sectional differences in Asian-Pacific real estate stock
returns and for portfolio management (e.g. for market timing strategies). Moreover, other risk factors
are also useful in explaining the return-generating process of Asian-Pacific real estate stocks, and
hence, are relevant to portfolio managers. Our results thus provide useful knowledge on investing in
the Asian-Pacific real estate stock markets.
ACKNOWLEDGEMENTS
The author would like to thank delegates at the July 2005 10th Asian Real Estate Society (AsRES) annual
conference and Professor James Shilling for helpful comments on an earlier version of this paper and Ms
Geraldine Shee for providing excellent research assistance
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20
Table 1 Economic & stock market statistics (2003)
Hong
Kong
GDP*
Malaysia
Australia
156.67
Singapore
93.56
Japan
4648.19
103.16
588.03
Exchange rate*
US $ Billion
Local per
USD
7.787
1.7008
107.1
3.8
1.333
Lending rate*
%
5
5.31
1.82
6.3
4.9
Unemployment rate*
%
7.9
5.4
5.3
3.5
5.9
Stock Market Captilization**
US $ Million
463,108
101,900
2,126,075
123,872
380,969
Value Traded **
US $ Million
210,622
56,129
1,573,279
27,623
294,658
0.45
1
1
0
1
968
434
3,058
865
1,355
478.4
235
695
143
281
Value Traded (/market cap)**
No. of companies**
Average firm Size**
US $ Million
Real Estate stock % of stock market***
%
P/E ratio of real estate stock***
Dividend yield of real estate stock***
%
11.44
8.49
1.27
2.68
8.95
22.60
21.60
35.50
14.20
17.10
2.47
2.58
0.94
2.96
5.69
Source: * data from IMF country database, the other data are extracted from Stock Market Factbook
** Source: Standard & Poor's Emerging Stock Markets Factbook 2003 and IMF
*** Source: Datasteam
Table 2
Real Estate Stock Sample: Sep 94 – Aug 04
Country
No of
stocks
No of
portfolio**
Australia
17
2
Hong Kong
75
8
Japan
34
4
Malaysia
43
5
Singapore
17
2
No of stocks in the portfolio*
Portfolio 1- (9)
Portfolio 2 - (8)
Portfolios (1-4) - (10) each
Portfolios (5-7) – (9) each
Portfolio 8 – (8)
Portfolios (1,2) – (9) each
Portfolios (3,4) – (8) each
Portfolios (1-3) – (9) each
Portfolios (4,5) – (8) each
Portfolio 1- (9)
Portfolio 2 – (8)
* Please refer to the “research data” section in the main text for the explanation on portfolio formation.
21
Table 3
Unconditional and Conditional CAPM: Hypotheses Testing
Unconditional regression:
~
R jt = α~0t + α~1t β j + α~2t (var iable j ) + ε jt
Hypothesis
Variable p
α~0t
1
Beta
2
Beta Squared
3
Unsystematic Risk
4
Skewness
5
Kurtosis
* Hypothesis 1 is tested jointly with hypotheses 2-5
** Null hypothesis is when the coefficients equal zero
Alternative Hypothesis**
≠ 0*
≠ 0*
≠ 0*
≠ 0*
≠ 0*
α~1t
α~2t
>0
>0
>0
>0
>0
-≠0
>0
<0
>0
Conditional regression:
~
R jt = α~0t + α~1ut β j + α~2ut (var iable j ) + α~1dt β j (1 − ϕ ) + α~2 dt (var iable j )(1 − ϕ ) + ε jt
Hypothesis
1
2
Variable p
α~0t
Beta
≠ 0*
Beta Squared
≠ 0*
Unsystematic
≠ 0*
3
Risk
4
Skewness
≠ 0*
5
Kurtosis
≠ 0*
* Hypothesis 1 is tested jointly with hypotheses 2-5
**Null hypothesis is when the coefficients equal zero
Alternative Hypothesis**
Market excess returns > 0
Market excess returns < 0
α~1ut
α~2ut
α~1dt
α~ 2 dt
>0
>0
-≠0
<0
<0
-≠0
>0
>0
<0
<0
>0
>0
<0
>0
<0
<0
>0
<0
Hypotheses 6 and 7 for the conditional CAPM
Hypothesis
6
7
Description
The slope coefficients under up and down markets are symmetrical
Average mean excess market returns are positive
22
Table 4
Risk-return characteristics of the portfolios: September 1995 – August 1998 (Estimation period)
Country
Australia
Hong
Kong
Japan
Malaysia
Singapore
Real
estate
stock
portfolio
Mean
Excess
Returns
Std Dev of
Excess
Returns
Mean Beta
Mean
Skewness
Mean
Kurtosis
Mean
Unsystematic
risk
1
2
1
2
3
4
5
6
7
8
1
2
3
4
1
2
3
4
5
1
2
0.0073
0.0062
-0.0105
-0.0162
-0.0096
-0.0162
-0.0033
-0.0024
0.0049
0.0011
0.0031
0.0124
0.0103
0.0098
0.0038
0.0035
0.0015
0.0091
0.0015
0.0107
0.0079
0.0622
0.0429
0.1168
0.1022
0.0902
0.1241
0.1073
0.0850
0.1031
0.1144
0.0561
0.0903
0.0857
0.1167
0.1267
0.1046
0.1214
0.1374
0.1169
0.1104
0.1233
0.4416
0.8205
0.5523
0.7254
0.8231
1.0139
1.0784
1.0374
1.1589
1.2553
0.6701
1.1343
1.1098
1.5524
1.3147
1.0640
1.2392
1.4357
1.2231
1.5544
1.6432
-0.1202
-0.1472
-0.7318
-0.1472
-0.9513
0.2204
-0.4793
-0.6420
-0.1396
-0.1094
0.4227
0.7863
0.4666
0.3397
0.5519
0.3382
0.5553
0.8104
0.3649
0.2328
0.7975
3.1158
4.3890
4.3891
6.6876
6.1701
5.5486
5.7882
7.5123
6.3862
7.0275
3.3309
4.2882
2.8987
4.1078
7.0649
6.1600
5.6619
7.5267
6.2102
7.9669
7.5315
0.0562
0.0376
0.1047
0.0099
0.0810
0.1015
0.0865
0.0758
0.0680
0.0843
0.0499
0.0748
0.0735
0.1100
0.0916
0.0841
0.0879
0.1114
0.0949
0.0639
0.0667
23
Table 5
Regression results on beta and other risk factors (unconditional CAPM)
~
R jt = α~0t + α~1t β j + α~2t (var iable j ) + ε jt
Panel A: Estimation results
Variable p
α~
0t
Beta
Beta-squared
Unsystematic
risk
Skewness
Kurtosis
Australia
α~
1t
-0.002
(-0.2)
-0.008
(-0.6)
-0.001
(-0.0)
0.009
(0.69)
0.012
(0.96)
0.053
(0.34)
0.012
(0.94)
-0.009
(-0.4)
0.017
(0.70)
0.010
(0.76)
α~
2t
α~
0t
Hong Kong
α~
1t
-0.04
(-0.8)
-0.03
(-0.2)
-0.02
(-1.3)
-0.03
(-2.0) B
-0.01
(-0.2)
0.032
(1.33)
-0.03
(-2.0) B
0.023
(1.58)
0.028
(-0.3)
0.014
(0.92)
0.024
(1.59)
-0.01
(-0.8)
-0.04
(-2.5) B
0.011
(0.62)
--
α~
2t
α~
Japan
α~
0t
1t
α~
2t
α~
0t
0.029
(0.59)
-0.56
(-3.0) A
-0.00
(-0.3)
0.014
(2.42) B
0.023
(3.37) A
0.038
(2.12)B
0.025
(2.78) A
-0.05
(-2.2) B
-0.04
(-1.5)
-0.07
(-2.6) A
-0.05
(-2.1) B
-0.20
(-2.4)B
-0.24
(-1.4)
-0.03
(-1.6)
-0.04
(-0.8)
0.086
(0.31)
-0.04
(-0.8)
-0.02
(-0.4)
0.006
(1.50)
0.032
(1.42)
-0.05
(-2.2) B
-0.01
(-0.8)
-0.03
(-0.7)
--
--
Malaysia
α~
1t
0.034
(0.88)
-0.17
(-0.4)
0.030
(0.73)
0.012
(0.30)
-0.12
(-2.5)B
α~
2t
-0.085
(0.65)
0.045
(0.38)
0.023
(1.30)
0.049
(5.3)A
α~
0t
Singapore
α~1t
α~2t
0.003
(0.07)
0.073
(0.27)
-0.06
(-1.2)
-0.11
(-1.9) C
0.004
(0.16)
-0.09
(-0.3)
0.240
(2.26) B
0.089
(2.16)B
0.032
(0.26)
-4.766
(-2.3) B
-0.05
(-2.7) A
-0.02
(-0.3)
0.003
(0.09)
0.005
(0.57)
--
Notes:
t - statistics are in parenthesis; significant coefficients are in bold
A statistically significant at 1%; B statistically significant at 5%; C statistically significant at 10%
Panel B: Adjusted R2 values
Variable p
Beta
Beta-squared
Unsystematic risk
Skewness
Kurtosis
Australia
-0.11%
-0.34%
-0.74%
0.43%
-0.27%
Hong Kong
0.26%
0.14%
1.58%
0.11%
0.47%
Adjusted R2 results
Japan
1.28%
2.94%
1.64%
1.83%
1.18%
Malaysia
-0.06%
-0.29%
-0.30%
0.13%
6.93%
Singapore
-0.69%
-1.35%
2.25%
3.54%
-1.17%
24
Table 6
Regression results on beta and other risk factors (conditional CAPM): excess market returns > 0 (up market)
~
R jt = α~0t + α~1ut β j + α~2ut (var iable j ) + α~1dt β j (1 − ϕ ) + α~2 dt (var iable j )(1 − ϕ ) + ε jt
Panel A: Estimation results
Variable p
Australia
α~
0t
Beta
0.046
(5.5)A
Beta-squared
0.027
(2.8)A
Unsystematic
risk
Skewness
0.017
(0.9)
0.043
(4.2)A
Kurtosis
0.060
(2.7)A
α~
1ut
Hong Kong
α~
2 ut
α~
α~
0t
1ut
Japan
α~
2 ut
α~
0t
α~
1ut
Malaysia
α~
2 ut
α~
0t
Singapore
α~
α~
1ut
2 ut
α~
0t
α~1ut
α~2ut
-0.005
(-0.5)
--
0.036
(2.3)B
0.052
(3.2)A
--
0.083
(14.0) A
-0.08
(-2.7)A
--
-0.124
(-2.3) B
0.186
(4.1) A
--
-0.037
(-0.6)
0.074
(2.2)A
--
0.102
(3.1)A
-0.09
(-3.4) A
0.121
(2.9)A
-0.160
(-1.6)
0.116
(2.1)B
0.080
(11.7) A
-0.09
(-2.9)A
0.089
(0.9)
0.311
(0.9)
-0.55
(-1.0)
0.305
(1.3)
0.173
(0.5)
-0.217
(-0.5)
0.096
(0.6)
-0.000
(-0.0)
0.502
(1.6)
0.026
(1.0)
0.054
(3.2)A
0.100
(0.5)
0.059
(3.1) A
-0.06
(-1.9)C
0.241
(1.3)
-0.124
(-2.3) B
0.184
(3.9)A
0.027
(0.2)
-0.071
(-1.2)
0.211
(1.9) C
-2.831
(-1.3)
0.001
(0.1)
0.006
(0.5)
0.034
(2.2)B
0.053
(3.3)A
-0.015
(-2.0) B
0.090
(9.7) A
-0.07
(-2.5) B
-0.02
(-0.9)
-0.08
(-1.5)
0.126
(2.6)B
0.061
(2.8)A
-0.200
(-2.6) B
0.187
(3.7)A
-0.067
(-2.8) A
-0.008
(-0.7)
-0.00
(-0.7)
0.038
(2.1) B
0.054
(2.9) A
-0.000
(-0.2)
0.060
(2.4)B
-0.08
(-2.7) A
0.008
(1.0)
-0.10
(-2.3) B
-0.09
(-2.1) B
0.086
(10.4) A
-0.038
(-0.5)
0.074
(2.1)B
0.001
(0.0)
Notes:
t - statistics are in parenthesis; significant coefficients are in bold
A statistically significant at 1%; B statistically significant at 5%; C statistically significant at 10%
Panel B: Adjusted R2 values
Variable p
Beta
Beta-squared
Unsystematic risk
Skewness
Kurtosis
Australia
-0.87%
10.45%
1.11%
-1.75%
-1.53%
Hong Kong
3.51%
4.89%
3.21%
4.64%
3.14%
Adjusted R2 results
Japan
4.22%
4.15%
4.67%
4.12%
4.18%
Malaysia
8.65%
9.09%
8.13%
12.36%
44.49%
Singapore
4.85%
4.04%
5.75%
13.28%
3.53%
25
Table 7
Regression results on beta and other risk factors (conditional CAPM): excess market returns < 0 (down market)
~
R jt = α~0t + α~1ut β j + α~2ut (var iable j ) + α~1dt β j (1 − ϕ ) + α~2 dt (var iable j )(1 − ϕ ) + ε jt
Panel A: Estimation results
Variable p
α~
0t
Beta
Beta-squared
Unsystematic
risk
Skewness
Kurtosis
-0.047
(-4.5)
-0.026
(-2.0)B
-0.05
(-4.0)A
-0.03
(-2.5)B
-0.04
(-1.8)C
Australia
α~
1dt
0.007
(0.5)
-0.13
(-2.2)B
0.007
(0.5)
-0.02
(-0.9)
0.006
(0.5)
α~
2 dt
-0.117
(2.4)B
0.017
(0.2)
-0.02
(-1.6)
-0.00
(-0.2)
α~
0t
-0.06
(-5.8)A
-0.06
(-2.2)B
0.007
(0.4)
-0.06
(-5.7)A
-0.07
(-5.1) A
Hong Kong
α~
1dt
-0.02
(-1.3)
-0.01
(-0.2)
-0.03
(-2.3)B
-0.02
(-1.3)
-0.02
(-1.5)
α~
2 dt
--0.00
(-0.0)
-0.65
(-4.3)A
0.003
(0.4)
0.003
(0.9)
α~
0t
-0.06
(-19)A
-0.05
(-17)A
-0.04
(-5.1)A
-0.05
(-9.3)A
-0.02
(-1.8)C
Japan
α~
1dt
0.194
(8.1)A
0.131
(4.9)A
0.182
(7.4)A
0.192
(8.2)A
0.191
(8.2)A
α~
2 dt
--0.29
(-4.3)A
-0.15
(-1.7)C
0.018
(-1.9)C
-0.01
(-2.8)A
α~
0t
0.081
(2.6)A
-0.26
(-1.5)
0.067
(2.2)B
0.043
(1.4)
0.092
(3.1)A
Malaysia
α~
1dt
-0.13
(-5.1)A
0.444
(1.5)
-0.09
(-3.1)A
-0.08
(-3.1)A
-0.06
(-1.9)C
α~
2 dt
--0.24
(-2.0)B
-0.38
(-3.0)A
-0.05
(-4.4)A
-0.03
(-4.1)A
α~
0t
0.058
(2.1)B
0.059
(0.7)
0.057
(2.1)B
0.036
(1.0)
0.081
(2.1)B
Singapore
α~1dt
-0.08
(-4.8)A
-0.08
(-0.8)
-0.09
(-2.6)B
-0.06
(-2.7)A
-0.08
(-4.7)A
α~ 2 dt
-0.001
(0.0)
0.245
(0.3)
-0.01
(-0.9)
-0.005
(-0.9)
Notes:
t - statistics are in parenthesis; significant coefficients are in bold
A statistically significant at 1%; B statistically significant at 5%; C statistically significant at 10%
Panel B: Adjusted R2 values
Variable p
Beta
Beta-squared
Unsystematic risk
Skewness
Kurtosis
Australia
-1.29%
6.49%
-3.02%
1.11%
-3.02%
Hong Kong
0.21%
-0.09%
5.44%
-0.04%
0.13%
Adjusted R2 results
Japan
31.36%
38.80%
32.24%
32.69%
34.48%
Malaysia
11.61%
12.97%
15.14%
19.48%
18.46%
Singapore
24.33%
23.19%
23.31%
24.21%
24.08%
26
Table 8
Test results of symmetry for slope coefficients in up and down markets
Beta
Australia
0.48(0.49)
Hong Kong
3.35 (0.07)*
F-statistic (p-value)
Japan
0.30(0.59)
Malaysia
19.76(0.00)*
Singapore
13.44(0.02)*
Beta
Beta-squared
3.98(0.05)*
2.11(0.15)
3.11(0.08)*
4.52(0.04)*
5.03(0.03)*
3.70(0.06)*
1.45(0.23)
2.55(0.11)
0.74(0.39)
0.69(0.41)
Beta
Unsystematic risk
0.16(0.68)
10.07(0.01)*
4.41(0.04)*
1.53(0.21)
13.39(0.00)*
3.51(0.06)*
12.72(0.01)*
1.09(0.29)
2.33(0.13)
0.07(0.79)
Beta
Skewness
0.04(0.95)
0.84(0.36)
3.46(0.06)*
1.80(0.18)
14.99(0.00)*
0.24(0.62)
6.07(0.02)*
8.05(0.01)*
3.95(0.05)*
0.31(0.57)
Beta
Kurtosis
0.32(0.57)
0.10(0.75)
4.69(0.03)*
1.41(0.23)
22.16(0.00)*
2.41(0.12)
0.45(0.50)
56.95(0.00)*
11.84(0.00)*
0.77(0.38)
Independent variable
Notes:
This table shows the test results of whether slope coefficients in the following regression equation are equal in the up and down markets (Hypothesis 6) for beta
~ = α~ ) and additional variables ( α~ = α~ ) for the conditional equation
(α
1ut
1dt
2 ut
2 dt
~
R jt = α~0t + α~1ut β j + α~2ut (var iable j ) + α~1dt β j (1 − ϕ ) + α~2 dt (var iable j )(1 − ϕ ) + ε jt
* denotes that the alternative hypothesis is accepted at the 10% level
27
Table 9
Average monthly real estate stock market excess returns
Annualised mean excess
return
Monthly mean excess
return
Monthly standard
deviation
T-statistic
P-value
Australia
Hong Kong
Japan
Malaysia
Singapore
0.0717
0.0954
0.0039
0.1682
0.1100
0.0058
0.0079
0.0003
0.0138
0.0087
0.0313
0.0754
0.0498
0.0789
0.0688
1.57
0.12
0.89
0.37
0.05
0.96
1.48
0.14
1.08
0.28
Notes:
This table shows both the annualized and monthly mean excess real estate stock returns. The test results of whether the monthly mean excess return is significantly
different from zero (hypothesis 7) is also reported.
28
Table 10
Pooled regression results on beta and other risk factors (unconditional CAPM)
~
R jt = α~0t + α~1t β j + α~2t (var iable j ) + ε jt
\
Variable p
Pooled sample
α~
α~2t
Adjusted R2
-0.018 (2.19) B
0.062 (0.82)
-0.003(-0.48)
0.007(3.20) A
4.98%
5.22%
4.97%
4.94%
5.57%
1t
Beta
Beta-squared
Unsystematic risk
Skewness
Kurtosis
0.044(9.49) A
0.016(1.23)
0.041(7.56) A
0.043(8.43) A
0.026(3.64) A
Notes:
~ ) cannot be tested as the risk free rate differs for each country. A fixed
The Sharpe-Lintner hypothesis ( α
0t
effect technique was used for this pooled regression. The fixed effect technique of the intercept allows the
~ and α~ ) nfor
intercept term to be different for each portfolio, but has only one slope coefficients each (i.e. α
1t
2t
the pooled regression
\t - statistics are in parenthesis; significant coefficients are in bold
A statistically significant at 1%; B statistically significant at 5%; C statistically significant at 10%
Table 11
Pooled regression results on beta and other risk factors (conditional CAPM)
~
R jt = α~0t + α~1ut β j + α~2ut (var iable j ) + α~1dt β j (1 − ϕ ) + α~2 dt (var iable j )(1 − ϕ ) + ε jt
Variable p
α~
Positive excess market returns
1ut
α~
2 ut
Adjusted
R2
α~
Negative excess market returns
1dt
α~ 2 dt
Adjusted R2
Beta
0.117(9.79)A
--
14.84%
-0.096(-11.31) A
--
16.89%
Beta-squared
Unsystematic
risk
Skewness
Kurtosis
-0.026(-1.10)
0.067(6.92)A
20.18%
0.020(1.02)
-0.053(-6.58)A
21.23%
-0.292(-4.03)A
18.51%
0.0104(2.56) B
0.005(0.22)
17.49%
16.79%
0.117(9.73) A
-0.009(-0.11)
14.72%
-0.087(-9.89) A
0.117(9.78) A
0.110(9.14) A
-0.004(-0.63)
0.014(4.69) A
14.76%
17.30%
-0.094(-10.92) A
-0.969 (-10.76) A
Notes:
~ ) cannot be tested as the risk free rate differs for each country. A fixed
The Sharpe-Lintner hypothesis ( α
0t
effect technique was used for this pooled regression. The fixed effect technique of the intercept allows the
~ and α~ ) nfor
intercept term to be different for each portfolio, but has only one slope coefficients each (i.e. α
1t
2t
the pooled regression
\t - statistics are in parenthesis; significant coefficients are in bold
A statistically significant at 1%; B statistically significant at 5%; C statistically significant at 10%
29
Table 12
Pooled regression testing results for slope coefficients in up and down markets
Independent variable
Pooled sample
F-statistic
P-value
Beta*
5.20
0.03*
Beta*
11.51
0.00*
Beta-squared*
7.10
0.01*
Beta*
3.68
0.06*
Unsystematic risk*
7.79
0.01*
Beta*
4.80
0.03*
Skewness
2.01
0.16
Beta*
4.58
0.04*
Kurtosis
0.37
0.54
Notes:
This table shows the test results of whether slope coefficients in the following pooled regression equation are
~ = α~ ) and additional variables ( α~ = α~ )
equal in the up and down markets (Hypothesis 6) for beta ( α
1ut
1dt
2 ut
2 dt
for the conditional equation
~
R jt = α~0t + α~1ut β j + α~2ut (var iable j ) + α~1dt β j (1 − ϕ ) + α~2 dt (var iable j )(1 − ϕ ) + ε jt
* denotes that the alternative hypothesis is accepted at the 10% level
30