An Evaluation of Opportunities to Improve Performance of Portfolios of Real Estate
Securities Through International Diversification
by
Robert L Rosenfeld, Jr.
A.B., Duke University, Accounting, Economics, 1979
J.D., University of Michigan Law School, 1982
Submitted to the Department of Urban Studies and Planning and the Department of
Architecture for the Degree of Master of Science in Real Estate
at the
Massachusetts Institute of Technology
September, 1997
C 1997 Robert L. Rosenfeld, Jr.
All rights reserved
The author hereby grants to MIT permission to reproduce and to distribute publicly paper
and electronic copies of this thesis document in whole or in part.
Signature of Author---------------Interdepartmental Degree Program in Real Estate
July 31, 1997
Certified by----------------
Accepted by---------
2
--------------------Blake Eagle
Chairman, MIT Center for Real Estate
-------------------
--------------William C. Wheaton
in Real Estate
Program
Chairman, Interdepartmental Degree
(Z P 16 1997
KC) ~
An Evaluation of Opportunities to Improve Performance of Portfolios
of Real Estate Securities Through International Diversification
by
Robert L. Rosenfeld, Jr.
Submitted to the Department of Urban Studies and Planning and the Department of
Architecture on July 31, 1997 in Partial Fulfillment of the Requirement for the Degree of
Master of Science in Real Estate
ABSTRACT
The current growth in securitization of real estate investments provides investors with
access to an increasing variety of liquid real estate investments. At the same time, the
end of the Cold War and the worldwide trend towards reduction or elimination of barriers
to foreign trade and investment have opened new national markets to real estate investors.
These dual trends of securitization and globalization, in the real estate capital markets,
have increased the investment alternatives available to managers of portfolios of real
estate securities. This thesis examines the application of modern portfolio theory to
improve the performance of portfolios of real estate securities by diversification across
national markets.
An analysis of recent literature and historical data reveals that international diversification
can improve the performance of a portfolio of real estate securities by reducing risk.
Generally, the correlations of the various countries' returns from real estate securities are
sufficiently low that diversification will substantially reduce portfolio risk. Efficient
frontier analysis using historical data shows how appropriate diversification would have
improved portfolio performance across most levels of risk. Efficient frontier analysis
using forecasted returns also shows the benefits of diversification.
International investing may also increase portfolio returns by broadening the field of
investment opportunities. An international investor would have the advantage of being
able to choose among countries with different risk/return characteristics and which are at
different points in market cycles. In general, for a fund manager with superior ability to
identify exceptional investment opportunities, an increase in the number of potential
markets available for investment should increase the number of exceptional investments
in the portfolio, thereby improving portfolio performance through higher expected
returns.
Thesis Supervisor: Blake Eagle
Title: Chairman, MIT Center for Real Estate
Acknowledgment
I would like to thank Russell Platt of Morgan Stanley Asset Management for sponsoring
this thesis and providing me with access to the resources of Morgan Stanley Asset
Management, including the GPR-LIFE international real estate indexes.
Table of Contents
A b stra c t ................................................................................................................................
A cknow ledgm ent .........................................................................................................
T able of C ontents ..........................................................................................................
2
3
4
Chapter 1-Introduction ....................................................................................................
5
Chapter 2-A Review of Recent Literature Regarding The Benefits of Global Investing ....7
2.1 The Impact of International Diversification in Reducing Portfolio Risk...................7
2.1.1 Historically Low Correlations of International Real Estate Returns.......................7
2.1.2 Historical Correlations are not Necessarily a Forecast of Future Correlations.........10
2.2 The Impact of International Diversification in Increasing Portfolio Return................11
Chapter 3-Analysis of Historical Data Regarding the Benefits of International
D iv ersificatio n ....................................................................................................................
14
3.1 D ata: The GPR -LIFE Index ......................................................................................
14
3.2 Risk/R eturn P rofiles.................................................................................................
. 18
3.2.1 Risk/Return Characteristics in First and Second Halves of Time Series..............23
3.3 C orrelations of R eturns...........................................................................................
27
3.3.1 Correlations of Monthly Returns ..........................................................................
27
29
3.3.2 Correlations of 12 Month Rolling Returns ..........................................................
3.3.3 Correlations of Returns in First and Second Halves of Time Series .................... 31
3.4 T he E fficient Frontier..............................................................................................
33
3.4.1 Efficient Frontiers Created From Historical Data.....................................................35
3.4.1.1 Efficient Frontier Based on Monthly Returns....................................................35
3.4.1.2. Efficient Frontier Based on 12 Month Rolling Returns....................................38
3.4.1.3 Efficient Frontiers for First and Second Halves of Time Series ....................... 41
46
3.4.2 Efficient Frontiers Created With Forecasted Returns ...........................................
46
3.4.2.1 Efficient Frontier Based on Country Returns....................................................
3.4.2.2 Efficient Frontier Based on Regional Returns .................................................
52
C hapter 4 -C onclu sion ........................................................................................................
55
B ib lio g rap hy .......................................................................................................................
58
CHAPTER 1-INTRODUCTION
The current growth in securitization of real estate investments provides investors with
access to an increasing variety of liquid real estate investments. At the same time, the
end of the Cold War and the worldwide trend towards reduction or elimination of barriers
to foreign trade and investment have opened new national markets to real estate investors.
These dual trends of securitization and globalization, in the real estate capital markets,
have increased the investment alternatives available to managers of portfolios of real
estate securities. In this environment, it would seem useful for real estate fund managers
to apply modern portfolio theory to improve portfolio performance through appropriate
diversification.
This thesis examines the application of modern portfolio theory to improve the
performance of portfolios of real estate securities by diversification across national
markets. This will involve an analysis of relevant data and a review of recent literature
exploring the impact of international diversification on a portfolio of real estate securities.
The data analysis will involve a review of historical real estate returns in various
countries and regions, in order to estimate the current means, standard deviations and
correlations of such returns. This analysis should lead to qualified conclusions regarding
opportunities to improve portfolio performance by international diversification. Any
conclusions would necessarily be qualified because the underlying data is imperfect.
Data on historical real estate returns is generally less available, and more flawed, than
data on other investment assets, such as stocks and bonds.
Generally, international diversification offers the real estate investor opportunities to
improve portfolio performance in two ways. First, by investing in countries which
exhibit low correlations of returns, an investor can reduce the risk of a portfolio for any
given level of expected return (or increase the expected return for any given level of risk).
Second, by expanding the investor's universe of potential investments, the investor
enhances his ability to uncover exceptional investments. This thesis will examine both
methods of improving portfolio performance.
CHAPTER 2- A REVIEW OF RECENT LITERATURE REGARDING THE
BENEFITS OF GLOBAL INVESTING
2.1 The Impact of International Diversification in Reducing Portfolio Risk.
Generally, diversification across international real estate markets should reduce portfolio
risk if returns in the various real estate markets do not move together. Such
diversification would eliminate the unique risk associated with a particular country. The
situation is analogous to diversification among stocks, which eliminates the unique risk
associated with a particular company's circumstances. Thus, if correlations of real estate
returns among countries are relatively low, diversification among such countries would
improve portfolio performance by reducing risk.'
2.1.1 Historically Low Correlations of International Real Estate Returns.
Piet Eicholtz of the Limburg Institute of Financial Economics at the University of
Limburg in the Netherlands, has performed a study which shows that the correlations
among real estate returns in various countries are lower than the correlations among stock
' Bodie, Z., Kane, A., Marcus, A., Investments, Irwin, 1996, Ch.7; Addae-Dapaah, K. and Kion, B.,
1996," International Diversification of Property Stock-A Singaporean Investor's Viewpoint", Real Estate
Finance, Fall, 54-66.
and bond returns in those countries. Eichholtz concluded that real estate investors can
receive substantial benefits from international diversification and that international
diversification reduces the risk of a real estate portfolio more than that of a stock and
bond portfolio. Eichholtz pointed out that this result was expected because: (i) real estate
markets are local in nature and (ii) the historic lack of international real estate investment
has caused real estate markets to be less integrated than stock and bond markets.
Eichholtz elaborated on these points by noting that, in real estate, significant events tend
to be local, such as the shocks endured by some (but not all) of the Texas real estate
market, in connection with a fall in oil prices in the 1980's. He indicated that, whereas
national real estate markets are influenced by national economic factors which do not
influence foreign real estate markets, stock and bond markets are less influenced by local
factors and are more influenced by global factors. 2
Jacques Gordon of Barings Institutional Realty Advisors wrote that, over the long term,
the performance of European property markets has not been highly correlated with U.S.
property returns. He further asserted that property markets will always be subject to local
supply and demand factors, which will assure that international real estate investments
will not be highly correlated in the future. 3
2
Eicholtz, P, 1996, "Does International Diversification Work Better for Real Estate than for Stocks and
Bonds?", Financial Analysts Journal, Jan-Feb, 56-62.
3 Gordon, J., 1991. "The Diversification Potential of International Property Investments," The Real Estate
Finance Journal, Fall, 42-48.
Charles Wurtzebach of JMB Institutional Realty and Andrew Baum of the University of
Reading stated that European real estate returns have historically performed
countercyclically to U.S. real estate returns, thereby providing investors with
opportunities to reduce portfolio volatility through international diversification. They
pointed out that the European cities have historically exhibited substantially more
stability in office vacancy rates than American cities. They suggested that this result may
be caused by differences in the structure of European markets. They speculated that the
causes of the greater stability in European markets are that: (i) European real estate
projects have primarily been demand driven, while real estate projects in the United
States have been driven by the supply of capital, and (ii) tighter land-use controls in
Europe and the lack of legislatively encouraged development has limited speculative
development. 4
Piet Eichholtz and Kees Koedijk of the University of Limburg used the GPR-LIFE Global
index of worldwide publicly-traded property shares to point out that an investor who was
internationally diversified would have been reasonably protected from the severe
downturns in certain real estate markets in the late 1980's, while still profiting from the
boom years in certain markets. 5
Wurtzebach, C. and Baum, A., 1994. "International Real Estate," Managing Real Estate Portfolios, Ed.
Hudson-Wilson, S. and Wurtzebach, C., 284-317
4
5 Eicholtz, P and Koedijk, K., 1996, "The Global Real Estate Securities Market", Real Estate Finance,
Spring, 76-82.
William Goetzmann of Yale and Susan Wachter of Wharton attempted to analyze
international real estate returns using a mathematical model based on a k-means
algorithm, which was designed to identify clusters of countries whose real estate returns
tended to move together. They concluded that more conservative portfolios should be
tilted towards the U.S. and Continental Europe, while more aggressive portfolios should
be tilted towards Asia and the Iberian countries.6
2.1.2 Historical Correlations are not Necessarily a Forecast of Future Correlations.
Goetzmann and Wachter pointed out that one should be cautious in interpreting the
results of a mean/variance optimizer for international real estate portfolios, since the data
set is likely to be flawed, and the results will be too likely to steer investors to past
winners.7
Wurtzebach and Baum cautioned investors against drawing definitive conclusions about
future relationships from historical data. For example, they suggested that, as markets
become more globally integrated, the correlation of real estate returns among countries
may increase, thereby reducing potential benefits from diversification. 8
6 Goetzmann,
W. and Wachter, S, 1994. "The Global Real Estate Crash: Evidence From an International
Data Base," Working Paper #196, Yale School of Management & The Wharton School.
7 Ibid.
8Op.cit.,Wurtzebach and Baum
Generally, circumstances could cause correlations of real estate returns among various
countries to change over time. Examples of reasons for returns to become more
correlated, include: (i) increasing global integration of economies, (ii) increasing global
integration of national and regional capital markets and (iii) increasing similarity of
governmental policies in various countries, associated with the fall of communism and
the growing worldwide acceptance of market-oriented policies. Real estate returns in
certain countries might become less correlated over time in connection with economic or
political changes.
Thus, a determination regarding the actual current benefits of international diversification
requires an estimate of the current correlations among real estate returns in various
countries. Such an estimate would be based on an evaluation of historical correlations,
trends of correlations and factors which may be affecting current correlations, including
economic and political factors.
2.2 The Impact of International Diversification in Increasing Portfolio Return.
Global investing allows an investor to choose among an expanded universe of investment
opportunities. Thus, an investor who is not limited by national borders may exercise
greater selectivity in making investment decisions. Such an investor would also have the
advantage of being able to choose among countries at different points in market cycles.
Andrew Baum emphasized that international real estate investors are likely to benefit
from having broader choices of investments and better perspectives on real estate markets
than local investors. He pointed out that, although foreign real estate investors are likely
to have an informational disadvantage relative to local investors, benefits can be obtained
by global real estate investors who are able to overcome any informational disadvantage
by employing local experts, because a "foreigner's global perspective can exploit the
inertia that exists in all local real estate markets because of inefficiency and local myopia,
or constraints that affect domestic players but do not bind the foreign institution." He
further explained that, "Mismatches in liquidity around the world can cause booms and
slumps, and occasionally cheap and dear markets, often at different times in different
places. The global player free of the capital supply constraint imposed by the local
liquidity shortage, and with a wider choice of target markets, can time large-lot size
transactions more effectively than the local investor." 9
Similarly, N.H. Seek emphasized the benefits to a foreign investor in Asian real estate
markets due to the wide variety of investment opportunities in markets at different stages
of development and the "gigantic markets for goods and services, including property of
all kinds-housing, shopping centers, office buildings, modern industrial facilities and
warehouses, hotels and resorts", caused by the "increasing affluence, staggering
population bases and changing lifestyles", in these markets. Seek pointed out that each
stage of the evolution of a typical real estate market is represented in the Asian countries,
from China and Vietnam, which have yet to establish functional market mechanisms, to
Australia, whose capital markets feature innovative approaches to packaging property
9 Baum, A., "Can Foreign Real Estate Investment Be Successful?", Real Estate Finance, 81-89
investments. Thus, the Asian countries offer investors unique choices and growth
opportunities.10
In general, for a fund manager with superior ability to identify exceptional investment
opportunities, any significant increase in the number of potential markets available for
investment should increase the number of exceptional investments in the portfolio,
thereby improving portfolio performance through higher expected returns. Thus,
international investment should improve the performance of a portfolio of real estate
securities by increasing expected returns.
0 Seek, N., 1996. "Institutional Participation in the Asia Pacific Real Estate Markets; Are the Benefits
Worth the Risks?" Real Estate Finance, Winter, 51-58.
CHAPTER 3- ANALYSIS OF HISTORICAL DATA REGARDING THE
BENEFITS OF INTERNATIONAL DIVERSIFICATION
The purposes of this chapter are: (i) to review historical data for the purpose of showing
how international diversification would have improved the performance of a portfolio of
real estate securities and (ii) to identify meaningful relationships among real estate returns
in various countries.
3.1 Data: The GPR-LIFE Index
This research is based on information contained in indexes of historical real estate
returns in 26 countries provided by Global Property Research in The Netherlands (the
"GPR-LIFE" indexes). The indexes for 14)of the countries begin in January, 1984; the
indexes for the other 12 countries begin on various dates after January, 1984.
The GPR-LIFE indexes include all publicly-traded property companies which have had a
market capitalization exceeding $50 million for at least twelve months. (Companies are
removed from an index when their market capitalization falls below $50 million for
twelve months.) The indexes include "Investor" companies, for which 75% or more of
the profits are derived from real estate investments and "Hybrid" companies, for which
75% or more of the profits are derived from investment and development activities. The
indexes exclude "Developers", for which 75% or more of the profits are derived from
construction and development and "Mortgage Investors", for which 75% or more of the
profits are derived from investments in mortgage loans. The distinction between
investment and development companies is important, because only the former represent
real estate portfolios, which are relevant to an analysis of real estate returns. Of the four
major international real estate indexes (GPR-LIFE, Datastream, Morgan Stanley Capital
International and Salomon Brothers), GPR-LIFE is the only index which makes a
distinction between property investment companies and property development
companies. The GPR-LIFE indexes are also the most representative, with information
from 333 companies. "
The GPR-LIFE indexes are available in local currency or US dollar denominations. The
indexes provide information regarding monthly total return, dividends and price. The
indexes have a variety of start dates, with the earliest starting with data from the month
ending January 31, 1984. The total return indexes assume reinvestment of all dividends.
The dollar denominated returns are computed in accordance with the following formula:
$
Ps++
Di,
-
1
In which:
r , = return of share i in U.S. dollars in period (t - 1,t)
" Eicholtz, P and Koedijk, K., 1996, "International Real Estate Securities Indexes", Real Estate Finance,
Winter, 42-50.
P$=price of share i in U.S. dollars at time t
Ds =dividend on share i in U.S. dollars at time t
P_, =price of share i in U.S. dollars at time t -1
t =last trading day of the month
The GPR-LIFE indexes are available in market-weighted and equal-weighted
formats. For a market capitalization-weighted index, each stock return is weighted by the
stock's fraction of the beginning-of-period market capitalization for the total index. The
return is computed by multiplying each company's return by it's beginning-of-period
market capitalization and adding the results. Finally, the sum is divided by the beginningof-period market capitalization. An equal-weighted index is the arithmetic average of the
separate company returns. It is called equal-weighted because each company, regardless
of size, exerts the same influence on the index return.
12
In my analysis, I used the market-weighted, local-currency, total-return indexes.
Although it is arguable whether the market-weighted or equal-weighted indexes are more
appropriate
13,
I chose the market-weighted indexes on the premise that they provide a
more accurate reflection of the domestic real estate market in a particular country. I used
the local currency indexes, to isolate the real estate returns from currency fluctuations.
The dollar denominated indexes would include the effects of currency fluctuations. (An
12 Giliberto,
" Ibid.
S. and Sidoroff, F., 1995, "Real Estate Stock Indexes", Real Estate Finance, Spring, 56-62.
investor who is considering foreign real estate investment would need to consider the
risks of currency fluctuations and the costs of hedging against such risks.) I used the total
return indexes, because total return is a more meaningful measure of return than either
dividend yield or price appreciation on its own.
The GPR-LIFE indexes for Germany, Austria and Switzerland are flawed, in that the
majority of the companies in these indexes consist of "open-end" funds. In the case of
open-end funds, shares are typically bought and sold at prices established by the issuing
company, based on its appraisal of property values. Shares of open-end funds tend to
exhibit lower volatility than shares of closed-end funds, because their values are
established by appraisals. Thus, the indexes for Germany, Switzerland and Austria exhibit
lower volatility than the local real estate markets due to the nature of the securities issued
by property companies in these countries. In addition, the German open-end funds tend
to make substantial investments in other European countries. I have chosen to include
these countries in my analysis, because they represent a large part of the European
economy. However, one should be cautious in interpreting the data for these countries.
It should also be noted that the companies included in GPR-LIFE indexes have changed
since the beginning of the data series. The following table shows the number of
companies included in each country's index in January, 1984 compared with the number
of companies included in the indexes in April, 1997.
Number of Companies included in GPR-LIFE Indexes
Australia
Canada
France
Germany
Hong Kong
Italy
Japan
Norway
Netherlands
Singapore
Switzerland
Sweden
UK
USA
Total
Jan., 1984
4
2
10
8
15
2
7
1
3
3
11
1
31
26
124
April, 1997
21
7
43
18
25
5
22
1
9
9
20
5
46
117
348
The changes in the GPR-LIFE indexes over time provide an additional reason to be
cautious in interpreting the GPR-LIFE data.
3.2 Risk/Return Profiles
Using the GPR-LIFE indexes, I determined the means, standard deviations and
correlation coefficients of the monthly real estate returns of each country. The mean
returns and standard deviations are listed in Exhibit 1 (ranked in order from the country
with the highest mean return, to the lowest).
To compare risk-adjusted returns, I computed the ratio of mean return to standard
deviation for each country. This provides a measure of return for each unit of risk. The
ratios for the various countries, in descending order, are listed in Exhibit 2.
Exhibit 1
Return/Risk Characteristics-Historical Monthly Returns
Hong Kong
Argentina
Norway
Singapore
Malaysia
Ireland
Portugal
Australia
Spain
Japan
New Zealand
USA
England
Sweden
France
Indonesia
Italy
Switzerland
Phillipines
Belgium
Germany
Netherlands
Austria
Canada
Mexico
Thailand
Mean Monthly Return Annualized Return
2.76
33.11
2.22
26.58
1.79
21.47
1.71
20.53
1.63
19.52
1.59
19.11
1.42
17.03
1.38
16.54
1.24
14.85
1.22
14.65
1.17
14.04
1.11
13.36
1.06
12.70
0.96
11.50
0.71
8.46
0.71~
8.46
0.64
7.74
0.62
7.40
0.59
7.07
0.58
6.94
0.48
5.79
0.43
5.20
0.35
4.24
-0.74
-8.91
-0.98
-11.79
-2.64
-31.73
Standard Deviation
10.37
11.47
10.09
10.60
13.81
11.22
10.12
3.78
10.32
10.41
20.69
4.40
5.98
12.31
3.81
14.61
6.53
2.15
8.09
4.93
0.52
3.00
2.35
7.67
9.50
15.89
Data Start Date
Jan-84
Sep-93
Jan-84
Jan-84
Feb-86
Jul-85
Mar-90
Jan-84
Ap-87
Jan-84
Feb-88
Jan-84
Jan-84
Jan-84
Jan-84
May-90
Jan-84
Jan-84
Nov-91
Mar-87
Jan-84
Jan-84
Mar-89
Jan-84
Jan-92
May-91
Exhibit 2
Return/Risk Ratios
Germany
Australia
Switzerland
Hong Kong
USA
Argentina
France
Norway
England
Singapore
Austria
Netherlands
Ireland
Phillipines
Spain
Malaysia
Japan
Belgium
Italy
Sweden
New Zealand
Mexico
Indonesia
Canada
Portugal
Thailand
0.94
0.36
0.29
0.27
0.25
0.19
0.19
0.18
0.18
0.16
0.15
0.14
0.14
0.14
0.12
0.12
0.12
0.12
0.10
0.08
0.07
0.06
0.05
-0.10
-0.10
-0.17
In reviewing Exhibit 2, it is interesting to note that Germany, which is near the bottom of
the list of countries in average return, dominates the other countries in risk-adjusted
returns, with a return/risk ratio more than 21/2 times that of the nearest country, Australia.
This result is probably caused by the presence of open-end funds in the Germany index.
Exhibit 3 shows a graphic representation of the historical returns and risk (measured by
standard deviation) in the 26 countries for which we have data. The chart exhibits a
reasonably strong relationship between risk and return. One can see that Germany,
Austria and Switzerland have the lowest standard deviation. This is probably attributable
to the presence of open-end funds in their indexes. Germany, Australia and Hong Kong,
respectively, dominate clusters at the low, medium and high ends of the risk spectrum.
Canada, Portugal and Thailand have experienced negative returns over the time period
represented by the data set. (In the case of Canada, this covers a substantial time periodbetween January, 1984 and the present.) Mexico has exhibited the highest level of
volatility in the data set. Generally, the more mature markets in Western Europe, the
United States, Australia and New Zealand have exhibited relatively low risk, low return
characteristics. The Scandinavian countries, the Iberian countries and the more
developed Asian countries (Japan, Hong Kong, Singapore) have exhibited higher risk,
higher return characteristics. The emerging markets (Argentina, Malaysia, Indonesia,
Thailand and Mexico) have exhibited high risk, with a wide variety of returns.
Exhibit 3
Return/Risk Characteristics-Historical Monthly Returns
+ Hong Kong
+ Argentina
Nowevningagoar
re% n diVI
*
i
aL06ysia
+ Aust alia
* USA
+Switz + Fran
+ GermanyAgh
New ZVANfd
+ Mexico
Japan, Spain
* England
* Sweden
ndonesia
* Belgium
0
+ Canada
+ F ortugal
* Thailand
Standard Deviation
25
3.2.1 Risk/Return Characteristics in First and Second Halves of Time Series.
For comparison, I reviewed the return/risk characteristics of the various countries for the
first and second halves of the period covered by the data set. Exhibit 4 shows a
comparison of the means, standard deviations and return/risk ratios, for the 14 countries
for which we have data since January, 1984, between the first half of the data period
(January, 1984- January, 1990) and the second half of the data period (February, 1990April, 1997). Exhibits 5 and 6 show this information in graphical form.
A review of Exhibits 5 and 6 indicates that certain characteristics of various countries'
returns appear consistent across the two periods. In particular, the risk characteristics of
most of the countries appear consistent. The countries of Western Europe, the U.S. and
Australia seem to have consistently low risk, low return characteristics. The Asian and
Scandinavian countries exhibit relatively high risk, high return characteristics. The chart
for the first half of the data set exhibits a very strong relationship between return and risk.
During the second half of the data set, the relationship between return and risk was much
weaker. During the second half of the data period, four of the countries (Italy, Japan,
Canada and Sweden) experienced negative average returns. Hong Kong had the highest
average return during both periods. Germany had the highest return/risk ratios during
both periods. Australia had the second highest return/risk ratio during both periods.
Exhibit 4
Return/Risk Characteristics-Comparison of First and Second Halves of Data Set
Total Avg. Return 1st Half Avq.Return
3.08
2.76
Hong Kong
2.55
1.79
Norway
2.21
1.71
Singapore
1.58
1.38
Australia
3.02
1.22
Japan
1.18
1.11
USA
1.44
1.06
England
2.26
0.96
Sweden
1.46
0.71
France
1.93
0.64
Italy
0.54
0.62
Switzerland
0.52
0.48
Germany
0.71
0.43
Netherlands
1.27
-0.74
Canada
Hong Kong
Norway
Singapore
Australia
Japan
USA
England
Sweden
France
Italy
Switzerland
Germany
Netherlands
Canada
Total Return/Risk 1st Half
0.27
0.18
0.16
0.36
0.12
0.25
0.18
0.08
0.19
0.10
0.29
0.94
0.14
-0.10
2d Half Avq.Return
2.49
1.15
1.29
1.21
-0.29
1.06
0.74
-0.13
0.07
-0.44
0.68
0.45
0.20
-2.43
Return/Risk 2d Half Return/Risk
0.27
0.27
0.11
0.27
0.16
0.17
0.45
0.33
-0.03
0.25
0.25
0.26
0.13
0.22
-0.01
0.30
0.02
0.36
-0.08
0.26
0.28
0.32
0.71
1.60
0.05
0.56
-0.30
0.19
Total Std Dev 1st Half Std.Dev 2d Half Std.Dev
9.40
11.48
10.37
10.49
9.62
10.09
7.97
13.10
10.60
2.68
4.79
3.78
8.78
11.89
10.41
4.26
4.59
4.40
5.54
6.47
5.98
15.19
7.45
12.31
3.52
4.01
3.81
5.62
7.31
6.53
2.46
1.72
2.15
0.63
0.33
0.52
3.90
1.27
3.00
8.18
6.52
7.67
Exhibit 5
Return/Risk Profile for First Half of Data Set (1/84-1/90)
3.5
+Hi npp
3
* Norway
2.5
* Sweden
* Italy
* Australia
+ France
+ UK
+ Canada
* USA
1
+ Netherlands
+ Germany * Switzerland
0.5
0
0
6
8
Standard Deviation
* Singapore
Exhibit 6
Return/Risk Profile for Second Half of Data Set (2/90-4/97)
2.5
2
1.5
* Singapore
* Australia
* USA
1
* UK
+ Switzerland
0.5
* Norway
* Germany
+ Netherlands
0
-
_-|
2
-0.5
i
4
-
-
j-
* Japan
* Italy
-1
-1.5
-2
-2.5
+ Canada
Standard Deviation
14
+Swey
3.3 Correlations of Returns
The degree to which diversification improves the risk-adjusted return profile of a
portfolio varies depending on the degree of correlation among the assets in the portfolio.
The lower the correlation among assets in the portfolio, the greater the benefits from
diversification.14 A real estate investor would obtain the maximum benefits from
international diversification by investing in countries with high expected returns, low
standard deviations and low correlations of returns.
3.3.1 Correlations of Monthly Returns
Exhibit 7 shows a matrix of the correlation coefficients for the monthly returns for the 14
countries for which we have data dating to January, 1984. (I only analyzed the
correlations among the countries with a time series beginning in January, 1984, because
any analysis which included additional countries would necessarily exclude meaningful
data on the countries for which the data series begins in 1984.) . None of the 91
correlation coefficients exceeds .5. The highest correlation is between Singapore and the
U.S.. Japan has the lowest total correlation with other countries. It is interesting to note
that negative correlations exist between Germany and the Netherlands, and between Hong
Kong and Japan. In the case of Germany, this is probably attributable to the
aforementioned problem with open-end funds. Exhibit 7 also includes an analysis of the
sum of correlations of the countries analyzed. This analysis gives an indication of the
14
op.cit. Bodie, Kane, Marcus
Exhibit 7
Correlation Coefficients-Monthly Returns
!Australia
Canada
England
France
Germany
Hong Kong
Italy
Japan
Netherlands
Norway
Singapore
Sweden
Switzerland
'USA
Australia
1
0.31
0.44
0.20
0.14
0.42
0.11
0.14
0.20
0.23
0.32
0.21
0.19
0.34
Sum of Correlations
Australia
.Canada
England
'France
Germany
Hong Kong
Italy
Japan
Netherlands
Norway
Singapore
Sweden
Switzerland
USA
I
3.25
3.25
3.83
3.60
3.15
1.82
2.39,
1.32
2.29,
3.01
2.78
2.52
1.89'
3.581
Canada
England
1.00
0.29
0.30
0.17
0.23
0.19
0.27
0.33
0.15
0.20
0.20
0.20
0.41
1.00
0.31
0.19
0.40
0.11
0.14
0.29
0.28
0.46
0.23
0.25
0.44
France
1.00
0.15
0.21
0.41
1.00
0.16
0.07
1.00
0.17
0.27
0.09
-0.01
0.36
0.22
0.15
0.21
0.27
0.42
-0.04
0.02
0.07
0.03
0.11
0.04
0.18
0.22
0.38
0.07
0.23
0.27
Ascending Order
Japan
Hong Kong
Switzerland
Netherlands
italy
Sweden
Singapore
Norway
Germany
Australia
iCanada
USA
France
England
Germany Hong Kong
1.32
1.82
1.89
2.29
2.39
2.52
2.78
3.01
3.15
3.25
3.25
3.58
3.60
3.83
Italy
1.00
0.02
0.17
0.11
0.12
0.00
-0.18
0.20
Japan
Netherlands
Norway
1.00
0.23
1.00
0.02
0.34
1.00
0.04
0.25
0.07
0.20
0.29
0.29
0.23
0.29
0.25
0.27
0.04
0.20
Singapore
Sweden
Switzerland
USA
1.00
0.11
0.16
0.48
1.00
0.18
0.16
1.00
0.12
1.00
countries in which investors would receive the greatest benefit from diversification;
investors in countries with the lowest correlations with other countries would receive the
greatest benefit from diversification
3.3.2 Correlations of 12 Month Rolling Returns
As an additional analysis, I computed the correlation coefficients among the countries' 12
month rolling returns, for each month between December, 1984 and the present. The
results of this computation are shown on Exhibit 8. The correlations for 12 month rolling
returns are quite different than for the monthly returns. The 12 month correlations, in
total, are 53.3% higher than the monthly correlations. 22% of the 12 month correlation
coefficients are .5 or higher. It is not surprising that the 12 month returns exhibit greater
correlation than the monthly returns, since the 12 month returns would tend to exhibit
more stability than the monthly returns. This analysis suggests that the degree of
correlation of real estate returns among countries varies substantially, depending on
whether monthly returns or annual returns are evaluated.
The highest 12 month correlations are between Sweden and Norway and Sweden and
England. Germany exhibits a negative total correlation with the other countries. Hong
Kong and Japan have a positive correlation in 12 month rolling returns. Germany and the
Netherlands exhibit an even stronger negative correlation in the 12 month returns than in
the monthly returns. Given the close ties between the German and Dutch economies, this
result provides additional evidence that the German data is problematic. The different
Exhibit 8
Correlation Coefficients-12 month rolling returns
I
Austral ia
Australia
1.00
0.26
Canada
0.59
England
0.26
France
0.09
Germany
Hong Kong
0.45
-0.12
Italy
0.40
Japan
0.33
Netherlands
0.38
Norway
0.47
Singapore
0.44
Sweden
0.45
Switzerland
0.38
USA
Sum of Correlations
Australia
Canada
England
France
Germany
Hong Kong
Italy
Japan
Netherlands
Norway
Singapore
Sweden
Switzerland
USA
4.38
4.30
5.491
5.64
-0.02,
3.73
1.98
5.49
5.61
4.77
3.44
6.10
3.44
4.98
Canada
England
France
1.00
0.33
0.54
-0.12
0.15
0.52
0.63
0.51
0.33
0.26
0.44
0.05
0.38
1.00
0.32
-0.15
0.39
-0.18
0.44
0.71
0.74
0.47
0.77
0.62
0.44
1.00
0.16
0.37
0.71
0.67
0.60
0.43
0.11
0.61
0.26
0.59
Germany Hong Kong
1.00
0.15
0.29
-0.13
-0.22
-0.12
0.02
-0.01
0.05
-0.03
I
1.00
0.00
0.28
0.36
0.18
0.29
0.25
0.42
0.43
Italy
Japan
Netherlands
Norway
Singapore
1.00
0.44
0.15
0.06
-0.06
0.21
-0.24
0.20
1.00
0.49
0.34
0.35
0.64
0.25
0.69
1.00
0.66
0.34
0.66
0.44
0.57
1.00
0.36
0.77
0.34
0.29
1.00
0.47
0.11
0.25
Sweden
Switzerland
USA
1.00
0.38
0.48
1.00
0.32
1.00
1
Ascending Order
Germany
Italy
Singapore
Switzerland
Hong Kong
Canada
Australia
Norway
USA
Japan
England
Netherlands
France
Sweden
-0.02
1.98
-
3.44,
3.441
3.73
4.30
4.38
4.77
4.98
5.491
5.49
5.61'
5.64
6.10
-
-
results between the correlations for the monthly returns and the 12 month rolling returns
are seen by reviewing the cases of Japan, Italy and Sweden. Japan went from having the
lowest total correlations in the monthly return data to the 10th lowest total correlations in
the 12 month data. Italy and Sweden are very close in terms of total correlations in the
monthly data; however they are far apart in terms of total correlations in the 12 month
data. (In the 12 month data, Italy has the second lowest total and Sweden has the highest
total of the 14 countries in the group.) There is no apparent reason for such discrepancies
between the data for monthly returns and for 12-month returns. Perhaps these results
indicate that caution should be exercised in drawing conclusions from this data, since the
same data can be interpreted to produce different results.
3.3.3 Correlations of Returns in First and Second Halves of Time Series
I also computed the correlation coefficients for the first and second halves of the data
series. Exhibit 9 shows a comparison of these correlation coefficients for each country.
A review of Exhibit 9 indicates that, in total, correlations have increased from the first
half to the second half of the time series. The total of the correlations among countries
increased by 13.7%. Ten of the fourteen countries showed increases in total correlations.
However, in each half of the time series, only 3 of 91 correlation coefficients were .5 or
higher.
Exhibit 9 reveals some interesting information. Hong Kong and Japan have very low
correlations of returns in both periods. The correlations between Australia and the other
Exhibit 9
Comparison of Correlations Between ist Half and 2nd Half of Data Set
Australia
Canada
England
France
Germany
Hong Kong
Italy
Japan
Netherlands
Norway
Singapore
Sweden
Switzerland
USA
Total
Australia
1184-1/90 2/90-4/97
1
1
0.19
0.45
0.54
0.29
0.13
0.30
0.27
0.08
0.43
0.42
0.16
0.00
0.14
0.14
0.23
0.28
0.20
0.29
0.33
0.31
0.36
0.18
0.19
0.24
0.41
0.27
4.82
3.99
Canada
1184-1/90 2/90-4/97
0.45
0.19
1.00
1.00
0.41
0.20
0.33
0.23
0.36
0.10
0.28
0.20
0.21
0.11
0.23
0.27
0.35
0.29
0.06
0.19
0.19
0.22
0.15
0.20
0.08
0.28
0.58
0.31
4.64
3.84
England
1/84-1/90 2/90-4197
0.29
0.54
0.41
0.20
1.00
1.00
0.11
0.53
0.11
0.36
0.37
0.43
-0.01
0.24
0.07
0.22
0.30
0.34
0.21
0.35
0.46
0.49
0.14
0.29
0.25
0.26
0.46
0.43
4.72
5.11
France
1/84-1/90 2/90-4/97
0.30
0.13
0.33
0.23
0.11
0.53
1.00
1.00
0.25
0.10
0.21
0.21
0.48
0.27
0.15
0.37
0.03
0.52
-0.03
0.42
0.02
0.36
-0.03
0.32
0.10
0.40
0.45
0.40
3.17
5.45
Germany
1/84-1/90 2/90-4/97
0
0.08
0.36
0.10
0.36
0.11
0.25
0.10
1.00
1.00
0.38
0.07
0.13
0.03
0.21
0.01
0.23
-0.08
0.17
-0.04
0.07
0.07
0.10
0.01
0.01
0.15
0.21
-0.04
3.72
1.56
Hong Kong
1/84-1/90 2/90-4/97
0.43
0.42
0.28
0.20
0.43
0.37
0.21
0.21
0.38
0.07
1.00
1.00
0.18
0.14
-0.03
0.01
0.26
0.19
0.17
0.28
0.53
0.29
0.01
0.1
0.04
011
0.04
0.38
0.30
0.24
3.95
4.14
Italy
1/84-1/90 2/90-4/97
0.16
0.00
0.21
0.11
-0.01
0.24
0.48
0.27
0.13
0.03
0.18
0.14
1.00
1.00
-0.06
0.06
0.00
0.25
0.08
0.11
0.06
0.21
-0.14
0.04
-0.12
-0.23
0.21
0.19
2.17
2.43
Australia
Canada
England
France
Germany
Hong Kong
Italy
Japan
Netherlands
Norway
Singapore
Sweden
Switzerland
USA
Total
1st half total
2nd half total
Japan
1/84-1/90 12190-4/97
0.14 | 0.14
0.23
0.27
0.07
0.22
0.37
0.15
0.21
0.01
-0.03
0.01
0.06
-0.06
1.00
1.00
0.28
0.23
0.11
-0.09
-0.07
0.23
0.28
0.25
0.08
0.08
0.24
0.18
3.27
2.30
47.47
55.00
Netherlands
1/84-1/90 2/90-4/97
0.23
0.28
0.35
0.29
0.30
0.34
0.03
0.52
0.23
-0.08
0.19
0.26
0.00
0.25
0.23
0.28
1.00
1.00
0.39
0.24
0.39
0.36
0.29
0.29
0.27
0.11
0.30
0.43
4.74
4.02
Norway
1184-1/90 2190-4/97
0.20
0.29
0.06
0.19
0.21
0.35
0.42
-0.03
-0.04
0.17
0.17
0.28
0.08
0.11
0.11
-0.09
0.24
0.39
1.00
1.00
0.21
0.31
0.11
0.34
-0.17
0.16
0.22
0.17
4.11
2.33
Singapore
Sweden
1/84-1/90 2/90-4/97
1/84-1/90 2/90-4/97
0.31
0.33
036
0.18
0.19
0.22
0.15
0.20
0.46
0.49
0.14
0.29
0.02
0.36
-0.03
0.32
0.07
0.07
0.10
0.01
0.29
0.53
0.01
0.11
0.04
-0.14
0.06
0.21
0.28
0.25
-0.07
0.23
0.29
0.29
0.39
0.36
0.11
0.34
0.31
0.21
0.04
0.19
1.00
1.00
0.04
0.19
1.00
1.00
0.21
0.17
0.22
0.12
0.14
0.25
0.47
0.50
3.59
5.0292.77
3.54
Switzerland
1/84-1/90 2/90-4/97
0.19
0.24
0.28
0.08
0.25
0.26
USA
1/84-1/90 190-4/97
0.41
0.27
0.58
0.31
0.43
0.10
-0.01
0.40
0.15
0.04
-0.12
0.08
0.38
-0.23
0.08
0.11
0.27
-0.17
0.16
0.12
0.21
1.00
0.15
2.03
0.22
0.17
1.00
0.12
3.50
I0.46
0.45
U.4U
0.21
0.30
0.21
0.18
0.43
0.17
0.50
0.25
0.15
1.00
5.28
-0.04
0.24
0.19
0.24
0.30
0.22
0.47
0.14
0.12
1.00
4.29
Asian countries (Hong Kong, Japan and Singapore) are extremely consistent across the
two periods. France exhibits substantial increases in correlations with a number of
countries, but shows a substantial decrease in its correlation with Italy, with which it had
previously exhibited the highest correlation coefficient. The Netherlands exhibits fairly
consistent correlation coefficients with the countries of Scandinavia, Asia and the British
Commonwealth, but shows a substantial increase in its correlation with France and a
substantial decrease in its correlation with Germany. The U.S. shows consistently high
correlations with England, France and Singapore. England shows substantial decreases in
correlations with the commonwealth countries, Canada and Australia.
Generally, the correlation coefficients which exhibit consistency across the two halves of
the data set are probably more meaningful than those which have changed substantially.
3.4 The Efficient Frontier
The "efficient frontier" refers to the set of portfolios which contain the maximum level of
portfolio expected return, for each level of portfolio risk (or the minimum level of risk,
for each level of return). An investor would always prefer to have an investment portfolio
on the efficient frontier because, for any portfolio which is not on the efficient frontier, an
investor could obtain a higher expected return, without incurring additional risk, or a
reduction in risk, without a reduction in expected return, by moving to a portfolio on the
efficient frontier. The actual efficient frontier at any point in time is unknown, because
the actual current expected returns, standard deviations and correlation coefficients are
unknown. The efficient frontier may be estimated by using estimates of expected returns,
standard deviations and correlation coefficients. Historical data is often used to estimate
the efficient frontier. 15 An efficient frontier derived from historical data provides useful
information, because it illustrates how diversification improves portfolio performance and
because some historical relationships may continue.
I created a model to derive points on the efficient frontier, using the solver function in
Excel. This model uses the formulas for the expected return of a portfolio and the
standard deviation of a portfolio, to determine the weightings of investment assets in the
portfolio which will provide the maximum return, for a given level of standard deviation.
The expected return of a portfolio equals the weighted average of the expected returns of
the assets in the portfolio. The standard deviation of a portfolio equals the square root of
the portfolio variance. The portfolio variance is defined as follows:
n
nn
W12 72
2
(=
=-
I
~~~c~
I
=
*J=
=
1
I-
In which:
2
Op
w
ortfolio variance
aiac
potflo
2 =weights
of investment assets in the portfolio.
a, ,o=standard deviations of investment assets in the portfolio.
16
p. =correlation coefficient for investment assets in the portfolio.
1 Hudson-Wilson, S. and Stimpson, J., 1996. "Adding U.S. Real Estate to a Canadian Portfolio: Does it
Help?" Real Estate Finance, Winter, 66-78.
16 op.cit.
Bodie, Kane, Marcus
3.4.1 Efficient Frontiers Created From Historical Data
3.4.1.1 Efficient Frontiers Based on Monthly Returns
Using the historical returns, standard deviations and coefficient correlations for the 14
countries for which I have data since January, 1984, I computed an estimate of the
efficient frontier for investments in international real estate securities. Exhibit 10 shows
a graph of points on this efficient frontier. Exhibit 11 shows the portfolio weightings of
each country, for each point on the efficient frontier. In reviewing Exhibit 11, one can see
that the lower risk portfolios are dominated by Germany and Switzerland, the medium
risk portfolios are dominated by Australia and the higher risk portfolios are dominated by
Hong Kong. The U.S. appears in the lower risk portfolios. Norway and Japan appear in
almost every portfolio, although never in a dominant position. As previously indicated,
the data from Germany and Switzerland are suspect. Therefore, the lower end of this
efficient frontier is probably not meaningful. Exhibit 10 shows that, for most levels of
risk, appropriate diversification would have substantially increased the return of the
portfolio over the time period covered by this data. However, it should be noted that, for
an investor to have obtained maximum returns over the relevant time period, the investor
would have had to invest the "correct" percentages of the portfolio in the "correct"
countries. It is far more difficult to identify these percentages and countries without the
benefit of hindsight.
Exhibit 10
Efficient Frontier-Historical Monthly returns
3
N
+ Hong Kong
N
2.5
--N
2
+ Norw ngapore
+ Australia
* Japan
* USA
+ England
* Sweden
--N
+ Germany
* France
+ Switzerland
* Netherlands
*ltaly
6
8
-0.5
* Canada
-1
Standard Deviation
Exhibit 11
Points on Efficient Frontier-Historical Monthly Returns
StdDev
1.00
2.00
3.00
4.00
4.99
6.00
7.00
7.99
9.00
10.00
Return
0.72
0.87
1.25
1.60
1.86
2.06
2.24
2.41
2.57
2.71
StdDev2
StdDev3
Portfolio Return
Portfolio Variance
Portfolio Std.Dev.
Portfolio Weights
12.32%
Australia
0.00%
Canada
0.00%
England
0.00%
France
74.51%
Germany
3.15%
Hong Kong
0.00%
Italy
0.98%
Japan
0.00%
Netherlands
Portfolio Return
Portfolio Variance
Portfolio Std.Dev.
Portfolio Return
Portfolio Variance
Portfolio Std.Dev.
Portfolio Weights
58.90%
Australia
0.00%
Canada
0.00%
England
0.00%
France
0.00%
Germany
0.00%
Hong Kong
0.00%
Italy
3.31%
Japan
0.00%
Netherlands
Norway
1.88%
Singapore
Sweden
0.00%
0.00%
Switzerland
USA
3.44%
3.71%
Portfolio Weights
24.06%
Australia
Canada
England
France
Germany
Hong Kong
Italy
Japan
Netherlands
Norway
Singapore
Sweden
Switzerland
USA
Portfolio Return
Portfolio Variance
Portfolio Std.Dev.
Portfolio Weights
33.88%
Australia
0.00%
Canada
0.00%
England
0.00%
France
0.00%
Germany
46.46%
2.06
36.00
6.00
2.24
49.00
7.00
Portfolio Weights
19.84%
Australia
Hong Kong
0.00%
0.00%
0.00%
0.00%
58.90%
Portfolio Return
Portfolio Variance
Portfolio Std.Dev.
Portfolio Weights
Australia
70.02%
Canada
England
France
Germany
0.00%
0.00%
0.00%
0.00%
Hong Kong
0.00%
7.25%
Japan
6.96%
Netherlands
0.00%
Netherlands
8.28%
Norway
Singapore
Sweden
0.00%
0.00%
Singapore
Sweden
Switzerland
USA
0.00%
0.00%
0.00%
0.00%
Singapore
Sweden
Switzerland
USA
2.41
63.84
7.99
Portfolio Weights
6.63%
Australia
Canada
England
France
Germany
Hong Kong
0.00%
0.00%
0.00%
0.00%
70.54%
Portfolio Return
Portfolio Variance
Portfolio Std.Dev.
Portfolio Weights
Australia
Canada
England
France
Germany
Hong Kong
Italy
0.00%
Italy
Japan
6.78%
Japan
6.58%
Japan
6.42%
0.00%
Netherlands
0.00%
Netherlands
Japan
Netherlands
Norway
Singapore
Sweden
Switzerland
USA
Singapore
Sweden
Switzerland
USA
0.00%
0.00%
0.00%
0.00%
Singapore
Sweden
Switzerland
USA
14.68%
0.00%
0.00%
0.00%
0.00%
Norway
Singapore
Sweden
Switzerland
USA
0.00%
16.40%
0.00%
0.00%
0.00%
0.00%
0.00%
10.86%
0.00%
0.00%
0.00%
0.00%
StdDev10
StdDev9
Portfolio Return
Portfolio Variance
Portfolio Std.Dev.
32.51%
Japan
0.00%
Norway
Hong Kong
14.44%
0.00%
0.00%
0.00%
0.00%
Italy
Italy
12.89%
Canada
England
France
Germany
Norway
14.83%
14.87%
1.86
24.90
4.99
Portfolio Weights
49.67%
Australia
0.00%
0.00%
Norway
Portfolio Return
Portfolio Variance
Portfolio Std.Dev.
Italy
Italy
Netherlands
1.60
16.00
4.00
8.09%
StdDev8
Portfolio Return
Portfolio Variance
Portfolio Std.Dev.
Canada
England
France
Germany
1.25
9.00
3.00
Norway
Switzerland
USA
StdDev7
StdDev6
Hong Kong
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
1.30%
0.00%
0.00%
0.00%
0.00%
62.55%
12.09%
StdDev5
StdDev4
StdDev1
0.00%
0.00%
0.00%
0.00%
0.00%
82.24%
0.00%
2.42%
0.00%
15.34%
0.00%
0.00%
0.00%
0.00%
2.57
81.00
9.00
Portfolio Return
Portfolio Variance
Portfolio Std.Dev.
Portfolio Weights
0.00%
Australia
0.00%
Canada
0.00%
England
0.00%
France
0.00%
Germany
Hong Kong
95.33%
Italy
Japan
Netherlands
Norway
Singapore
Sweden
Switzerland
USA
0.00%
0.00%
0.00%
4.67%
0.00%
0.00%
0.00%
0.00%
2.71
100.00
10.00
3.4.1.2. Efficient Frontiers Based on 12 Month Rolling Returns
For comparison, I also computed an efficient frontier using 12 month rolling return data,
instead of monthly returns. The graph of this efficient frontier is shown on Exhibit 12.
Exhibit 13 shows the portfolio weightings of each country, for each point on this
efficient frontier. This efficient frontier, which omits points at the low end of the risk
spectrum, is almost entirely made up of investments in Australia and Hong Kong. The
efficient portfolios are dominated by Australia at the middle risk levels and Hong Kong
at the higher risk levels. Italy appears in the portfolio at the lower end of this efficient
portfolio. This result occurs because Italy exhibits significantly lower correlation
coefficients in the 12 month data than in the monthly data. Norway and Japan no longer
appear in any efficient portfolios. One can observe from the chart on Exhibit 12 that
Norway and Japan have much higher standard deviations, relative to Hong Kong, than in
the chart on Exhibit 10 for the efficient frontier derived from monthly returns. In
addition, Japan has much higher correlation coefficients with Australia and Hong Kong,
using 12 month returns instead of monthly returns. (For 12 month returns, Japan's
correlation coefficients are .40 with Australia and .28 with Hong Kong; for monthly
returns, Japan's correlation coefficients are .14 with Australia and -.01 with Hong Kong.)
The higher standard deviations of Japan and Norway, and the higher correlation
coefficients of Japan, associated with the 12 month data, explains why Japan and
Norway have dropped out of the efficient portfolios derived from the 12 month data. In
general, the lower level of diversification in the efficient portfolios derived from the 12
Exhibit 12
Efficient Frontier-Rolling Returns
* Hong Kong
25
Fpor
* Sing
+t
+ Norway
* Australia
* Japan
15
* USA
wed
* UK
10
* France
* Switzerland
5
* Italy
* Germany
* Netherlands
5
10
15
20
25
14
30
35
-5
+ Canada
-10
-15
Standard Deviation
40
4
Exhibit 13
Points on Efficient Frontier-12 Month Rolling Returns
Eff. Frontier
Eff. Frontier
Eff. Frontier
Eff. Frontier
Australia
Canada
England
France
Germany
Hong Kong
Italy
Japan
Netherlands
Norway
Singapore
Sweden
Switzerland
USA
StdDev
10.00
15.00
20.00
25.00
9.87
33.53
24.70
20.81
2.52
28.25
29.98
39.29
14.69
42.43
42.96
44.03
9.48
18.17
Return
17.82
23.35
27.49
31.31
16.41
-10.34
11.96
7.80
5.92
33.63
7.49
15.12
3.80
19.63
24.64
12.10
7.57
13.47
Portfolio Return
Portfolio Variance
Portfolio Std.Dev.
Portfolio Weights
Australia
80.96%
0.00%
Canada
0.00%
England
0.00%
France
0.00%
Germany
11.88%
Hong Kong
7.16%
Italy
0.00%
Japan
0.00%
Netherlands
0.00%
Norway
0.00%
Singapore
0.00%
Sweden
0.00%
Switzerland
0.00%
USA
StdDev20
StdDev15
StdDev10
17.82
100.00
10.00
Portfolio Return
Portfolio Variance
Portfolio Std.Dev.
Portfolio Weights
59.71%
Australia
0.00%
Canada
0.00%
England
0.00%
France
0.00%
Germany
Hong Kong
40.29%
0.00%
Italy
0.00%
Japan
0.00%
Netherlands
0.00%
Norway
0.00%
Singapore
0.00%
Sweden
0.00%
Switzerland
0.00%
USA
23.35
225.00
15.00
Portfolio Return
Portfolio Variance
Portfolio Std.Dev.
Portfolio Weights
Australia
34.62%
0.00%
Canada
0.00%
England
0.00%
France
0.00%
Germany
63.39%
Hong Kong
0.00%
Italy
0.00%
Japan
0.00%
Netherlands
0.00%
Norway
1.99%
Singapore
0.00%
Sweden
0.00%
Switzerland
0.00%
USA
StdDev25
27.49
400.00
20.00
Portfolio Return
Portfolio Variance
Portfolio Std.Dev.
Portfolio Weights
10.94%
Australia
0.00%
Canada
0.00%
England
0.00%
France
0.00%
Germany
84.26%
Hong Kong
0.00%
Italy
0.00%
Japan
0.00%
Netherlands
0.18%
Norway
4.62%
Singapore
0.00%
Sweden
0.00%
Switzerland
0.00%
USA
31.31
625.00
25.00
month data is largely attributable to the higher correlations of the 12 month returns
compared to the monthly returns.
3.4.1.3 Efficient Frontiers for First and Second Halves of Time Series.
Exhibit 14 shows a graph of the efficient frontier derived from data for the first half of the
data series. Exhibit 15 shows the portfolio weightings of the points on this efficient
frontier. Exhibit 14 shows that, for most levels of risk, appropriate diversification would
have substantially increased the return of the portfolio over the time period covered by
this data. At the higher return levels, diversification would have substantially reduced the
risk of the portfolio. The portfolio weightings on Exhibit 15 show that for most risk
levels, a relatively high level of diversification would have been appropriate. Nine of the
fourteen countries would have been represented in these portfolios, with substantial
positions. At the higher risk levels, Hong Kong and Japan dominate the portfolios. For
this data set, the efficient frontier analysis clearly shows the potential benefits of
diversification.
Exhibit 16 shows a graph of the efficient frontier derived from data for the second half of
the data series. Exhibit 17 shows the portfolio weightings of the points on this efficient
frontier. For this data set, the efficient frontier is dominated by Australia, at the low and
middle risk levels, and Hong Kong at the middle and upper risk levels. ( Interestingly,
although Hong Kong had a prominent position in the high risk portfolios on the efficient
frontier for the first half data set, Australia was one of only five countries which did not
Exhibit 14
Efficient Frontier Based on First Half Data (1/84-1/90)
3.50
+ HgnIgg
3.00
* Norway
2.50
* Sweden
2.00
* Singappre
* Italy
* Australia
+ France
1.50
+ UK
+ Canada
* USA
1.00
* Netherlands
0.50
0.00
0.00
* Germany * Switzerland
2.00
4.00
6.00
8.00
Standard Deviation
10.00
12.00
14.00
Exhibit 15
Points on Efficient Frontier- First Half Data
Efft Frtr
Efft Frtr
Efft Frtr
Efft Frtr
Efft Frtr
Australia
Canada
England
France
Germany
Hong Kong
Italy
Japan
Netherlands
Norway
Singapore
Sweden
Switzerland
USA
Std Dev
2.01
4.01
6.01
8.01
10.01
4.79
6.52
6.47
4.01
0.33
11.48
7.31
11.89
1.27
9.62
13.10
7.45
1.72
4.59
Return
1.30
2.32
2.83
3.04
3.07
1.58
1.27
1.44
1.46
0.52
3.08
1.93
3.02
0.71
2.55
2.21
2.26
0.54
1.18
Portfolio Return
Portfolio Variance
Portfolio Std.Dev.
Portfolio Weights
0.00%
Australia
0.00%
Canada
0.00%
England
France
18.80%
Germany
Hong Kong
Italy
Japan
Netherlands
Norway
Singapore
Sweden
Switzerland
USA
9.60%
0.00%
8.40%
8.12%
28.09%
11.15%
0.00%
0.00%
15.83%
0.00%
1.30
4.04
2.01
Switzerland
USA
2.32
16.08
4.01
46.01%
0.00%
0.00%
0.00%
1.84%
0.00%
0.00%
3.04
64.16
8.01
Australia
Canada
England
France
Germany
Hong Kong
Italy
Japan
Netherlands
Norway
Singapore
Sweden
Switzerland
USA
21.48%
0.00%
0.00%
Portfolio Return
Portfolio Variance
Portfolio Std.Dev.
Portfolio Weights
Australia
Canada
England
France
Germany
Hong Kong
Italy
Japan
Netherlands
Norway
Singapore
Sweden
Switzerland
USA
0.00%
0.00%
0.00%
0.00%
0.00%
86.52%
0.00%
13.48%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
Portfolio Return
Portfolio Variance
Portfolio Std.Dev.
Portfolio Weights
StdDev1O
Portfolio Return
Portfolio Variance
Portfolio Std.Dev.
Portfolio Weights
0.00%
Australia
0.00%
Canada
0.00%
England
0.00%
France
0.00%
Germany
52.15%
Hong Kong
0.00%
Italy
Netherlands
Norway
Singapore
Sweden
Switzerland
USA
Portfolio Return
Portfolio Variance
Portfolio Std.Dev.
Portfolio Weights
Australia
0.00%
0.00%
Canada
0.00%
England
18.24%
France
0.00%
Germany
Hong Kong
12.98%
16.74%
Italy
14.17%
Japan
0.00%
Netherlands
16.39%
Norway
0.00%
Singapore
Sweden
StdDev8
Japan
StdDev6
StdDev4
StdDev2
3.07
100.20
10.01
0.00%
0.00%
0.00%
0.00%
0.00%
31.50%
1.33%
31.51%
0.00%
24.95%
0.00%
10.71%
0.00%
0.00%
2.83
36.12
6.01
Exhibit 16
Efficient Frontier Based on Second Half Data (2/90-4/97)
HongKong
2.50
2.00
1.50
* Singapore
* Norway
* USA
1.00
* Switzerland
0.50
* UK
* Germany
+ Netherlands
0.00
-0
2.00
0.
-*-Frgnce
4.00
-
_
6.00
8.00
+ Japan
+ Swo
14.00
12.00
10.00
* Italy
-0.50
-1.00
-1.50
-2.00
-2.50
--
Canada
-
Standard Deviation
-
-
_~
~
~
~
~
Exhibit 17
Points on Efficient Frontier- Second Half Data
Eff Frtr
Eff Frtr
Eff Frtr
Eff Frtr
Australia
Canada
England
France
Germany
Hong Kong
Italy
Japan
Netherlands
Norway
Singapore
Sweden
Switzerland
USA
StdDev
2.01
4.01
6.01
8.01
2.68
8.18
5.54
3.52
0.63
9.40
5.62
8.78
3.90
10.49
7.97
15.19
2.46
4.26
Return
1.03
1.60
1.95
2.28
1.21
-2.43
0.74
0.07
0.45
2.49
-0.44
-0.29
0.20
1.15
1.29
-0.13
0.68
1.06
StdDev2
Portfolio Return
Portfolio Variance
Portfolio Std.Dev.
Portfolio Weights
Australia
67.01%
Canada
England
France
Germany
Hong Kong
Italy
Japan
Netherlands
Norway
Singapore
Sweden
Switzerland
USA
0.00%
0.00%
0.00%
20.87%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
12.11%
1.03
4.04
2.01
Portfolio Return
Portfolio Variance
Portfolio Std.Dev.
Portfolio Weights
Australia
68.95%
Canada
0.00%
0.00%
England
0.00%
France
Germany
Hong Kong
Italy
Japan
Netherlands
Norway
Singapore
Sweden
Switzerland
USA
StdDev8
StdDev6
StdDev4
0.00%
30.44%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.61%
1.60
16.08
4.01
Portfolio Return
Portfolio Variance
Portfolio Std.Dev.
Portfolio Weights
41.98%
Australia
Canada
0.00%
0.00%
England
0.00%
France
Germany
0.00%
Hong Kong
58.02%
0.00%
Italy
0.00%
Japan
Netherlands
0.00%
0.00%
Norway
0.00%
Singapore
0.00%
Sweden
0.00%
Switzerland
0.00%
USA
1.95
36.12
6.01
Portfolio Return
Portfolio Variance
Portfolio Std.Dev.
Portfolio Weights
Australia
16.89%
Canada
England
France
Germany
Hong Kong
Italy
Japan
Netherlands
Norway
Singapore
Sweden
Switzerland
USA
0.00%
0.00%
0.00%
0.00%
83.11%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
2.28
64.16
8.01
appear in any of the portfolios on the first half efficient frontier). As noted earlier, the
second half data set does not exhibit as strong a relationship between risk and return as
the first half data set. Perhaps we can conclude that the data from the first half of the time
period represents a better representation of a "true" efficient frontier than the data from
the second half of the time series.
3.4.2 Efficient Frontiers Created With Forecasted Returns.
3.4.2.1 Efficient Frontier Based on Country Returns.
The efficient portfolios derived in 3.4.1 above were created using historical mean returns
to approximate expected returns. A portfolio manager with opinions regarding current
expected returns in various markets, based on a current analysis of economic factors in
such markets, would be likely to reach different conclusions regarding the optimum
portfolio mix. The U.S. and international real estate portfolio managers at Morgan
Stanley Asset Management have provided current estimates of expected returns in various
sectors of the U.S. market and in various foreign markets. These returns have been
computed by providing data into a model which takes into account: (i) the forecasted
change in discount or premium between property shares and underlying real estate values,
(ii) the forecasted change in property values attributable to a change in local capitalization
rates, (iii) the average leverage ratio of publicly-owned real estate companies, and (iv) the
average dividend yield of property shares.
Based on the analysis of the Morgan Stanley portfolio managers, I divided the expected
returns into five categories: (i) negative- below 0%, (ii) poor- 0% to 8%, (iii) average- 8%
to 15%, (iv) above average- 15% to 23% and (v) superior- above 23%. I then assigned
each country an "average" return for its category. I chose this method of grouping
forecasted returns, to lessen the impact of a single incorrect forecast. Exhibit 18 shows
the various countries' expected returns, computed in this manner. Exhibit 19 shows this
information in graphical form. Exhibit 18 also contains weighted average returns for
Europe and Asia, computed by using the weights used by GPR-LIFE in calculating their
Europe and Asia indexes.(The GPR-LIFE weightings are based on the market
capitalizations of property companies in the various countries in each region.)
Exhibit 20 shows an efficient frontier computed using the various countries' forecasted
expected returns, historical standard deviations and historical correlation coefficients.
Exhibit 21 shows the portfolio weightings of the points on this efficient frontier. Exhibit
20 shows that, for this data set, appropriate diversification is quite effective in increasing
return at the low end of the risk spectrum and reducing risk at the high end of the risk
spectrum. Exhibit 21 shows that this efficient frontier is generally made up of welldiversified portfolios. Nine of the twelve countries for which we had data are represented
in a portfolio. (I lacked forecasted returns for Canada and Italy). Generally, France, the
Netherlands and Switzerland are strongly represented at the lower end of the risk
spectrum, Australia and France are strongly represented in the middle risk levels and the
countries with superior estimated expected returns, Hong Kong, Singapore, Japan and
Sweden, dominate the higher risk levels.The U.S. is not represented in any portfolio. The
Exhibit 18
Forecasted Annual Returns
Life weights
USA
34.28%
17.44%
1.50%
8.76%
0.66%
0.85%
0.18%
28.88%
1.22%
5.90%
0.32%
0%
0%
48.56%
21.68%
12.66%
9.42%
4.56%
0.00%
2.14%
0.12%
0.86%
Category
average
Assumed Return
11.5%
11.5%
average
UK
19.0%
above average
France
28.0%
superior
Sweden
11.5%
average
Netherlands
19.0%
above average
Belgium
4.0%
poor
Spain
28.0%
superior
Portugal
-4.0%
negative
Germany
4.0%
poor
Austria
4.0%
poor
Switzerland
19.0%
above average
Norway
28.0%
superior
Denmark
28.0%
superior
Finland
European Weighted Average(Based on LIFE weights)
8.08%
28.0%
superior
Hong Kong
28.0%
superior
Japan
28.0%
superior
Singapore
19.0%
above average
Australia
19.0%
above average
Phillipines
28.0%
superior
Taiwan
-4.0%
negative
Malaysia
4.0%
poor
Thailand
-4.0%
negative
Indonesia
Asian Weighted Average(Based on LIFE weights)
25.75%
Exhibit 19
Return/Risk Characteristics with Forecasted Returns
0.025
* ++K,Sing,Jap + Sweden
0.020
* Aust,Fr* Belgium
* Phillipines
* Norway
0.015
0'.010
+Neth
* USA
+UK
0.005
0.000
0.C
-A-
-----------------4
2.000
ThailE
* Spain
++ Austria, Switzerland
4.000
6.000
8.000
10.000
12.000
14.000
)00
Malasia, lndon sia
* Germany
-0.005
Standard Deviation (Based on Historical Data)
Exhibit 20
Efficient Frontier Based on Forecasted Returns
2.50
** HK,Sing,Jap * Sweden
2.00
+ Norway
* Australia, France
1.50
1.00
* Netherland, USA
* UK
0.50
+ Switzerland
-- +-+-4---
0.00
2.00
0.
4.00
6.00
--
++
8.00
+ Germany
-0.50
Standard Deviation (Based on Historical Data)
10.00
12.00
Exhibit 21
Points on Efficient Frontier Based on Estimated Returns
Eff. Frtr
Eff. Frtr
Eff. Frtr
Eff. Frtr
Australia
Canada
England
France
Germany
Hong Kong
Italy
Japan
Netherlands
Norway
Singapore
Sweden
Switzerland
USA
StdDev
2.00
3.50
5.00
6.50
3.78
7.67
5.98
3.81
0.52
10.37
6.53
10.41
3.00
10.09
10.60
12.31
2.15
4.40
Return
0.85
1.82
2.09
2.33
1.58
0.00
0.96
1.59
-0.33
2.33
0.00
2.33
0.96
1.58
2.33
2.33
0.33
0.96
StdDev3.5
Portfolio Return
Portfolio Variance
Portfolio Std.Dev.
Portfolio Weights
0.00%
Australia
0.00%
Canada
0.00%
England
29.71%
France
13.15%
Germany
0.00%
Hong Kong
0.00%
Italy
2.97%
Japan
28.16%
Netherlands
0.00%
Norway
0.00%
Singapore
0.00%
Sweden
26.01%
Switzerland
0.00%
USA
Portfolio Return
Portfolio Variance
Portfolio Std.Dev.
Portfolio Weights
32.26%
Australia
0.00%
Canada
England
France
Germany
Hong Kong
Italy
Japan
Netherlands
Norway
Singapore
Sweden
Switzerland
USA
StdDev6.5
StdDev5
StdDev2
0.00%
36.59%
0.00%
7.01%
0.00%
11.16%
0.00%
0.00%
8.09%
4.89%
0.00%
0.00%
1.82
12.26
3.50
Portfolio Return
Portfolio Variance
Portfolio Std.Dev.
Portfolio Weights
32.55%
Australia
0.00%
Canada
0.00%
England
0.00%
France
0.00%
Germany
17.46%
Hong Kong
0.00%
Italy
23.54%
Japan
0.00%
Netherlands
0.00%
Norway
15.39%
Singapore
Sweden
11.06%
0.00%
Switzerland
0.00%
USA
2.09
25.01
5.00
Portfolio Return
Portfolio Variance
Portfolio Std.Dev.
Portfolio Weights
0.00%
Australia
0.00%
Canada
0.00%
England
0.00%
France
0.00%
Germany
24.08%
Hong Kong
0.00%
Italy
41.37%
Japan
0.00%
Netherlands
0.00%
Norway
20.71%
Singapore
13.84%
Sweden
0.00%
Switzerland
0.00%
USA
2.33
42.26
6.50
reason for the absence of the U.S. from any portfolios is evident from Exhibit 20.
Australia and France dominate the U.S. with substantially higher returns and virtually the
same level of risk. The Netherlands dominates the U.S. with a substantially lower level
of risk and the same return.
3.4.2.2 Efficient Frontier Based on Regional Returns.
Some investors may be interested in looking at a diversified portfolio made up of
representative investments in Europe, Asia and the U.S.. I computed an efficient frontier
made up of investments in these three regions, using the weighted average expected
returns for each region shown in Exhibit 18 and the historical standard deviations and
correlation coefficients computed from the GPR-LIFE indexes for Europe, Asia and the
U.S.. This efficient frontier is shown on Exhibit 22. Exhibit 23 shows the portfolio
weightings of the points on this efficient frontier. As might be expected, Europe is
prominent at the low end of the risk spectrum, Asia is prominent at the high end of the
risk spectrum and the U.S. is prominent throughout the lower and middle levels of risk.
Exhibit 22
Regional Efficient Frontier Based on Forecasted Returns
2.50 r-
Asia
2.00
1.50
1.00
* USA
* Europe
0.50 1
0.00
Standard Deviation(Based on Historical Data)
Exhibit 23
Points on Regional Efficient Frontier Based on Estimated Returns
Eff Frtr
Eff Frtr
Eff Frtr
Eff Frtr
Asia
Europe
USA
StdDev
2.31
4.01
5.01
6.01
7.59
2.71
4.40
Mthly Return Annlzd Return
9.02
0.75
15.15
1.26
18.00
1.50
20.74
1.73
25.75
2.15
8.08
0.67
11.50
0.96
Portfolio Return
Portfolio Variance
Portfolio Std.Dev.
Portfolio Weights
0.00%
Asia
72.43%
Europe
27.57%
USA
0.752
5.335
2.310
Portfolio Return
Portfolio Variance
Portfolio Std.Dev.
Portfolio Weights
Asia
33.69%
Europe
33.69%
32.62%
USA
StdDev6
StdDev5
StdDev4
StdDev2.3
1.262
16.080
4.010
Portfolio Return
Portfolio Variance
Portfolio Std.Dev.
Portfolio Weights
49.89%
Asia
Europe
17.75%
USA
32.35%
1.500
25.100
5.010
Portfolio Return
Portfolio Variance
Portfolio Std.Dev.
Portfolio Weights
65.42%
Asia
2.48%
Europe
32.10%
USA
1.728
36.120
6.010
CHAPTER 4- CONCLUSION
An analysis of recent literature and historical data reveals that international diversification
can improve the performance of a portfolio of real estate securities by reducing risk.
Generally, the correlations of the various countries' returns from real estate securities are
sufficiently low that diversification will reduce portfolio risk. An analysis of the GPRLIFE indexes since 1984 shows that no two countries have had monthly returns with a
correlation coefficient exceeding .5. The historically low correlations of international
real estate returns can be attributed to the local nature of real estate markets. Efficient
frontier analysis using historical data shows how appropriate diversification would have
improved portfolio performance across most levels of risk.
This finding must be qualified by the facts that, in general, the correlation coefficients are
substantially higher when computed from 12 month rolling returns than from monthly
returns and the correlation coefficients were higher in the second half of the time series
than in the first half. It is likely that correlation coefficients among the various countries
would generally increase over time due to: (i) increasing global integration of economies,
(ii) increasing global integration of national and regional capital markets and (iii)
increasing similarity of governmental policies in various countries, associated with the
growing worldwide acceptance of market-oriented policies. An accurate determination
regarding the actual current benefits of international diversification requires an estimate
of the current correlations among real estate returns in various countries. Such an
estimate would be based on an evaluation of historical correlations, trends of correlations
and factors which may be affecting current correlations, including economic and political
factors.
International investing can also increase portfolio returns by broadening the field of
investment opportunities. An international investor would have the advantage of being
able to choose among countries with different risk/return characteristics and which are at
different points in market cycles. An analysis of historical data has indicated that: the
more mature markets in Western Europe, the United States, Australia and New Zealand
have exhibited relatively low risk, low return characteristics; the Scandinavian countries,
the Iberian countries and the more developed Asian countries (Japan, Hong Kong,
Singapore) have exhibited higher risk, higher return characteristics; and the emerging
markets (Argentina, Malaysia, Indonesia, Thailand and Mexico) have exhibited high risk,
with a wide variety of returns. In general, for a fund manager with superior ability to
identify exceptional investment opportunities, an increase in the number of potential
markets available for investment should increase the number of exceptional investments
in the portfolio, thereby improving portfolio performance through higher expected
returns.
Efficient frontier analysis using historical standard deviations and correlation coefficients
and forecasted returns shows well-diversified efficient portfolios, with substantially
improved performance compared with investments in individual countries. The actual
performance of a global investment strategy is dependent on the skill of the portfolio
manager in identifying exceptional investment opportunities and forecasting returns.
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