GLOBAL FTSE EPRA / NAREIT - IDENTIFY ANALYZE QUANTIFY - REIT Risk Model
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GLOBAL FTSE EPRA / NAREIT REIT Risk Model IDENTIFY ANALYZE QUANTIFY NORTHFIELD
Aug-25-2015
Global FTSE EPRA / NAREIT REIT Risk Model
Table of Contents
INTRODUCTION .............................................................................................................................2
MODEL DEVELOPMENT ..................................................................................................................3
MODEL STRUCTURE ......................................................................................................................5
REGRESSION.................................................................................................................................7
STOCK SPECIFIC RISK ....................................................................................................................8
REIT UNIVERSE ............................................................................................................................9
FACTOR VARIANCE ADJUSTMENTS ............................................................................................... 10
MODEL TESTING ......................................................................................................................... 10
WHY NORTHFIELD IS RIGHT FOR YOU ............................................................................................ 12
Powerful, Integrated, Consistent & Comparable Risk Models ....................................... 12
Open Models: Open Systems. No Black Boxes! ............................................................. 12
Global, Regional, Country & Asset Coverage ................................................................. 12
Sophisticated, Flexible, Robust, Open Analytical Systems ............................................ 12
Partners .............................................................................................................................. 12
Innovation .......................................................................................................................... 12
Excellent Training, Support and Solutions ...................................................................... 12
1 www.northinfo.comGlobal FTSE EPRA / NAREIT REIT Risk Model
Introduction After originating in the United States in 1960, Real Estate Investment Trusts
(REITs) were launched in Australia in 1971, Canada and Brazil in 1993, but
only relatively recently in Asia: for example in Japan in 2001, Singapore in
2002, and Hong Kong in 2005, and Europe: Bulgaria in 2004, and the UK in
2007. Various other countries such as Germany and India have also launched
public REITs. The United States remains the largest REIT market with
approximately one third of the world’s listed property market.
France, Japan, Australia, Canada, and the UK make up another 40% of the
global market. Australia remains the most active secondary public property
market behind the U.S. with a growing number of property companies
expanding through offshore property acquisitions in order to diversify and to
spend surplus capital which is the bane of any REIT. Investing overseas also
allows their shareholders to effectively escape the tax and management
headaches of foreign investing while simultaneously reaping the benefits of
the REIT tax structure. Cross-border investing also takes place in Europe,
although it is more common for continental REITs to stay on the mainland
and shy away from the UK and the same is also the case in reverse.
Canadian REITs are also making investments in the U.S. Like their Australian
counterparts, the impetus is to gain economies of scale and improved
diversification that they cannot achieve by limiting their investment choices
to their home countries. This makes Australian, European, and Canadian
REITs different than their counterparts in the U.S.
The REIT concept is relatively simple and straightforward inasmuch as REITs
were designed to provide the average investor an opportunity to secure the
benefits of income-producing properties. In the U.S., these benefits included
the ability to purchase interests in companies with professionally managed
properties, the potential to create diversified property portfolios by investing
in companies that span across property types and geographies, and a strong
dividend stream since the enabling legislation required that 90% of a REIT’s
funds from operations (FFO) be distributed to shareholders on a pre-tax
basis. Virtually all countries have modeled their enabling legislation based on
the U.S. model such that similar benefits have inured investors around the
world.
Despite being in the real estate sector, REITs are traditionally low leverage
vehicles with gearing ratios ranging from 35% to 50% in most countries
depending on cyclical factors. These leverage ratios are comparable to what
conservative “core” institutional investors use when buying property. REITs
can be sector or geographic-specific, although in recent years the tendency is
for large sector-specific vehicles.
The Northfield Global FTSE EPRA/NAREIT REIT Risk Model is a multi-factor
risk model developed specifically for the Global Real Estate Investment Trust
market. It relates a security’s return to a set of pervasive factors determined
to explain the covariance among global REITs. The model is solidly founded
on the classification of global REITs into different sector and regional
2 www.northinfo.comGlobal FTSE EPRA / NAREIT REIT Risk Model
segments constructed using FTSE EPRA/NAREIT Indices. For more
information about FTSE EPRA/NAREIT indices please visit FTSE website at
www.ftse.com.
The model is a sophisticated tool which, when used in conjunction with
Northfield’s optimizer, allows the user to monitor the active exposures of
their portfolios relative to a benchmark, and to construct portfolios according
to their risk/reward preferences, although it can be used in conjunction with
any optimization tool, as none of the file formats are proprietary. Please
contact your nearest Northfield office for further information about the
models, data file formats, and related analytical tools.
Model Northfield Information Services employs linear factor models as our preferred
method of estimating, analyzing, and controlling risk. Risk for our purposes
Development
is defined as return volatility (the annualized standard deviation of returns)
which can be estimated in either absolute terms or relative to a benchmark
market index. The term tracking error is often used for benchmark relative
volatility. Other measures of risk such as parametric Value-at-Risk can be
derived from the volatility value. As risk management is focused on future
events, the models are calibrated so as to have the greatest accuracy in
predicting future realizations of tracking error, rather than to maximize the
model’s power in explaining portfolio returns in the past over some historic
observations period.
Northfield’s decision to build standalone U.S. and Global REIT models comes
in large part from academic research which supports our explicit choice of
risk factors and reinforces the importance of independent factor models for
this asset class. Successful applications of multi-factor models to U.S.
commercial real estate have a long history going and include papers by Chan,
Hendershott and Sanders (1990), a macro factor model by Karolyi and
Sanders (1996) which included factors such as inflation, bond term, and
default risk, Ling, Naranjo, and Ryngaert (2000), as well as the Northfield U.S.
REIT Model (1996). On the international front, studies by Eichholtz,
Huisman, Koedijk, and Schuin (1998), Liu and Mei (1996), and Ling and
Naranjo (2002) identify global market risk as well as country/region-specific
market risk, but do not explore whether these market risks are related to
fundamental or economic risk factors. Lin and Naranjo as well as Eichholtz et
al., and Case, Goetzmann, and Rouwenhorst (1999) demonstrated a strong
global REIT market factor as well as country/region factors.
Risk models are statistical models that employ a common set of themes or
“factors” that affect the performance of the securities that are being
analyzed. The models measure the volatility of security returns associated
with chosen factors, the expected correlation between the factors, and the
sensitivity or “exposure” of each security to each factor. In addition, the
idiosyncratic (firm specific) portion of each security’s observed volatility is
also evaluated. The model’s output allows the user to quantify the expected
risk of a particular security or a portfolio of securities over a future time
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period, given the potential distribution of factor outcomes, or across a set of
specific user-defined scenarios.
While not the only methodology available to measure risk, factor models
have certain structural and statistical advantages over other techniques. By
correlating security returns to structural (industry, region, property type, etc.)
or macroeconomic variables (e.g. interest rates or GDP), linear factor models
produce a host of valuable statistics necessary for both security and portfolio-
level analytics. For example, investors could choose to tilt their portfolio
towards or away from a particular strategy by over or underweighting their
exposure to a risk factor. Such models are also convenient and informative
for attribution analysis of past portfolio returns. How well did my portfolio
perform relative to the benchmark because of my property type selection?
Factor models are a better predictor of portfolio risk than simply observing
past volatility because the factor structure filters out historical events that are
unlikely to be repeated in the future. Finally, factor models also produce
covariance matrices among the securities that are a key input to most
methods for allocating amounts of capital to particular assets within a
portfolio.
There are three basic approaches to estimating factor models (cross-
sectional/fundamental, time series/macro, and statistical). In time series
models, we chose the factors (e.g. GDP) so we observe the behavior of the
factors over time, and make clear assessments of factor relationships. In
this type of model, we must use statistical methods such as regression
analysis to estimate the level of exposure (or beta) of a particular security to
a given factor. In cross-sectional models, we chose factors for which the
exposures can be observed for each security at each moment in time (e.g.
market capitalization). For these models we use statistical methods to
estimate the returns associated with each factor during time period and
eventually understand the return relationships between factors. In purely
statistical models, we don’t choose the factors at all, but assume that a set
of unobservable factors exists. We can then jointly estimate both the factor
exposures and the factor return behaviors over time using mathematical
procedures, without ever defining what the factors represent in the real
world.
Each method has its strengths and weaknesses. Cross-sectional factor
models only use historical observations of factors and hence can incorporate
new securities more accurately than time series models. The main
disadvantage is that if market conditions change any inaccuracy in the model
is likely to manifest in the factor relations (the factor covariance matrix). This
will result in biased risk assessments irrespective of whether the portfolio is
well diversified or highly concentrated.
Time series models use historical observations at the security level and
assume that a security’s exposure to a factor is stationary over time. To the
extent these assumptions lead to inaccuracies, such errors only impact one
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security at a time and will tend to diversify away as the portfolio becomes
more diverse. Another advantage of time series models is that they allow
every security to have its own exposure to industry membership variables
that are often treated as binary (you are either in or not in a particular group)
in cross-sectional models. Both time series models and cross-sectional
models involve statistical estimation that can impact the accuracy of the
estimates and therefore care must be given to avoid these problems when
estimating any factor model. 1
The advantage of purely statistical approaches to factor modeling is that they
use only blind mathematical relationships to measure factor exposures.
Therefore these models have no priors with respect to what factors may or
may not be important at a given moment in time. They are also good tools
for capturing transient short-term trends in the market conditions. The
disadvantage of statistical models is the explicit assumption that the future
will be exactly like the past observation period. In addition, statistical models
do nothing to add to our intuitive understanding of source of portfolio risk,
since the factors are never defined.
Starting about ten years ago, Northfield began the use of “hybrid” models
where we combine the time-series and statistical model approaches. First,
we select defined factors that we believe are appropriate and likely to be
relevant to investor risk across all time periods. We then take the residual
portions of the observed security returns that are not explained by our
factors, and build a statistical model of any latent factors found in the
residuals to capture any transient effects. Adoption of the hybrid approach
for this model provides both the intuitiveness of a specified factor model,
while insuring that no significant factors are omitted.
Numerous back tests for sample period lengths and observation frequencies
looking for a model that would accurately predict the ex-post tracking errors
at various points in history were performed. The tests consisted of
constructing random portfolios of different sizes and optimizing them versus
a benchmark, thus generating ex-ante estimates of tracking errors. The
realized out of sample tracking errors were then computed.
Model Structure The model relates each security’s return time-series to the returns of a global
real estate market index factor, a global sector-grouping index factor, a size
factor, a regional index factor and a currency factor. We have used weekly
security and factor return data to construct the model. In order to estimate
the regression coefficients for each security, we use a historical window
1
Multicolinearity occurs when two variables in a time series regression are highly correlated. Economic data are highly
susceptible to this condition since they tend to be influenced by the same forces as well as interact. For example,
population and real GDP are highly correlated. Including both of them as explanatory variables in a regression explaining
shoe sales would most likely lead to colinearity problems, since either variable would be highly correlated with shoe
sales. If the problem is great enough, it can affect the precision of the estimators and therefore lead to biased results.
Heteroskedasticity occurs when the error term does not have a constant variance. In cross-sectional data this often
occurs when there are outliers in the data or the data is stratified; the classic example being data with small and large
firms.
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spanning the preceding 104 weeks. The model is updated on a monthly
basis. The model covers all the constituents of FTSE EPRA/NAREIT Index.
Mathematically, the structure of the model is as follows:
R = C + βmkt*Global REIT Market Factor + βind*Sector Factor +
βsze*Size Factor + βrgn*Regional Factor + βst1*Statistical Factor1 +
βst2*Statistical Factor2 + βst3*Statistical Factor3 + βst4* Statistical
Factor4 + βst5* Statistical Factor5 + βcrn*Currency Factor + ε
Where
• R = Security Return
• C = constant
• Global REIT Market Factor = Return on FTSE EPRA/NAREIT Market
Index
• Sector Factor = Residual return on FTSE EPRA/NAREIT Sector index
• Size Factor = Return spread between the top quartile and bottom
quartile of the global REIT market
• Regional Factor = Residual return on FTSE EPRA/NAREIT regional index
• Statistical Factor1-5 = Return on statistical factors resulting from PCA
• Currency Factor = Return on security’s denomination currency against
U.S. Dollar
• ε = error term
Global REIT Market factor represents return on FTSE EPRA/NAREIT Global
Index. This factor is constructed using the same weights for each security as
in FTSE EPRA/NAREIT global index. This is the first factor in the model
against which security returns are regressed. Each security is then regressed
against one of the ten sector factors.
It should be stressed that even though there are ten such groupings, each
security only participates in one. For a REIT to be included in one of the ten
property sectors, more than 75% of its gross invested book assets have to
be invested in that sector. For a REIT to be included in the diversified sector
more than 75% of its invested assets need distributed among nine defined
sectors. The list of FTSE EPRA/NAREIT sectors is as follows:
1. Diversified
2. Healthcare
3. Self-Storage
4. Industrial
5. Office
6. Residential
7. Retail
8. Lodging/Resorts
9. Specialty
10. Industrial/Office Mixed
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Each security is also assigned one of the three global REIT regions. A
particular security also participates in only one of the three regions. Global
REIT sectors and regions are defined according to FTSE EPRA/NAREIT
indices. Each security’s weight in global and regional factors is directly
obtained from FTSE EPRA/NAREIT real estate global sector and regional
indices.
Below is the list of three FTSE EPRA/NAREIT regions:
1. Europe
2. Asia
3. North America
Each sector factor return represents the residual return of FTSE
EPRA/NAREIT sector index. Residual return is return of each sector factor
that cannot be explained by the market index factor. It is obtained by running
a simple regression of each FTSE EPRA/NAREIT sector index against FTSE
EPRA/NAREIT global index individually. Returns on size factor are obtained
by creating two indices representing top and bottom quartiles of the global
REIT market. Size factor returns are equal to top quartile minus bottom
quartile. All the securities in the top and bottom quartile indices are equally
weighted. Regional factors represent residual returns on FTSE EPRA/NAREIT
regional indices. Residual return on each regional factor is calculated the
same way as with sector factors. Please note that all returns are total returns
which include dividends as well as price change. Statistical factor returns are
estimated by performing a Principal Components Analysis on the residuals
remaining after the preceding series of regressions against all the other
factors. Each currency factor represents return of each currency against U.S.
Dollar.
Regression We use 104 weekly return data points to estimate the security regression
betas. All data points are equally weighted – meaning that each historical
observation is given the same weight or significance. We require at least 10
weeks of return data for a security to be included in the regression and have
beta estimates to each factor. If a security has less than 10 weeks of return
data it is not included in our estimates. For securities that have more than 10
weeks of return history but still less than 104 weeks, we use an additional 50
weeks of filled-history using industry averages data which is then used to
estimate factor exposures. We first perform a multiple regression in which
each security’s return is regressed against Global REIT Market Factor, one of
the ten REIT Sector Factors and REIT Size Factor. This gives us βmkt, βind
and βsze.
Estimating the Global REIT model is a three step process. We first regress
the individual securities against the FTSE EPRA/NAREIT Market Index to
obtain beta estimates to the market index. Using the residuals from this first
regression, we then estimate a second regression which includes the three
REIT regional factors to which a security belongs as well as the size factor.
This result is our beta estimate to the regional factor (i.e. βrgn).
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The residuals from the second regression are then used to create the
covariance matrix that is then employed in the final step: the estimation of
the Statistical Factors using Principal Components Analysis (PCA). Note that
only those securities that have a complete history of 104 weekly returns are
included in Principal Components Analysis. The PCA results in a time series
(104 weeks) of five Statistical Factor returns. Each security’s beta sensitivity
to each of the five statistical factors is then estimated.
We run five simple regressions, each one regressing residuals from previous
regression against each of the five Statistical Factors. This results in βst1,
βst2, βst3, βst4, and βst5. Note that each security is exposed to all of the
five statistical factors. Factor sensitivity to a currency factor is not estimated
through a regression and always assumed to be 1 (i.e. βcrn = 1) to the
security’s home currency, and 0 to all other currencies.
Stock Specific The security-specific risk for each security is calculated by taking the
standard deviation of the residual return remaining after the estimation of the
Risk
statistical factors described above. For security’s that received industry
average data to complete a sufficient history, we upwardly adjust security-
specific risk by a multiplier consisting of the square root of the ratio of total
history required to the amount of real historical returns actually available. For
example if security had 40 available returns and 20 were patched industry
averages, we upwardly adjust the residual risk by 1.22 which is square root
of 1.5 = 60 ÷ 40. We make one further adjustment to stock specific risk by
adopting the Parkinson volatility estimator. In the presence of serial
correlation, heteroskedasticity, and fat tails in time-series data, the Parkinson
volatility estimator is a better measure of historical volatility than traditional
measures. In this context “better” means “larger”. The Parkinson method
utilizes a function of the high and low price recorded over a particular time
period to measure volatility without forcing any distributional assumptions.
This is in contrast to the Normal i.i.d. assumptions that underlie the more
common use of standard deviation of period end price-changes upon which
traditional return based volatility measures are based. Details of the
Parkinson estimator can be found in “The Extreme Value Method for
Estimating the Variance of The Rate of Return;” Journal of Business; 1980; v
53(1); 61-66. We calculate the Parkinson estimator, P, using high and low
prices as follows:
Where:
P = Parkinson volatility estimator
N = number of highs and lows
Hi = High price
Li = Low price
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To apply the Parkinson estimator to our risk model, we first estimate the
total risk using our regular factor model including the stock-specific risk. We
then estimate the Parkinson estimator for each security. In cases where P is
higher than our risk model estimate, we upwardly adjust the stock specific
risk to reflect the higher estimate from Parkinson method.
REIT Universe As of November 2010 our Global FTSE EPRA/NAREIT REIT risk model
covered about 368 globally traded REITs. This includes all the REITs included
in the FTSE EPRA/NAREIT global index. The following table represents
geographical distribution of all REITs by country:
Country REITs
Australia 14
Belgium 6
Brazil 14
Canada 20
China 11
Egypt 1
Finland 3
France 9
Germany 8
Greece 3
Hong Kong 19
India 9
Indonesia 7
Israel 1
Italy 2
Japan 21
Malaysia 13
Mexico 5
Netherlands 7
Norway 1
New Zealand 1
Austria 2
Philippines 6
Poland 2
South Africa 7
Singapore 15
Spain 1
Sweden 6
Switzerland 4
Thailand 10
Turkey 3
Taiwan 1
United Arab Emirates 2
United Kingdom 30
United States 104
Total 368
9 www.northinfo.comGlobal FTSE EPRA / NAREIT REIT Risk Model
Factor Variance Efficient market theory suggests that mean alphas (returns net of market
risk) to a particular factor should be close to zero over time. However, in a
Adjustments
bubble or trending market, a particular factor may exhibit a high mean return,
with low variance around the mean for a substantial period of time. For this
reason we estimate factor variances using the average of the squared value
of the factor returns over the sample period. This is equivalent to assuming
that the mean is zero in the usual formula. Empirically, most factor returns do
have a mean close to zero, so the change will not be noticeable. However,
when a factor return is consistently large and of one sign (i.e. positive returns
to the internet factor during tech bubble), this procedure will inherently bias
the factor variance values upwards to provide a warning of the unusual factor
behavior.
We also employ a weighting scheme while estimating factor variances. Since
most recent observations are more relevant than past observations, we
weigh newer data points more heavily than older ones. To accomplish this,
we use e-nr scaling, where n ranges from 1 to T for 1 is the newest
observation and T is oldest and r is the decay rate. This algorithm results in
giving more weight to newer observations while giving less weight to older
data points. We use a decay rate of 0.015 for 104 weekly factor returns. The
concept of Half Life is relevant in the discussion of decay rates. The half-life
of a quantity whose value decreases over time is the interval required to
decay the quantity to half its original value. In the discussion of weighing
observations, half-life would be the time interval required to decay the
weight to 0.5 from the original weight of 1 (i.e. to reduce it by half). With the
decay rate of 0.015 and a total of 104 weekly observations, the half life is 47
weeks.
Model Testing The Northfield Global FTSE EPRA/NAREIT REIT model was thoroughly tested
by comparing realized and estimated risk numbers. The model was tested for
the period 12/31/2006 to 5/31/2008. We created 100 portfolios each month
and compared their estimates and realized risk both at absolute and relative
levels. Each portfolio was comprised of 25 to 125 randomly selected Global
REITs. Our benchmark represented the total Global REIT market as defined
by the FTSE EPRA/NAREIT Global Market Index. Each month we estimated
total and active risk of portfolios based on Northfield’s Global FTSE
EPRA/NAREIT REIT model. We then calculated realized absolute and active
risk numbers based on the next 12 months of active and absolute portfolio
returns. We repeated the experiment for each month starting from
12/31/2006 and ending on 12/31/2007.
10 www.northinfo.comGlobal FTSE EPRA / NAREIT REIT Risk Model 11 www.northinfo.com
Global FTSE EPRA / NAREIT REIT Risk Model
Why Northfield
is right for you
Powerful, Northfield’s family of risk models has been helping clients construct and
Integrated, analyze portfolios in many countries across the world for over 15 years. The
Consistent & risk models are based on sound theoretical and academic foundations. They
Comparable Risk are clear, intuitive, informative and comparable. Diverse portfolios can be
Models analysed, using appropriate metrics, relative to standard and or customised
benchmarks. Sources of systematic and security specific risk are identified
quickly, clearly and easily.
Open Models: Open Northfield maintains a philosophy of openness and partnership with our
Systems. No Black clients. Northfield offers and supports “glass boxes” – there is nothing
Boxes! hidden. Should you want to know the full detail of how a model is put
together, we will tell you, clearly. Northfield is not in the “black box”
business.
Global, Regional, The coverage of assets in the Northfield family of risk models is huge. From
Country & Asset the Everything Everywhere (“EE”) global fixed income and equity risk model,
Coverage to the Global, Single Country / Regional, and specialist equity risk models,
coverage includes over 57,000 equities and about 400,000 fixed income
instruments. Additional EE data coverage includes 1,100,000 U.S. muni
bonds, 1,000,000 mortgage backed securities and agency pass-throughs, and
100,000 U.S. collateralized mortgage obligations and asset backed securities.
Should your portfolios contain assets not included in the system (private
equity holdings, very new IPO’s etc. etc.) we give you the tools and
understanding to add them yourself.
Sophisticated, “Just like it says on the box” - Northfield systems are flexible, robust and
Flexible, Robust, open. Inputs can be managed and changed to reflect your views. Output can
Open Analytical be saved as text files and used in any manner of your choosing. Available on
Systems the PC, Unix, Linux and multiple partner platforms, Northfield’s analytical
tools are widely respected for their reliability and functionality.
Partners Northfield has partnered with selective business information services
companies to enhance clients’ ability to access Northfield analytics via
multiple platforms. Northfield partners include FactSet, ClariFi, Quantitative
Services Group, SoftPak, Thomson Reuters and others.
Innovation Northfield constantly strives to add more useful features and functions for
your use. Examples of recent innovation include: The ability to manage long-
short hedge funds appropriately as a single entity, accurately and
conveniently managing composite assets as part of a portfolio, the ability to
manage non-linear transaction costs during the optimization process.
Excellent Training, Northfield staff attentively assist customers with excellent training and
Support and support, based on many years experience.
Solutions
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