CRES:2004-006
IMPACT OF INTEREST RATE LEVEL AND VOLATILITY ON TIME-VARYING EXCESS RETURNS
FOR PROPERTY STOCKS – SOME INTERNATIONAL EVIDENCE
Kim Hiang, LIOW and Qiong, HUANG, Department of Real Estate, National University of Singapore
Contact author
Dr Kim Hiang LIOW
Associate Professor and Deputy Head (Academic)
Department of Real Estate
National University of Singapore
4 Architecture Drive
Singapore 117566
Tel: (65)68743420
Fax: (65)67748684
E-mail: [email protected]
17 May 2004
IMPACT OF INTEREST RATE LEVEL AND VOLATILITY ON TIME-VARYING EXCESS RETURNS
FOR PROPERTY STOCKS – SOME INTERNATIONAL EVIDENCE
Abstract
This study attempts to investigate whether the level and volatility of interest rates affect the excess returns of
property stocks within a time-varying risk framework. Specifically, a three–factor APT model is developed with
excess return volatility, interest rate level and interest rate volatility as its factors. Using the generalized
autoregressive conditionally heteroskedastic in the mean (GARCH-M) methodology on monthly excess returns of
property stock indexes of Singapore, Hong Kong, Japan and the United Kingdom for the period 1987-2003 and
two shorter-sample periods, there is some evidence of a positive trade-off between the excess returns and
conditional variances for Japan, Singapore and the UK. Strong time-varying conditional volatility is found in the
excess return series of all four markets On the whole property stock market volatility is more persistent in
Singapore, relative to the UK, HK and Japan. Property stocks are generally sensitive to changes in the long-term
and short-term interest rates and to a lesser extent, their volatility. In addition, there are disparities in the
magnitude as well as direction of sensitivities in interest rate level and volatility across regional property stocks
and different market conditions. Overall, results indicate changes in the ARCH parameter, risk premia, persistence
of volatility and interest rate level and volatility effects before and after the 1997 Asian Financial crisis. However
these noted changes are not uniform and depend upon the individual property stock markets. Our findings
enhance the investors’ understanding in equilibrium asset pricing and complements existing evidence in
international real estate.
Introduction
Investors in real estate can choose to hold it directly by investing in physical (unsecuritized) property, or
indirectly through the purchase of shares in Real Estate Investment Trusts (REITs) or real estate operating
companies, in short, real estate companies. In countries such as the UK, Hong Kong and Singapore, given the
relative absence of REITs, the stocks of these companies, commonly known as property stocks, provide an
important investment opportunity to obtain exposure to the stock market and the underlying property assets that
comprise these portfolios. Specifically listed real estate companies have become an increasingly important
property investment vehicle in Asia and internationally. With recent studies such as Steinert and Crowe (2001) and
Conover et al. (2002) highlighting the diversification benefits and added value of including international listed
property in a mixed asset portfolio, considerable research has focused on performance analysis in Asian markets
and the inter-relationship between the respective securitized and unsecuritized real estate markets.1 However,
little attention has been given to the lack of knowledge by international investors on the return volatility, timevarying excess returns and return-generating process of property stocks in Asian markets. Another key concern is
that with two parallel markets (i.e. stock market and physical real estate market) for trading real estate assets, it is
very likely that property stock return and volatility characteristics are different from those of stock markets
(especially) in the long term. Thus, research results from the stock markets should not be automatically extended
to the real estate stock markets. 2 Additionally, real estate stocks are also different from REITs in their
organizational form, tax status, institutional framework and investment performance. 3 A body of empirical
knowledge in time-varying risk-return dynamics and equilibrium asset pricing of property should add greatly to
international real estate literature.
In a different vein, one interesting issue appeared in the financial asset pricing literature is the impact of
interest rate risk and its pricing in the stock markets for banks and financial institutions.4 Similarly, several studies
in the US, UK and Singapore have observed that returns of direct real estate, REITs and property companies are
2
influenced by interest rate movements.5 However, many of these studies did not include an assessment of the
effect of the changes in the interest rate volatility on the time-varying excess returns of property companies. As
high interest rate volatility can adversely affect spending and economic activity and thereby affect property
company earnings and excess stock returns, it is important to incorporate the volatility effect, in addition to the
level effect, in asset pricing models.
The resulting key investment issue is whether the level and volatility of interest rates affect the excess
returns of property stocks within a time-varying risk framework. Specifically, a three–factor APT model is
developed with excess return volatility, interest rate level and interest rate volatility as its factors. Using the
generalized autoregressive conditionally heteroskedastic in the mean (GARCH-M) methodology on monthly
excess returns of real estate stock indexes of Singapore, Hong Kong, Japan and the UK for the period 1987-2003
and two shorter-sample periods (i.e. pre-1997 Asian financial crisis and post-1997 Asian financial crisis periods),
the specific objectives of this research are:
(a)
to develop a three-factor APT model that includes excess return volatility, interest rate level and interest
rate volatility as its factors in a time-varying framework
(b)
to assess and compare the property stock excess return volatility, persistence of volatility and risk
premia in three Asian markets (HK, Singapore, Japan) and one European market (the UK) and across
the two short-sample periods (i.e. pre-crisis period and post-crisis period). Since the long-term and
short-term interest rates and their volatility might affect real estate stock returns differentially, these
variables are included in alternative specifications
(c)
to assess whether the changes in interest rate level and volatility have significant effects on the excess
returns of property stocks.
(d)
to compare significance and magnitude of the interest rate effects across the four real estate markets
and for the pre- and post-crisis periods
To establish a background for the study, the next section provides a brief review of relevant empirical
literature. This is followed by presentations of research data and methodology. The empirical results are then
reported and discussed. The final section concludes the study.
Literature Review
The literature on stock market volatility and the studies regarding interest rate sensitivity and pricing on
stock returns provide an appropriate empirical foundation for this study.
Over the last ten years there has been substantial growth in the number of empirical studies examining
the volatility of stock returns, particularly those conditionally heteroskedastic models such as ARCH or GARCH
processes to model conditional variances and covariances.6 Essentially the ARCH or GARCH processes allow the
conditional variance of a stock return series to depend on the past realizations of the error process. For a stable
process, the conditional variance will eventually decay to the long term (unconditional) variance. Todate, there is
considerable evidence in the finance literature to suggest that clustering, predictability and persistent in
conditionally volatility exist in international stock markets (Poon and Taylor; Theodossiou and Lee, 1995).
Specifically, stock return volatility is highly persistent and probably is an integrated process. Thus risk premium are
highly persistent and volatility shocks can have large effects on prices. Another important development is that the
ARCH and GARCH effects have been included in a regression framework to test hypothesis involving risk-return
3
trade-off. In the spirit of asset pricing, the CAPM or APT with time-varying conditional variances would thus appear
to be an improvement on the assumption that equilibrium returns are constant. The GARCH-in mean (GARCH-M)
model, introduced by Engle, Lilien and Robins (1987), links explicitly the conditional variance to the conditional
mean of returns and provide a framework to examine the relationship between volatility and expected returns. The
relevant trade-off parameter is interpreted as the coefficient of relative risk aversion (Merton, 1980). It can take a
positive, a negative or a zero value depending on agents’ utility function and the supply condition of the assets.
For example, Choudhry (1996) use a GARCH-M model to studies volatility, risk premia and the persistence of
volatility in six emerging markets before and after the 1987 stock market crash. He fails to find a significant
positive relationship between risk and return (as advocated by the CAPM) in any one of the six markets during any
period. However, significant negative risk premium coefficients are found for two of the markets in the post-1987
crash period.
Similar research in securitized real estate is relatively limited. Liu and Mei (1992) examine the time variation
in both the expected and unexpected REIT returns using a multifactor latent-variable model. They find that the
capitalization rate on equity REITS is significant in explaining the variation in the REIT returns and small
capitalization stock returns. Karolyi and Sanders (1998) investigate the time-varying risk premiums in stock, bond
and REIT returns. They employ a multi-beta asset-pricing model that allows for time variation in economic risk
premiums and asset betas. Devaney (2001) appeals to a GARCH-M model to examine the return generating
process of REITs. They find a positive trade-off between conditional variance and excess returns for both EREITs
and MREITs. Finally, Mei and Hu (2000) examine the time variation of expected returns for Asian property stocks.
They find strong evidence of a time-varying risk premium, suggesting property development based on constant
discount rate may underestimate the cost of capital.
In a different vein, Interest rate is an important macroeconomic indicator that influences both stock
market and real estate market. It has been popularly included in previous studies of macroeconomic forces on
asset returns. Many similar studies on the interest rate sensitivity and pricing have also appeared in the securitized
real estate literature (McCue and Kling, 1994; Li and Wang, 1995; Mueller and Pauley, 1995; Ling and Naranjo,
1997; Lizieri and Satchell, 1997; Devaney, 2001; Eichholtz and Huisman, 2001; Swanson, et. al., 2002 and Liow
et al. 2003). However, there is lack of consensus as to the significance and direction of the interest rate effects on
stock returns For examples, Li and Wang (1995) and Mueller and Pauley (1995) find little correlation between
interest rate movements and REIT returns. On the other hand, McCue and Kling (1994) and Ling Naranjo (1997)
find a negative interest rate influence on REIT returns. Lizieri and Satchell (1997) find that the real interest rate
has an influence on property company share prices but the behavior differs in high interest rate and low interest
rate regimes. During periods of relatively high interest rates, property stock prices fall sharply and exhibit little
volatility, while price movements are more erratic during periods of relatively low interest rates. Devaney (2001)
finds that changes in the interest rate level and interest rate volatility are both inversely related to EREIT and
MREIT excess returns. Liow et al. (2003) examines the relationship between the unexpected changes in the longterm interest rate and property stock returns from an asset pricing perspective. Their results reveal that property
stock returns are sensitive to the unanticipated movement in the long-term interest rate. Additionally, interest rate
risk is a factor in capital asset pricing and that the pricing of the interest rate risk is sensitive to the prevailing
market conditions. Finally, Eichholtz and Huisman (2001)’s results on international property stock returns show
4
that interest rate variables especially the changes in interest rates and the term structure have an impact on
excess property stock returns.
This research combines the two veins of literature. In contrast to the previous studies, we appeal to the
standard GARCH-M framework that includes interest rate volatility (in addition to interest rate level) in a threefactor pricing model. The effects of interest rate volatility has been overlooked in the previous securitized real
estate studies; in that sense, we extend the literature by jointly investigating the impact of the changes in the first
moment and second moment of the interest rate distribution on the excess returns of property stocks. Additionally,
a joint study on the interest rate effects and time-varying volatility behavior of property stocks in the pre-crisis and
post- crisis periods such as in the current paper is expected to offer significant insights to international investors in
understanding the macroeconomic and portfolio implications of the four major property stock markets in the world.
Research Data
The raw data used in this study are the monthly stock indices for four property stock markets from
Datastream. The markets (indexes) examined are: Hong Kong (Hang Seng Property Index), Singapore (Singapore
All-Equity Property), Japan (Tokyo SE Real Estate Index) and the United Kingdom (UK) (Financial Times SE
Properties). Property companies play a relative important role in the general stock indexes for HK and Singapore.
The fundamental difference between Japan and HK/Singapore is that Japan is a significantly developed economy
in the Asian region while HK and Singapore are major Asian (emerging) tiger economies. The main motivation for
including Japan in our sample is to examine whether differences exist between the emerging Asian markets and
Japan, the highly developed country in the region. Finally, the UK property stock market is one of the major and
established European securitized real estate markets. Its inclusion in our study can provide comparative evidence
and generate significant investor interest in international real estate. The time period of the study is from
December 1987 to April 2003. Monthly stock return is computed as the natural logarithm of the price index relative.
Excess returns on real estate stocks are defined as returns minus yields to risk-free asset. The three-month
Treasury bill yield is utilized as the risk free rate for Singapore and UK. However, it is not available for Hong Kong
and Japan. The three-month Euro-yen deposit is used for the risk-free rate for Japan. For Hong Kong, as the
three-month Euro-yen deposit rate was not available before 1997 from DataStream, the three-month Euro-Hong
Kong Dollar Deposit average rate is used as the risk-free rate. All the data are extracted from Datastream.
The two-year HK Exchange Fund Bill rate (available from November 1991)7, the Singapore five-year
Government Bond yield (available from January 1988), the 10-year Japanese Government Bond yield (available
from December 1987) and the 10-year UK Government yield (available from December 1987) are utilized as the
long-term interest rate indices, respectively.8 In addition, this study utilizes the HK three-month Euro-Yen deposit
rate, the Japan three-month money market rate, the Singapore three-month Treasury Bill rate, and the UK threemonth Treasury Bill rate as the short-term interest rate indices, respectively. All the four short-term interest indices
cover the full-period data from December 1987 to April 2004. Exhibit 1 presents the interest rate movements in the
four countries. Finally, the total period (1987-2003) is further broken down into a pre-Asian financial crisis period
(December 1987 – July 1997) and a post-Asian financial crisis period (August 1997 – April 2004), so that changes
in the volatility, persistence of shocks in volatility before and after the July 1997 financial crisis and the influence of
interest rate level and volatility on the excess returns of the property stock markets may be investigated.
(Exhibit 1 here)
5
Exhibit 2 presents the monthly descriptive statistics of excess returns from the four real estate stock
markets during all three periods. They include the mean, standard deviation, maximum and minimum of excess
returns, the measures for skewness and kurtosis, the Jarque-Bera normality test and the Ljung-Box statistics for 6,
12, and 18 lags applied on the excess return series. Over the full period, the sample average of excess returns per
month is only positive for HK (ranges between -0.9% for Japan and 0.1% for HK). The mean monthly excess
returns are positive for HK (1.4%) and Singapore (0.5%) in the pre-crisis period. However, all the mean monthly
excess returns decline after the 1997 financial crisis. For the full period, the standard deviations of excess returns
are 5.4% (UK), 8.7% (Japan), 10.8% (SG) and 11.2% (HK), respectively. Hence HK and Singapore property stock
markets are more volatile than Japan and the UK. In the post-crisis period, HK and Singapore markets become
more volatile as evidenced from higher standard deviation of excess returns for Singapore (post crisis:15.4%; precrisis: 6.8%) and HK (post-crisis: 13.8%; pre-crisis: 9.1%). The results for the measure of skewness indicate that
the distributions of excess returns are positively skewed for HK and Singapore (except in the pre-crisis period),
although the skewness values are small. The HK excess return series is skewed to the right in all three periods
while the opposite is true for the UK series. Excess kurtosis of greater than 3 is found in all series during all three
periods except for Japan and UK in the post-crisis period. In other words, the excess returns series have thicker
tails than a normal distribution.
Based on the Jarque-Bera statistics, the hypothesis of a normal distribution is rejected for HK, Singapore
and the UK for all three periods except in the case of UK in the post-crisis period. The Ljung-Box portmanteau
statistics, Q (k) for K = 6, 12, and 18 lags, are used to test for serial correlation in the excess return series. The
statistics follow a chi-squared distribution with K degrees of freedom under the null hypothesis of no serial
correlation. As the figures in Exhibit 2 shows, for the full period, the null hypothesis of uncorrelated returns is
rejected at the conventional statistical levels for all markets, except for k = 6 (for HK, Singapore and Japan) and
k=12 (for Japan). Overall, results indicate that the excess return series of all markets displays conditional
heteroskedasticity and that a GARCH process is a suitable candidate for modeling their time-series behavior.
(Exhibit 2 here)
Research Methodology
In the spirit of asset pricing, the GARCH-M methodology introduced by Engle, Lilien and Robbins (1987)
links the conditional variance to the conditional mean of returns and provide a basic framework to examine the
relationship between volatility and expected returns. In the present context, a basic GARCH (1, 1)-M model of
property stock excess returns can be described by the following system of equations:
Rt = θX t + γht + ε t
(1)
ht = α 0 + α 1 ε t2−1 + α 2 ht −1
(2)
ε t Ω t −1 ~ N (0, ht )
(3)
where R t is the excess returns or risk premia,
is a random error,
X t is an exogenous, or predetermined, vector of variables, ε t
ht is the conditional variance of ε t , and Ω t −1 is the information set at period (t-1). The
parameters are. θ , γ ,
α 0 , α1
and
α2 .
6
There are two notable features of the GARCH (1, 1)-M model. First, equation (1) expresses the excess
return as function of vector
the coefficient
γ . If γ
X t and own conditional variances that allow a time-varying risk premium captured by
is statistically significant, then volatility (h t) does contribute to the risk premium so that the
premia might reflect the changing risk-return trade off under different market conditions. Hence this model
specification is closer to the CAPM or the APT that relates ex-ante returns to the conditional variance of returns
(Elyasiani and Mansur, 1998). Second, the conditional variance equation (2) is a function of three terms: (a) the
mean, (b) news about volatility from the previous period, measured as the lag of the squared residual from the
mean equation:
ε t2−1 (the ARCH term), and (c) last period’s forecast variance: ht −1 (the GARCH term).9 Equation
2 implies that if the innovations have been large, they are likely to be large in the next period. This is described as
volatility clustering. The sum of coefficients in the conditional variance equation ( α 1 +
α 2 ) measures the degree
of persistence in shocks to volatility which is important in determining the relationship between return and volatility
since only persistent volatility changes would bring about changes in the risk premium. To ensure the process is
well defined, the parameters α 0 ,
α1
and
α2
must be non-negative.
The above basic GARCH (1, 1)-M model is expanded into a three-factor APT factor with property stock
excess return volatility, interest rates and interest rate volatility as its factors:
Model 1(long-term interest rates)
n
R j ,t = µ + θ i ∑ R j ,t −i + β 1 ∆LTRt −1 + β 2 ∆CVLTRt −1 + γh j ,t + ε j ,t
(4a)
h j ,t = α 0 + α 1ε 2j ,t −1 + α 2 h j ,t −1
(5a)
ε j ,t Ω t −1 ~ N (0, ht )
(6a)
i =1
Model 2 (short-term interest rates)
n
R j ,t = µ + θ i ∑ R j ,t −i + β1 ∆STRt −1 + β 2 ∆CVSTRt −1 + γh j ,t + ε j ,t
(4 b)
h j ,t = α 0 + α ε
(5 b)
i =1
2
1 j ,t −1
+ α 2 h j ,t −1
ε j ,t Ω t −1 ~ N (0, ht )
(6 b)
where R j ,t is the excess returns on jth property stock index ( j=1,2,3,4; Hong Kong, Japan, Singapore,
UK property stocks respectively) and R j ,t −i is the autoregressive lag of excess returns in the mean equations (4a
and 4b). 11 periods was determined to be the optimal autoregressive lag for HK and Singapore while 6 and 0
autoregressive lags were determined for UK and Japan, respectively. The variable h t measures stock return
volatility (risk). In addition, the effects of the long-term and short-term interest rates (LTR and STR) and their
volatility are examined in model 1 and model 2, respectively. In model 1,
long-term interest rates with a lag and
∆LTRt −1 is the first difference of the
∆CVLTRt −1 is the first difference of the conditional variance of the long-
term interest rates. Similarly, in model 2,
∆STRt −1 and ∆CVSTRt −1 represent lagged one-period of the first
7
difference of the short-term interest rates and lagged one-period of the first difference of the conditional variance
of the short-term interest rates, respectively. There are three main reasons for differencing. First, differencing
facilitates comparison with stock returns. Second, first differencing renders the series stationary. Third, as only the
innovations or unexpected changes in the interest rates are of relevance to the APT, their first differences are
good proxies of the unexpected changes. Additionally, the series are lagged one-period to avoid possible error-inthe-variable problem resulting from contemporaneous correlations of the error term and changes in the interest
rates (Elyaiani and Mansur, 1998). This specification is similar to Devaney (2001) who also suggests a one-month
lag in interest rates.
As interest rate contains information about future economic conditions and captures the state of
investment opportunities, higher interest rates lower property company’s profits and in turn lead to lower stock
returns. Hence interest rates are expected to negatively affect the excess returns of property stocks. On the other
hand, higher interest rates increase the income to investors in money market funds and thus in turn might
stimulate the economy. In the longer term, higher interest rates might lead to higher property stock returns
associated with growth in the economy and property markets. Hence, the magnitude and direction of the long-tern
and short-term interest rate effects (measured by
β 1) are to be determined empirically especially in our present
studies where the four markets have different states of economy, stock and property markets.
Investigation of the effect of interest rate volatility on property stock risk premia provides fresh insights
into the behavior of property companies in response to interest rate fluctuation. At the macro level, interest rate
volatility reflects fluctuation in the economy due to uncertainty in monetary policy. If interest rate volatility affects
the expected bond returns, it should also affect the returns on other investment assets such as finance stocks and
property stocks (Flannery et al., 1997). At the micro level, interest rate volatility impacts the leverage of
corporations in their risk exposure. Empirically, the extant literature indicates that the returns to financial
institutions are inversely related to changes to interest rate volatility. Devaney (2001) find that changes in interest
rate volatility are inversely related to REIT excess returns. However, the effect of interest rate volatility on property
stock excess returns is not known and deserves attention. In this study, the conditional variances of interest rates
are derived from GARCH (1, 1) models. The coefficient
β 2 measures the effect of the changes in the long- term
and short-term interest rate volatility (CVLTR and CVSTR) on the excess returns. The magnitude and the direction
of
β2
for the four property stock portfolios are to be determined and compared empirically.
Empirical Results and Discussion
The coefficient estimates for Model 1 and Model 2 over the full period (1987:12-3:4), the pre-crisis
period (1987:12-1997:7), and the post-crisis period (1997:8-2003:4) are presented in Exhibits 3 and 4 respectively.
Additionally, Exhibits 5 and 6 display the time-varying conditional variances. The findings are discussed below.
(Exhibits 3 and 4 here)
(Exhibits 5 and 6 here)
Time-varying conditional variances, shock persistence and risk-return trade off
As the figures in Exhibit 3 (Model 1: long-term interest rate), the coefficient estimates ( α 0 ,
α1
and
α 2 ) are
all positive, satisfying the specification requirement of non-negativity for all of the models. The intercept term,
α0 ,
8
α0
in the volatility equation, constitutes the time-dependent component of volatility. Over the entire sample period
is significantly positive for Hong Kong but insignificant for the other three portfolios (Japan, Singapore, and UK).
While the ARCH parameter, α 1 , is significantly positive for Hong Kong and Singapore, the GARCH parameter,
α 2 , is statistically significant for all four portfolios. Another related observation is that the magnitude of α 2
considerably larger than that of the parameter
α1
is
in the four volatility equations. The implication is that volatility in
the four property stock markets is more responsive to its own lagged values than it is to new surprises in the
market place. Next, the sum ( α 1 + α 2 ) which measures the change in the response function of shocks to volatility
per month, is found to be less than unity for all four portfolios implying that shock decays with time. The highest
and lowest volatility persistence are 0.9270 (Singapore) and 0.6785 (UK) respectively. Hence, in the case of UK,
after one year the proportion of shock remains at 0.96% (0.6785)
^ 12.
A shock reaches its half life in only about
1.78 months. In Singapore, however, after one year the proportion shock remains at 40.3% (0.927) ^ 12. Half life of
the impact is reached in about 9.14 months, a relatively longer time than that of the UK market.
The two shorter sub-period results are qualitatively similar although the significance and magnitude of the
parameters ( α 0 , α 1 and
α 0 (time-variant
α 2 ) vary across the four portfolios.
factor) and
statistically significant
α0
α 1 (ARCH
Both the UK and Japan portfolios have a significant
effect) each in the pre-crisis period. However, only the UK has a
in the post-crisis period. The GARCH parameter ( α 2 ) is highly significant for all four
portfolios across both sample periods. Again, all the
α2
values are considerably larger than the respective
α1
values, suggesting some evidence of long memory in property stocks. Finally, the magnitude of volatility
persistence ranges between 0.6172 (HK) and 0.8749 (Singapore) during the pre-crisis period; and between
0.7154 (Japan) and 0.8837 (UK) during the post-crisis period.
Results from Exhibit 4 (Model 2: short-term interest rate) also suggest, with some exceptions, presence
of a time-variability component, ARCH and GARCH effects in excess returns. In particular, the GARCH parameter
( α 2) is positive and significantly different from zero at the 1% significance level for all 4 portfolios over the full
period, the pre- and post-crisis periods. The average persistence measures ( α 1 + α 2 ) for the 4 portfolios are
0.8509 (full-period), 0.7984 (pre-crisis period) and 0.9016 (post-crisis period) respectively. For example, in the
case of Singapore and Japan property stocks, the persistence of an initial shock remaining after 6 months is
69.6% [(0.9414)6] and 19.8% [(0.7636)6] respectively during 1987-2003.
The risk premium coefficient
variance. In Exhibit 3,
γ
γ
describes the trade-off between excess return and its own conditional
is found to be positive and vary in statistical significance and magnitude across Japan,
Singapore and the UK over the full period, the pre-crisis period and the post-crisis period. For the full period,
γ
is
significantly positive at the 10% level for Singapore and Japan. On the other hand, the influence of volatility on
excess returns ( γ ) is found to be inverse but insignificant for HK. In the pre-crisis period, a significant and positive
influence of volatility on excess returns is found for Japan and UK, while the risk-premium coefficient ( γ ) is again
significantly negative for HK. In the post-crisis period all four risk premium coefficients are positive regardless of
the significance level (statistically significant at the conventional levels for Japan, Singapore and the UK). Thus, it
appears that an increase in conditional volatility of excess returns is a factor in explaining a higher risk premium of
9
property stocks. A further point to note is that as the magnitude and sign of the trade-off parameter ( γ ) are
dependent on the investors’ risk preference, the heterogeneous nature of investors’ expectations about the future
performance of property stocks of the 4 markets could have resulted in different trade-off values.10 The volatility
risk premium parameter ( γ ) is thus portfolio-specific in magnitude and sign as the four property stock markets
have different institutional, economic and micro-structural features. In Exhibit 4 (short-term interest rate model),
the sign of the risk-return trade-off parameter ( γ ) for the 4 portfolios is similar to those reported in Exhibit 3.
However, some of the significance levels differ. For example, over the full period while γ becomes significant for
the UK and HK, it is found to be insignificant for Singapore.
The interest rate effects
Of particular interest to this study are the magnitude and the direction of the effects of interest rate and
their volatility on the distribution of property stock excess returns. The null hypotheses are that (a) changes in
interest rate level has no effect on property stock excess returns(i.e.
volatility has no effect on property stock excess returns (i.e.
that over the full period, the parameter
β 1 = 0) and (b) changes in interest rate
β 2 = 0). The estimates reported in Exhibit 3 show
β 1 which measures the effect of the changes in the long-term interest
rates on the excess returns is negative in all cases and only statistically significant for the UK portfolio. Increases
in the long-term interest rates are thus associated with lower excess returns. In the pre-crisis period a highly
significant and negative influence of changes in the long-term interest rate on excess returns is found for the UK,
HK and Japan. However, the interest rate coefficient ( β 1) appears to have changed significantly in the postcrisis period. In this period all four interest rate coefficients are positive but are not statistically different from zero.
As the figures in Exhibit 4 shows, the impact of the changes in the short-term interest rates on excess
returns is somewhat different from the long-term interest rate impact. The main differences observed are (a) over
the full period, a significant negative interest rate coefficient (at the 10% level) is found for HK while an
insignificant inverse relationship is found for UK, (b) In the pre-crisis period, the impact of the changes in the shortterm interest rates on excess returns is negligible for HK and the UK, and (c) Except for HK, the remaining three
interest rate coefficients are negative but are not statistically different from zero.
The results are contrasted with those of Devaney (2001) who find that the coefficients on the monthly
changes in the US ten-year Treasury yield (proxy for long-term interest rate) are both highly significant and
negative for mortgage REITS and equity REITs. However, no sub-period evidence is available in his study. In
property stock research, Liow et al. (2003) report that many property stocks included in their study are negatively
related to the long-term interest rate movement but the proportion of those companies varies across different
sample periods.
The impact of interest rate volatility on excess return can be measured through the parameter
β 2.
It is
different in sign and magnitude across the four portfolios. According to the figures displayed in Exhibit 3, for the full
sample period,
β 2 is not statistically different from zero for HK, Japan and Singapore (regardless of sign); only a
significant positive
β 2 is found for the UK market. Another observation is that the effects of interest rate volatility
on excess return in both the pre-crisis and post-crisis periods are not uniform across the four markets. Specifically,
while the interest rate volatility coefficients ( β 2) for UK and Singapore have the same sign and significance in
10
both the pre-crisis and post crisis periods (significantly positive for UK and insignificantly negative for Singapore,
respectively), the significance and sign of
β 2 for Japan change from significantly negative (probability level =
0.000) in the pre-crisis period to insignificantly positive (probability level = 0.840) in the post crisis period. On the
other hand, the significance and sign of
β 2 for HK change from insignificantly positive (probability level = 0.680)
in the pre-crisis period to insignificantly negative (probability level = 0.12) in the post-crisis period. Thus an overall
picture emerge from these results is that while increases in the long-term interest rate volatility, as measured by
changes in the conditional variance of interest rate, is associated with higher property stock risk premia for UK; the
risk premia remain probably unaffected when the long-term interest rates become more volatile in HK, Singapore
and Japan. The lack of significance of the interest rate volatility effect on property stock excess returns for these
three markets may also indicate insignificant exposure to interest rate risk due to stronger risk aversion and
hedging action on the part of this group of property firms.
In Exhibit 4, the short-term interest rate volatility parameter ( β 2) is negative and highly significant for
HK (full-period) and Japan (pre-crisis period). On the other hand, significant positive
β 2 are found for the UK in
the full period and in the pre-crisis period. In the post-crisis period, once again no significant effect of the shortterm interest rate volatility on excess returns is found in any of the four cases.
In summary, our results suggest that property stocks are generally sensitive to changes in the long-term
and short-term interest rates and to a lesser extent, their volatility. Further, the disparity in the magnitude as well
as direction of sensitivities in interest rate level and volatility across regional property stocks and different market
conditions should be considered in portfolios construction and management so as to reduce interest rate exposure.
One possible explanation for the lack of significance in the interest rate volatility effect on excess returns for the
Asian property stocks in the post-crisis period is that the July 1997 Asian Financial Crisis has escalated the
volatility of real estate returns in the region, with its impact felt in varying degree across the various economies.
This period was characterized by significant devaluation of regional currencies, the flight of foreign capital, the
closing down of many banks and rapid deterioration in employment rates and domestic economies. Entering into
the new millennium, many of the markets in East Asia are still undergoing restructuring and consolidation.
Although interest rate is one of the important factors affecting real estate market and stock market risk premia,
other factors include political stability, financial market deregulations, property supply and property prices and
alternative investment opportunities. Hence, changes in interest rates volatility alone might not be significant
enough to cause changes in property stock excess returns during this volatile period.
Nevertheless, the studies concerning interest rate volatility extend the literature in at least two important
ways. First, by investigating the effect of changes in the second moment of the long-term and short-term interest
rate distribution on the return generating process of property stocks, they highlight the importance of incorporating
the interest rate volatility effect in APT. Second, they expose the dependence of property stock excess returns on
the volatility of the interest rate and indicate the importance of estimating the risk-return trade-off jointly in a timevarying framework and under different market regimes.
Conclusions
In this paper, a three–factor APT excess return model is investigated for its sensitivity to the interest rate
level and volatility in a time-varying framework. We focus on four major international property stock markets with
11
respect to their excess return volatility, time-varying risk premia, persistence of shocks and the effects of changes
in the level and volatility of interest rates on the return-generating process of property stocks. Such extension of
previous literature across international property stocks enhances investors’ understanding in equilibrium asset
pricing and complements existing evidence in international real estate. With the increased significance of property
stocks as property investment vehicles for international investors to gain property exposure in Asia and
internationally, the paper is timely and provides the basis for more advanced research in international investment
strategies and capital asset pricing.
The conclusions obtained from this study may be summarized as follows. The excess return distribution
is heteroskedastic as there is presence of significant of GARCH effect in all series and ARCH effect exists in some
series. Strong time-varying conditional volatility is found in the excess return series for all markets. On the whole
property stock market volatility is more persistent in Singapore, relative to the UK, HK and Japan. There is some
evidence of a positive trade- off between the excess returns and conditional variances for Singapore, Japan and
the UK. Volatility is thus a factor real estate stock asset pricing. However, the volatility risk premium trade-off
parameter is portfolio - specific in magnitude and differs before- and after- the financial crisis. Consideration of
interest rate movements and Asian financial crisis in the model provide a better description of the data. According
to our findings, property stocks are generally sensitive to changes in the long-term and short-term interest rates
and to a lesser extent, their volatility. In addition, the disparities in the magnitude and direction of sensitivities in
the interest rate kevel and volatility among regional / international property stocks and across different market
conditions should be considered in portfolios so as to reduce interest rate exposure and/or hedge interest rate risk.
Finally, results indicate changes in the ARCH parameter, risk premia, persistence of volatility and interest rate
level and volatility effects before and after the 1997 Asian Financial crisis. However these noted changes are not
uniform and depend upon the individual property stock markets. Factors other than the 1997 financial crisis might
have been contributed to the changes.
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.
14
87
12
88 M
19 8M
8
19 9 4
89 M
19 12M
90
19 8M
9
19 1 4
91 M
19 12M
92
19 8M
9
19 3 4
93 M
19 12M
94
19 8M
9
19 5 4
95 M
19 12M
96
19 8M
97
19 4
97 M
19 12M
98
19 8M
9
19 9 4
99 M
20 12M
00
20 8M
0
20 1 4
01 M
20 12M
02
20 8M
03
4M
19
19
87
19 12M
88
19 8M
8
19 9 4
89 M
19 12M
90
19 8M
9
19 1 4
91 M
19 12M
92
19 8M
9
19 3 4
93 M
19 12M
94
19 8M
95
19 4
95 M
19 12M
96
19 8M
97
19 4
97 M
19 12M
98
19 8M
9
19 9 4
99 M
20 12M
00
20 8M
0
20 1 4
01 M
20 12M
02
20 8M
03
4M
19
87
12
88 M
19 8M
8
19 9 4
89 M
19 12 M
90
19 8M
9
19 1 4
91 M
19 12M
92
19 8M
93
19 4
93 M
19 12M
94
19 8M
9
19 5 4
95 M
19 12 M
96
19 8M
9
19 7 4
97 M
19 12M
98
19 8M
99
19 4
99 M
20 12M
00
20 8M
0
20 1 4
01 M
20 12M
02
20 8M
03
4M
19
19
87
19 12M
88
19 8M
8
19 9 4
89 M
19 12 M
90
19 8M
9
19 1 4
91 M
19 12
92 M
19 8M
9
19 3 4
93 M
19 12M
94
19 8M
9
19 5 4
95 M
19 12M
96
19 8 M
9
19 7 4
97 M
19 12M
9
19 8 8
99 M
19 4
99 M
20 12M
00
20 8 M
0
20 1 4
01 M
20 12M
02
20 8M
03
4M
19
Exhibit 1
18
16
14
12
10
8
6
4
2
0
% p.a.
% p.a.
9
8
7
6
5
4
3
2
1
0
% p.a.
7
6
5
4
3
2
1
0
% p.a.
Long-term Interest Rates and Short-term Interest Rates
Hong Kong Interest Rate
Tim e
Short-term
Short-term
Short-term
Short-term
Long-term
Japan Interest Rate
Tim e
Long-term
Singapore Interest Rate
Time
Long-term
16
14
12
10
8
6
4
2
0
United Kingdom Interest Rate
Time
Long-term
15
Exhibit 2 Descriptive statistics of monthly excess returns on property stocks
Hong Kong
Full period: 1987:12—2003:4
Mean
0.001
Std. Deviation
0.112
Maximum
0.452
Minimum
-0.469
Skewness
0.041
Kurtosis
6.030
Jarque-Bera
70.823***
Ljung-Box Q Statistics
Q (6)
5.253
Q (12)
20.458*
Q (18)
25.624*
Q (24)
28.663
Pre-crisis period: 1987:12—1997:7
Mean
0.014
Std. Deviation
0.091
Maximum
0.359
Minimum
-0.311
Skewness
0.178
Kurtosis
5.144
Jarque-Bera
22.829***
Ljung-Box Q Statistics
Q (6)
8.301
Q (12)
17.979
Q (18)
25.971*
Q (24)
31.421
Post-crisis period: 1997:8—2003:4
Mean
-0.020
Std. Deviation
0.138
Maximum
0.452
Minimum
-0.469
Skewness
0.233
Kurtosis
5.341
Jarque-Bera
16.372***
Ljung-Box Q Statistics
Q (6)
4.746
Q (12)
10.413
Q (18)
14.038
Q (24)
23.014
Japan
Singapore
United
Kingdom
-0.009
0.087
0.207
-0.299
-0.184
3.308
1.780
-0.002
0.108
0.476
-0.389
0.300
7.801
180.447***
-0.004
0.054
0.128
-0.169
-0.553
3.210
9.754***
2.738
4.708
26.458*
18.957
7.009
26.376***
29.028**
31.544
12.960**
21.721**
26.186*
28.080
-0.006
0.090
0.207
-0.299
-0.321
3.710
4.433
0.005
0.068
0.192
-0.217
-0.333
3.877
5.863*
-0.003
0.058
0.128
-0.169
-0.655
3.310
8.756**
2.545
6.436
24.353*
19.798
10.187
15.772
22.247*
25.317
15.616**
27.695***
36.170***
40.872**
-0.014
0.082
0.146
-0.198
0.084
2.342
1.327
-0.013
0.154
0.476
-0.389
0.506
5.044
14.953***
-0.007
0.049
0.095
-0.120
-0.298
2.659
1.354
3.366
6.995
13.197
20.076
3.181
16.207
18.310
20.396
5.437
17.794
23.901*
29.026
Note:
*** Indicates two-tailed significance at the 1% significance level
** Indicates two-tailed at the 5% significance level
* Indicates two-tailed significance at the 10% significance level
16
Exhibit 3 Results of GARCH (1, 1)—M model of excess returns with long-term interest rates
Model 1:
n
R j ,t = µ + θ i ∑ R j ,t −i + β 1 ∆LTRt −1 + β 2 ∆CVLTR t −1 + γh j ,t + ε j ,t
i =1
h j ,t = α 0 + α 1ε 2j ,t −1 + α 2 h j ,t −1
ε j ,t Ω t −1 ~ N (0, ht )
Estimated
Parameter
Full period:
γ
β1
β2
α 0 ( × 10 −3 )
α1
α2
α1 + α 2
Hong Kong
Japan
Singapore
United Kingdom
-3.0355 (p=0.22)
6.9063
1.9028 (p= 0.10*)
9.8482
-21.8501(p=0.14)
-11.7732 (p=0.68)
24.0417 (p= 0.16)
-31.3707 (p= 0.07*)
-0.0372 (p=0.73)
-0.3959 (p=0.68)
0.1871 (p=0.18)
0.5862
(p= 0.09*)
2.009
1.377
(p=0.99)
0.822
0.853
(p= 0.99)
0.0519 (p=0.00***)
0.0899
(p=0.56)
0.2404 (p= 0.07*)
0.1027
(p= 0.42)
0.7970 (p=0.00***)
0.6913
(p=0.00***)
0.6866 (p=0.00***)
0.5758
(p= 0.08*)
(p=0.00***)
(p=0.09*)
0.8489
0.7812
(p=0.96)
0.9270
(p= 0.37)
0.6785
Pre-crisis period:
γ
β1
β2
α 0 ( × 10 −3 )
α1
α2
α1 + α 2
-24.2266 (p=0.00***)
3.2442
-137.2854 (p=0.00***)
-41.8309 (p=0.00***)
-27.4617 (p= 0.34)
-50.2235 (p= 0.00***)
0.5233
(p=0.68)
-1.1892
(p=0.00***)
-0.1042
(p=0.64)
0.8432
(p= 0.00***)
2.319
(p=0.98)
1.069
(p=0.00***)
0.566
(p=0.49)
0.847
(p= 0.00***)
0.1040
(p=0.45)
0.0697
(p=0.00***)
0.0665
(p= 0.54)
0.2272 (p= 0.00***)
0.5132
(p=0.00***)
0.7769
(p=0.00***)
0.8084
(p=0.00***)
0.4406 (p= 0.00***)
0.6172
(p=0.06*)
0.6399
0.8466
(p= 0.95)
3.6112
0.8749
(p= 0.02**)
0.6678
Post-crisis period:
γ
β1
β2
α 0 ( × 10 −3 )
α1
α2
α1 + α 2
18.1506
(p=0.41)
14.7755 (p=0.07*)
7.1548
31.0636
(p=0.64)
57.7565 (p=0.23)
115.8017 (p= 0.38)
7.2408
(p= 0.88)
-0.4864
(p=0.12)
0.1631
(p=0.84)
-0.0641
(p=0.98)
1.8812
(p= 0.09*)
2.150
(p=0.99)
1.842
(p=0.99)
2.837
(p=0.43)
0.306
(p= 0.00***)
0.0502
(p=0.72)
0.0929
(p=0.34)
0.1703
(p= 0.73)
0.0041
(p= 0.30)
0.7223
(p=0.00***)
0.6225
(p=0.00***)
0.5907 (p= 0.08*)
0.8796
(p= 0.00***)
0.7725
0.7154
Notes:
1. R j , t is the excess returns on the property stocks;
R j ,t − i
(p= 0.06*)
0.7610
57.9758 (p= 0.00***)
0.8837
is lags of excess returns; ∆LTRt −1 is one lag of the first
difference in long-term interest rates; ∆CVLTRt −1 is one lag of first difference in conditional variance of the long-term interest
rates; ht is conditional variance of excess returns; ε t −1 is ARCH term; ht −1 is GARCH term
2
2. P values in the parentheses
3. ***at the 1% significance level; ** at the 5% significance level; * at the10% significance level
17
Exhibit 4 Results of GARCH (1, 1)—M model of excess returns with short-term interest rates
Model 2:
n
R j ,t = µ + θ i ∑ R j ,t −i + β 1 ∆STR t −1 + β 2 ∆CVSTR t −1 + γh j ,t + ε j ,t
i =1
h j ,t = α 0 + α 1ε 2j ,t −1 + α 2 h j ,t −1
ε j ,t Ω t −1 ~ N (0, ht )
Estimated
Parameter
Full period:
γ
β1
β2
α 0 ( × 10 −3 )
α1
α2
α1 + α 2
Hong Kong
Japan
Singapore
United Kingdom
-2.0783 (p=0.02**)
18.6726 (p=0.03**)
1.7764 (p= 0.13)
26.8005 (p= 0.04**)
-7.2916 (p=0.09*)
-50.9372 (p=0.30)
-16.5202 (p= 0.26)
1.9731
(p= 0.90)
0.0491 (p=0.00***) -0.6293 (p=0.45)
0.0473 (p=0.57)
0.2862
(p= 0.02**)
2.148
(p=0.99)
0.701
0.295
(p= 0.99)
0.1002 (p=0.00***) 0.0260
(p=0.87)
0.2331 (p= 0.07*)
0.0345
(p= 0.31)
0.7066 (p=0.00***) 0.7376
(p=0.00***)
0.7083 (p=0.00***)
0.8575
(p= 0.00***)
(p=0.00***) 1.787
0.8068
0.7636
(p=0.88)
0.9414
0.8920
Pre-crisis period:
γ
β1
β2
α 0 ( × 10 −3 )
α1
α2
α1 + α 2
-4.0505 (p=0.24)
1.8678
-12.5470 (p=0.47)
-44.8868 (p=0.00***)
-21.7670 (p= 0.13)
8.0953
(p= 0.65)
0.2795
(p=0.37)
-1.1385
(p=0.00***)
0.0972
(p=0.28)
0.2629
(p= 0.04**)
3.412
(p=0.97)
1.284
(p=0.00***)
0.530
(p=0.99)
0.266
(p= 0.99)
0.2663
(p=0.06*)
0.0087
(p=0.00***)
0.0977
(p= 0.60)
0.0449
(p= 0.23)
0.3009
(p=0.00***) 0.8334
(p=0.00***)
0.7768
(p=0.00***)
0.8648
(p= 0.00***)
0.5672
(p=0.64)
2.4757
0.8421
(p= 0.69)
24.4496 (p= 0.09*)
0.8745
0.9097
Post-crisis period:
γ
β1
β2
α 0 ( × 10 −3 )
α1
α2
α1 + α 2
13.8211 (p=0.12)
1.3613
0.8480 (p=0.97)
(p= 0.17)
33.2995 (p= 0.34)
-182.0887 (p=0.20)
-9.6868 (p= 0.87)
-7.2105 (p= 0.90)
0.0271 (p=0.58)
8.3438
(p=0.30)
0.4709
(p=0.68)
0.4492
(p= 0.82)
0.0157 (p=0.99)
1.698
(p=0.61)
0.666
(p=0.99)
0.0767
(p= 0.00***)
0.0632 (p=0.00***) 0.2394
(p=0.39)
0.0982
(p= 0.22)
0.0202
(p= 0.00***)
0.9285 (p=0.00***) 0.4884
(p=0.04**)
0.8088
(p=0.00***)
0.9595
(p= 0.00***)
0.9917
Notes:
1. R j , t is the excess returns on the property stocks;
(p=0.78)
0.7278
R j ,t − i
7.2517
0.9070
0.9797
is lags of excess returns; ∆STRt −1 is one lag of the first
difference in short-term interest rates; ∆CVSTRt −1 is one lag of first difference in conditional variance of the short-term
interest rates; ht is conditional variance of excess returns; ε t −1 is ARCH term; ht −1 is GARCH term
2
2. P values in the parentheses
3. ***at the 1% significance level; ** at the 5% significance level; * at the10% significance level
18
Exhibit 5 Conditional Variance of property Stocks
- From model 1: long-term interest rate
Full period
0.030
0.014
0.012
0.025
0.010
0.020
0.008
0.015
0.006
0.010
0.004
92 93 94
95 96 97
98 99 00 01
02 03
88
90
92
94
Hong Kong
96
98
00
02
Japan
0.07
0.006
0.06
0.005
0.05
0.04
0.004
0.03
0.02
0.003
0.01
0.002
0.00
88
90
92
94
96
98
00
88
02
90
92
94
96
98
00
02
United Kingdom
Singapore
Pre-crisis period:
0.016
0.012
0.014
0.011
0.010
0.012
0.009
0.010
0.008
0.008
0.007
0.006
0.006
0.004
0.005
1992
1993
1994
1995
1996
1997
88
89
90
91
92
Hong Kong
93
94
95
96
97
Japan
0.008
0.008
0.007
0.007
0.006
0.006
0.005
0.004
0.005
0.003
0.004
0.002
0.003
0.001
88
89
90
91
92
93
94
Singapore
95
96
97
88
89
90
91
92
93
94
95
96
97
United Kingdom
19
Post-crisis period:
0.016
0.011
0.010
0.014
0.009
0.012
0.008
0.010
0.007
0.008
0.006
0.006
0.005
1998
1999
2000
2001
2002
2003
1998
1999
2000
Hong Kong
2001
2002
2003
2002
2003
Japan
0.10
0.0028
0.08
0.0026
0.06
0.0024
0.04
0.0022
0.02
0.0020
0.00
1998
1999
2000
2001
Singapore
2002
2003
1998
1999
2000
2001
United Kingdom
20
Exhibit 6
Conditional Variance of property Stocks
-- From model 2: short-term interest rate
Full period
0.040
0.0095
0.035
0.0090
0.030
0.0085
0.025
0.0080
0.020
0.0075
0.015
0.0070
0.010
0.005
0.0065
88
90
92
94
96
98
00
02
88
90
92
94
96
98
00
02
98
00
02
Japan
Hong Kong
0.08
0.0040
0.06
0.0035
0.04
0.0030
0.02
0.0025
0.00
0.0020
88
90
92
94
96
98
00
88
02
90
92
94
96
United Kingdom
Singapore
Pre-crisis period:
0.04
0.0088
0.0086
0.03
0.0084
0.02
0.0082
0.0080
0.01
0.0078
0.00
0.0076
88
89
90
91
92
93
94
95
96
88
97
89
90
91
92
93
94
95
96
97
Japan
Hong Kong
0.008
0.0045
0.007
0.0040
0.006
0.0035
0.005
0.0030
0.004
0.0025
0.003
0.002
0.0020
88
89
90
91
92
93
94
Singapore
95
96
97
88
89
90
91
92
93
94
95
96
97
United Kingdom
21
Post-crisis period:
0.012
0.018
0.016
0.010
0.014
0.012
0.008
0.010
0.008
0.006
0.006
0.004
0.004
0.002
1998
1999
2000
2001
2002
2003
1998
1999
2000
Hong Kong
2001
2002
2003
2002
2003
Japan
0.030
0.0032
0.025
0.0030
0.020
0.0028
0.015
0.0026
0.010
0.0024
0.005
0.000
0.0022
1998
1999
2000
2001
Singapore
2002
2003
1998
1999
2000
2001
United Kingdom
22
Endnotes
Examples of these studies include Singapore (Liow, 2001a; Liow, 2001b), Hong Kong (Newell and Chau, 1996,
Chau, et al. 2003, Schwann and Chau, 2003), Australia (Newell and Acheampong, 2001) and Asia (Garvey et al,
2001)
1
Examples of stock market studies include Poon and Taylor (1992), Theodossiou and Lee (1995), Koutmos (1999)
and Lee, Chen and Rui (2001)
2
Examples of REIT performance studies include Liu and Mei (1992), Young and Graff (1996), Li and Wang (1995),
Liu and Mei (1998), Glascock et al. (2000) and Stevenson (2002)
3
Examples of these studies include Chance and Lane (1980), Flannery and James (1984), Mansur (1995),
Flannery et al. (1997) and Elyasiani and Mansur (1998)
4
These studies include McCue and Kling (1984), Mueller and Pauley (1995), Liang and Webb (1995), Ling and
Naranjo (1997), Brooks and Tsolacos (1999) and Liow et al. (2003).
5
The ARCH model was first proposed by Engle (1982) and generalized to GARCH by Bollerslev (1986). The
framework was further extended to ARCH and GARCH in mean (ARCH-M and GARCH-M) by Engle, Lilien and
Robins (1987) and allows for a time-varying risk premium.
6
The two-year Exchange Fund Bill rate is chosen as the long-term interest rate index for HK since Exchange Fund
Bill with longer maturity period is not available, For example, the data for a five-year Exchange Fund Bill are only
available from 1994 onward.
7
Hence, the first date of the long–term interest rate data (Singapore: 01/1988; HK: 11/1991; Japan and the UK:
12/1987) dictates the length of analysis for the full period and pre-crisis period analyses.
8
9 Accordingly to Bollerslev et al. (1992), GARCH (1, 1) as opposed to higher order models, is parsimonious and
allow for long memory in the volatility process and fits most economic time series
Similarly, there is no consensus reached in the stock market literature about the parameter γ . For example,
Baillie and DeGennaro (1990), Poon and Taylor (1992) and Lee, Chen and Rui (2001) find an insignificant and
positive relationship between conditional returns and conditional volatility; whereas Fama and Schwart (1977) and
Campbell (1987) find a negative relationship ( γ <0).
10
23
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CRES:2004-006 IMPACT OF INTEREST RATE LEVEL AND VOLATILITY ON TIME-VARYING EXCESS... FOR PROPERTY STOCKS – SOME INTERNATIONAL EVIDENCE