CRES: 2004-004
Regime Changes in International Securitized Property Markets
Kim Hiang LIOW1, Haihong ZHU, David Kim Hin, HO and Kwame, Addae-Dapaah, Department of Real Estate,
National University of Singapore
1 Contact
author
Dr Kim Hiang LIOW
Associate Professor
Department of Real Estate
National University of Singapore
4 Architecture Drive
Singapore 117566
Tel: (65)68743420
Fax: (65)67748684
Email: rstlkh@nus.edu.sg
20 May 2004
1
Regime Changes in International Securitized Property Markets
Abstract
This paper investigates the existence and the nature of return and volatility shifts in international securitized property
market returns over the period 1987-2003 .We find that international securitized property markets have strong
switching behavior in volatility. The results indicate that the conditional variance is state-dependent but the conditional
mean is state-dependent for the US REIT and the UK property stock markets only. Securitized property markets are
either in low return-high volatility state or in high return-low volatility state. In addition, the two regimes are persistent
with differences observed in the expected duration and the frequency of shifts between the states among markets.
Further examinations of the correlations of mean-variance state probabilities suggest intermarket interactions between
some pairs of securitized property markets. Finally, the response of returns to past price / dividend ratio is asymmetric.
Hence it is important for international investors to assess the fuller investment perspective of optimal asset allocation
and securitized property portfolio performance after accounting for state-dependent switching.
1.
INTRODUCTION
Listed real estate companies make a significant contribution to the market capitalization of Asian stock
markets (Newell and Chau, 1996; Liow, 2001 and Steinert and Crowe, 2001). Similarly, securitized real estate has
become an increasingly important property investment vehicle in Asian and internationally (Steinert and Crowe, 2001),
particularly through the success of REITs (Real Estate Investment Trusts) in USA, LPTs (Listed Property Trusts) in
Australia, the recent development of equivalent listed vehicles in Japan, Malaysia, Korea and Singapore, and the longestablished track record of listed property companies in Asia and Europe.
With recent studies highlighting the portfolio diversification benefits of including international listed real estate
in a mixed portfolio (Conover et al, 2002; Steinert and Crowe, 2001; Worzala and Sirmans, 2003 and Bond et al, 2003),
attention has been given to examining various aspects of securitized real estate performance in Asia and internationally.
While much of this property company research has focused on performance analysis in specific Asian markets and the
inter-relationship between the respective indirect and direct property markets, it is also important to assess impact of
regime changes in international securitized property markets. This is because prior empirical evidence has indicated
that securitized property markets perform differently in different economic environment (e.g. bull and bear markets) and
this change in behavior results in discrete changes in the time-series risk-return characteristics of securitized property
indexes. A regime change is thus associated with a significant shift in the fundamental relation between the risk and
return trade-off of securitized real estate, and there is a probability each period that a switch would happen from one
regime to another. For example, the effect of 1997 Asian Financial crisis was to reduce real estate returns and to
increase real estate volatility and correlation with other asset classes (Kallberg, et al.2002), while prior to the crisis, the
opposite occur. In addition, regime changes in securitized property markets might occur due to changes in
macroeconomic conditions, government intervention in the direct property market,1 highly cyclical nature of physical
property market and sudden external shocks like the 1987 stock-market crash and the 1997 Asian financial crisis.
For example, on May 15, 1996, the Singapore Government introduced a series of measures to curb the speculation in
the residential property market. These measures include a tax levied on gains from the sale of property within the first
three years of purchase, additional stamp duties, a limit of housing loans to 80% of property value and a restriction on
granting Singapore dollar loans to permanents residents and foreigners. The curbs affected both the residential market
and the property stock market significantly, with the benchmark SES All-property price index tumbling 40.24 points or
5.5% to 690.61 on that day.
1
2
Hence, failure to consider changing behaviors and interactions of the markets due to regime shifts might result in suboptimal asset allocation and inaccurate portfolio performance measurement.
In the paper, we allow the movement of securitized property markets to be characterized by multiple
structures. By permitting switching between these structures, we hope to capture more complex dynamic patterns, i.e.
regime changes, in the securitized property markets. The objective of this paper is thus to investigate the securitized
property market behavior in light of discrete regime shifts. Employing a monthly return datasets that cover the US, UK,
Australia, Japan, Singapore and Hong Kong securitized property markets over 1987-2003, the specific objectives of
this paper are:
(a)
To model distinct regimes in securitized property risk and returns
(b)
To assess how the regimes differ among the different markets
(c)
To assess and compare the frequency and timing of regime shifts
(d)
To assess the level of intermarket correlations of regimes
(e)
To determine whether securitized property market returns are predictable after accounting for
regime switches
To establish a background for the study, Section 2 provides a review of relevant literature. The underlying
regime switching models are discussed in Section 3. The data requirements are discussed in Section 4. The
presentation of results and conclusion appear in Sections 5 and 6 respectively.
2.
LITERATURE REVIEW
Hamilton (1989) proposes a two-state switching-regime Markov model to consider changes in regime. Under
this approach, the parameters of a non-stationary time series are viewed as the outcome of a discrete-state Markov
process.2 The shifts are not to observe directly, but instead probabilistic inference is drawn about whether and when
the shifts have occurred based on the observed behavior of the series. Hamilton (1989) employs the model to
investigate the US business cycle. Goodwin (1993) employs the Hamilton Markov-switching model to analyze the
business cycles of 8 developed market economies. Filardo (1994) extends the Hamilton model to incorporate timevarying transitional probabilities between the expansionary and contractionary phases of the business cycle. Engel
(1994) investigates whether the Markov switching model is a useful tool for modeling the behavior of floating exchange
rates. Finally, Garcia and Perron (1996) allow three possible regimes in their Markov switching model that affects both
the mean and variance of the US real interest rate from 1961 to 1986.
The issue of regime changes has also been examined in the stock market literature. Schwert (1989) explores
a model whereby returns could have either a high or low volatility and the switches between these return distributions
are controlled by a two-state Markov chain process. Turner et al (1989) consider a Markov switching model in which
either the mean, the variance or both may differ between two regimes. Using S&P monthly index data over the period
1946-1989, they investigate univariate specifications with constant transition probability. Hamilton and Susmel (1994)
consider a model with sudden discrete changes in volatility. They estimate models with two to four regimes in which
2A
Markov process (or chain) is a stochastic process in which the probabilities associated with the outcomes at any
stage of the process depend only on the outcomes of the preceding stage.
3
the latent innovations come from Gaussian and Student t-distributions. They find that Markov switching model provides
a better statistical fit to the data than ARCH models without switching. Schaller and Van Norden (1997) find strong
evidence of switching behavior in the US stock market excess returns. Additionally, they develop a multivariate
regression model to investigate whether price/dividend ratio has marginal predictive power for stock market return after
accounting for state-dependent switching. Finally, in a study that covers five industrialized countries’ stock market
returns (Canada, Germany, Japan, United Kingdom and United States), Nishiyama (1998) finds that each market
exhibits distinct regimes in volatility, but not in expected mean return. The persistence of the regimes and the
frequency of regime shifts are significantly different among the markets. Additionally, the inter-market correlations of
regimes are significantly higher in the post 1987 crash period.
Although prior studies have extensively investigated the risk-return performance of REITS and property
stocks (Gyourko and Keim, 1992; Han and Liang, 1995; Glascock and Davidson, 1985; Kapplin and Swartz, 1999 and
Liow, 2001), they are mainly based on the assumption that the relationship between risk and return is linear and give
little attention to the issue of structural or regime changes. To the best of our knowledge, only three studies consider
regime changes in real estate performance measurement. Lizieri et al. (1998) test for the existence of two-regime real
interest rate in the US REITs and UK property companies using a threshold autoregressive (TAR) model. MaitlandSmith and Brooks (1998) find that the Markov switching model is better able to capture the non-stationary features of
their US and UK commercial real estate return series than the TAR. Finally, Kallburg, Liu and Pasquariello (2002)
employ BLS technique to identify regime switches in securitized real estate and stock markets if eight Asian countries
over 1992-1998.
In summary, similar to the stock market, regime changes in securitized property markets and volatility might result
in different states of the markets with different patterns of risk-return behavior and state interactions. Hence it is
necessary to consider the securitized market behavior in light of discrete regime shifts. On further reflection, although
evidence of regime shifts using Markov switching model has existed in stock market, its application to international
securitized real estate markets is relatively new and will create new frontier in international real estate research.
3.
BASIC REGIME SWITCHING MODELS
The underlying structure of a regime-switching model is characterized by a latent variable, S t, the state or
regime. Although it is possible to estimate models with n regimes, using two regimes is standard in the literature. We
first use likelihood ratio tests to determine the three specifications (Equations 2-4) given below are best characterized
as having one or two regimes. Each regime has its own return distribution with different expected return and /or
variance. In addition, changes in the regimes are governed by a discrete Markov process with constant transition
probabilities.
First, assume returns are drawn from a single Gaussian distribution with mean
µ 0 and
variance
σ
0,
equation (1) is the specification of no switching:
Rt = µ 0 + σ 0 ε t ……………………………(1)
4
Next, contraction and expansion are modeled as switching regimes of the stochastic process generating the
securitized real estate return R t. In the following equations, st denotes an unobservable state or regime, which is
denoted by 0 (contraction) or 1(expansion). The transition between the states is governed by a first-order Markov
process, which is reported in equation 5. Three different models of switching will be tested - regime switching in mean
(equation 2), switching in variance (equation 3) and switching in mean and variance (equation 4) respectively.
Rt = µ 0 (1 − s t ) + µ1 st + σ 0 ε t
(2)
Rt = µ 0 + [σ 0 (1 − st ) + σ 1 s t ]ε t
(3)
Rt = µ 0 (1 − st ) + µ1 s t + [σ 0 (1 − st ) + σ 1 st ]ε t
(4)
P[ st = 0 | st −1 = 0] = p
P[ st = 1 | st −1 = 0] = 1 − p
P[ st = 1 | st −1 = 1] = q
(5)
P[ st = 0 | st −1 = 1] = 1 − q
The underlying intuition behind a regime-switching model is that each securitized property market will be
characterized by two different regimes (states), S t. State 0 is identified as the low return – high volatility regime and
State 1 as the high return – low volatility regimes. For each of the states we modeled, three regime specifications are
examined. Equation (2) indicates securitized property returns are drawn from two different normal distributions that
differ only in their mean returns (switching in means). In Equation (3), securitized property returns come from two
distributions that differ only in their variances (switching in variance). Finally in Equation (4), securitized property
returns are drawn from two distributions that differ in both mean returns and variances (switching in means and
variances). In addition, either state 0 or state 1 will not persist all the time as there is a probability each period that the
market will switch from one regime to another. The transition probability, p, (given in equation 5) is the probability of
remaining in regime 0 today given that the market was in regime 0 in the previous month. Similarly, q is the probability
of remaining in regime 1 today given that the market was in regime 1 in the previous month. The expected duration is
the number of periods during which each state is expected to persist once that state sets in. According to Hamilton
(1989), the expected duration and unconditional probability for state 0 are calculated as
p ( s t = 0) =
and
p( st = 1) =
and
4.
D( st = 0) = (1 − p ) −1
1− q
−1
2 − p − q , respectively. For state 1, the two formulae are D( st = 1) = (1 − q)
1− p
2 − p − q , respectively
RESEARCH DATA
The four Asian-Pacific markets analyzed are Singapore, Hong Kong, Japan and Australia. Of them,
Singapore and Hong Kong are major Asian developing economies and have reasonably long-established track records
of listed property investment and development companies. We use monthly property stock returns for the period from
5
January 1987 to December 2003. In addition, these Asian-Pacific markets are compared with two well established
securitized markets of USA and UK. All data are extracted from Datastream.
Exhibit 1 contains a description of the securitized property indexes of the six markets which represents about
91% of the global securitized property market.3 Exhibit 2 displays the index movement over the study period.
(Exhibits 1 and 2 here)
Exhibit 3 reports several descriptive statistics for the monthly return series of the six markets. These include
the mean, the standard deviation of the return, the range (maximum and minimum) of returns, and the measures of
skewness and kurtosis. As can be seen, the US REIT market reports the highest average monthly returns (0.8%) and
lowest standard deviation (3.44%). Hong Kong and Singapore appear to be the 2 most volatile markets (standard
deviations are 11.79% and 9.99% respectively). The skewness statistic shows that all the returns series are negatively
skewned although the respective skewness statistics are not large (between -0.7783 and -0.0939). Finally, the kurtosis
measure is more than 3 in all the return series. This evidence suggests that for all the six securitized property markets,
the distribution of returns has fat tails compared with the normal distribution.
(Exhibit 3 here)
5.
EMPIRICAL RESULTS
5.1
Test of regime switching
Exhibit 4 reports the likelihood ratio (LR) and probability for the null hypothesis of no regime switching for the
three alternatives.4 When we test Equation 2 against the null hypothesis, the likelihood ratio (LR) tests fail to reject the
null of no regime shifts for the US and UK markets. On the other hand, the LR tests on Equation 3 (switching in
variances) and Equation 4 (switching in both means and variances) imply consistent evidence of rejection of no state
switching. Another observation is the US and UK markets have lower variance switching. Overall there is reasonable
evidence of regime switching in international securitized property markets. However, the expected returns are not state
dependent for the Asian-Pacific markets.
(Exhibit 4 here)
5.2
Evidence of regime switching
Estimates of the regime shifts are presented in Exhibit 5 (switching in means), Exhibit 6 (switching in
variances) and Exhibit 7 (switching in means and variances).
(Exhibits 5 – 7 here)
(a)
Switching in means
3 According
to the 2003 report of UBS Investment Bank, the shares of global listed real estate market are 49%(USA),
8% (Continental Europe), 10% (Japan), 11% (HK /China), 13% (UK) and 8% (Australia).
4
Using Ox, we first develop a sample likelihood function for each case. Each log-likelihood function is a function of
µ 0 , µ1 , σ 0 , σ 1 , p, q and is maximized numerically using expected maximization (EM) algorithm (Hamilton, 1989).
In addition, the filter generates the conditional probability of each state occurring given all the information up to time t.
6
The first specification is one in which securitized property returns are drawn from two distributions that differ
only in their means (Equation 2). According to the figures shown in Exhibit 5, there is some evidence of significant
regime swifts in the mean returns for the USA and UK securitized property markets. In state 0, monthly returns are 7.61% (UK) and -1.81% (US), implying annual (compounded) returns of -141.2% (UK) and -24.02% (USA). When state
1 occurs, the implied annual returns become 28.02% (UK) and 22.41% (USA). Additionally, the probabilities of
remaining in state 1 (q) is higher (between 0.6640 for Australia and 0.9216 for the USA). For state 0, the probability will
persist for one more month is between 0.4380 (UK) and 0.7693 (USA).
(b)
Switching in variances
The second specification is one in which securitized property returns are draw from two distributions that
differ only in their variances (Equation 3). A picture of two regimes with sharply different variances emerges from
Exhibit 6 (i.e. the difference between
σ 0 and σ 1 is statistically significant at the conventional probability levels). For
all six markets, state 0 is characterized by a variance about 1.7 times to 2.9 times as large as the variance in state 1.
The differences in variance between the two states are statistically significantly at the one-percent level for all six
markets. The estimates of the transitional probabilities show that state 1 (low variance state) is highly persistent with an
average q value of 0.9376. Similarly, state 0 (high variance state) is also reasonably persistent with a smaller average
p value of 0.8345.
(c)
Switching in means and variances
In the third specification where securitized property returns are characterized by switching means and
variances (Equation 4), the results in Exhibit 7 reveals the variance in high-volatility state (state 0) is between 1.4
times (USA) and 2.8 times (HK) as large as the variance in low-volatility state (state 1). The mean return in state 0 is
negative for all markets (between -3.70% and -0.10%). In addition, the difference in the mean annual (compounded)
returns between the two regimes ranges from 5.59% (Australia) to 56.51% (HK). Hence, we have a situation in one
state the returns are low / negative and the variance is high (state 0), and in the other state the returns are high and
variance is low (state 1). The estimates of the transitional probabilities are very similar to the specification of switching
in variances only. Specifically, the estimates suggest that low-variance regime dominates (q is between 0.8070: UK
and 0.9763: Australia). In addition, all high–variance probabilities estimates are reasonably high (p is between 0.7343:
HK and 0.9057: Singapore). This result indicates once the low-variance or high-variance state sets in there is a high
probability that the same state continues in all markets. Our evidence here is also consistent with the stock market
studies of Turner et al (1989) and Nishiyama (1998)
5.3
Further Evidence for Mean-Variance Switching
(a)
Expected duration of the states
Exhibit 8 provides estimates of the expected duration of the two states in the context of mean-variance
regime swifts. The expected duration provides a useful measure of the duration of each state. As observed, the Japan
securitized property return series has the longest expected duration of low return-high volatility state (state 0) of about
7
10.6 months. This is followed by Australia (8.3 months), USA (5.5 months), UK (4.4 months), Singapore (4.2 months)
and HK (3.8 months). For the high return-low volatility state (state 1), the longest and shortest expected duration are
approximately 29.1 months (Australia) and 8.5 months (UK) respectively. Hence, the property stock return series in
Japan exhibits long volatility in both high- and low-volatility states.
(Exhibit 8 here)
(b)
Unconditional probabilities of the regimes
The unconditional probabilities of the two regimes to prevail are provided in Exhibit 9. The most distinct case
is HK. As observed, HK shows the highest probability of being in the low volatility- high return regime (state 1), which is
84.62 percent of the time. On the hand, HK has the lowest probability of being in the high volatility-low return regime
(state 0 – 15.4 percent). The US REIT market is expected to be in its low volatility-high return state about 76.7 percent
of the time.
(Exhibit 9 here)
(c)
Volatility persistence
For each market, the probabilities of being in state 1 (high return-low volatility) are shown over the sample
period in Exhibit 10. Exhibit 11 graphs the return series as well as the probability for each market. There are two key
observations. First, all the market’s returns are dominated by the low volatility-high return state. The probability of being
in good years (state 1) is reasonably close to 1 for most of the sample period especially in HK, Australia and Singapore
markets.5 Second, the high-volatility state persists in the Singapore and HK markets after the 1997 Asian financial
crisis, with the Singapore property stock market exhibits stronger post-crisis high volatility. Panels A and B of Exhibit 12
display the return-probability trend over the Asian financial crisis period for Hong Kong and Singapore.
(Exhibits 10 and 11 here)
(Exhibit 12 here)
In summary, our investigations have revealed that the two regimes are persistent with significant differences
observed in the degree of regime persistence and the frequency of switches between the regimes among the six
markets. However, the low volatility-high return state dominates all the six markets between 65.7 and 84.6 percent of
the time.
(d)
US REIT market in the period 1998-2000
As the figure in Panel C of Exhibit 12 shows, shortly after the abrupt of the Asian financial crisis, the US REIT
market was in a “recession” for a period of 19 months (April 1998-October 1999, both months inclusive)6. Over the
period 1991-2000, the average mean return for REIT stocks and their standard deviation were 1.06% and 3.48%,
respectively. However, the average monthly return for the REIT stocks was -1.64% and -0.49% for 1998 and 1999 with
standard deviation of returns of 4.21% (1998) and 3.83% (1999), respectively. Hence, the years 1998 and 1999
5 For example, for the full period (204 months), the probability of being greater than 0.9 is 62%, 59% and 57% of the
time for HK, Australia and Singapore markets.
Based on our analysis, the unconditional probability of State 0 (low return-high volatility) of each of the 19 months is
between 0.0182 and 0.4573.
6
8
corresponded to the low-return-high volatility regime (State 0). One popularly cited reason for the weak performance of
the REIT industry during these two years was the rotation of institutional funds out of REIT stocks to technology and ecommerce stocks. According to Howard (1998), during these periods many US technology and internet stock prices
soared to unrealistic level. Investors’ enthusiasm on these stocks and the liquidity crunch in the market had caused
REIT shares tumble nearly 20 percent for the first quarter of 1998. The huge decline in REIT stock prices was thus
mainly due to the relatively poor performance of real estate value increases during the 1990s compared with the prices
of competitive stock investments, especially technology and e-commerce stocks (Downs, 2000). The technological
bubble had caused institutional investors rotate their funds to the high-technology sectors. In 2000, REIT stock prices
recovered with an average monthly return of 2.01%.
5.4
State dependent mean-variance correlation
In the context of mean-variance regime shifts, Exhibit 13 presents the cross-market Pearson correlation
coefficients of state 1 (low volatility) for the entire period, the 3-year period after October 1987 stock market crash and
the 3-year period after July 1997 Asian financial crisis. For the full period (Panel A), the correlation of mean-variance
state dependence is the highest between HK and Singapore (0.524), followed by US and UK (0.447), US and Japan
(0.448) and HK and Australia (0.446). On the other hand, some pairs of securitized property markets show negligible
correlations. They include HK and Japan (0.118), Singapore and Japan (0.109) and HK and UK (0.088). A final
observation is that the US mean-variance state dependence shows stronger positive relationship with all the other five
markets (correlation coefficients range between 0.272 and 0.447, all are statistically significant at the 5 percent level)
(Exhibit 13 here)
For the three-year post October 1987 crash period, Panel B of Exhibit 13 reveals that mean-variance state
correlations for Singapore, Japan and UK improve substantially with the US securitized real estate market. The USJapan correlation become the highest (0.781), followed by US-UK (0.701) and US-Singapore (0.686) correlations. The
Japan-Singapore state correlation also improves tremendously for the post crash period (0.627) On the other hand, the
state correlations for other pairs of securitized property returns decrease or turn out negative for the post-crash period.
Our findings are hence different from earlier stock market evidence that increasingly interdependency and volatility
spillovers among international stock markets in the post-crash era are documented (Theodossiou and Lee, 1993;
Nishiyama, 1998).
When the data are confined to the 3-year post July 1997 Asian financial crisis period, a different picture
emerges. As observed in Panel C, the most striking evidence is the mean-variance state correlations of Australia with
other three Asian-Pacific markets (HK, Singapore and Japan) are significantly higher (between 0.427 and 0.589) in the
post crisis period. However, the Japan-HK and Japan-Singapore state correlations show weaker positive relationship.
As expected, the US and UK securitized markets display weak state correlations with other pairs of Asian-Pacific
markets as they were much less affected by the Asian financial crisis. Finally, as noted earlier, this post Asian financial
crisis period is coincided with the US REIT technological bubble period. Hence the state correlations of other markets
with the US REIT market might have been affected by this event.
9
5.5
Predictability of Returns
Securitized properties are valued in the same way other public traded firms are valued. The two popular
stock market valuation parameters are price/dividend (P/D) and price / earning (P/E) ratios. In the context of this paper,
the relevant question is: Could securitized returns be predicted with P/D or P/E ratios after allowance is made for statedependent heteroscedasticity? Schaller and Van Norden (1997) find that after controlling for regime switching in
variance, P/D ratio could still predict stock market returns. In this study, we expand the investigation by developing
three multivariate specifications that include P/D ratio (equation 6), P/E ratio (equation 7), P/D and P/E ratios (equation
8) in the switching mean-variance specification. Our objective is to examine whether the P/D, P/E, P/D and P/E ratios
have predictive power for securitized property returns after accounting for state-dependent switching. In addition, the
asymmetric effect of the P/D and P/E ratio on the returns could be examined. Exhibits 14-16 present the estimation
results. The focus is on the significance of
β
and
φ
coefficients and their economic interpretations.
R t = α 0 (1 − s t ) + α 1 s t + β 0 ( P / D ) t −1 (1 − s t ) + β 1 ( P / D ) t −1 s t + [σ 0 (1 − s t ) + σ 1 s t ]ε t
R t = α 0 (1 − s t ) + α 1 s t + φ 0 ( P / E ) t − 1 (1 − s t ) + φ 1 ( P / E ) t − 1 s t + [σ 0 (1 − s t ) + σ 1 s t ]ε t
Rt =α0 (1− st ) + α1st + β0 (P/ D)t −1(1− st ) + φ0 (P/ E)t −1(1− st ) + β1(P / D)t −1st + φ1(P/ E)t −1s + [σ0 (1− st ) + σ1st ]εt
(6)
(7)
(8)
(Exhibits 14 -16 here)
Exhibit 14 indicates that there is some strong evidence of predictability with the P/D ratio. As observed, the tstatistics for β 0 for HK (-2.05), Japan (-2.15), Singapore (-1.96) and Australia (-2.29) are statistically significant at the
5 percent level. Similarly,
β 1 estimates for HK, Japan, Singapore, Australia and UK are at least statistically significant
at the 10% level. Further, the influence of P/D ratio between the two regimes is different. For HK, in regime 0 (high
volatility state), an increase in one standard deviation in the Log (P/D) implies a fall in securitized property price of
about 28.3 percent per year. In regime 1 (low volatility state), a similar increase in the P/D ratio implies a fall of only
about 8.7% per year. Similarly, the implied annual estimates
β0
and
β1
for Singapore market are -16.8 and -4.9%
respectively. Hence, there is a fairly high asymmetric response to the lagged P/D ratio. The asymmetric effect is at
least 3 times larger in state 0 than in state 1. The difference between µ1 and
µ0
is also economically significant for
HK, Japan and Singapore markets. The estimates implies that annual stock prices would be about 42.8% (Singapore),
58.8% (HK) and 62.9% (Japan) higher in state 1 than in state 0. However, as observed from Exhibit 15, the P/E ratio
has no predictive power for state-dependent securitized property returns because the relevant estimates
φ 0 and φ1
are largely statistically insignificant. Finally, in equation 8 where both P/D and P/E ratios are jointly examined, with
some minor exceptions we find little evidence of predictability (Exhibit 16).
To summarize, we are only able to obtain a switching model in which the price-dividend (P/D) ratio predicts
securitized property returns. Additionally, the response of returns to past P/D ratio is asymmetric; the effect is at least
three times larger in state 0 than in state 1. This finding implies that there is even greater variability in expected returns
conditional on the P/D ratio and state 0. In addition, as state 0 is between 1.4 times and 2.8 times riskier than in state 1,
for more than about 97.2% to 98.6% of the values of the lagged P/D ratio, the expected return in state 0 is lower than
10
the expected return in state 1. An investment implication is that real estate investors should buy securitized property
when P/D ratios decrease and sell securitized property when P/D ratios increase; especially in the “bad” state since the
response effect of return to past P/D ratio is strongly asymmetric. Our findings are thus similar to those of Schaller and
Van Norden (1998) reported in the stock market literature.
6.
CONCLUSION
This paper examines the existence and nature of return and volatility regime swifts in international securitized
property returns in the period January 1987 to December 2003. With the increased significance of international
securitized property as a real estate investment vehicle for institutional investors to gain worldwide real estate
exposure, this paper is important to help investors understand the differential risk-return performance of securitized
property after accounting for state dependent regime switching and consider structural mean-variance implications in
their optimal asset allocation and performance measurement exercise.
The main findings are: (a) international securitized property markets have strong switching behavior in
volatility. The results indicate that the conditional variance is state-dependent but the conditional mean is statedependent for the US REIT and the UK property stock markets only, (b) securitized property in our sample exists in one
state (state 0) where the returns are low/negative and the variance is high, and in the other state (state 1) the returns
are high and the variance is low, (c) the two regimes (low return-high volatility; high return-low volatility are persistent
with differences observed in the expected duration and the frequency of shifts between the states among the six
international markets. However, the high return-low volatility (state 1) regime dominates the six markets between 65.7
and 84.6 percent of the time, (d) examinations of the correlations of mean-variance state probabilities suggest
intermarket interactions between some pairs of securitized property markets. There is also some evidence of changes
in correlations among some pairs of securitized property markets after the 1987 stock market crash and the 1997 Asian
financial crisis.
In a specification where we allow for switching in both means and variances, the response of securitized
property returns to the past price / dividend (P / D) ratio is strongly asymmetric; the effect of the P/D ratio is about three
times larger in the low return-high volatility state than in the high return-low volatility state. Hence, after controlling for
switching, securitized property returns can be predicted using the P/D ratio. The predictability of returns can also come
from time-varying excess returns in an efficient securitized property market. Our results are preliminary but indicative
and for which more studies are required to explore the influence of macroeconomic factors on securitized property
return and volatility with other forms of regime switching models such as MS-GARCH and MS-VAR.
11
References
Bond, S., Karolyi, A. and A. Sanders (2003), International real estate returns: a multifactor, multi-country approach,
Real Estate Economics 31(3): 481-500
Conover, C., Friday, H. and Sirmans, G. (2002), Diversification Benefits from Foreign Real Estate Investments, The
Journal of Real Estate Portfolio Management, 8(1), pp.17-25
Downs, A (2000), What Led to the REIT Stock Recovery, National Real Estate Investor 42(9), p. 50
Engel, C. (1994), Can the Markov Switching Model Forecast Exchange Rates? Journal of International Economics, pp.
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Filardo, A.J. (1994), Business Cycle Phases and their Transitional Dynamics, Journal of Business and Economic
Statistics 12(3), pp. 299-308
Garcia, R. and P. Perron (1996), An Analysis of the Real Interest Rate under Regime Swifts, The Review of Economics
and Statistics 78(1), pp. 111-125
Glascock, J.L. and W.N., Davisdon (1985), Performance Measures of Real Estate Firm Common Stock Returns, (eds)
Schwartz and Kapplin, Alternative Ideas in Real Estate Investment, Research Issues In Real Estate Series, Kluwer
Academic Publishers
Goodwin, T.H. (1993), Business Cycle Analysis with a Markov Switching Model, Journal of Business and Economic
Statistics 11(3), pp. 331-339
Gyourko, J. and D., Keim (1992), What Does the Stock Market Tell Us about Real Estate Returns, AREUEA Journal
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Estate Economics 30(2), pp. 263-292
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Alternative Ideas in Real Estate Investment, Research Issues In Real Estate Series, Kluwer Academic Publishers
Lizieri, C. Satchell, S. Worzala, E. and R Dacco (1998), Real Interest Regimes and Real Estate Performance: A
Comparison of UK and US Markets, Journal of Property Research 16(3), pp. 339-355
Maitland-Smith, J.K. and C. Brooks (1999), Threshold Autoregressive and Markov Switching Models: An Application to
Commercial Real Estate, Journal of Property Research 16(1), pp. 1-19
Newell, G. and K.W. Chau (1996), Linkage between Direct and Indirect Property Performance in Hong Kong, Journal of
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Property Finance 7(4), pp.9-29
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(40), pp.1115-1149
13
Exhibit 1
Hong Kong
Japan
Singapore
US
UK
Australia
Sample Description of Securitized Property Indices
Hang Seng Property Index is a capitalization-weighted index of all the stocks designed to measure
the performance of the property sector at the Hong Kong Stock Exchange. The index consists of 6
members and its total market capitalization was HK$315.8 billion as at 11/07/03.
Topix Real Estate Index is a capitalization-weighted index designed to measure the performance of
the real estate sector of the Topix Index. The index was developed with a base value of 100 as of
04/02/68. It consists of 34 members with a total market capitalization of $2.98 trillion yen as at
11/07/03.
Singapore Property Equities Index is a capitalization-weighted index of all the stocks traded on the
Stock Exchange of Singapore’s property sector. The index was developed with base value of 1000 as
of 03/01/97. It consists of 21 members with a total market capitalization of S$16.65 billion as at
11/07/03.
The NAREIT Index includes all REITs trading on the New York Stock Exchange, the NASDAQ
National Market System and the American Stock Exchange. The index provides a standard with
which to measure the REIT industry's growth and performance. It consists of 50 members with a total
market capitalization of US$135.0 billion as at 30/06/03.
FTSE 350 Real Estate Index is a capitalization-weighted index of stocks designed to measure the
performance of the real estate sector of the FTSE 350 Index. The index was developed with a base
value of 1000 as of 31/12/85. It consists of 18 members and its total market capitalization was 16.96
billion pounds as at 11/07/03.
ASX 300 Real estate index is a capitalization weighted index of property equity traded on the
Australian Stock Exchange. The index was developed with base value of 3133.25 as of 31st March
2000. It consists of 35 members and its total market capitalization was A$59.01 billion at of 12/09/02
Source: Datastream
Exhibit 2 Securitized Real Estate Price Indices
14
Exhibit 3 Descriptive Statistics of Monthly Securitized Property Returns (1987:1 to 2003:12)
Hong Kong
Japan
Singapore
Australia
UK
US
Exhibit 4
Mean
0.72%
-0.75%
-0.01%
0.3%
0.43%
0.80%
Maximum
45.79%
19.16%
47.8%
9.8%
16.09%
9.96%
Minimum
-61.52%
-33.33%
-38.63%
-19.71%
-20.26%
-14.28%
Std Dev
11.73%
8.50%
9.99%
3.47%
5.95%
3.44%
Skewness
-0.6813
-0.4642
-0.0939
-0.7783
-0.4394
-0.2702
Kurtosis
8.4253
3.7627
7.4651
7.7503
3.4179
4.6427
Likelihood Ratio Tests of Regime Switching in Securitized Property Returns
Switching in
p-value
Switching in
p-value
Switching in Means and
p-value
Means
Variances
Variances
Hong Kong
-0.0128
1.000
47.66**
0.000
48.85**
0.000
Japan
-0.0458
1.000
5.88**
0.015
8.78*
0.012
Singapore
0.3120
0.576
59.49**
0.000
61.24**
0.000
Australia
-0.0084
1.000
23.77**
0.000
23.53**
0.000
UK
11.8349**
0.006
8.97**
0.003
5.75**
0.004
US
7.4025**
0.007
9.13**
0.003
9.67**
0.008
**,* indicates two-tailed significance at the 1% and 5% level respectively This table reports tests of the null hypothesis
of no switching in property stock market returns against three alternative specifications.
Exhibit 5 Regime Switching in Means1
Rt = u0 (1 − st ) + u1 st + σ 0ε t
u0
u1
p
q
σ
Loglikelihood
Hong Kong
-0.70%
(-0.16)
1.90%
(0.47)
0.6449
(0.94)
0.7021
(0.2162)
11.64%**
(2.75)
-719.38
Japan
-2.25%
(-0.56)
0.36%
(0.03)
0.5951
(0.41)
0.6978
(0.04)
8.39%
(0.27)
-725.76
Singapore
-1.64%
(-0.76)
1.27%
(0.81)
0.7305
(1.19)
0.7244
(0.39)
9.71%**
(4.98)
-758.47
Australia
-0.15%
(0.09)
0.34%
(0.18)
0.6591**
(3.77)
0.6640
(0.06)
3.44%
(0.21)
-541.50
UK
-7.61%**
(-4.83)
2.08%**
(3.32)
0.4340
(1.15)
0.8848
(1.66)
4.68%**
(8.63)
646.76
U.S.
-1.81%
(-1.60)
1.70%**
(3.80)
0.7693**
(3.98)
0.9216
(1.15)
3.07%**
(3.95)
537.32
The mean return is µ 0 in state 0 and µ1 in state 1. The standard deviation of returns is σ . The transitional
probabilities are p (sate 0) and q (state 1) that follow a standard Gaussian distribution function. The figures in
parentheses are t-statistics.
1
** Indicates two-tailed significance at the 1% level.
15
Exhibit 6 Regime Switching in Variances
Rt = u0 + [σ 0 (1 − st ) + σ 1 st ]ε t
u
p
q
σ0
σ1
Log-likelihood
Hong Kong
1.21%
(1.83)
0.7904*
(1.96)
0.9503**
(2.62)
23.58%**
(5.22)
8.05%**
(15.27)
-764.04
Japan
-0.47%
(-0.82)
0.7509
(0.65)
0.9078
(0.82)
11.71%**
(5.21)
6.84%**
(8.30)
-719.13
Singapore
0.40%
(0.77)
0.9114*
(2.21)
0.9595*
(2.22)
15.48%**
(8.23)
5.77%**
(8.77)
-724.32
Australia
0.22%
(0.99)
0.9037
(0.81)
0.9854**
(3.81)
5.70%**
(5.16)}
2.78%**
(2.31)
-526.86
UK
0.37%
(0.92)
0.8875
(0.83)
0.9897
(0.76)
9.55%**
(5.10)
5.24%**
(14.7)
-643.63
U.S.
0.61%**
(2.56)
0.7630
(1.19)
0.8332**
(3.20)
4.43%**
(4.34)
2.38%**
(2.64)
-530.68
The mean return is µ .The standard deviation of returns is σ 0 in state 0 and σ 1 in state 1. The transitional
probabilities are p (sate 0) and q (state 1) that follow a standard Gaussian distribution function. The figures in
parentheses are t-statistics
1
** Indicates two-tailed significance at the 1% level.
Exhibit 7 Regime Switching in Means and Variances 1
Rt = u0 (1 − st ) + u1 st + [σ 0 (1 − st ) + σ 1 st ]ε t
u0
u1
p
q
σ0
σ1
Log-likelihood
Hong Kong
-3.70%
(-0.87)
1.54%**
(2.29)
0.7343
(1.76)
0.9517**
(3.00)
Japan
-3.76%
(-1.41)
0.38%
(0.49)
0.7630
(0.79)
0.9114
(1.01)
Singapore
-1.82%
(-0.74)
0.67%
(1.18)
0.9057*
(1.76)
0.9651
(1.35)
Australia
-0.10%
(-0.03)
0.36%
(0.71)
0.8793
(1.25)
0.9656***
(3.48)
UK
-2.52%
(-1.66)
1.87%**
(2.25)
0.7735
(1.62)
0.8816*
(1.80)
U.S.
-1.30%
(-0.92)
1.45%**
(1.98)
0.8175
(0.61)
0.9445
(1.04)
22.57%**
(6.26)
7.98%**
(15.25)
-766.85
11.22%**
(6.71)
6.84%**
(9.57)
-721.35
16.16%**
(7.42)
6.07%**
(8.08)
-728.00
5.26%**
(5.56)
2.61%**
(2.37)
-531.08
8.17%**
(6.42)
4.27%**
(6.64)
-652.16
3.99%**
(2.81)
2.95%**
(12.60)
-536.19
The mean return is µ 0 in state 0 and µ1 in state 1. The standard deviation of returns is σ 0 in state 0 and σ 1 in state
1. The transitional probabilities are p (sate 0) and q (state 1) that follow a standard Gaussian distribution function.
( The figures in parentheses are t-statistics.
1
** Indicates two-tailed significance at the 1% level.
16
Exhibit 8 Expected duration (in months) 1
Hong Kong
Japan
Singapore
Australia
UK
U.S.
Low return—High volatility
Regime (State 0)
3.76
10.60
4.22
8.28
4.42
5.48
High return—Low volatility
Regime (State 1)
20.71
28.68
11.29
29.08
8.45
18.01
The expected duration is the number of periods (months) during which each state is expected to persist once that
state sets in.
1
Exhibit 9 Unconditional Probability of each Regime
Hong Kong
Japan
Singapore
Australia
UK
U.S.
Low return—High volatility
Regime (State 0)
0.1538
0.2699
0.2721
0.2271
0.3433
0.2333
High return—Low volatility
Regime (State 1)
0.8462
0.7301
0.7279
0.7783
0.6569
0.7667
17
Exhibit 10 Probability of High Return-Low volatility state ( P ( S t
Hong Kong
Japan
Singapore
Australia
= 1 |ψ t )
UK
UK
US
18
Exhibit 11 Probability of P ( S t
= 1 | ψ t ) and Return
Hong Kong
Singapore
Japan
19
Australia
UK
US
20
Exhibit 11
Examples of Return– probability in recession / crisis periods
Panel A Asian Financial Crisis and Hong Kong Property Stock Market
P( S t = 1 |ψ t )
Recession because of
Asian Financial Crisis
Panel B Asian Financial Crisis and Singapore Property Stock Market
P( S t = 1 |ψ t )
Recession because of
Asian Financial Crisis
21
Panel C US Technological Bubble and REIT Stocks
P( S t = 1 |ψ t )
Recession because of
high-tech bubble in US
22
Exhibit 13
Pearson Correlation Coefficients P ( S t = 1 | ψ t ) for Switching in Means and Variances
Panel A: Full period
HK
Singapore
Japan
Australia
UK
US
HK
1
Singapore
0.524**
1
Japan
0.118
0.109
1
Australia
0.446**
0.276**
0.296**
1
UK
0.088
0.147*
0.356**
0.166*
1
US
0.272**
0.440**
0.448**
0.344**
0.477**
1
Panel B: Post-Stock Market Crash Period (Nov 1987—Nov 1990)
Hong Kong
Singapore
Japan
Australia
UK
US
Hong Kong
1
Singapore
-0.47
1
Japan
-0.249
0.627**
1
Australia
-0.037
-0.205
0.270
1
UK
-0.123
0.327*
0.003
0.061
1
US
-0.260
0.686**
0.781**
-0.146
0.701**
1
Panel C: Post Asian Financial Crisis Period (Aug 1997—Aug2000)
Hong Kong
Singapore
Japan
Australia
UK
US
Hong Kong
1
Singapore
0.435**
1
Japan
0.311
0.272
1
Australia
0.589**
0.459**
0.427**
1
UK
0.092
0.311
0.631**
0.183
1
US
-0.001
0.312
0.493**
0.326
0.498**
1
**,* indicates two-tailed significance at the 1% and 5% level respectively
23
Exhibit 14 Price/Dividend (P/D) Ratio and Regime Switching in Means and Variances1
Rt = µ 0 (1 − s t ) + µ1 st + β 0 ( P / D) t −1 (1 − st ) + β 1 ( P / D) t −1 st + [σ 0 (1 − s t ) + σ 1 st ]ε t
µ0
β0
µ1
β1
p
q
σ0
σ1
Log-likelihood
Hong Kong
-3.71%*
(-1.92)
-0.021**
(-2.05)
0.33%***
(2.92)
-0.007***
(-2.76)
0.7821
(1.19)
0.9705**
(1.99)
22.25%***
(6.71)
8.18%
(1.53)
354.88
Japan
-3.92%**
(-1.98)
-0.011**
(-2.15)
0.30%*
(1.86)
-0.0031*
(-1.78)
0.7848**
(1.97)
0.8864*
(1.76)
9.74%***
(8.54)
6.53%***
(5.05)
446.79
Singapore
-2.51%*
(-1.85)
-0.013**
(-1.96)
0.66%**
(1.97)
-0.0034*
(-1.85)
0.8168**
(2.15)
0.9454*
(1.69)
16.05%***
(8.76)
6.33%**
(2.07)
378.07
Australia
-1.01%**
(-2.32)
-0.004**
(-2.29)
1.10%
(1.59)
-0.0028*
(-1.71)
0.6039***
(2.57)
0.5005
(1.50)
3.78%***
(14.59)
2.79%***
(5.73)
923.29
UK
-0.72%
(-0.23)
-0.0009
(-0.41)
2.56%***
(3.54)
-0.0034***
(-2.89)
0.8822**
(1.97)
0.8601**
(2.10)
6.87%***
(13.87)
3.37%***
(3.69)
568.84
US
-2.10%
(-0.47)
-0.0008
(-0.35)
1.49%
(0.61)
0.0019
(0.76)
0.5430*
(1.91)
0.6912**
(2.10)
3.69%***
(9.28)
3.00%***
(9.76)
986.45
The mean return is µ 0 in state 0 and µ1 in state 1. The standard deviation of returns is σ 0 in state 0 and σ 1 in state
1. P/D is log (price / dividend) ratio. The transitional probabilities are p (sate 0) and q (state 1) that follow a standard
Gaussian distribution function. The figures in parentheses are t-statistics.
1
***, **, * indicates two-tailed significance at the 1%, 5% and 10% levels respectively
24
Exhibit 15 Price/Earning (P/E) Ratio and Switching in Means and Variances1
R t = α 0 (1 − s t ) + α 1 s t + φ 0 ( P / E ) t − 1 (1 − s t ) + φ 1 ( P / E ) t − 1 s t + [σ 0 (1 − s t ) + σ 1 s t ]ε t
µ0
φ0
µ1
φ1
p
q
σ0
σ1
Log-likelihood
Hong Kong
-2.46%
(-1.08)
-0.036
(-1.02)
1.0%
(2.68)
-0.0012**
(-2.63)
0.9928
(1.72)
0.9950
(1.50)
11.91%**
(16.60)
10.64%**
(12.99)
474.95
Japan
-0.51%
(-0.14)
-0.01
(-0.06)
0.33%
(0.77)
-0.015
(-0.97)
0.2622
(1.52)
0.7586
(1.73)
8.82%
(1.67)
7.08%**
(9.52)
583.02
Singapore
-0.27%
(-0.0037)
-0.009
(-0.05)
0.38%
(0.32)
-0.002
(-0.28)
0.5963
(1.73)
0.6727**
(2.40)
12.42%**
(12.33)
7.41%**
(3.34)
426.26
Australia
-1.47%*
(-2.29)
-0.071**
(-2.33)
1.06%
(1.07)
0.023
(1.09)
0.3973
(1.89)
0.6863
(1.57)
3.88%**
(11.02)
3.05%**
(4.09)
946.50
UK
-0.70%
(-1.40)
-0.135
(-1.46)
0.75%
(0.03)
0.0033
(0.13)
0.124**
(3.17)
0.7993**
(3.90)
5.99%**
(5.11)
5.77%**
(2.49)
704.98
1 The mean return is µ in state 0 and µ in state 1. The standard deviation of returns is σ in state 0 and σ in state
0
1
0
1
1. P/E is log (price / earning) ratio. The transitional probabilities are p (sate 0) and q (state 1) that follow a standard
Gaussian distribution function. The figures in parentheses are t-statistics. The US market was excluded from the
analysis as no time series data for P/E were available.
**, * indicates two-tailed significance at the 1% and 5% levels respectively
25
Exhibit 16 Price/ Dividend Ratio, Price/Earning Ratio and Regime Switching in Means and Variances1
Rt =α0 (1− st ) + α1st + β0 (P/ D)t −1(1− st ) + φ0 (P/ E)t −1(1− st ) + β1(P / D)t −1st + φ1(P/ E)t −1s + [σ0 (1− st ) + σ1st ]εt
µ0
β0
φ0
µ1
β1
φ1
p
q
σ0
σ1
Log-likelihood
Hong Kong
-0.94%*
(-1.77)
-0.076
(-1.05)
0.006
(0.09)
2.50%***
(4.48)
-0.0033***
(-4.21)
0.002***
(3.00)
0.9681
(1.00)
0.9497
(1.40)
12.19%***
(15.25)
9.05%***
(11.37)
779.39
Japan
-1.0%
(-1.10)
-0.054
(-1.10)
0.017
(0.66)
2.26%
(0.99)
-0.019
(-0.69)
-0.006
(-0.27)
0.2672
(1.56)
0.7408*
(1.80)
8.78%***
(17.95)
7.12%***
(14.00)
809.34
Singapore
-2.20%***
(-2.62)
-0.018***
(-3.28)
0.069**
(2.13)
0.28%
(1.66)
-0.008
(-0.33)
-0.035
(-1.58)
0.6590**
(2.01)
0.7883*
(1.78)
12.52%***
(23.87)
6.65%***
(8.89)
603.04
Australia
-1.78%***
(-4.02)
-0.017
(1.60)
0.013
(0.14)
0.57%
(1.57)
-0.0049*
(-1.90)
0.004
(0.10)
0.9279
(1.67)
0.9709**
(2.23)
3.43%***
(18.60)
3.11%***
(10.07)
1261.64
UK
-0.60%
(-0.17)
-0.029
(-0.05)
-0.031
(-0.38)
0.40%
(1.19)
-0.0037*
(-1.81)
0.014
(0.41)
0.2037
(1.10)
0.8240**
(2.02)
6.89%***
(19.02)
5.37%***
(11.99)
980.37
1 The mean return is µ in state 0 and µ in state 1. The standard deviation of returns is σ in state 0 and σ in state
0
1
0
1
1. P/D is log (price / dividend) ratio. P/E is log (price / earning) ratio. This specification allows returns to be influenced
by both P/D and P/E ratios in the context of regime switching in means and variances. The transitional probabilities are
p (sate 0) and q (state 1) that follow a standard Gaussian distribution function. The figures in parentheses are tstatistics. The US market was excluded from the analysis as no time series data for P/E were available.
***, **, * indicates two-tailed significance at the 1%, 5% and 10% levels respectively
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