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Are REITs a Distinct Asset Class?

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  • Buckingham Strategic Wealth

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Are REITs a Distinct Asset Class?
Jared Kizer, CFA
Chief Investment Officer, Buckingham Asset Management, LLC
8182 Maryland Avenue Suite 500 St. Louis, MO 63105
jkizer@bamadvisor.com - (314) 743-2204
Sean Grover
MBA student, McDonough School of Business, Georgetown University
December 6, 2017
Abstract
Real estate investment trusts (REITs) are often considered to be a distinct asset class.
But, do REITs deserve this designation? While exact definitions for asset class vary,
a number of statistical methods can provide strong evidence either for or against the
suitability of the designation. The authors step back from the established real estate
and REITs literature and answer this broader question. Beginning with a set of asset
class criteria, the authors then utilize a variety of statistical methods from the litera-
ture and factor-based asset pricing to evaluate REITs for their candidacy as a distinct
asset class. REITs fail to satisfy almost all of the relevant criteria leading the authors
to conclude that REITs, in fact, are not a distinct asset class but do deserve a market
capitalization weighted allocation in a diversified investment portfolio.
Please send any comments to jkizer@bamadvisor.com. This analysis is for academic purposes
only. The research, opinions and data shared within this paper are those of Mr. Kizer and
Mr. Grover and do not directly reflect those of Buckingham Asset Management, LLC.
Many investors think of real estate investment trusts (REITs) as a distinct asset class be-
cause, in aggregate, they have historically had relatively low correlation with both stock and
bond markets. However, this is a far too simplistic definition for what defines a distinct asset
class. Many individual stocks have low correlation with the overall stock and bond markets,
yet no one would (hopefully) consider a single stock, or a small handful of stocks, to be an
asset class. For individual equities, a better definition would be a well diversified portfolio
of securities that has historically demonstrated statistically significant excess return relative
to what is explained by a generally accepted factor model like the Carhart [1997] four-factor
model. For example, early research on the size and value premiums argued that these two
types of equity securities are distinct equity asset classes because their excess returns were
not fully accounted for by the CAPM.
On a relative basis, public REIT equities are a young investment vehicle. The REIT Act
title law of 1960 allowed the creation of REITs and accordingly, the ability for investors to
gain access to diversified real estate portfolios. The first REIT was formed shortly thereafter
and the first public REIT debuted in 1965.1Early research into public real estate invest-
ment, such as Webb and Rubens [1987], tends to use appraisal-based individual property
data and suggests that real estate provides diversification benefits for traditional stock and
bond portfolios. Following the growth of the industry and accumulation of sufficient returns
histories, REIT indexes debuted. Subsequent studies often used REIT indexes, tending to
confirm earlier findings concerning diversification benefits and suggesting sizable portfolio
allocations.
There is an important distinction to be made here as broad real estate and REITs are not
synonymous. REIT indexes are better suited for research purposes as they feature up-to-
date pricing and do not exhibit the positive autocorrelation found in appraisal-based series.
1reit.com
1
Gyourko and Keim [1993] demonstrate this and actually find that REITs are highly corre-
lated with the S&P 500 Index. Much of the relevant research makes the distinction that
REITs data is used as an imperfect proxy for real estate or in conjunction with other mea-
sures. Notable examples from the literature that use REIT data in this manner, with results
in support of real estate as a portfolio diversifier, are Goetzmann and Ibbotson [1990] and
Hudson-Wilson et al. [2005]. But many pieces implicitly treat REITs as a near-perfect sub-
stitute for real estate or explicitly treat REITs as an asset class. For example, using a
mean-variance framework, Feldman [2003] suggests a 12 percent allocation to REITs in a
balanced portfolio of global developed country equities and US government bonds. With a
finding nearer to the market capitalization weight of U.S. REITs, Mull and Soenen [1997],
using a nonparametric technique, suggest a REIT allocation of 2.2 percent in a US stock
and bond portfolio. Whether implicit or explicit, the sentiment and results of these works
has taken root in practical application, especially in the large and growing indexing and
evidence-based management spaces; consider for example the Vanguard REIT Index Funds
and ETF which, as of early 2017, collectively hold nearly 100 billion in assets representing
about 13 percent of the MSCI U.S. REIT Index.2
As mentioned, it is not surprising that individual REITs, or a small handful of REITs,
would improve a portfolio from a CAPM perspective, as many individual equities would do
the same. Further, so long as REITs are not perfectly correlated with a chosen benchmark
portfolio and have a similar Sharpe Ratio, the addition of REITs to that portfolio, in some
specific amount, will improve the original portfolio’s Sharpe Ratio. These are standard re-
sults from modern portfolio theory. Works attempting to determine an optimal allocation
to REITs and the diversification benefits of REITs are important for both academics and
practitioners but we think that the body of literature has skipped an important step. In
this study we step back from previous work and evaluate a more general question: should
2Bloomberg
2
public REIT equities be considered a distinct asset class? In this evaluation, we draw on
methodologies present in the literature but also utilize some more advanced techniques that,
to our knowledge, have not been applied to REITs in a diversified portfolio context. Our
results suggest that REITs themselves should not hold the distinct asset class moniker. The
main contribution of this article is the result that, on a statistically inferred basis, REITs
do not improve the mean-variance frontier of a standard benchmark stock and bond portfolio.
Section 2 of this paper reviews the data used in this evaluation. Section 3 presents a variety
of analytical procedures and key findings and Section 4 concludes.
Data
Focusing on a more comprehensive methodology and staying consistent with the body of
literature, we use standard benchmarks in our analysis. The Dow Jones U.S. Select REIT
Index, henceforth REITs, represents public REITs. The S&P 500 Index (SP500) and 5-
year Treasury bond (5YT) returns are the chosen representors of stock and bond markets,
respectively. Data for these indexes is obtained from Thomson Reuters Lipper. Returns for
12 other industries, U.S. equity market factor data and U.S. small-cap value (SV) returns
are obtained from Ken French’s data library. Long-term corporate bond (CORP) returns
and the investment grade default premium (IGDEF) are taken from Barclay’s Capital Live.
All data used is at a monthly frequency and all data, with the exception of IGDEF, begins
in January 1978 and ends in July 2017. The IGDEF series begins in August 1988.
Analyses
This research steps back from much of the REITs literature in that the goal is not to an-
alyze the extent to which REITs should be included in a generalized portfolio nor is it to
comment on the diversification benefits of REITs. Rather, we seek to provide a measured
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look at REITs qualifications for consideration as a distinct asset class. To do so, we utilize
an array of statistical techniques and relevant comparisons. The analysis begins with more
common techniques, such as correlation, to address the current literature and common in-
vestor views, but then moves to more advanced techniques to provide deeper insight and
add to the body of REITs literature. The first step though, is to define the term asset class,
as this definition frames the work that follows. The broad but typical definition for an asset
class is a group of similarly characterized securities whose behavior is similar in the market-
place and is distinct from other asset classes. Here, we already run into a circular definition
issue as a comparison to other asset classes is required. But if we establish more careful
criteria we can build a better definition. The criteria that we use to define an asset class
incorporates the broader definition, and common techniques of its measurement, but con-
siders more modern analytical finance techniques. While not perfect, the list below provides
a number of key criteria for asset class distinction and the frame of reference for this research.
1. Low correlation with established asset classes such as broad market equities and gov-
ernment bonds.
2. Statistically significant positive alpha with respect to generally accepted factor models.
3. Inability to be replicated, on a comovement basis, by a long-only portfolio holding
established asset classes.
4. Improved mean-variance frontier when added to a portfolio holding established asset
classes.
Correlation and Factor Analysis
Beginning with criteria one, our analysis first examines the historical correlation between
REIT returns and the returns of both the S&P 500 Index and 5-year Treasury bonds. Exhibit
1 presents these figures.
4
Exhibit 1: Monthly Correlations (January 1978–July 2017)
REITs SP500 5YT
REITs 1.00 0.58 0.07
SP500 0.58 1.00 0.07
5YT 0.07 0.07 1.00
We see that REITs have indeed had low correlation with stocks and bonds, particularly with
bonds. These simple but important results have led many investors to jump to the conclusion
that REITs are indeed a distinct asset class. But in reality, many sectors have had relatively
low correlations with stocks and bonds. Exhibit 2 shows an expanded correlation matrix
that includes the three series from Exhibit 1 but adds 12 other sectors from Ken French’s
data library. These sectors are defined based upon SIC codes and span the historical cross-
section of the U.S. equity market. A non-abbreviated listing is included in Exhibit 7 in the
appendix.
Exhibit 2: Monthly Correlations (January 1978–July 2017)
REITs SP500 5YT
REITs 1.00 0.58 0.07
SP500 0.58 1.00 0.07
5YT 0.07 0.08 1.00
BUSEQ 0.40 0.83 -0.04
CHEM 0.54 0.85 0.08
DURB 0.59 0.79 -0.05
ENRG 0.40 0.64 -0.03
HLTH 0.40 0.76 0.17
MANUF 0.61 0.92 0.00
MONEY 0.62 0.87 0.11
NDUR 0.52 0.80 0.20
OTHER 0.64 0.91 0.02
SHOPS 0.53 0.85 0.08
TELCM 0.39 0.77 0.08
UTIL 0.46 0.53 0.29
Focusing on the column of correlations with the S&P 500, observe that a number of other sec-
tors have had relatively low correlation with this index. In particular, ENRG and UTIL have
had correlations with the S&P 500 that are roughly similar to that of REITs at 0.64 and 0.53,
5
respectively. Using just correlation, one might argue that all three of these sectors are their
own asset classes. But as noted earlier, classification based on correlation alone is too simple.
Small capitalization and value stocks once presented researchers with a classification issue
as the one-factor CAPM could not adequately explain their respective excess returns. The
seminal Fama and French [1993] study expanded the CAPM to include size (SMB) and
value (HML) factors and ushered in the risk factor asset pricing era. Since, much research
has built upon and improved factor models, such as the Carhart [1997] four-factor model
which adds a momentum (UMD) factor. Researchers and practitioners alike now use factor
models extensively as a tool for examining cross-sectional asset returns. Compared to simple
correlation analysis, evaluating REITs in a factor model specification provides much more
advanced insight into the drivers of their return. Exhibit 3 presents the results of Carhart
four-factor regression analyses for REITs as well as each of the 12 sectors from Ken French’s
data library.
Exhibit 3: Carhart Four-Factor Analysis (January 1978–July 2017)
Alpha (bps) t-stat MKT t-stat SMB t-stat HML t-stat UMD t-stat R-squared
NDUR 373 2.6 0.78 28.3 -0.19 -4.7 0.13 3.1 0.06 2.2 64%
HLTH 420 2.4 0.80 24.4 -0.23 -4.9 -0.18 -3.6 0.08 2.4 60%
BUSEQ 286 1.8 1.12 36.2 0.22 4.9 -0.69 -14.4 -0.18 -6.1 83%
SHOPS 170 1.2 0.96 33.2 0.05 1.3 0.04 0.9 -0.02 -0.6 73%
TELCM 176 1.0 0.86 25.0 -0.19 -3.8 0.02 0.3 -0.08 -2.5 60%
UTIL 117 0.7 0.56 16.4 -0.24 -4.9 0.35 6.6 0.12 3.6 37%
CHEM 83 0.6 0.92 34.3 -0.16 -4.2 0.16 3.9 0.00 -0.1 73%
REITs 27 0.1 0.76 18.1 0.43 7.3 0.67 10.3 -0.07 -1.7 51%
MANUF 9 0.1 1.13 52.0 0.10 3.2 0.20 5.8 -0.07 -3.5 87%
ENRG -34 -0.1 0.89 18.6 -0.12 -1.7 0.34 4.6 0.10 2.1 43%
MONEY -130 -1.1 1.17 49.8 -0.09 -2.8 0.58 15.9 -0.06 -2.6 85%
DURB -259 -1.3 1.21 31.1 0.20 3.7 0.52 8.6 -0.26 -7.1 72%
OTHER -265 -2.7 1.10 56.4 0.21 7.5 0.15 5.1 -0.03 -1.6 89%
Exhibit 3 sorts the regression results by the t-statistic, from highest to lowest, of each series’
estimated annualized alpha from the Carhart four-factor specification. The intuition is that
statistically significant alphas may signify that the factor model is not able to sufficiently
explain the excess returns of a given sector and thus, could be evidence for considering a
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given sector to be a distinct asset class. With this consideration, there are three sectors
with statistically significant alphas, two of which are positive (NDUR and HLTH) and one
negative (OTHER). REITs, however, are not one of the three, with an alpha t-statistic of
only 0.1, which is close to a fatal blow in arguing that REITs should be treated as a distinct
asset class. Additionally, NDUR, HLTH and OTHER show sizable estimates of annualized
alpha compared to the 27 bps estimate for REITs. We do note that the REITs regression
shows the third lowest R-squared (51 percent) of the industries considered, UTIL and ENRG
being the two lower, which indicates a relative deficiency in the ability for the factor model
to explain the variance in REIT returns. But looking further into the regression results, it
could be argued that REIT returns are somewhat well explained by the Carhart four-factor
model in that they show statistically significant loading estimates for the equity market pre-
mium (MKT), SMB and HML, just as most of the 12 industries do.
Expanding on the four-factor model, Exhibit 4 presents a six-factor regression analysis for
REITs and each of the 12 sectors from Ken French’s data library. The two additional factors
are the TERM (5YT less the risk free rate) and IGDEF (investment grade-corporate bonds
less 5YT) premiums. The reason to include these two fixed income factors is that some equity
sectors may have exposure to fixed income oriented risks, given the underlying nature of the
businesses, and so explanatory power may be gained over the equity-only four-factor model.
Exhibit 4 shows the results from these regressions, which are again sorted from highest to
lowest estimated annualized alpha t-statistic.
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Exhibit 4: Six-Factor Analysis (August 1988–July 2017)
Alpha (bps) t-stat MKT t-stat SMB t-stat HML t-stat UMD t-stat TERM t-stat IGDEF t-stat R-squared
BUSEQ 363 1.9 1.26 29.5 0.20 4.0 -0.72 -13.3 -0.15 -4.4 -0.30 -2.3 -0.32 -1.9 84%
HLTH 384 1.9 0.77 16.3 -0.23 -4.2 -0.16 -2.7 0.07 1.9 0.16 1.1 -0.03 -0.2 52%
NDUR 290 1.8 0.72 19.0 -0.20 -4.5 0.13 2.8 0.02 0.5 0.34 2.9 -0.12 -0.8 58%
SHOPS 222 1.3 0.93 24.5 0.01 0.3 0.07 1.4 -0.04 -1.4 -0.12 -1.0 -0.42 -2.8 70%
CHEM 166 1.0 0.83 21.9 -0.17 -3.6 0.24 5.0 0.00 -0.1 -0.01 -0.1 0.02 0.2 66%
MANUF 107 0.8 1.08 35.6 0.07 2.0 0.27 7.0 -0.06 -2.5 -0.08 -0.8 0.24 2.0 86%
UTIL 57 0.3 0.42 8.6 -0.20 -3.4 0.32 5.2 0.12 3.1 0.66 4.4 0.78 4.0 35%
ENRG 32 0.1 0.69 11.0 -0.09 -1.2 0.38 4.8 0.09 1.7 0.03 0.2 0.85 3.4 40%
TELCM -8 0.0 0.98 21.5 -0.21 -3.8 -0.07 -1.2 -0.02 -0.5 0.01 0.1 0.07 0.4 67%
REITs -133 -0.5 0.60 10.1 0.41 5.8 0.71 9.4 -0.08 -1.7 0.76 4.1 0.96 4.0 51%
MONEY -124 -0.9 1.20 36.2 -0.11 -2.8 0.64 15.2 -0.06 -2.4 0.00 0.0 -0.22 -1.7 85%
DURB -260 -1.1 1.11 20.8 0.22 3.5 0.64 9.4 -0.24 -5.6 -0.14 -0.8 0.72 3.4 74%
OTHER -271 -2.4 1.06 41.5 0.14 4.5 0.22 6.7 -0.06 -3.0 -0.08 -1.1 -0.15 -1.5 88%
Interestingly, now only one industry (OTHER) has statistically significant annualized alpha
and the estimate is negative. Similar to the four-factor specification, the annualized alpha
estimated t-statistic for REITs is near zero. Also similar to the four-factor specification, the
R-squared figures are still relatively low for REITs but also for other industries including
ENRG, UTIL and HLTH. But the results in Exhibit 4 show that virtually all industries are
well explained by four equity factors and two fixed income factors; most have statistically
significant loadings on MKT, SMB and HML and many have statistically significant load-
ings on the TERM and IGDEF, including REITs which has statistically significant loadings
on all five. In consideration of industries with non-statistically significant annualized alpha
estimates and statistically significant factor loading estimates, the low R-squared ratios seem
to indicate diversifiable risks present in each industry, not uniqueness in underlying return
drivers. So, while the relatively low correlation with the S&P 500 Index and 5YT was en-
couraging, with respect to criterion two, the four- and six-factor regression models indicate
that REITs are likely not a distinct asset class, especially when compared to the results of
other industries.
Exhibit 4, however, provides us with other clues as to how the returns and systematic risk
characteristics of REITs could be replicated with standard long-only positions in stocks and
bonds. As mentioned, Exhibit 4 shows that REITs have positive and statistically significant
exposure to the SMB, HML, TERM and IGDEF premiums. This indicates that a certain
8
portfolio of small-cap value stocks and long-term investment grade corporate bonds should
be able to closely replicate the returns of REITs, from a comovement perspective.
Portfolio Replication
As a term, replication is a bit of a misnomer. The basic idea is to use optimization techniques
to identify a combination of assets that has historically behaved like a target portfolio or
strategy, with respect to returns comovement. However, rarely (if ever) will the identified
portfolio exactly replicate the returns stream of the target portfolio. Nevertheless, replication
is typically the term that is used so we use that convention. As noted in the prior section, the
six-factor regression analysis tells us that a portfolio of small-cap value stocks and long-term
corporate bonds should do a decent job at replicating the returns of REITs. With respect to
criterion three, a distinct asset class should not be easily replicated by a long-only portfolio
of established asset classes. The ability to replicate a security (or portfolio) with a broader
portfolio implies that the security is redundant in the given portfolio. For this reason, we
evaluate REITs on their ability to be replicated, as suggested by the six-factor regression
results.
We begin with returns for U.S. small-cap value stocks (SV) from Ken French’s data library
and the Barclay’s Capital Long-Term Corporate Bond Index (CORP). To attempt a repli-
cation of REITs returns with these two returns series, we specify a constrained least squares
regression and utilize linear optimization to minimize the objective function with respect
to the portfolio weights. The portfolio weights are designated by the vector w, we define
A= [ι, SVt, C ORPt] and B=REITtwhere ιis a ones vector and the subscript tdesignates
the month. We define the linear equality constraint matrix as u= [0,1,1]. The specified
objective function is shown below.
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ˆw=argmin
| {z }
w
(Aw B)2subject to: uw = 1 (1)
The ˆwthat minimizes the objective function produces a portfolio which allocates about 66
percent to SV and consequently 34 percent to CORP. This optimal replicating portfolio has
a monthly correlation with REITs of 0.72. Exhibit 5 presents other statistics that compare
this optimal replicating portfolio to REITs over this same time period.3
Exhibit 5: Monthly Return Summary Statistics (January 1978–July 2017)
REITs Portfolio
Average Return 1.11 1.19
Annualized Return 12.2 14.2
Annualized Std. Dev. 18.4 13.2
t-stat 3.0 4.6
Annualized Sharpe Ratio 0.48 0.74
Min. Return -32.4 -17.2
Max. Return 32.8 12.6
Max DD -70.5 -46.0
Skewness -0.7 -0.9
Kurtosis 10.7 5.9
% Neg. Periods 39 32
The statistics in Exhibit 5 are compelling. The replicating portfolio dominates REITs from
almost every imaginable angle. It earns higher compound returns, has lower volatility,
achieves a higher Sharpe Ratio, has lower kurtosis, and wins on most historical risk char-
acteristics. A skeptic might note that the replicating portfolio has 34 percent allocated to
long-term corporate bonds during a period where interest rates have declined significantly.
Regression results reported in Exhibit 8 in the appendix, however, show the TERM loading
for the replicating portfolio is lower than the TERM loading for REITs, so interest rate risk
exposure cannot account for the results in Exhibit 5. Speaking to criterion three, REITs
appear to be a complete miss. Using the six-factor regression results, we were able to create
a simple long-only two-asset portfolio that not only comoves well with REITs but dominates
3Note that compound return, standard deviation and Sharpe Ratio are all annualized.
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REITs from a historical return and risk perspective. Note, again, we are not arguing that the
allocation to REITs should be zero. We are, arguing, however, that there is scant analytical
evidence for overweighting REITs above market-cap weighting (with the possible exception
of overweighting as part of a more general strategy of tilting a portfolio toward small and
value stocks).
Mean-Variance Spanning
As mentioned, the motivation behind the portfolio replication exercise is to determine if
REITs are redundant in the sense that a combination of other assets in a portfolio can be
weighted to replicate the comovement of REITs. While interesting to our specific research
question, this exercise may be narrow in that we explicitly chose the assets for our replicating
portfolio and did not evaluate the broader investable universe in our comparison. A more
complete technique requires us to step back and evaluate REITs in the context of an over-
all investment portfolio, specifically with respect to modern portfolio theory. Many studies
have evaluated the diversification benefits of REITs by attempting to quantify the optimal
portfolio allocation to REITs, generally in the mean-variance sense, such as Goetzmann and
Ibbotson [1990] and Feldman [2003]. In order to evaluate criterion four, we also evaluate
REITs’ role in a portfolio in a mean-variance sense but do so with a more advanced technique
that allows us to evaluate diversification benefits and optimal weighting simultaneously and
with accompanying statistical inference. The technique used to do so are tests of mean-
variance spanning.
At a high level, the idea is to statistically determine if the addition of a test asset (or assets)
to a given portfolio (the benchmark asset) improves the efficient frontier. If the efficient
frontiers are statistically similar, one would not be able to conclude that the test asset
improves portfolio efficiency. Kan and Zhou [2012] review these techniques in extensive
detail and we use their findings for guidance in this work. Speaking more formally, consider
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Kbenchmark assets and Ntest assets. The Kbenchmark assets span the larger set of K+N
assets if the mean-variance frontiers of both portfolios are statistically identical. With the
existence of a risk-free rate and unlimited lending and borrowing at that rate, then investors
solely seek the tangency portfolio of the mean-variance frontier, or rather, the portfolio with
maximum Sharpe ratio. With these assumptions in place and because we are only interested
in one test asset (the REITs index), we can move forward with the mean-variance spanning
test of Huberman and Kandel [1987] with N= 1. Define R1as the T×Kmatrix of
benchmark asset returns and R2as the T×1 matrix of test asset returns. We first specify
the regression R2=α+R1β+where we assume that is mean-zero and iid. We then define
δ= 1 ιβ where ιis a 1 ×kvector of ones. With this specification, we use a Likelihood
Ratio test statistic having χ2
2×N=2 distribution under the following null hypothesis:
H0:α= 0 and δ= 0 (2)
The calculation of the test statistic is omitted for brevity.4The null hypothesis presents
a joint test of 1) whether the tangency portfolio has zero weight in the test asset and 2)
whether the minimum-variance portfolio has zero weight in the test asset. Together, we test
whether every portfolio on the mean-variance frontier of the K+ 1 assets has zero weight
in the test asset i.e. the Kasset portfolio spans K+ 1 asset portfolio. In simpler terms, a
failure to reject the null hypothesis suggests that addition of the test asset to the benchmark
does not improve portfolio efficiency.
Chen et al. [2005] utilize tests of mean-variance spanning with the FTSE NAREIT All RE-
ITs Index as the test asset and find evidence for improved portfolio efficiency. But we find
their benchmark assets to be unrealistic in a practical portfolio context. The benchmark
used in that study are the 25 portfolios resulting from a 5x5 sort of size and book-to-market,
from Ken French’s data library. We would assert that an investor seeking to diversify their
4Refer to Kan and Zhou [2012] for a detailed derivation.
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equity portfolio would first look to fixed income (a very widely used diversifier of equity
risk) and thus, a simple benchmark comprised of broad equities and fixed income is much
more realistic. In a replication of their results over our sample, we indeed find that while the
null hypothesis is rejected using their original benchmark and test assets, when Long-Term
Corporates or Five-Year US Treasuries are included in their benchmark, the null hypothesis
is not rejected.
We conduct mean-variance spanning tests for three separate benchmarks with REITs as
the test asset. The benchmarks are chosen to compliment other analyses from this study
that, we would argue, are practical starting points for an investor seeking to diversify their
portfolio. Exhibit 6 shows the makeup of each benchmark and the associated p-value from
the Likelihood Ratio test of mean-variance spanning from Huberman and Kandel [1987].
For additional perspective, Exhibit 6 also shows the unconstrained mean-variance optimal
portfolio weights for a portfolio comprised of the respective benchmark assets and REITs.
Exhibit 6: Mean Variance Spanning Tests (January 1978–July 2017)
Benchmark Assets Test Asset p-value
K= [SP500, 5YT, SV] REITs 0.9464
-8%, 38%, 73% -3%
K= [SP500(60%), 5Y(40%)] REITs 0.1309
83% 17%
K= [SV(66%), CORP(34%)] REITs 0.8935
111% -11%
The K= [SP500, 5YT, SV] benchmark allows an unconstrained view into a portfolio with
holdings in standard asset classes. The K= [SP500(60%), 5YT(40%)] benchmark looks at
an industry standard 60/40 stock and bond portfolio. The K= [SV(66%), CORP(34%)]
benchmark allows us to dive deeper on our REITs replicating portfolio. The null hypothesis
is not rejected in any of the tests meaning that we cannot statistically say that the addition of
REITs improves the mean-variance frontier for any of our benchmark portfolios. Because we
know that REITs load on SMB and HML, the failure to reject the null in the first benchmark
13
test is expected. The surprising result in the first specification though, is that even in an
unconstrained mean-variance optimization, REITs do not receive a positive allocation. The
second test is most surprising: the null is not rejected when REITs are added to a standard
60/40 S&P 500 and 5YT portfolio. As mentioned, because REITs load on SMB and HML, ex
ante, we expected the addition of REITs to improve the mean-variance frontier of this second
benchmark. Of note, the unconstrained mean-variance optimization allocates 17 percent to
REITs in this case, a number far above the market capitalization weight of REITs. This is
because the stock/bond portfolios Sharpe Ratio is highest at a portfolio allocation of 30/70
(see Exhibit 9 in appendix). As we overweight S&P 500 to arrive at a stock/bond allocation
of 60/40 and the correlation between S&P 500 and REITs is low, we would expect the
addition of REITs to significantly reduce volatility and improve the Sharpe Ratio. The third
test result fell in-line with expectations as we tested REITs against a portfolio specifically
designed to resemble REITs, from a comovement perspective. The failure to reject the null
in any of these tests, specifically the second, leads us to conclude that REITs fail to meet
our fourth asset class criterion.
Pre-2007 Analyses
For robustness, one other question worth exploring is whether REITs’ performance during
and after the financial crisis drives the long-term results. We repeat our correlation, four- and
six-factor analyses for the pre-2007 period, the results of which are in Exhibits 10, 11 and 12
in the appendix, respectively. The correlation of REITs with stocks over the pre-2007 period
was lower but roughly similar to the result over the full period. In the four-factor model,
REITs had an annualized alpha not distinguishable from zero and roughly similar factor
exposures when compared to the full-period analysis. In the six-factor regression results
for the pre-2007 period, we again see an annualized alpha estimate that is not statistically
significant. We do see, however, that the loading on the IGDEF premium is now negative
(but not statistically significant) compared to the full period six-factor regression that showed
14
positive exposure to the IGDEF premium. This means that the post-2006 period is driving
the full-period relationship for this particular factor. Overall, we do not find any results
which suggest a structural break in the data and conclude that the period during and after
the financial crisis does not drive the long-term results.
Post-May 1996 Analyses
Another question worth exploring is whether the earlier portion of our sample — when
REITs were a meaningfully smaller portion of investable markets — is driving our findings.
The introduction of REIT mutual funds in the 1990s allows us to address this question.
We consider the period after the inception of Vanguard REIT Index Fund (VGSIX) to be a
point-in-time at which the REIT market was large and diverse enough to allow individual
and institutional investors to easily access diversified exposure to REITs. We repeat our
correlation, four- and six-factor analyses, the results of which are in Exhibits 13, 14, and 15
in the appendix, respectively. The correlation of REITs with stocks over the post-May 1996
period was lower but roughly similar to the result over the full period. We do see however,
correlations with 5YT have now become negative, which is consistent with the changes in
the interest rates environment. In both the four-factor and six-factor model, REITs had
an annualized alpha that is not statistically significant and roughly similar factor exposures
when compared to the full-period analysis. Overall, we do not find any results which suggest
a structural break in the data and conclude that post-May 1996 period did not produce
significantly different results.
Conclusion
This study steps back from the body of REITs literature and evaluates a broader ques-
tion: are REITs a distinct asset class? Studies tend to generally accept REITs as an asset
class and seek to make comments on their diversification benefits or deserved allocations
15
in a portfolio. We establish a pragmatic list of criteria for consideration as an asset class
and then use an array of techniques to evaluate REITs as such. While REITs do indeed
exhibit relatively low correlation with traditional equity and fixed income, a deeper dive
into their returns reveal shortfalls in their qualifications for asset class distinction. Four-
and six-factor regression analyses reveal no statistically reliable alpha generation in REIT
returns and coefficient estimates point to REITs being well explained by traditional risk
factors. Taking direction from the regression results and attempting a long-only replication
of REIT returns with small-value and equities and long-term corporate bonds produces a
portfolio that comoves well with REIT returns and exhibits historically superior return and
risk characteristics. Utilizing tests of mean-variance spanning, we also examine the diversifi-
cation properties of REITs on a statistically inferred basis. These tests suggest that REITs
do not reliably improve the mean-variance frontier when added to a benchmark portfolio of
traditional stocks and bonds. These results, and the associated failure to satisfy our asset
class criteria, lead us to conclude that REITs are not a distinct asset class.
We would like to point out that this study used only U.S. based returns data. A large body
of evidence suggests that an investor wishing to diversify their portfolio would do well to add
developed international and emerging market equities. This study focused on U.S. stocks,
bonds, and REITs primarily for increased sample lengths, as international REIT indexes are
quite young. A global evaluation of REITs in the spirit of this study would be helpful but
we leave this to future work.
In conclusion, we want to make clear that we are not suggesting that REITs deserve no
allocation in an investment portfolio. Nor are we suggesting that any results previously
brought forth in the literature are spurious or incorrect. The results of this study lead us
only to suggest that REITs, as an equity security with only marginal diversification benefits,
should not receive a weighting in investor portfolios that significantly deviates from market
16
capitalization based weights. The Dow Jones U.S. Select REIT Index represents a non-
trivial approximately 2.5 percent of the Russell 3000 Index, as of early 2017, on a market
capitalization basis, which we would argue is a valid starting point for a REITs allocation
in a diversified portfolio.5
Appendix
Exhibit 7: SIC Industry Classifications
Designation Industry
NDUR Consumer NonDurables - Food, Tobacco, Textiles, Apparel, Leather, Toys
DURB Consumer Durables - Cars, TVs, Furniture, Household Appliances
MANUF Manufacturing - Machinery, Trucks, Planes, Office Furniture, Paper, Commercial Printing
ENRG Energy - Oil, Gas, and Coal Extraction and Products
CHEM Chemicals and Allied Products
BUSEQ Business Equipment - Computers, Software, and Electronic Equipment
TELCM Telephone and Television Transmission
UTIL Utilities
SHOPS Wholesale, Retail, and some Services (Laundries, Repair Shops)
HLTH Healthcare Medical Equipment, and Drugs
MONEY Finance
OTHER Other - Mines, Construction, Building Material, Business Services, Entertainment
Exhibit 8: Replicating Portfolio Exercise - Six-Factor Analysis (August 1988–July 2017)
Alpha (bps) t-stat MKT t-stat SMB t-stat HML t-stat UMD t-stat TERM t-stat IGDEF t-stat R-squared
[SV(66%), CORP(34%)] 63 1.6 0.64 70.7 0.57 52.6 0.48 41.5 -0.01 -1.0 0.57 20.4 0.52 14.4 98%
REITs -133 -0.5 0.60 10.1 0.41 5.8 0.71 9.4 -0.08 -1.7 0.76 4.1 0.96 4.0 51%
5Bloomberg
17
Exhibit 9: Sharpe Ratio of Stock/Bond Portfolio By Allocation (January 1978–July 2017)
Exhibit 10: Pre-2007 Analysis - Monthly Correlations (January 1978–December 2006)
REITs SP500 5YT
REITs 1.00 0.51 0.16
SP500 0.51 1.00 0.17
5YT 0.16 0.17 1.00
BUSEQ 0.35 0.81 0.03
CHEM 0.49 0.83 0.14
DURB 0.47 0.78 0.04
ENRG 0.43 0.60 0.03
HLTH 0.35 0.76 0.24
MANUF 0.55 0.91 0.08
MONEY 0.57 0.86 0.25
NDUR 0.50 0.79 0.27
OTHER 0.60 0.90 0.10
SHOPS 0.50 0.84 0.14
TELCM 0.26 0.73 0.17
UTIL 0.45 0.50 0.37
18
Exhibit 11: Carhart Four-Factor Analysis (January 1978–December 2006)
Alpha (bps) t-stat MKT t-stat SMB t-stat HML t-stat UMD t-stat R-squared
BUSEQ 452 2.2 1.10 26.4 0.24 4.5 -0.75 -11.4 -0.23 -6.0 83%
HLTH 440 2.1 0.78 18.4 -0.29 -5.3 -0.22 -3.3 0.09 2.2 59%
NDUR 217 1.2 0.85 23.6 -0.12 -2.6 0.28 4.8 0.04 1.1 63%
TELCM 239 1.0 0.83 18.1 -0.20 -3.3 0.00 0.0 -0.13 -3.0 55%
SHOPS 50 0.3 1.05 27.6 0.08 1.6 0.16 2.6 -0.05 -1.4 73%
ENRG 46 0.2 0.88 14.6 -0.10 -1.4 0.40 4.1 0.08 1.5 39%
REITs -2 0.0 0.65 15.1 0.46 8.3 0.63 9.3 0.00 -0.1 47%
MONEY -30 -0.2 1.15 39.3 -0.12 -3.3 0.52 11.1 -0.03 -1.2 82%
CHEM -55 -0.3 0.95 26.6 -0.13 -2.9 0.25 4.4 0.00 0.0 69%
MANUF -55 -0.4 1.11 40.4 0.08 2.3 0.22 5.1 -0.06 -2.3 85%
UTIL -139 -0.7 0.64 15.5 -0.16 -3.0 0.59 9.1 0.08 2.0 42%
DURB -375 -1.7 1.18 25.8 0.14 2.4 0.57 7.8 -0.22 -5.1 68%
OTHER -298 -2.3 1.10 43.3 0.23 7.1 0.15 3.8 -0.03 -1.3 88%
Exhibit 12: Six-Factor Analysis (August 1988–December 2006)
Alpha (bps) t-stat MKT t-stat SMB t-stat HML t-stat UMD t-stat TERM t-stat IGDEF t-stat R-squared
BUSEQ 517 1.9 1.26 18.4 0.23 3.3 -0.76 -8.7 -0.19 -3.8 -0.13 -0.7 0.12 0.2 83%
HLTH 486 1.7 0.70 9.8 -0.33 -4.5 -0.26 -2.9 0.09 1.7 0.11 0.5 -0.13 -0.3 47%
NDUR 161 0.7 0.79 13.5 -0.10 -1.7 0.30 4.1 -0.03 -0.8 0.28 1.8 -0.83 -2.0 52%
ENRG 231 0.7 0.73 8.3 0.02 0.3 0.50 4.4 -0.03 -0.5 0.07 0.3 -0.28 -0.4 28%
MANUF 61 0.4 1.15 27.0 0.10 2.4 0.39 7.2 -0.08 -2.5 -0.35 -3.0 -0.91 -2.9 82%
SHOPS 75 0.3 1.01 17.0 0.02 0.3 0.21 2.7 -0.05 -1.2 -0.26 -1.6 -0.31 -0.7 66%
CHEM 48 0.2 0.91 15.4 -0.10 -1.6 0.40 5.3 -0.01 -0.2 -0.32 -2.0 -0.92 -2.1 57%
REITs 37 0.1 0.49 7.4 0.46 6.6 0.67 7.7 -0.08 -1.6 0.43 2.3 -0.12 -0.2 36%
TELCM -34 -0.1 0.96 13.3 -0.25 -3.4 -0.10 -1.1 -0.04 -0.8 0.07 0.3 0.48 0.9 61%
MONEY -35 -0.2 1.20 24.9 -0.13 -2.6 0.60 9.7 -0.04 -1.0 0.14 1.1 -0.32 -0.9 80%
UTIL -106 -0.4 0.56 8.1 -0.03 -0.5 0.64 7.3 0.00 0.1 0.53 2.9 -0.32 -0.6 35%
DURB -527 -1.9 1.17 16.8 0.21 2.9 0.84 9.4 -0.23 -4.4 -0.35 -1.8 0.41 0.8 69%
OTHER -329 -2.1 1.05 27.2 0.14 3.6 0.23 4.6 -0.06 -2.0 -0.23 -2.2 -0.11 -0.4 84%
19
Exhibit 13: Post-May 1996 Analysis - Monthly Correlations (June 1996–July 2017)
REITs SP500 5YT
REITs 1.00 0.55 -0.08
SP500 0.55 1.00 -0.25
5YT -0.08 -0.25 1.00
BUSEQ 0.33 0.83 -0.26
CHEM 0.53 0.78 -0.19
DURB 0.60 0.78 -0.31
ENRG 0.35 0.59 -0.19
HLTH 0.39 0.69 -0.10
MANUF 0.58 0.90 -0.29
MONEY 0.59 0.85 -0.25
NDUR 0.50 0.72 -0.07
OTHER 0.61 0.91 -0.28
SHOPS 0.50 0.83 -0.24
TELCM 0.40 0.82 -0.24
UTIL 0.45 0.43 -0.01
Exhibit 14: Carhart Four-Factor Analysis (June 1996–July 2017)
Alpha (bps) t-stat MKT t-stat SMB t-stat HML t-stat UMD t-stat R-squared
NDUR 354 1.9 0.63 16.7 -0.21 -4.5 0.22 4.3 0.03 0.9 56%
HLTH 377 1.6 0.70 15.0 -0.21 -3.5 -0.03 -0.5 0.08 2.0 49%
BUSEQ 298 1.5 1.29 31.9 0.14 2.8 -0.80 -14.4 -0.12 -3.6 88%
UTIL 364 1.3 0.47 8.5 -0.16 -2.3 0.34 4.5 0.09 1.8 26%
SHOPS 199 1.0 0.85 22.4 -0.04 -0.8 0.14 2.8 -0.01 -0.2 70%
CHEM 168 0.9 0.78 19.9 -0.15 -3.0 0.28 5.1 0.00 -0.1 65%
REITs 287 0.8 0.72 10.6 0.37 4.3 0.76 8.2 -0.10 -1.7 48%
MANUF 135 0.8 1.11 33.7 0.09 2.1 0.30 6.6 -0.07 -2.4 85%
ENRG 99 0.3 0.82 11.7 0.00 0.0 0.40 4.2 0.05 0.8 39%
TELCM -1 0.0 0.98 20.7 -0.18 -3.0 -0.13 -2.0 -0.06 -1.6 68%
DURB -278 -1.0 1.20 20.9 0.24 3.3 0.59 7.5 -0.29 -6.0 74%
MONEY -164 -1.0 1.15 35.0 -0.16 -3.9 0.67 14.8 -0.04 -1.6 86%
OTHER -325 -2.5 1.04 39.3 0.11 3.2 0.23 6.3 -0.05 -2.4 89%
20
Exhibit 15: Six-Factor Analysis (June 1996–July 2017)
Alpha (bps) t-stat MKT t-stat SMB t-stat HML t-stat UMD t-stat TERM t-stat IGDEF t-stat R-squared
BUSEQ 384 1.9 1.33 29.2 0.14 2.8 -0.80 -14.6 -0.13 -3.9 -0.29 -1.9 -0.40 -2.4 88%
HLTH 301 1.2 0.70 13.1 -0.20 -3.3 -0.03 -0.4 0.08 1.9 0.24 1.3 0.11 0.6 50%
NDUR 235 1.2 0.64 15.2 -0.19 -4.0 0.23 4.5 0.02 0.6 0.37 2.6 0.03 0.2 57%
SHOPS 213 1.1 0.88 20.5 -0.03 -0.6 0.15 2.8 -0.02 -0.5 -0.06 -0.5 -0.27 -1.8 71%
MANUF 150 0.9 1.07 28.7 0.07 1.7 0.30 6.5 -0.05 -1.8 -0.02 -0.2 0.28 2.1 86%
UTIL 220 0.8 0.39 6.4 -0.17 -2.4 0.34 4.6 0.11 2.3 0.49 2.4 0.77 3.5 30%
CHEM 133 0.7 0.76 17.0 -0.15 -3.0 0.28 5.1 0.00 0.1 0.12 0.8 0.21 1.3 65%
ENRG 110 0.3 0.72 9.1 -0.04 -0.4 0.39 4.1 0.08 1.4 0.02 0.1 0.77 2.7 41%
TELCM 42 0.2 0.97 17.9 -0.19 -3.1 -0.13 -2.0 -0.06 -1.4 -0.13 -0.7 0.02 0.1 68%
REITs -22 -0.1 0.64 8.6 0.38 4.5 0.77 8.6 -0.08 -1.4 1.02 4.2 1.03 3.9 53%
DURB -229 -0.8 1.10 17.0 0.20 2.7 0.58 7.4 -0.25 -5.1 -0.09 -0.4 0.75 3.2 75%
MONEY -140 -0.8 1.17 31.2 -0.16 -3.7 0.67 14.8 -0.05 -1.7 -0.09 -0.7 -0.16 -1.2 87%
OTHER -323 -2.4 1.05 34.8 0.11 3.3 0.23 6.4 -0.06 -2.5 -0.01 -0.1 -0.10 -0.9 89%
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