2004 V32 3: pp. 437–462
REAL ESTATE
ECONOMICS
What Factors Determine International Real
Estate Security Returns?
Foort Hamelink∗ and Martin Hoesli∗∗
We use constrained cross-sectional regressions to disentangle the effects of
various factors on international real estate security returns. Besides a common
factor, pure country, property type, size and value/growth factors are considered. The value/growth measure that is used in this paper provides for each
security the relative importance of the value and growth components, rather
than a binary classification. The value/growth factor is found to be volatile and
to have a substantial effect on returns over the period February 1990–April
2003. Country factors are the dominant factors, and size is shown to have
a negative impact on returns. Statistical factors derived by means of cluster
analysis explain about one third of specific returns on international real estate
securities. The implication for portfolio managers is that failing to recognize
the importance of the various factors leads to the portfolio being exposed to
systematic risk.
For stock portfolio managers executing a top-down approach, it is crucial to
decide whether the strategy will be based primarily on countries, sectors, industries or some other factor such as size or value/growth. Diversification by
sectors is growing in importance, but geographical allocation remains important
despite the globalization of international financial markets. In this context, real
estate securities are considered as one industry, but they are too often discarded
from the strategic portfolio allocation. This is surprising given that real estate
securities have been shown to be effective diversifiers of common stock portfolios (Liang, Chasrath and McIntosh 1996, Gordon, Canter and Webb 1998).
Moreover, the correlation of U.S. REITs with common stocks has been declining (Ghosh, Miles and Sirmans 1996, Brounen 2003). Also, the market value of
publicly traded real estate companies has grown substantially in recent years,
with an estimated figure of US$340 billion as of April 2003.
Extensive research has been conducted since the 1970s on the benefits of
international diversification for stock portfolios. There is also more recent
∗
Lombard Odier Darier Hentsch & Cie, 1204 Geneva, Switzerland, also Vrije Universiteit and Tinbergen Institute, Amsterdam, The Netherlands, and FAME, Switzerland
or foort@hamelink.com.
∗∗
University of Geneva, HEC, 1211 Geneva 4, Switzerland, also University of Aberdeen
Business School, U.K., and FAME, Switzerland or martin.hoesli@hec.unige.ch.
evidence on the benefits of international diversification for portfolios of both
direct and indirect real estate investments. The cross-country correlations are
usually lower for real estate investments than for common stocks. There is evidence, however, of an international real estate factor (Ling and Naranjo 2002)
and also of continental factors (Eichholtz et al. 1998). Country-specific factors
remain important, however, which explains the diversification benefits. Eichholtz and Huisman (2001) show, for instance, that country dummy variables
are usually significant in a model that also includes beta, size and interest rate
variables.
When constructing a portfolio of publicly traded real estate stocks, much emphasis is placed on the analysis of the correlation coefficients across countries (or across continents). We argue that while these correlations are useful, it would be important to disentangle the effects of various factors on real
estate company returns and hence on cross-country correlation coefficients.
The aim of this paper is to calculate the pure effects of various factors on
international real estate security returns. For this purpose, we use real estate
security returns for the 10 countries with the highest market capitalization
for the period from February 1990 to April 2003, and we extract such pure
effects using a cross-sectional factor estimation technique. The factors that
we consider are the following: a common factor affecting all securities, the
well-known size effect first analyzed by Banz (1981), the value/growth factor of Fama and French (1992), the main property type in which the company invests and the country of origin of the security. Cluster analysis is
used on the residuals of this analysis to ascertain whether an additional factor can be extracted once the effect of the common and pure factors has
been eliminated. The relative importance of each pure factor is highlighted.
Such an analysis is of great importance as changes in cross-country correlation coefficients may be due to changes in any of the other factors. By
extracting the influence of other factors on cross-country correlations, it is
possible to ascertain the true potential of international real estate portfolio
diversification.
The pure factor approach developed in this paper has important implications
for portfolio management. The active portfolio manager will have to decide
according to which factor(s) he or she wants to make a bet. If countries with
positive expected returns are selected, for instance, then he or she has to make
sure that this strategy is neutral with respect to all other factors influencing
returns (property type, growth and size). For instance, if it is decided to overweight Japan, it should be recognized that the growth exposure of this country
is substantially larger than that of the world and that the Japan bet also results
in a bet being made on growth.
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438 Hamelink and Hoesli
The paper is organized as follows. In the following section, we discuss related
work on international real estate diversification. Next, we present our data, while
the method that we use to assess the risk of real estate portfolios is discussed
in the following section. We then present our results. The last section contains
some concluding remarks.
International Real Estate Diversification
The issue of international diversification of stock portfolios has received substantial attention in the financial economics literature since the seminal work by
Solnik (1974). The general conclusion is that widening the investment spectrum
to nondomestic stocks permits an increase in risk-adjusted returns. Moreover,
geographical diversification has been shown to be more effective than diversification by industry (Heston and Rouwenhorst 1994, 1995). Recent work has
shown that the world economy is becoming increasingly global, with international stock markets becoming more and more correlated with each other
(Solnik and Roulet 1999). In such a context, industrial factors have gained
in importance (Cavaglia, Brightman and Aked 2000, Hamelink, Harasty and
Hillion 2001).
Far less attention has been given to this issue in the real estate literature due
to the relative lack of quality international data on the performance of real
estate. Case, Goetzmann and Wachter (1997) find that returns to commercial
real estate tend to move together (although not perfectly) across property types
within each country and that international diversification within three segments
of the real estate market (industrial, office and retail) would have been beneficial over the period 1986–1994. Quan and Titman (1997) report that U.S.
real estate returns are less highly correlated with real estate returns in other
countries than is the case of U.S. stocks with international stocks, suggesting
significant benefits from international real estate diversification (see also Newell
and Webb 1996). Goetzmann and Wachter (2001) also find that cross-border
real estate diversification is useful. They show that cross-border correlations
are due in part to common exposure to fluctuations in the global economy, but
that country-specific GDP changes help explain more of the variation in real
estate returns than the global factor. This would indicate a stronger impact of
local factors than has been reported for common stocks (Beckers, Connor and
Curds 1996). Goetzmann and Wachter (2001) report that international real estate diversification is more beneficial than international stock diversification for
industrial real estate but not for other property types. Several studies have also
looked at whether international real estate portfolios should be hedged against
currency fluctuations (see, e.g., Ziobrowski, Ziobrowski and Rosenberg 1997).
The results concerning the usefulness of hedging are mixed. When it is decided
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International Real Estate Security Returns 439
to hedge, then currency swaps have been shown to be best suited given the
long-term nature of real estate investments.
Securitized real estate has been shown to be quite highly correlated with common stocks on an international basis (Eichholtz 1997), although there is evidence for U.S. REITs and also for real estate securities in other countries that
this correlation has been declining (Ghosh, Miles and Sirmans 1996, Brounen
2003). Also, and as is the case for direct real estate (Goetzmann and Wachter
2001), there is evidence of a worldwide factor in international indirect real estate
returns (Ling and Naranjo 2002). The latter authors also find that a countryspecific factor is highly significant, which would suggest that international
diversification is useful when constructing portfolios of real estate securities.
In a study of the excess returns on securitized real estate in six countries,
Eichholtz and Huisman (2001) find that country dummy variables are significant in almost all instances. They also show that the level of interest rates
and the change in that level negatively impact on excess returns, whereas term
structure is positively related to returns. Related to this study, Eichholtz and
Huisman report a negative relationship between size and excess returns, a
result that is consistent with the financial economics literature. Importantly,
beta does not appear to be an important factor in explaining excess return
on international real estate securities. Bond, Karolyi and Sanders (2003) also
find that global and country-specific market risk factors are important, and
they report that a country-specific value risk factor adds some explanatory
power.
Correlations of real estate securities across countries are lower than cross-border
correlations between common stocks (Eichholtz 1996, Gordon, Canter and
Webb 1998). Additionally, Eichholtz (1996) finds that international real estate
security diversification is more effective than international stock diversification.
Wilson and Okunev (1996) use cointegration tests and show that international
real estate markets are segmented. Benefits are to be gained from diversification,
although potential gains are dependent on the exchange rate risk. Stevenson
(2000) also reports evidence on the benefits of international diversification for
real estate security portfolios (although he finds that these benefits are greater
for common stocks) and on the positive impact of including international real
estate stocks in global equity portfolios (see also Liu and Mei 1998).
With respect to the most efficient way of constructing a well-diversified portfolio
of real estate securities by geographical areas, Eichholtz et al. (1998) analyze
whether a strategy that is based on continents is more useful than one that is
based on countries. They find clear evidence of a continental factor in Europe
and in North America but not in the Asia–Pacific region. The results of Eichholtz
et al. also suggest growing integration within Europe. This would seem to
indicate that a parsimonious international real estate security diversification
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440 Hamelink and Hoesli
strategy is most beneficial when conducted across continents rather than within
continents.
Data
We use the Global Property Research (GPR) database of international real estate
securities for the period February 1990–April 2003. This database is the most
comprehensive database of international real estate stocks and includes for each
company such information as the country of origin, the type of fund (investment,
development, hybrid), the main property type in which the company invests
(office, retail, residential, industrial, hotel, health care, other and diversified), the
structure of the company (open-end and closed-end) and the market capitalization. We place the emphasis on investment companies and hence have excluded
from the analysis development and hybrid companies. Also, we only include
stocks for the 10 countries with the largest market capitalization. These countries are the United States, Germany, the United Kingdom, Australia, France,
Switzerland, the Netherlands, Canada, Hong Kong and Japan. Total returns (i.e.,
including dividends) calculated on monthly time increments are of course also
available from the database. All returns are in U.S. dollars. We use unhedged
returns as we consider that this is the most realistic assumption: In most cases
the benchmark against which the portfolio manager is evaluated is unhedged.
This generally makes sense, as for a well-diversified international benchmark
the currency risk tends to be diversified away. Therefore, managers who decide
to include real estate stocks in their portfolio will hardly decide to hedge these
positions. As unhedged returns are used, the currency effects will be included
in the pure country effects. In this framework, an exposure to a given country
entails an exposure to the country’s currency.
As the main objective of this study is to examine the impact of the value/growth
factor on international real estate security returns, the GPR database is matched
with the Salomon Smith Barney (SSB) Developed World Equity database (recently taken over by S&P). As the SSB database begins in February 1990, the
beginning of the analysis is set at that date. The main feature of the SSB database
is that for each stock a growth weight and a value weight are provided, the total
of weights for each stock being equal to one. Any given stock is therefore not
either a growth stock or a value stock as is the case when other style classifications are used, but is some combination of both attributes (the method used
to compute weights is discussed below). Thus, this analysis uses a database
that combines the advantages of the GPR database (data on the type of fund,
predominant property type and the structure of the company are provided) and
of the SSB database (value/growth weights are available).
Summary statistics for property investment companies are presented in Table 1.
These are presented on a worldwide basis, but also for the various continents and
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International Real Estate Security Returns 441
Table 1 Summary statistics, February 1990–April 2003.
Std. Current Current
Current
Annualized Dev. No. of Market Cap
% Matched Growth
Mean (%) (%) Stocks (US$million) with SSB
Weight
World
9.3
North America
9.9
Europe
6.6
Oceania
13.2
Asia
7.0
United States
12.5
Germany
3.3
United Kingdom
7.9
Australia
13.4
France
7.8
Switzerland
6.3
Netherlands
3.0
Canada
−10.5
Hong Kong
13.1
Japan
−3.5
Office
6.7
Retail
11.8
Deversified
8.8
Residential
10.2
Industrial
10.5
Health care
10.6
Hotel
5.5
Other
13.4
10.3
14.6
10.4
14.7
30.7
14.3
10.2
19.7
14.8
14.6
11.6
13.7
28.6
39.4
28.5
11.8
10.1
11.4
11.6
16.8
16.6
27.6
14.4
302
156
142
30
25
137
22
39
25
11
22
10
19
4
13
86
63
59
40
20
12
16
6
319,839.1
164,173.4
130,485.6
26,569.9
17,570.7
157,548.4
57,760.8
27,224.1
25,900.4
12,043.6
10,533.5
9,862.6
6,625.0
6,307.7
6,033.1
109,163.3
77,622.6
56,815.1
37,589.3
22,190.9
7,536.8
7,107.9
1,183.1
75.5
96.9
43.9
91.8
82.0
97.4
2.3
89.1
92.9
87.9
25.3
86.5
85.2
100.0
74.3
52.8
92.5
71.2
91.6
95.7
98.6
92.1
96.7
0.24
0.18
0.36
0.28
0.39
0.17
0.70
0.36
0.28
0.26
0.38
0.16
0.22
0.03
0.61
0.29
0.26
0.27
0.21
0.12
0.14
0.18
0.15
Note: For each of the 10 countries with the largest securitized real estate market, for
continental groupings and on a worldwide basis the following statistics are reported:
annualized mean return, standard deviation, current number of stocks, current market
capitalization, percentage of market capitalization for which the matching with the
value/growth weights was successful and current growth exposure. Note that the
continental approach is conducted with data from more than 10 countries. Hence, the
figures for North America, for instance, do not correspond to the sum of the figures for
the United States and Canada.
countries, as well as for the property types. Continental returns are computed
as the weighted average of returns in the constituent countries. For the continental analysis, all countries from the GPR database are considered, not only
the 10 countries with the largest market capitalization. This table shows that
the performance of real estate securities worldwide varies substantially across
continents and countries. Real estate stocks in the Oceania area (i.e., Australia
and New Zealand) have performed well during the period, while real estate
stocks in Asia have performed poorly. On a country basis, Canadian real estate
stocks exhibit a dismal performance. The performance of the various property
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442 Hamelink and Hoesli
350
350,000
300
300,000
250
250,000
200
200,000
150
150,000
100
Market Cap (US$ million)
Number of stocks
Figure 1 Number of real estate stocks in the sample and their market capitalization,
and market capitalization of firms for which value/growth weights are available,
February 1990–April 2003.
100,000
# of Stocks
Total Market Capitalization
50
50,000
Market Capitalization with
Value/Growth
0
02/1990
0
02/1992
02/1994
02/1996
02/1998
02/2000
02/2002
types is quite similar, with the hotel and office sectors performing, however,
significantly worse than the average.
As of the end of April 2003, the total number of investment real estate securities
included in the database for the 10 countries with the highest market capitalization amounts to 302, and the market capitalization amounts to US$320 billion.
Table 1 also contains the percentage of the market capitalization for which we
were able to match both databases, and hence for which we have a value/growth
weight. The matching between both databases was successful for most countries
as we were able on average to assign value/growth weights to stocks representing approximately 70% of market capitalization in Asia and Oceania and 56%
in North America.1 The current figures are much higher (82% for Asia, 92%
for Oceania and 97% for North America). For Europe, these figures are lower
(26% on average and 44% currently). This is largely due to the fact that the
matching was unsuccessful for most German and Swiss companies. Many real
estate companies are open-ended in these two countries, and SSB does not
report value/growth weights for these companies. Figure 1 shows the evolution
1
Companies for which no value/growth weights were available were not discarded from
the analysis, but were assigned equal value and growth weights. By so doing, retaining
these companies in the sample does not affect the estimation of the value and growth
factor returns.
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International Real Estate Security Returns 443
of the number of investment real estate companies and their market capitalization in the 10 largest real estate security markets worldwide, as well as
the market capitalization of stocks for which the matching with the value and
growth weights from the SSB database was possible. The number of investment companies has increased from 204 in February 1990 to a high of 317 in
January 2000, but it has diminished slightly in recent years. Also, the percentage of market capitalization for which the matching was possible has increased
substantially over the period.
Table 1 also reports the current growth probability weight of real estate stocks.
The growth and value probability weights of each company are reported on
a 0 to 1 scale by Salomon Smith Barney. For each company, the total of the
growth and value weights is 1. The procedure that is used by SSB is as follows
(Salomon Smith Barney 2000). First, a set of 10 variables related to growth and a
set of 5 variables related to value are identified. As these variables have different
measurement units, they have to be standardized. Standardization also leads to
all variables having approximately the same influence upon the measurement
of the style characteristics. Ideally, standardization should be undertaken on
a worldwide basis, but this is impossible as different accounting principles
prevail across countries. Thus, standardization is undertaken by country when
the number of companies is sufficiently large, else it is achieved by groupings
of countries that are geographically and culturally similar and that have similar
accounting standards (an example of one such grouping is Denmark, Finland,
Norway and Sweden). Cluster analysis is then applied to both sets of variables,
and three growth and four value variables are retained. The growth variables
are:
5-year earnings per share growth rate,
5-year sales per share growth rate and
5-year internal growth rate = ROE × (1 − payout ratio),
and the value variables are:
book value to price,
cash flow to price,
sales to price and
dividends to price (yield).
Growth and value scores are computed for each stock as the equally weighted
average of the value of these variables. A stock that is clearly either a growth
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444 Hamelink and Hoesli
Figure 2 Average growth exposure for real estate stocks in Europe, Asia, North
America, Oceania and the World, February 1990–April 2003. Note: Growth exposure
(on a scale from 0 to 1) as defined by Salomon Smith Barney (SSB). Five-year earnings
per share growth rate, 5-year sales per share growth rate and 5-year internal growth rate
are taken into account. Measure is relative to other stocks in the country or region, and
the sum of growth rate and value weight for each stock is 1.
1
0.9
0.8
World
North America
Europe
Oceania
Asia
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
02/1990
02/1992
02/1994
02/1996
02/1998
02/2000
02/2002
or a value stock will be considered as a pure growth or value stock, and it is
assigned a probability weight of 1 for that characteristic. If a stock is not clearly
a growth or a value stock, then the weight is split according to distances from
pure growth and value stocks. The final step is to ensure that (1) each SSB
country-style index represents exactly 50% of the total float-adjusted market
capitalization of the corresponding country,2 and (2) for each stock the sum of
probability weights is equal to 1. The above procedure is applied each year in
June.
Figure 2 depicts the exposure to the growth factor over time (on a scale from
0 to 1) for real estate companies in the four continents and on a worldwide
basis for the period from February 1990 to April 2003. Real estate companies
have become generally less and less growth companies (as defined by SSB)
2
Ideally, the measurement of growth and value weights should not be country specific,
but global. As stated above, this is hardly possible due to different accounting practices
across countries, and SSB has decided to measure the probability weights within countries. It is acknowledged here that biases may occur if the relative importance of growth
and value dimensions varies dramatically from one country to another.
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International Real Estate Security Returns 445
Figure 3 Growth exposure for office, retail and residential properties,
February 1990–April 2003.
1
0.9
Office
Retail
Residential
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
02/1990
02/1992
02/1994
02/1996
02/1998
02/2000
02/2002
during the 1990s, and this trend is striking for Asian companies. For Oceania,
the average growth weight has increased over the period, while a slight increase
of the weight is observed in the last 2 years for Europe. Real estate companies
appear to be clearly less growth companies at the end of the period as compared
to what was the case at the beginning of the period (the growth weight has been
cut by more than half on a worldwide basis). Figure 3 shows the exposure to
the growth factor over time for the three main property types (office, retail and
residential). The exposure to growth clearly diminishes in time for office and
retail properties, while the exposure is quite volatile for residential buildings.
Assessing the Risk of Real Estate Portfolios
The Model
Modern Portfolio Theory (MPT) provides us with the theoretical tools to estimate an asset’s, and hence a portfolio’s, risk. On the one hand, we have
systematic sources of risk (i.e., sources of risk that influence a large number of
assets), and on the other we have the stock’s specific risk. As these two sorts of
risk are independent, the total risk of a stock or that of a portfolio is simply the
sum of the two types of risk. Systematic risk originates from the behavior of
the common factor(s) influencing the returns. In the case of the Capital Asset
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446 Hamelink and Hoesli
Pricing Model (CAPM), the common factor is the market return in excess of the
risk-free rate, while in multifactor models a larger number of common factors
determine the total level of systematic risk.
Determining the common factors in a multifactor model may be done using a
variety of techniques, depending on the initial assumptions. All models have
in common that there are common factor returns and factor loadings, that is,
the exposure of each stock to each factor. We may either observe factor returns
and estimate the factor loadings (such as in the CAPM, where the betas are the
loadings), observe the loadings and estimate the returns (loadings are usually
country or sector dummy variables) or estimate both the loadings and the factor
returns (as in the Arbitrage Pricing Theory, APT, class of models). In some
cases it is possible to give a specific meaning to the factors, for instance, the
price of one unit of risk (in which case it is argued that the factor is “priced”).
Extending the model developed by Heston and Rouwenhorst (1994),3 the model
we propose in this paper is based on observed exposures, and the factor returns
are estimated. No assumption is made as to whether these estimated factors are
priced. The model considers a common factor, country factors, property-type
factors, a size factor and a value/growth factor. Formally, the model is written
as follows:
Ri,t = Ft +
NC
k=1
DikC × FktC +
NS
DihS × FhtS + pitG + FtG
h=1
+ pitV × FtV + Si,t × FtS + εi,t ,
(1)
where Ri,t is the return on stock i at time t. NC is the number of countries.
DikC is a dummy variable, set to one if stock i belongs to country k, with k =
1, . . . , NC. NS is the number of property types. DihS is a dummy variable, set to
one if stock i belongs to property-type h, with h = 1, . . . , NS. pitG and pitV are
the SSB Growth and Value probability weights of stock i at time t. Si,t is the
size exposure of stock i at time t. In the above equation, the unknowns are F t
(the return on the common factor, which is equivalent to the weighted average
of all real estate stock returns), FktC and FhtS (the returns on the pure country
factors and property-type factors), FtG and FtV (the returns on the pure growth
3
Heston and Rouwenhorst (1994) assess the relative importance of diversification by
country and by industry for international common stock portfolios. Country and industry
dummy variables are used. A similar methodology is used to investigate the benefits of
sector and regional diversification for U.S. private real estate portfolios by Fisher and
Liang (2000) and for U.K. private real estate portfolios by Lee (2001).
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International Real Estate Security Returns 447
and value factors) and FtS (the return on the pure size factor). Finally, ε i,t is the
stock-specific return, which means the return on stock i at time t once its country,
property type, value/growth and size attributions are taken into account.
The above model is estimated under the constraint that for the market portfolio
(i.e., the portfolio containing all stocks in the sample weighted by their relative
market caps) the value-weighted sums of exposures to the country factors, to
the property-type factors, to the value/growth factors and to the size factor are
all equal to zero. In other words, the market portfolio does not have any global
country, property type, value/growth or size exposure. This translates into the
constraints:
N NC
C
wi,t Dik
× FktC = 0
for the country exposures,
wi,t DiSh × FhtS = 0
for the property type exposures,
i=1 k=1
N NS
i=1 h=1
N
wi,t pitG FtG + pitV FtV = 0
for the value and growth exposures and
i=1
N
wi,t Si,t = 0
for the size exposure.
(2)
i=1
Recognizing that, by definition, pitG = 1 − pitV , we may simplify Equation (1)
and the constraints in (2). In particular, it can be shown that if the model is
estimated using the full SSB universe, then the return on the value factor is
the opposite of the return on the growth factor.4 Furthermore, each stock’s
exposure to size is a transformation of its relative market weight w i,t such that
the exposure to the size of the largest real estate stock in the universe is equal
to one.5
4
In our case, the return on the value factor will be close but not exactly equal to the
opposite of the return on the growth factor.
5
It can be shown that for the size variable we have to set a scaling arbitrarily. Indeed,
we may have very small stock exposures and a large return on the size factor or large
stock exposures and a small return on the size factor. The constraint that the largest stock
has an exposure of one yields a better economic interpretation of the returns on the size
factor.
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448 Hamelink and Hoesli
To estimate Equation (1), we have to make sure there are enough representative
observations for each country. For instance, if there is a single real estate stock
in a given country, then estimating a pure country effect would not be relevant
(in fact, the country factor would also pick up the specific return). We therefore
require that there be at least four stocks belonging to any country for any
given month. If there are less than four, then the country is dropped and the
corresponding real estate stocks have no country exposure (in which case part
of the country effect, if there is any, will be found in the real estate stock’s
specific return ε i,t ). Finally, Equation
N(1) is estimated using a value-weighted
OLS regression scheme, such that i=1
wi,t εi,t = 0. The latter ensures that a
large cap real estate stock has a larger effect than a small cap one. The equation
is estimated in a cross-sectional way, that is, each month the regression is
performed and the factor returns at that time estimated independently from
observations for other time periods.
The interpretation of the pure factors is as follows. The factors are pure in the
sense that they are not influenced by any of the other factors. For instance, the
pure U.S. factor represents what is really due to the fact that a stock is U.S.
based. If U.S. stocks tend to be concentrated on a particular property type, if
there are more growth or value stocks or more large or small caps in the U.S.
than worldwide, then the property type, growth or size effects will be captured
by the corresponding pure factors, and hence the country factors will not be
influenced by these dimensions. There is also a “common factor,” which is the
factor to which all stocks are exposed. Another interpretation of the pure factor
concept is that the return on U.S. real estate stocks would be equal to the sum
of the common factor and the pure U.S. factor had the United States the same
property-type, size and value/growth characteristics as the World.
Additional Factors
The cross-sectional regression in Equation (1) decomposes the return on an
asset i at time t into returns on the various factors, and an error term denoted
εi,t . This term represents the return that cannot be explained by the common
factor and pure factors, and it is therefore also referred to as the stock’s specific
return. The idea is to investigate whether there are other common characteristics
among real estate stocks that are not captured by the pure factors and to extract
such “hidden” factors from the specific returns. This is also the basic technique
underlying APT models.
We argue that although it may be difficult to find an economic interpretation
for such statistical factors, they are of foremost importance to the portfolio
manager. If some stocks behave differently because they have an exposure
to some statistical factor, and if the return on that factor is statistically and
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International Real Estate Security Returns 449
economically important, then a portfolio manager should actively manage the
portfolio’s exposure to that factor. If he/she does not have a specific view on the
expected return on the factor, then he/she should make sure that the portfolio
has the same exposure to that factor as the benchmark. If he/she does have a
view, on the other hand, then he/she may bet on the performance of the factor
by overweighting (relative to the benchmark) the exposure of the portfolio to
that factor. Not doing so will inevitably result in higher tracking error for the
portfolio without a higher expected return. This is an important issue in active
management, and whether a factor is merely a statistical one (without economic
interpretation) or not is of little relevance here.
The most straightforward way to extract statistical factors is Principal Component Analysis. It is a powerful technique, but it uses the variance as the measure
of risk and therefore assumes normality of the data. This may be a strong assumption indeed, and therefore we use cluster analysis, a method that requires
that no distributional assumption be made. Cluster analysis allows us to form
groups of observations, the degree of similarity of which is similar within each
group but dissimilar across groups. Once the membership of each stock to a
cluster is determined, then we calculate the average return of all observations
within each cluster. These are the factor returns, and each stock has an attribute
(one or zero) for each cluster.
Applying cluster analysis to a set of data will always reveal some kind of ex post
structure in the data. What is important, however, is the out-of-sample usefulness
of the techniques. We apply therefore the following estimation procedure: We
use the first 36 months of returns on all assets for which we have returns
for all months, apply the cluster algorithm and measure the equally weighted
average return within each group over the subsequent 12 months. We then move
the estimation window forward by 12 months and reestimate the groups. If the
clustering approach had no predictive power (in other words, if the membership
of each stock to a particular cluster were highly unstable over time), then there
would be no reason to expect any out-of-sample difference in estimated factor
returns.
Results
Common Factor and Pure Factors
The mean return and standard deviation of the pure factors are reported in
Table 2. For pure country and property-type factors, the mean returns in most
cases are similar to those reported in Table 1 provided that an adjustment be
made for the common factor, and therefore they are not discussed again here.
For example, the return on the pure Japanese factor would equal the return
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450 Hamelink and Hoesli
Table 2 Summary statistics for the common factor and the pure factors, February
1990–April 2003.
Pure
Factor
Annualized
Mean (%)
Std. Dev.
(%)
Pure
Factor
Annualized
Mean (%)
Std. Dev.
(%)
Office
Retail
Deversified
Residential
Industrial
Health care
Hotel
Other
−0.2
2.1
0.4
0.8
0.9
−2.2
−9.5
3.1
3.8
5.2
2.0
5.2
8.1
14.2
20.6
13.3
Growth
Size
−1.0
−1.7
6.3
8.2
Common factor
5.0
10.3
United States
Germany
United Kingdom
Australia
France
Switzerland
Netherlands
Canada
Hong Kong
Japan
4.0
−2.1
−0.7
5.7
−1.8
−1.2
−4.2
−19.1
4.2
−11.8
11.7
12.7
13.6
13.4
10.5
11.9
11.7
27.1
33.4
26.6
Note: Annualized mean return and standard deviation for the common factor, the pure
country factors, the pure property-type factors, the pure growth factor and the pure size
factor. These are time-series moments on pure factor returns, which are estimated
cross-sectionally by means of the following model:
Ri,t = Ft +
NC
k=1
DikC × FktC +
NS
DihS × FhtS + pitG × FtG + pitV × FtV + Si,t × FtS + εi,t
h=1
on Japanese real estate stocks minus the common factor if the property-type
structure, the exposure to value/growth and the size were identical to that of
the world index. The return on the pure growth factor is negative on average,
indicating that real estate securities that have a large growth weight are negatively affected over the period. Importantly, the standard deviation is quite large
(6.3%), indicating that the growth factor truly constitutes a risk factor, at least
as much as property types (the pure office, retail, diversified and residential
factors have lower standard deviations). The average return on the size factor
is also negative: All things held constant, large capitalization real estate stocks
perform worse than smaller capitalization real estate securities. This is consistent with the results usually reported in the financial economics literature, and
also with the results of Eichholtz and Huisman (2001) for real estate securities.
Table 3 contains the correlation coefficients between the common factor and
pure country, property-type, growth and size factors. The correlation coefficients between pure country factors and growth and size factors are generally
close to zero. This indicates that if an active portfolio manager makes a bet
according to any of the three factors (country, growth or size), this does not
imply that he or she is making simultaneously a bet according to any of the
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International Real Estate Security Returns 451
France
Canada
Australia
Common Factor
−0.10
1
0.06
0.15
1
−0.06
0.05 −0.17
1
−0.57 −0.03 −0.22
0.39
1
0.27
0.15
0.01 −0.27 −0.33
Germany
Hong Kong
1
U.K.
Switzerland
Netherlands
Japan
−0.07
1
−0.17 −0.06
1
−0.24 −0.01
0.20
1
−0.06
0.11 −0.13 −0.19
1
−0.07 −0.25 −0.22 −0.32 −0.25
U.S.
1
Hotel
Health Care
Diversified
Industrial
1
Office
0.17
0.27
0.20
0.09
0.06
0.17 −0.27
0.08 −0.19 −0.37
0.10 −0.19
0.09 −0.18
0.03
0.01 −0.20
0.06
0.06
0.04
0.06 −0.17
0.00
0.17 −0.05 −0.06
0.07
0.19
0.01 −0.14
Residential
1
0.00
1
0.07 −0.16
1
Retail
0.11 −0.20 −0.14
0.04
0.12
0.05
0.18 −0.15
0.18
0.13
0.15 −0.16 −0.34
0.16 −0.15 −0.09 −0.13 −0.14
0.20 −0.24 −0.31 −0.20 −0.03
1
−0.25
0.16 −0.01
0.01
0.33
0.09 −0.33
0.10
0.30 −0.09 −0.13 −0.08
0.26 −0.28 −0.08 −0.13
0.00
0.03 −0.12
0.03
0.04
0.05
0.08
0.04 −0.12
0.09 −0.16 −0.36
0.08 −0.06
0.03 −0.09
−0.23 −0.16 −0.44
0.19
0.37 −0.16
0.09
0.01
0.21
0.02 −0.23 −0.27
0.31 −0.20 −0.12 −0.40
Note: Pure factors are country factors, property-type factors, a growth factor and a size factor.
Growth
Size
Office
Other
Residential
Retail
Diversified
0.01 −0.09
0.23 −0.03 −0.03 −0.10 −0.02 −0.06
0.02 −0.04
0.18
1
Health Care −0.08 −0.08 −0.21
0.01
0.29 −0.04
0.02
0.11
0.23
0.12 −0.40 −0.34
1
Hotel
0.21 −0.07
0.05
0.00 −0.26
0.13 −0.05 −0.03 −0.12
0.19
0.00 −0.09 −0.10
1
Industrial
0.00
0.04
0.09 −0.11 −0.09
0.11
0.03 −0.02 −0.17
0.08
0.04 −0.09 −0.03 −0.18
Japan
0.08 −0.06 −0.03
0.09
0.04
Netherlands −0.23
0.17
0.03
0.34
0.30
Switzerland −0.40
0.05 −0.07
0.24
0.61
U.K.
0.24 −0.19 −0.10 −0.03 −0.24
U.S.
−0.05 −0.01
0.19 −0.33 −0.40
Australia
Canada
France
Germany
Hong Kong
Other
Table 3 Correlation coefficients between the returns on the common factor and on pure factors, February 1990–April 2003.
1
0.02
Growth
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452 Hamelink and Hoesli
other two dimensions. For instance, if one believes that a country will perform
well in the future and a decision is made to overweight this country, this does
not imply that a bet is made with respect to growth or size.
Correlation coefficients between pure country factors are generally low. This
is particularly true between the returns on the pure Hong Kong factor and the
returns on the pure factor for several other countries. In fact, many of these
correlations are negative. The returns on the pure country factors are highly
correlated in two instances only (0.61 between Germany and Switzerland and
0.34 between France and the Netherlands). The correlations indicate that diversification opportunities exist within continents, although results not reported
here show that correlations across pure continental factors are even lower. This
is consistent with the conclusions by Eichholtz et al. (1998).
The pure property-type factors are also lowly correlated with the growth and
size factors. The correlations between pure property-type factors are in several
instances negative, but the average of the correlations is only marginally lower
than the average of the cross-country correlations (−0.11 vs. −0.03). This
discussion is, of course, based on pure factors. In reality, it is not possible
to gain exposure to the pure factors, but rather when a decision is made, for
instance, to overweight one country, then this will have in most cases an effect
on the property-type, growth and size exposures of the portfolio. To overcome
this difficulty, constrained optimization techniques may be used to construct a
model portfolio that takes active bets on specific pure factors, while keeping
the exposures to other factors neutral (relative to the benchmark).
We now focus on the cumulative returns for the various factors. Figure 4 depicts
the index of cumulative returns for the common factor and the pure size factor.
There is a strong upward trend in cumulated returns for the common factor, with
two slumps. The cumulative returns for the size factor are quite stable until the
end of 1997 before declining by more than 30% (from 116 in September 1997
to 80 in April 2003). As large stocks are more exposed to this factor than smaller
ones, they will suffer more from this drop in value. As explained above, the
maximum exposure to size is for the largest real estate stock in the sample at
any given month (size exposure = 1). For smaller stocks the exposure is less,
and it is even negative for many stocks as by construction the weighted average
of the exposure to size is zero.
Figure 5 shows the index of cumulative returns for the growth factor both when
the analysis is based on countries and on continents. When the analysis is done
using country factors (the main method used in this paper), the index shows in
some instances large variations over short periods. For instance, the index drops
by 15% between February 1990 and September 1993, then increases by 22%
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International Real Estate Security Returns 453
Figure 4 Index of cumulative returns on the common factor and the pure size factor,
February 1990–April 2003.
200
Common Factor
Size
175
150
125
100
75
01/1990
01/1992
01/1994
01/1996
01/1998
01/2000
01/2002
Figure 5 Index of cumulative returns on the growth factor when countries or
continents are considered, February 1990–April 2003.
105
95
85
75
65
55
Growth (country analysis)
Growth (continental analysis)
45
01/1990
01/1992
01/1994
01/1996
01/1998
01/2000
01/2002
before the Asian crisis in September 1997 and then drops again by 13%. Growth
thus appears to be an important risk factor to account for when constructing a
portfolio of real estate stocks. This is even more striking when a continental
approach is considered (i.e., when dummy variables for continents are used
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454 Hamelink and Hoesli
Figure 6 Index of cumulative returns on the pure country factors,
February 1990–April 2003. Note: Cumulative returns on the pure country factors are
reported for the five countries with the largest securitized real estate market
capitalization (the United States, Germany, the United Kingdom, Australia and France).
225
200
United States
Germany
United Kingdom
Australia
France
175
150
125
100
75
50
01/1990
01/1992
01/1994
01/1996
01/1998
01/2000
01/2002
in lieu of country dummy variables). Such an analysis is often suggested and
motivated by the fact that intercontinental correlations are lower than crosscountry correlations. The drop by more than 50% of the growth index over the
period is a clear indication that caution should be exercised when implementing
a continental strategy, as such a strategy involves an exposure to a very risky
growth factor.
Figure 6 shows the cumulative returns for the pure country factors for the five
largest countries in terms of market capitalization. Differences across countries
are important despite the fact that factors such as property type, growth and size
have been controlled for. Figure 7 depicts the cumulative returns on the pure
property-type factors for five property types (office, retail, residential, industrial
and hotel). Again, the differences across property types are substantial. The
office category shows a clear positive trend from December 1992 to September
2000, but then the return index decreases by 13%. During the latter period the
pure retail factor has increased by more than 25%.
It is of particular interest to analyze the importance of the market cap weighted
average absolute returns on the pure country, property-type, size, growth and
value factors as a percentage of the total of these absolute returns. The relative
importance of each factor is depicted in Figure 8. The (weighted) average pure
country factor appears to be the most important factor, but its importance has
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International Real Estate Security Returns 455
Figure 7 Index of cumulative returns on the pure property factors, February
1990–April 2003. Note: Cumulative returns on the pure property-type factors are
reported for the following five property types: office, retail, residential, industrial and
hotel.
140
120
100
80
60
40
01/1990
Office
Retail
Residential
Industrial
Hotel
01/1992
01/1994
01/1996
01/1998
01/2000
01/2002
Figure 8 Average absolute returns on each factor as a percentage of the sum of
absolute returns, February 1990–April 2003 (12-month moving averages). Note:
Importance of the average absolute returns on the pure country, property-type, size,
growth and value factors as a percentage of the sum of absolute returns.
100%
80%
60%
40%
Size
20%
Value + Growth
Property Types
Countries
0%
01/1991
01/1993
01/1995
01/1997
01/1999
01/2001
01/2003
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456 Hamelink and Hoesli
diminished slightly during the period. The property-type factor is less important,
but it has gained in importance during the period. The size factor is the third
most important factor, and it exhibits no clear trend during the period. Growth
and value account for up to 9% of the total of absolute returns (this figure is as
high as 20% when the analysis is performed by continents). There is thus clearly
a value/growth factor in real estate securities, and that factor should be taken
into consideration when building real estate stock portfolios. When the above
analysis is performed including the specific factor, it turns out that the specific
factor accounts for approximately 50% of absolute returns. This indicates that
stock picking remains a very important issue when constructing real estate
security portfolios, but also that additional factors may be able to explain the
cross section of real estate security returns. This latter issue is investigated in
the following section.
Additional Factors
Although the data included in the GPR database, together with the SSB
value/growth weights, make it possible to account for most of the effects related
to real estate stock characteristics, additional factors may influence their returns.
Examples of such factors are related to the tax status and macroeconomic factors
such as interest rate-related variables. In our specification, the impact of these
characteristics will not necessarily be included in the specific return. Indeed,
characteristics of real estate companies that are specific to a country will have
been included into the pure country factor. This will be the case, for instance, of
the tax status, which will apply to all real estate companies in a given country.
Similarly, if some omitted characteristic of real estate securities is related to
the growth or the size characteristics, then it will have been captured by these
factors. The specific factor will capture any remaining effects, as well as the true
specific component. In this section, we analyze whether it is possible to extract
an additional factor from the specific component that remains after taking into
consideration the common factor and pure country, property-type, growth and
size factors. For this purpose, we use cluster analysis.
The clustering algorithm used in this study can be summarized as follows:
k-means clustering is applied iteratively on the N−by−(T = 36) dataset of
logarithmic asset returns until the largest group contains close to 50% of the
observations. This first cluster is referred to as Cluster 1. The next two clusters
contain the second and third largest number of observations, respectively. The
final cluster (Cluster 4) contains the remaining observations and is probably
the least homogeneous group. The estimation period is then moved forward
by 12 months, and we use the 24 overlapping months to insure that Clusters 2
and 3 correspond to the same clusters as in the previous estimation period by
measuring the correlation of the estimated factor returns. If necessary, we swap
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International Real Estate Security Returns 457
Figure 9 Out-of-sample cumulative returns on the first three cluster factors, February
1993–April 2003. Note: The first year of out-of-sample returns (02/1993 to 01/1994)
are obtained through cluster analysis of the real estate returns from 02/1990 to
01/1993. The 36-month rolling window is then moved forward by 12 months to obtain
the cluster factor returns over the full period.
130
Cluster 1
Cluster 2
Cluster 3
120
110
100
90
01/1993
01/1995
01/1997
01/1999
01/2001
01/2003
the memberships of Clusters 2 and 3. By so doing, we minimize the percentage
of stocks that change clusters from one year to another, and this results in an
average of 40% of stocks changing clusters annually.
The results are represented in Figure 9, which shows the cumulative returns on
the first three cluster factors. Cluster 4 is not represented, as it is a heterogeneous
cluster containing the remaining observations. Not surprisingly, Cluster 1 shows
little variability over time. It is probably also the least interesting cluster to
analyze, as by construction it contains most of the observations. Cluster 2 is
clearly more variable and its returns are economically important; for instance, it
increases by more than 30% from February 1996 to October 2001. Cluster 3 is
more volatile, with a sharp decline of almost 20% in the mid 1990s and a sharp
increase thereafter. Clearly, the constructed clusters behave differently. From a
portfolio management point of view, it is important to measure the risk of being
over- or underexposed to these factors, relative to the benchmark. A portfolio
manager who, between May 1994 and June 1997, would have picked by chance
and without him or her being aware of it stocks that belong to Cluster 3 that
would have significantly lowered his/her portfolio return. This is important,
even if it is difficult to attribute any economic “label” to a cluster factor.
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458 Hamelink and Hoesli
Figure 10 Average absolute returns on each of the cluster factors and on the residual
returns as a percentage of total absolute returns, February 1994–April 2003 (12-month
moving averages). Note: Each stock’s residual return is defined as its specific return,
from which the returns on the estimated cluster factor returns is subtracted. A
substantial percentage (up to 40%) of the stock’s specific returns can be explained by
the four cluster factors.
100%
80%
Residual
Cluster 4
Cluster 3
Cluster 2
Cluster 1
60%
40%
20%
0%
01/1994
01/1995
01/1996
01/1997
01/1998
01/1999
01/2000
01/2001
01/2002
01/2003
Finally, to assess the economic importance of the above methodology, we show
in Figure 10 the relative importance of the absolute return on the four cluster
factors, as well as the absolute unexplained residual, as a percentage of the
total. Between 30% and 40% of the total is explained by the returns on the
four cluster factors. Without being a formal test, it sheds some light on what a
portfolio manager, who is measured against a benchmark, might expect from
applying a cluster attribution of the specific returns: One third of the portfoliospecific risk is explained by the cluster factors, which is a risk that can be hedged
simply by ensuring that the portfolio has the same exposure to the cluster factors
as the benchmark portfolio.
Concluding Remarks
The benefits of international real estate diversification have been documented
in the literature, albeit to a lesser extent than for common stocks. We argue that
while it is important to recognize the advantages of cross-country diversification, it would be at least equally important to isolate the effect of various factors
on international real estate security returns. A low cross-country correlation coefficient between real estate securities in two countries, for instance, could be
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International Real Estate Security Returns 459
due to the fact that real estate stocks in both countries differ with respect to the
property types in which companies invest, but also with respect to other factors such as size, value/growth or to any remaining effect. We use constrained
cross-sectional regressions to disentangle a common factor and pure country,
property-type, size and value/growth effects.
It is found that country factors dominate property-type factors in importance,
but other factors are important, too. This is the case of the size factor and the
value/growth factor, but even after accounting for all these factors, statistical
factors determined by means of cluster analysis emerge as factors explaining the
cross section of international real estate security returns. The pure value/growth
factor is of particular interest as it has not been examined previously in the
literature. We find that value/growth exhibits substantial levels of volatility,
much more so than some of the property-type factors, and therefore not taking into account a portfolio’s exposure to this factor can be very risky. The
value/growth factor plays an even more important role when diversification is
conducted across continents rather than across countries. Not taking into account the value/growth factor is therefore even more risky when a continental
strategy is implemented.
For portfolio management, it is important to recognize the importance not only
of the country factors (as opposed to continental factors), but also of the other
factors discussed above, in particular the value/growth and the cluster factors.
The volatilities of these factors are such that a manager that would inadvertently
over- or underexpose his or her portfolio to these factors, relative to a benchmark,
would take a significant amount of risk. Controlling for the portfolio exposure
to these factors is even more crucial when a continental approach is used rather
than a country approach.
Substantial work on this paper was undertaken while Martin Hoesli was the Hans
Dalborg Visiting Professor of Financial Economics, Stockholm Institute for Financial
Research (SIFR), Sweden. The paper benefited from useful comments from an anonymous
referee, Peter Englund (SIFR and Stockholm School of Economics), Åke Gunnelin and
Göran Robertsson (SIFR), as well as from participants at the 2002 European Real Estate
Society (ERES) conference in Glasgow (Scotland).
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