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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

3

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

6

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.

7

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.

9

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.

10

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

11

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.

12

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

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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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