The Determinants of Cointegrating Relation among U.S. Real ... · To further test the determinants of cointegrating relation, we obtain six U.S. equity market risk factors and five

The Determinants of Cointegrating Relation among U.S. Real Estate Sectors

Paul Gallimore Department of Real Estate

Robinson School of Business Georgia State University

PO Box 3991 Atlanta, GA 30302

[email protected]

J. Andrew Hansz* Gazarian Real Estate Center &

Department of Finance and Business Law Craig School of Business

California State University, Fresno 5245 N. Backer Avenue PB7

Fresno, CA 93740 [email protected]

Wikrom Prombutr

Department of Finance College of Business Administration

California State University, Long Beach Long Beach, CA 90840 [email protected]

Ying Zhang

Department of Finance Dolan School of Business

Fairfield University 1073 North Benson Road

Fairfield, CT 06824 [email protected]

Contact author

This Draft April 01, 2012

Acknowledgment We thank seminar participants at the 2011 Annual Meeting of the American Real Estate Society (ARES) conference in Seattle, Washington and the 2011 annual Financial Management Association (FMA) Conference in Denver, Colorado.

mailto:[email protected]



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The Determinants of Cointegrating Relation among U.S. Real Estate Sectors

Abstract

With substantial attention in the literature on the existence of cointegrating real estate markets which shatter real estate portfolio diversification benefits, this study focuses on the determinants of cointegrating relation and cointegration-based portfolio construction and performance among U.S. real estate sectors. First, cointegration approaches identify cointegrating vector, leading cointegrated sectors, and redundant cointegrated sectors. Third, a proposed vector autoregressive model suggests a stronger cointegrating relation during down markets. Fourth, analyses on error correction model residuals suggest that certain macroeconomic factors, but not the U.S. equity market risk factors, explain the long-term cointegrating relation. Lastly, we conclude a cointegration-based portfolio outperformed the all-sector REIT market portfolio and provided protection to investors under market down turns in which investors need diversification most. Keywords: Cointegration, Domestic real estate sector, Error correction model, Portfolio

construction and diversification, Vector autoregressive model

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1. Introduction

There has been a recent research interest in integration of global real estate markets and

international real estate portfolio diversification (Glascock and Kelly 2007, Yunus 2009, Gallo

and Zhang 2010, Gallo, Lockwood, and Zhang 2012 and Yunus and Swanson 2007, 2012). The

resulting extension of knowledge in these areas has been facilitated in particular by two

developments. First, econometric advances have improved upon correlation analysis and

cointegration analysis has emerged as a productive tool for detecting and understanding long-term,

time-series return relations (Yunus 2009 and Gallo and Zhang 2010). At the same time, public real

estate equity return indices in developed global markets have matured to the point where they are

now available and appropriate for cointegration analysis to reveal underlying long-term relations.

Despite the at-least-equal relevance of these developments to domestic market analysis, there has

been comparatively modest attention to U.S. domestic real estate sector portfolio diversification

(Hartzell, Hekman, and Miles, 1986 and Eichholtz and Hoesli, 1995). With substantial attention in

the recent literature on the existence of cointegrating real estate markets (Yunus, 2009; Gallo and

Zhang, 2010 and Gallo, Lockwood and Zhang, 2012), this study focuses on the determinants of

cointegrating relation and cointegration-based portfolio construction and performance among U.S.

real estate sectors.

This study offers several important findings to the real estate literature. First, we

implement cointegration analyses to evaluate cointegrating relation among seven real estate sector

indices and identify, over the long term, 1. sectors those are segmented of any cointegrating

relation, 2. sectors as the representation of a cointegrating vector (CIV, hereafter), referred to as

market-leading (weak exogenous) sectors, and 3. subordinate sectors that are cointegrated within a

CIV, referred to as redundant sectors or followers. Second, the results of two novel residual

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analyses reveal that stronger cointegrating relation during down markets and long-term

disequilibrium among cointegrated real estate sectors is driven by certain macroeconomic factors

but not the U.S. equity market risk factors. Third, by eliminating redundant property sectors and

constructing a portfolio with market segmented and leading (weak exogenous) sectors, we produce

a cointegration-based real estate sector portfolio (COI, hereafter) with excess and risk adjusted

returns greater than the CRSP/Ziman market portfolio (MKT, hereafter). Tested with a

REIT-based four-factor model, our COI portfolios provided significant abnormal returns to

investors under market down turns in which investors need diversification most. We argue that the

inferior performance of the all-property-sector MKT portfolio stems from containing the

redundant cointegrated sectors which shatter portfolio diversification.

The next section is a review of the portfolio diversification and cointegration methods used

in the real estate literature. The literature review is followed by a description of the data, methods,

and results. The paper ends with a discussion of the results and conclusions.

2. Literature review

Concern about the reliability of correlation structures in studying asset returns has led to studies

adopting the alternative of cointegration analysis. Tarbert (1998) applied this to two different

series of UK direct property returns (1971-1995 and 1977-1995) and found, in general, a tendency

for returns to be cointegrated across both regions and property, indicating restricted diversification

potential. Using the same cointegration method, Myer, Chaudry, and Webb (1997) examine the

1987-1992 time-series of both aggregated and property sector disaggregated direct property values

for the US, UK, and Canada and find a common factor – inflationary expectations - between these

markets indicating reduced cross-diversification benefits in the long-run. Wilson and Okunev

(1996), using the same method, demonstrate segmentation between the indirect property markets

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and stock markets of the US, UK, and Australia, indicating diversification potential across these

assets within the national markets. They also show, in support of international diversification, that

the same is true for indirect property across these countries1.

Yunus and Swanson (2007) investigate long-run relations and short-run linkages across the

US and several Asia-Pacific2 indirect real estate markets over the period 2000-2006. Over this

period, they find that these markets are not cointegrated. They conclude that this is progressively

becoming less so, although it is not happening across all sub-markets, meaning some long-run

diversification opportunities still exist. Using a longer time period (1990 through 2007), Yunus

(2009) extends this analysis, adding the Netherlands, France and the UK to a similar

US/Asia-Pacific market set3.They find that most international public real estate markets are

cointegrated, and this trend to integration is increasing over time.4 Other studies adopting the

cointegration method in the real estate literature include D’Arcy and Lee (1998), Chaudhry,

Christie-David, and Sackley (1999), Wilson and Zurbruegg (2001), Kleiman, Payne and Sahu

(2002), Gallo and Zhang (2010), Gallo, Lockwood, and Zhang (2012) , and Yunus and Swanson

(2012).

As the foregoing reveals, relatively few studies since Hartzell, Hekman, and Miles (1986)

and Eichholtz and Hoesli (1995) have focused exclusively on domestic real estate sector

diversification and no domestic studies have employed a cointegration approach.5 Studies that do

1 Wilson and Okunev (1996) uses different sets of times series, dictated by availability. The longest is 1969-1993. 2 Australia, Japan, Hong Kong and Singapore. 3 Yunus (2009) does not include Singapore. 4 The exceptions are France and the Netherlands, a circumstance that Yunus (2009) suggests may be associated with their convergence with the real estate markets of the Euro zone. 5 Tarbert (1998) uses this approach for the UK market, applying it to returns from direct real estate investment.

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address real estate sector diversification also include or focus on international markets making the

property sector results difficult to isolate and interpret. This present study fills this gap in the

literature by examining, exclusively, the existence of cointegrating relation and the determinants

of such relation among U.S. real estate sectors.

3. The data

We examine the period from March 1984 to December 2009. We obtain monthly return and

market capitalization series for seven REIT property sector indices6 (healthcare, industrial/office,

residential, lodging/resort, retail, self-storage, and unclassified) from the Center for Research in

Securities Prices (CRSP)/Ziman US Real Estate Data Series.7

Importantly, the CRSP/Ziman database also includes return series for the universe of all

individual REITs trading on the NASDAQ, New York Stock Exchange, and American Stock

Exchange.8 Following Hartzell, Mühlhofer and Titman (2010) and Cici, Corgel and Gibson (2011),

we create Fama-French-Carhart REIT-based four factors from the universe of all individual REITs

over the 1984 to 2009 period. First, we use the value-weighted CRSP/Ziman REIT market index as

6 Although we focus on seven property type indices, each specialized property type index contains all individual REITs categorized in this particular property type in the CRSP/Ziman database. A portfolio contains seven property indices would include the universe of all individual REITs trading on the NASDAQ, New York Stock Exchange, and American Stock Exchange. 7 A note on the unclassified sector is warranted. We contacted CRSP to ask about the definition and composition of the ‘unclassified’ category. CRSP informed us that this was a catchall category for assets returns that do not fit into the any of the six explicit classifications. No further information was available. Following Ro and Ziobrowski (2011) who also use the CRSP/Ziman data series, we include the ‘unclassified’ category in our analysis. 8 Combining stock price and returns data with carefully researched information regarding the population,

characteristics, and history of REITs, the CRSP/Ziman database provides firm-specific information and indices essential to analyses involving this important asset class. This database includes several qualitative measures detailing market capitalizations, concentrations, and changes in index composition particularly important for evaluating the information in thinly populated index series which were common during the 1980s. the CRSP/Ziman database includes all REITs that have traded on the NYSE, AMEX and NASDAQ exchanges since 1980, contains a series of indices based on REIT type and property type, contains underlying individual security information for the indices, and includes qualitative measures important for evaluating information in the thinly populated index series: market capitalization, concentration, and changes in index composition.

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the market portfolio (MKT).The other factors are the return differentials between the small cap and

large cap REITs (Size), high and low book-to-market REITs (Book-to-Market), and positive and

negative prior year return-momentum REITs (momentum). The method for constructing these

factors is based exactly on Fama and French (1993) and Carhart (1997).9

To further test the determinants of cointegrating relation, we obtain six U.S. equity market

risk factors and five U.S. macroeconomic data. In particular, we obtain CRSP equity market index,

equity SMB (small minus big), HML (high minus low), and UMD (up minus down) factors from

the website of Professor Kenneth French. Pastor and Stambaugh (2003)’s equity liquidity data is

downloaded from Professor Lubos Pastor’s website. Five U.S. macroeconomic factors, industrial

production growth rate, unexpected inflation rate, change in expected inflation, term structure, and

risk premium, are downloaded from Professor Laura Xiaolei LIU’s website.

4. Research methods

4.1 Unit Root and Cointegration Tests

The objective of our study is to examine the determinants of cointegrating relation and

cointegration-based portfolio performance among U.S. real estate sectors. Cointegration methods,

developed by Engle and Granger (1987), are based on error correction models (ECM, hereafter),

rather than correlations, to identify long-term equilibrium among a set of non-stationary variables

(REIT price indices in this study).

Cointegrated markets share a linear combination of nonstationary variables. Stationarity of

variables can be identified with unit root tests. We first conduct four unit root tests, Augmented

Dickey-Fuller (1981), Phillips-Perron (1988), Kwiatkowski, Phillips, Schmidt, Shin (1992), and

Zivot-Andrews (1992), to test for price series stationary. Each REIT’s returns are converted to

price series, which is then converted to natural logarithms for unit root tests. All price level REIT

9 Our four REIT-based factors are different from the US equity-based factors used in Ro and Ziobrowski (2011).

8

indices with unit roots are shown to be nonstationary and therefore merit cointegration tests.10

Second, we conduct Johansen (1988, 1992a) cointegration rank tests to assess any long-run

equilibrium relations or CIVs among nonstationary real estate sector indices. Second, Johansen

(1991) exclusion tests are then performed to identify sectors independent of cointegrating

relations. Third, a Johansen (1992b) weak exogenous test is conducted to differentiate the leading

property type REIT index from other cointegrative indices (followers) within the CIV. Similar to

Johansen, Mosconi and Nielsen (2000), we use likelihood-ratio (L-R) tests to identify any possible

structural breaks in the CIV. Dummy variables are added as controls for large residual shocks

(significant at the 0.01 level) that could induce non-normally distributed residuals. The Bartlett

small sample correction Johansen (2002) test is included in each cointegration rank test to mitigate

potential small sample size bias. We report test statistics for both the Johansen Trace and the

Bartlett-corrected Trace.

4.2 Determinants of cointegrating relation

This study is the first one in the literature to investigate determinants of cointegrating relationships

among domestic real estate sectors. Cointegration ECM residuals generated from the above

cointegration tests allow us to further examine both market conditions and macroeconomic factors

that possibly drive the cointegrating relation among real estate sectors. In the U.S. equity market,

Campbell, Koedijk, and Kofman (2002) and Butler and Joaquin (2002), among others, show

increased correlation and reduced diversification benefits in down markets. Many studies also

show that there is a strong linkage between the U.S. equity market as well as macroeconomic

factors and the U.S. real estate market, such as Ling and Naranjo (1999) among others. We want to

identify the level of cointegration during down markets and reveal any equity market factors or

10 Previous literature (e.g. Chen, Firth and Rui (2002)) indicates nonstationarity among index price series.

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macroeconomic factors that impact the cointegrating relation.

First, to discern the extent to which cointegration changes in varying market conditions (up

versus down), we propose a novel vector autoregression (VAR) analysis with an interactive

dummy as the past CIV residual to examine the influence down markets have on cointegrating

relation. As described by Engle and Granger (1987), the CIV of the property sector indices, Yit,

takes a long-run equilibrium form

β1*

Y1t+ β2* Y 2t+ … + βn

* Y nt+ δ*D = 0 (1)

where Y1t … Ynt are real estate sector indices price levels, β1…βn are the Eigenvector coefficients

and D is the deterministic component (i.e., constant, linear time trend, etc.). The CIV residual, ϑ ,

or deviation from long-run equilibrium is equal to B*Yt’ where B and transposed Yt’ denote the

vectors (β1, β2,…,βn) and (Y1t , Y 2t ,…,Ynt)’ respectively. Although not reported, the CIV residual or

deviation from long-run cointegration equilibrium is proved to be a stationary process by our unit

root test.

Given a previous residual is positive (negative) at time t-1, meaning the sector deviated

from its bonded long-term equilibrium with a positive (negative) error or shock, the current time t

sector price level should move down (up) with a negative (positive) return towards its long-term

equilibrium to correct for its past error should the cointegrating relation hold. Therefore, we expect

there is an inverse relation between current index return at time t and past CIV residual at time t-1.

We want to discern the extent to which cointegration varies in different market conditions, which

is whether the error correction is effective under an up or down market. Up (down) markets are

defined collectively as months in which the excess return of the broad property market index is

positive (negative), as specified by Fabozzi and Francis (1977). Specifically, a vector

autoregression (VAR) model is as follow:

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t

k

i

ititttt YYt ψρϖϑρϖρϑρρ +∆++++=∆ ∑=

−−−4

132110 *)*( , (2)

where, for time t, Yt is the vector of real estate sector price levels in a VAR system, Yt∆ is the

vector of real estate sector returns in a VAR system at time t, 1−tϑ is the lagged CIV residual

(disequilibrium) at time t-1, ϖ is a binary dummy variable at time t (1 = declining market and 0 =

rising market), )*( 1 tt ϖϑ − is the interactive term between past disequilibrium and current market

condition dummy, ∑=

−∆k

i

iti Y4

*ρ is the sum of k lagged real estate sector returns in the VAR

system, and ψ represents the error term of the system. When ϖ =0, 1ρ depicts how sector REIT

returns response to the past disequilibrium in rising market condition; when ϖ =1, depicts how

sector REIT returns response to the past disequilibrium in declining market condition. In general, a

positive 1ρ implies real estate sectors tend to become more segmented in rising markets. On the

contrary, a negative )( 31 ρρ + implies property sectors tend to become more cointegrated in

declining markets.

Second, to examine other determinants of cointegration disequilibrium, we conduct two

regression analyses with the White noise CIV residual tϑ from the ECM model as the dependent

variable. We first examine if traditional equity market factors have impact on the cointegration

disequilibrium. We perform the following regression by running cointegration residual against

the Fama-French-Carhart-Pastor-Stambaugh equity market five factors:

=θ0+θ1(REquityMkt–Rft)+θ2EquitySMBt+θ3EquityHMLt+θ4EquityUMDt+θ5EquityLIQ+εpt (3)

where is the CIV residual (disequilibrium) at time t. REquityMkt – Rft is the CRSP equity market

risk premium, the EquitySMB is the equity size premium measured as the difference in returns of

small cap and large cap equity portfolios, the EquityHML is the equity value premium calculated

tϑ

tϑ

tϑ

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as the difference in returns of high book-to-market and low book-to-market equity portfolios, and

the equity momentum factor, EquityUMD, is the difference between equity returns of last year

high return and low return portfolios. EquityLIQ is the value-weighted Pastor and Stambaugh

(2003) equity liquidity factor that invests long in equities with high liquidity betas and short sells

equities with low liquidity betas.

Next, with Liu and Zhang (2008)’s data, we test the impact of changes in traditional

macroeconomic factors on the disequilibrium. We perform the following regression by running the

cointegration residual against the Chen, Roll, and Ross (1986) five US macroeconomic factors:

= λ0+ λ1MPt+ λ2UIt + λ3DEIt + λ4UTSt + λ5UPRt + τpt, (4)

where MPt is the industrial production growth rate, UIt is unexpected inflation rate, DEIt is the

change in expected inflation, UTSt is the term structure, and UPRt is the risk premium at time t. All

five factors are measured on a monthly basis.

4.3 Tests of portfolio performance

The investment value of applying a cointegration approach to real estate sectors can be

measured by testing the performance of the portfolio consists of only the essential real estate

sectors (non-cointegrated plus leading cointegrated sectors). The cointegrated real estate sectors

offer limited diversification potential and should be minimized in diversified portfolios while the

only cointegrated sectors deserving allocations are leading markets (weak exogenous) that are the

source of common trends among cointegrated markets (Pesaran, Shin, and Smith 2000, Gallo,

Phengpis and Swanson, 2007, Yunus 2009, Gallo, Lockwood, and Zhang, 2012). With essential

property sectors, at the beginning of every year, we form an active value-weighted portfolio based

on each sector’s prior year-end market value, the portfolio is held for the next 12 months and

rebalanced annually. In addition, we also construct a passive equally weighted portfolio using

tϑ

tϑ

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equal weight on each real estate sector.

On the portfolio level, we examine two risk-adjusted performance measures. First, we

perform significance tests of Sharpe ratio differences across portfolios using the Jobson and

Korkie (1981) Z-statistics. Second, we examine portfolio performance after controlling for the

portfolio’s exposures to the REIT-based market, size, style and momentum factors:

Rpt - Rft = a+ b1(RMKT – Rft) + b2ReitSMBt + b3ReitHMLt + b4ReitUMDt + ept, (5)

where Rpt is the monthly property portfolio raw return, Rft is the monthly Citigroup 3-month

Treasury bill return, RMKT is the value-weighted CRSP/Ziman REIT Market Index, SMB (small

minus big) is the REIT size factor, HML (high minus low) is the REIT style factor, and UMD (up

minus down) is the REIT momentum factor. We test the performance of each portfolio by

examining the sign and significance of the estimate of the intercept, a. The intercept measures the

incremental performance (abnormal return) of the portfolio after controlling for exposures

(b1…b4) to the broad market, size, style, and momentum factors. A significant positive (negative)

t-statistic for the intercept estimate indicates superior (inferior) risk-adjusted performance.

Finally, we hypothesize that cointegrated real estate sector indices become more

cointegrated in down markets so that cointegrated redundant sectors are lack of diversification

benefit during down markets while essentials ones should outperform. We therefore perform an

intertemporal performance test by running equation (5) over varying market conditions based on

the performance of the benchmark MKT. As defined above, an up market is defined as months in

which the excess MKT return is positive. Down markets are defined as months in which the excess

MKT return is non-positive. Between 01/1995 and 12/2009, our sample is demarcated with 108

months of up market and 72 months of down market.

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5. Results

Descriptive statistics are calculated over the 310-month sample period, March 1984 to December

2009, for each REIT sector index and are reported in Table 1. Other than means, standard

deviations, market capitalizations, and Sharpe ratio (SHP, hereafter), we also report the

Jobson-Korkie z-statistics for equality of the REIT sector’s SHP versus that of the market portfolio

MKT.

--- Insert Table 1 here ---

The MKT’s mean monthly return equaled 0.82% with a 0.09 SHP over the full sample

period. The sector REIT’s mean returns exhibit substantial variation, ranging from a low of 0.25%

for LODG to a high of 1.33% for HEAL. Jobson-Korkie z-statistics indicate that only the HEAL’s

SHP is significantly larger than that of the MKT (z-test=2.24). The SHP of other sector indices are

either smaller than or indifferent from that of the MKT. Mean market capitalization shows that

INDU has the highest market value with 27.39% market share among all other REIT sectors while

SELF with 5.21% market share is ranked the lowest. In the spirit of Glascock and Kelly (2007), we

run the MKT returns against each real estate sector returns to see by how much the MKT can be

explained by each sector separately. We find large R-squares under each real estate sector

regression with significant model F-test statistics meaning that real estate sectors explain a large

portion of the domestic real estate market portfolio return variation. These findings are different

from Glascock and Kelly (2007)'s 6% explanatory power of sectors in the international real estate

markets. We conclude that real estate sectors provide important diversification within the U.S.

REIT market. The time series plot of the log of price for these seven sector REITs is exhibited in

Figure 1. The plots provide mixed visual evidence of comovement among these REITs and a

systematic drop during the global financial crisis occurring between 2008 and 2009.

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--- Insert Figure 1 here ---

The cointegration methodology begins with unit root tests on the seven sector price level

indices. Although results are not reported, we find that each of the seven sector price indices has a

unit root representation (non-stationary). Therefore, unit root tests merit the implementation of the

cointegration methodology to further detect long-run equilibrium among non-stationary price

indices.


The results of cointegration tests are presented in Table 2. To ensure that our cointegration

tests are not look-ahead biased and are suitable for an out-of-sample portfolio formation (Phengpis

and Swanson, 2010), we run cointegration tests using a 120-month rolling windows approach with

the first window which is from 03/1984 to 12/1994 which instructs us to form the COI portfolios

on 01/1995 and hold it for the next 12 months and the second window is from 01/1986 to 12/1995

for 01/1996 formation, so on and so forth until the last window is from 01/2000 to 12/2008 for

01/2009 formation. From fifteen separate rolling windows cointegration tests, we find consistent

results in terms of cointegrated/non-cointegrated and leading/following sectors. This finding is in

line with the essence of cointegration framework that a long-term stable cointegrating relation is

warranted should the cointegrating ECM hold. Furthermore, we present a recursive cointegration

test of CIV stability to show that cointegration test results are stable over time from 1995-2009.

We also run full period (03/1984-12/2009) cointegration tests and find consistent results. To

conserve space, we only report the first window cointegration tests results. Other subsequent

windows and the full period results are available from the authors upon request.

Panel A of Table 2 shows a significant CIV among all real estate sector indices (Bartlett

λtrace=152.22, p-value=0.04) with insignificant G(r) common linear trend components

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(p-value=0.17). Results from the cointegration exclusion tests are reported in Panel B of Table 2.

Sector indices with significant (insignificant) L-R test statistics are cointegrated

(non-cointegrated). On the one hand, the findings indicate that five sectors HEAL (L-RHEAL=5.81),

INDU (L-RINDU=7.15), LODG (L-RLODG=5.49), RETL (L-RRETL=3.62) and SELF (L-RSELF=4.27)

are cointegrated and share one CIV. On the other hand, L-R statistics are insignificant for UNCL

(L-RUNCL=0.55) and RESI (L-RRESI=0.39), which implies their independence from the CIV. The

robustness test, presented in Panel C, confirms there is one and only one significant CIV among all

five cointegrated real estate sectors (Bartlett λtrace=72.07, p-value=0.03) with a similar

insignificant G(r) common linear trend component (p-value=0.28). Panel D further confirms that

none of the cointegrated REITs are segmented (non-cointegrated) from the CIV. Cointegration

tests identify five cointegrated real estate sectors (HEAL, INDU, LODG, RETL, and SELF) and

two independent ones (UNCL and RESI).

We contend that cointegrated real estate sectors share common underlying trends and thus

comove temporally, undermining diversification benefits. However, leading indices within a CIV

do not respond to deviations from the cointegrating relation, and, although cointegrated, may still

offer diversification benefits (Pesaran, Shin, and Smith 2000, Yunus 2009, Gallo, Lockwood, and

Zhang 2012). To differentiate leading sectors from subordinate following sectors, we conduct

Johansen (1992b) weak exogenous and Granger (1969) causality tests.


Panel A of Table 3 presents exogeneity test results with a null hypothesis of weak

exogeneity (Engle, Hendry and Richard 1983). An insignificant L-R statistic supports the

hypothesis that the index is weakly exogenous and the sector is a leading index within its CIV.

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Findings indicate that HEAL (L-RHEAL=0.25), RETL (L-RRETL=1.22), and the SELF

(L-RSELF=2.02) are the leading sectors in the CIV which sufficiently represent the entire CIV while

INDU (L-RINDU=9.44) and LODG (L-RLODG=5.81) are subordinate followers which are redundant

diversifiers. Other than the non-cointegrated markets (UNCL and RESI), the only cointegrated

sectors deserving allocations are weak exogenous indices that are the source of common trends

and representations of the CIV. Weak exogenous indices are the leaders and do not respond to

other followers’ deviations from the long-run cointegrating equilibria which possess of certain

diversification benefits. As a robustness test, we conduct the Granger causality test to verify the

leading role of HEAL, RETL, and SELF. Significant F-test represents Granger causality from

variable Y to X. Panel B of Table 3 shows that other than its own lags (F-stat=149.33), HEAL is

not significantly Grange caused by any other cointegrated sectors. Similar results can be found on

RETL (F-stat=106.89) and SELF (F-stat=171.47) sectors. INDU, however, is not only Granger

caused by its own lags (F-stat=37.65), but also significantly caused by HEAL (F-stat=3.77), RETL

(F-stat=3.02) and SELF (F-stat=2.17). LODG is also significantly Granger caused by itself

(F-stat=77.51) and RETL (F-stat=3.14). Granger causality test further confirms the leading role of

HEAL, RETL, and SELF and subordinate role of INDU and LODG in the CIV. Based on above

results, we conclude that diversified real estate sector portfolios should consist of two independent

sector REITs (UNCL and RESI) and the three other leading sector REITs (HEAL, RETL, and

SELF) as the essential real estate sectors.

--- Insert Figure 2 here ---

From the essence of cointegration theory and ECM model, we know that cointegrating

relation is intertemporal stable. To show that our findings of cointegrated/non-cointegrated and

leading/following sectors in the first window are not time dependent, we present a recursive

17

cointegration analysis in Figure 2. The recursive stability test of the cointegration parameters

(Hansen and Johansen, 1999) is performed. Based on the notion that the parameters should be

stable if the model is valid and useful, the test is implemented by assuming that short-run

parameters are held constant at their full-sample estimates but that the long-run relations are

allowed to change over time, then calculating the Trace statistic over the base period (03/1984–

12/1994) and keeping the initial observations in the base period fixed and increasing one

additional observation at each iteration to re-estimate the Trace statistic until the last Trace statistic

is computed over the full sample period. In Figure 2, conditional on the presence of one CIV in the

partial VAR, the recursive likelihood ratio Trace test statistics (scaled by the 5% critical value) are

plotted against the end of each estimation window. The number of lines above the critical value

line of one would indicate the number of CIVs determined at the 5% significance level. Figure 2

shows that one and only one CIV is consistently above line of one from 1995 to 2009, which

indicates stable cointegrating relations. This shows us that our cointegration tests are consistent

and unbiased.

Next, we perform an examination on the determinants of the cointegrating relation. As

presented in Table 2, there is a CIV among five sector indices. A time series of residuals (CIV

disequilibrium) of the ECM model over the full period is computed to proxy for the deviation from

the bonded cointegrating relation among these five cointegrated sectors. We therefore are

interested in identifying driving factors that affect the ECM residuals over the long run.

First, we present a VAR analysis with an interactive dummy with the past CIV residuals.

The purpose of this test is to examine the effects of down markets on the cointegrating relation.

The influx of downside risk questions the importance of a domestic real estate sector investment

strategy in down markets, precisely the market conditions in which investors need diversification

18

most. Therefore, we test the strength of the cointegrating relation in down versus up market

conditions. Within the cointegrating relation, we compute the CIV residuals and lag the residuals

by one month (t-1) to account for past disequilibria, and then regress each cointegrated sector

REIT return against the CIV’s past disequilibria, a market condition dummy, an interactive term,

and other lagged REIT market returns.11


As presented in Table 4, two (three) out of five real estate sectors’ returns significantly

(insignificantly) and positively respond to their past disequilibria in up markets, as indicated by the

dummy variable ρ1. In particular, in up markets, HEAL (ρ1=0.0378, t-test HEAL,ρ1=1.70) and RETL

(ρ1=0.0350, t-testRETL,ρ1=1.70) deviates from its bonded long-term equilibrium. However, all five

cointegrated sectors significantly and negatively react to their post disequilibria in down markets,

captured by the interactive term ρ1+ρ3. For instance, in down markets, HEAL moved towards its

long-term equilibrium by (ρ1+ρ3) =0.0378-0.0505=-0.0127 (t-testHEAL,ρ1=1.70, t-testHEAL,ρ3=-2.03).

These findings suggest cointegrated sectors become more cointegrated in down markets as

evidenced by movement towards their long-term equilibria. We are the first one in the literature

report that cointegrating relation among cointegrated real estate sectors is in fact induced by down

markets. This finding suggests that cointegrated sectors are lack of diversification benefit during

down markets while essential ones should provide better downside risk protection. Therefore, we

ought to look into different market conditions when examining cointegration-based portfolio

performance.


11 We also test the VAR system with up to 12 lagged market returns and these results are consistent with the original model.

19

Second, we further examine other determinants of the cointegraing relation by running the

current month CIV residuals against current month common equity market risk factors and

macroeconomic factors. In Panel A of Table 5, we find that the cointegration disequilibrium is not

due to any equity market premium as evidenced by insignificant t-tests on each of the five equity

market factors. In Panel B, however, we find that the disequilibrium error is smaller (indicating

greater cointegrating effect) when unexpected inflation (λUI=18.8750, t-test=3.07) or risk premium

(λUPR=19.1280, t-test=5.58) is high. On the other hand, the disequilibrium error is larger (moves

away from their equilibrium) when change in expected inflation is high (λDEI=-33.8751,

t-test=-2.23). In summation, the long-term disequilibrium among cointegrated real estate sectors

are not affected by equity market risk factors but responds to both expected and unexpected

inflation changes and risk premium changes.12


Next, based on above cointegration rank, exclusion, weak exogenous, and Granger

causality tests results, we contend that only essential property sectors which are non-cointegrated

and leading cointegrated sectors should be included in diversified real estate sector portfolios. Two

cointegrated sectors are redundant diversifiers that should be excluded. We form our annual

rebalanced portfolios: EWCOI and VWCOI. VWCOI is a value-weighted portfolio consists of five

essential real estate sectors suggested by the cointegration framework while EWCOI is an

equally-weighted portfolio.13 The benefits of including leading (weakly exogenous) sectors can be

examined by comparing the performance of the cointegration-based portfolios to portfolios

12

We also conduct the same tests under sub-periods and varying market conditions, we find similar results. Unreported results are

available upon request. 13

We also formed an all sector value-weighted VWALL portfolio according to each sector’s prior year-end market value. Since

this portfolio’s construction is almost the same as the MKT index portfolio, which contains all real estate sectors, they performed indifferently. We do not further report VWALL results but they are available from the authors upon request.

20

consists of only non-cointegrated sectors (UNCL and RESI). Although not reported, we find that

cointegration-based portfolios outperformed the portfolios contain only two non-cointegrated

sectors which support the inclusion of leading sectors into well-diversified real estate sector

portfolios.


We compare the performance of our COI portfolios with the market portfolio over 01/1995

to 12/2009 in Table 8.14 Panel A of Table 7 reports the average monthly return, standard deviation,

Sharpe ratio, Jobson-Korkie z-test statistics, and risk premium t-test statistics. The mean monthly

return for both the VWCOI (1.02% versus 0.93%, z-test=1.67) and EWCOI (1.05% versus 0.93%,

z-test=1.73) portfolio significantly exceeds the mean return for the MKT. Annualized returns

equal 12.95% for the VWCOI portfolio, 13.35% for the EWCOI portfolio and 11.75% percent for

the MKT respectively. Both VWCOI and EWCOI risk premium are significantly positive

(t-statVWCOI=1.71; t-statEWCOI=1.87) while the market portfolio is less attractive with insignificant

risk premium (t-statMKT=1.44). Jobson-Korkie z-tests indicate that the SHP is significantly higher

for both the VWCOI portfolio (12.72% vs. 10.78%) and EWCOI (13.95% vs. 10.78%) versus the

MKT, which is because that cointegration-based portfolios have higher return (RET) as well as

lower risk (SD) than the MKT benchmark. In sum, Panel A indicates that domestic real estate

investors would prefer the COI portfolios over the all-sector MKT portfolio. These results confirm

that the inclusion of two non-leading cointegrated sectors (INDU and LODG) leads to suboptimal

asset allocations resulting in inferior portfolio performance.

Panel B and C present results of the REIT-based four-factor tests which control for

14 Similar to Ro and Ziobrowski (2011)’s study that uses data from 1997 to 2006, this study examines the data from 1995 (the

beginning of our portfolio formation) to 2009. However, unlike Ro and Ziobrowski (2011) who use equity market factors, MKTRP, SMB, HML and UMD, in their four-factor asset pricing model, we use REIT-based market factors as suggested by recent studies Hartzell, Mühlhofer & Titman (2010) and Cici, Corgel and Gibson (2011).

21

exposures to the broad REIT-based market, size, style and property momentum factors. Results are

consistent with the total risk findings reported in Panel A. Importantly, both VWCOI

(aVWCOI=0.14%, t-test=1.92) and EWCOI (aEWCOI=0.20%, t-test=1.85) portfolios exhibited

superior significant abnormal return. Compounded annually, the abnormal returns equal 1.69% for

the VWCOI and 2.43% for the EWCOI portfolios, respectively. Not surprisingly that each of the

two COI portfolios has a significant beta loading which shows that REIT market premium

significantly explain two portfolios’ return variations. Notably, both cointegration-based

portfolios VWCOI (bVWCOI,1=0.9699) and EWCOI (bEWCOI,1=0.9215) have a beta smaller than one,

a proxy for less systematic market risk than the all-sector MKT portfolio. On the one hand, both

COI portfolios have an insignificant size loading (bVWCOI,2=0.0329, t-test=1.02; bEWCOI,2=0.0995,

t-test=-1.63) and momentum loading (bVWCOI,4=0.0820, t-test=0.13; bEWCOI,4=0.7479, t-test=0.69)

which implies that COI portfolios consist of different size REITs and both last year winners and

losers REITs. Both COI portfolios also have a significant style loading (bVWCOI,3=-0.1581,

t-test=-4.68; bEWCOI,3=-0.1831, t-test=-2.67) which implies these portfolios tend to hold REITs

with low Book-to-Market ratios. In sum, any rational investor would prefer VWCOI and EWCOI

over the market portfolio MKT.

From Table 4, we understand that cointegrated real estate sectors become more

cointegrated in down market conditions. Non-cointegrated real estate sectors are expected to

extend better performance (protection) for investors during down markets. To further determine

the extent to which general market conditions impact on portfolio performance, we run tests based

on up and down market conditions. Results are reported in Panel B and C of Table 7. Interestingly,

no significant abnormal alpha is evident for both COI portfolios during up markets which imply

that these portfolios performed indifferently from the market portfolio under good market

22

conditions. This finding also suggests that the COI portfolios’ overall outperformance must come

from their down market superior performance. Importantly, both the VWCOI and EWCOI

portfolios significantly outperformed the 4-factor model during down markets

(aVWCOI,Down=0.23%, t-test=1.69; aEWCOI,Down=0.39%, t-test=3.02). Therefore, the COI portfolios

performed in line with the 4-factor benchmark in up markets, but significantly outperformed it by

23 basis points per month for VWCOI and by 39 basis points for EWCOI during down markets,

effectively providing a downside risk protection. Results in Table 7 provide an important finding

that better diversified cointegration-based portfolios, VWCOI and EWCOI, which eliminate

redundant diversifiers, provides superior protection to investors than a market portfolio, during

unfavorable market conditions, in which investors need diversification benefits most.

6. Conclusionss

This study focuses on the determinants of coinetrating relation and cointegration-based portfolio

performance among U.S. real estate sector REITs from March 1984 to December 2009. Real estate

sector price indices were found to be non-stationary with unit root. Using a cointegrative approach,

we find a significant cointegrating relation among five real estate property sectors (retail,

industrial/office, lodging/resort, healthcare and self storage) and the residential and unclassified

sectors are segmented from this cointegrating relation. Among the five cointegrated sectors, retail,

healthcare, and self-storage sectors are found to be weakly exogenous and leading indices while

the industrial/office and lodging/resort sectors are identified as followers which are redundant

diversifiers. We provide sufficient evidence that it is necessary to include leading cointegrated

sectors but to exclude redundant cointegrated ones in a well-diversified real estate sector portfolio.

Therefore, two non-cointegrated and three leading cointegrated sectors are sufficient for

constructing well-diversified domestic real estate sector portfolios.

23

Furthermore, this study is the first one in the literature to investigate the determinants of

cointegrating relation among five cointegrated real estate sectors. Based on our proposed vector

autoregressive model, we find that cointegrated sectors have become more cointegrated during

downmarket conditions and our error correction model residuals analysis suggests that expected,

unexpected inflation changes and risk premium changes, but not the equity market factors, explain

the long-term cointegrative relation among cointegrated real estate sectors.

Finally, we provide evidence that a cointegration-based portfolio has a higher raw return as

well as a smaller standard deviation, as compared to a traditional all-property-sector market

portfolio. We argue that the inferior performance of the market portfolio stems from two redundant

cointegrated sectors: industrial/office and lodging/resort. Moreover, using a REIT-based 4-factor

asset-pricing model with different market conditions, the cointergration-based strategy provided

protection to investors under market downturns, in which investors need diversification most.

Since many REITs operate exclusively in the U.S. and institutional investment portfolios

often have specific US real estate allocation mandates, our results help clarify real estate portfolio

selection and allocation policy important to institutional investors and real estate portfolio

managers. The implications of this study are limited to U.S. domiciled investors. It is of interest to

consider how these results hold for global real estate sector diversification, especially when

emerging real estate markets are considered. A better understanding of the real estate sector

integration convergence process could also be beneficial to academicians and practitioners. These

proposed extensions remain promising areas of future research.

24

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27

Figure 1

Seven Property Type REITs Log of Price (03/1984-12/2009)

Test period is from 03/1984 to 12/2009 that includes 310 monthly observations. Figure 1 plots seven property type REITs log of price: LPUNCL is the log price of unclassified REIT index; LPHEAL is the log price of healthcare REIT index; LPINDU is the log price of industrial/office REIT index; LPLODG is the log price of lodging/resort REIT index; LPRESI is the log price of residential REIT index; LPRETL is the log price of retail REIT index; LPSELF is the log price of self-storage REIT index.

Figure 2

Trace Test Statistics (01/1995-12/2009)

Recursive cointegration tests of Cointegrating Vectors (CIVs) stability in the group of REIT property sector indices: healthcare, industrial/office, residential, lodging/resort, retail, self-storage, and unclassified (recursive trace tests). The figure shows the plots of recursive trace statistics scaled by 5% critical values against the passage of time. The 03/1984– 12/1994 is the base period. The number of lines above 1 would indicate the number of CIVs determined at the 5% significance level.

28

Table 1 Descriptive Statistics

INDEX RET(%) SD (%) SHP J-K z-test (vs. MKT)

Mkt. Cap. Mkt. Share Count ConRatio R-Sqr P-value

Market Index 0.82% 4.95% 0.09 $124,000 100% 170.19 17.31%

3MTB 0.38% 0.19%

REIT Type

Unclassified (UNCL) 0.54% 5.21% 0.03 -1.36 $5,790 5.41% 18.17 73.71% 0.52 0.00***

Health Care (HEAL) 1.33% 5.56% 0.17 2.24** $8,480 7.93% 10.88 70.21% 0.63 0.00***

Industrial/Office (INDU) 0.57% 6.30% 0.03 -2.16** $29,300 27.39% 29.43 53.72% 0.79 0.00***

Lodging/Resorts (LODG) 0.25% 9.10% -0.01 -2.41** $9,214 8.61% 10.01 85.69% 0.52 0.00***

Residential (RESI) 0.97% 5.23% 0.11 0.84 $19,900 18.60% 22.16 58.79% 0.77 0.00***

Retail (RETL) 1.04% 5.79% 0.11 1.31 $28,700 26.83% 31.19 51.11% 0.88 0.00***

Self Storage (SELF) 1.11% 6.00% 0.12 0.76 $5,577 5.21% 7.26 88.04% 0.50 0.00***

This table summarizes the monthly performance of the value-weighted property-type REIT indices examined over the 310-month period 03/1984-12/2009. Market Index is the CRSP/Ziman value-weight market index. 3MTB is the 3-Month Treasury Bill. For each index, we report the raw mean return (RET), standard deviation of returns (SD), Sharpe ratio (SHP), and Jobson-Korkie z-statistic (J-K z-test) for equality of Sharpe ratio with the Mkt’s Sharpe ratio. Mkt. Cap. represents the average market value of each REIT in millions. Count represents the average number of REITs eligible for inclusion in the index. ConRatio is the Concentration Ratio which is the ratio of the market value of the largest four securities in the portfolio versus the market value of the entire portfolio computed using the beginning of period market caps. To examine by how much the market return can be explained by a certain property type return, we adopt a single factor model as follow:

RtMKT = AlphaP + BetaP*RtP + Errp

where RtMKT represents REIT market raw return and RtP is the property type index P’s raw return. R-sqr shows the goodness of fit of the single factor model. P-value is for F-test of model fitness. ***and ** and * denote statistical significance at the 1%, 5%, and 10% levels, respectively.

29

Table 2 Cointegration Rank and Exclusion Tests (from 03/1984 to 12/1994)

Panel A. Cointegration rank tests on all indices

I(1)-Analysis (n=7, lag=1) G(r) p-r r Eig. Value Trace Bartlett Trace P-Value Bartlett P-Value

1.90 7 0 0.29 156.63 152.22 0.02** 0.04**

P-value=0.17 6 1 0.25 111.63 108.99 0.11 0.16

Panel B. Exclusion tests among all indices

REIT Indices (n=7) r DF 5% C.V. UNCL HEAL INDU LODG RESI RETL SELF

L-R statistic 1 1 3.84 0.35 5.81 7.15 5.49 0.76 3.62 4.27

P-value 0.55 0.02** 0.01** 0.02** 0.39 0.06* 0.04*

Panel C. Cointegration rank tests on five cointegrated indices

I(1)-Analysis (n=5, lag=1) G(r) p-r r Eig. Value Trace Bartlett Trace P-Value Bartlett P-Value

1.15 5 0 0.26 73.49 72.07 0.02** 0.03**

P-value=0.28 4 1 0.11 34/86 34.34 0.46 0.49

Panel D. Exclusion tests among five cointegrated indices

REIT Indices (n=5) r DF 5% C.V. HEAL INDU LODG RETL SELF

L-R statistic 1 1 3.84 8.20 13.49 10.38 3.28 4.83

P-value 0.00*** 0.00*** 0.00*** 0.07* 0.03**

The G(r) statistic is distributed chi-square with r degrees of freedom and is used to detect common linear trends among any of the property market indices, p is the number of dimensional vectors of property market indices, r is the number of cointegrated vectors, Eig Value is the Eigenvalue obtained from maximum likelihood estimation of the error correction model. Trace is Johansen trace statistic for cointegration rank test; Bartlett Trace is the Bartlett-small-sample-corrected Trace statistics, P-value is the probability value for Johansen trace statistics. The final column reports the p-value for the Bartlett Trace statistic. Panel B presents the exclusion test results based on the rank tests in Panel A. Insignificant likelihood-ratio (L-R) statistics affirm the null hypothesis the index is independent from cointegrating relations. Corresponding p-values are shown under the L-R test statistics. DF is the degrees of freedom, while 5% C.V. represents the critical value at a 5% level. Panel E reports results of Johansen’s (1992c) weak exogenous test. The weak exogenous variable (indicated by insignificant likelihood ratio, L-R, test statistics) is the source of common trend and does not respond to deviations from long-run equilibria. Insignificant L-R statistics are associated with leading countries within the CIV. ***, ** and * denote statistical significance at the 1%, 5%, and 10% levels, respectively.

30

Table 3 Leading Sector within the CIV (from 03/1984 to 12/1994)

Panel A reports results of Johansen’s (1992b) weak exogenous test. The weak exogenous variable (indicated by insignificant likelihood ratio (L-R) test statistics) is the source of common trend and does not respond to deviations from long-run equilibria. Insignificant L-R test statistics are associated with leading countries within the CIV. Panel B shows Granger (1969) causality F-test statistics with maximum of 12 lags, (X) represents explainable variables; (Y) represents dependent variables. Significant F-test statistics represents granger causality.

Panel A. Weak exogenous test within the CIV

REIT Indices (n=5) r DF 5% C.V. HEAL INDU LODG RETL SELF

L-R statistic 1 1 3.84 0.25 9.44 5.81 1.22 2.02

P-value 0.62 0.00*** 0.02* 0.27 0.16

Panel B: Ganger causality F-test within the CIV

HEAL(X) INDU(X) LODG(X) RETL(X) SELF(X)

HEAL(Y) 149.33*** 1.92 0.65 1.30 0.88

INDU(Y) 3.77*** 37.65*** 1.26 3.02** 2.17*

LODG(Y) 1.33 1.15 77.51*** 3.14** 0.77

RETL(Y) 1.12 0.91 1.48 106.89*** 0.34

SELF(Y) 0.98 0.98 1.35 1.51 171.47***

31

Table 4 Cointegration under Different Market Conditions

tY∆ ρ0 ρ1 ρ2 ρ3 ρHEAL(t-1) ρINDU (t-1) ρLODG(t-1) ρRETL(t-1) ρSELF(t-1)

0.0142 0.0378 -0.0302 -0.0505 -0.1327 -0.1715 -0.0473 0.2137 0.1661

0.69 1.70* -0.99 -2.03** -1.76* -2.09** -1.14 2.24** 2.60***

0.0548 -0.0173 0.0088 -0.0771 -0.1321 0.0788 -0.0682 0.1818 -0.0352

2.40** -0.77 0.26 -2.35** -1.59 0.87 -1.49 1.73* -0.50

-0.0156 -0.0254 0.0447 -0.1295 -0.2212 0.4152 0.0272 -0.0472 0.0119

-0.45 -1.25 0.87 -2.61*** -1.75* 3.03*** 0.39 -0.30 0.11

0.0058 0.0350 -0.0019 -0.0651 -0.1234 -0.0011 -0.0282 0.1599 0.0141

0.27 1.70* -0.06 -2.16** -1.61 -0.01 -0.67 1.65 0.22

0.0398 0.0031 -0.0423 -0.0160 -0.0180 -0.2104 0.0212 0.2273 -0.0188

1.71* 0.13 -1.23 -1.88* -0.21 -2.28** 0.45 2.13** -0.26

This table presents a vector autoregression (VAR) analysis with an interactive dummy with the past CIV residual. The VAR model is as follow:

t

k

i

itittttt YY ψρϖϑρϖρϑρρ +∆++++=∆ ∑=

−−−3

132110 *)*(

where tY is the vector of property sector price levels in a VAR system at time t;

tY∆ is the vector of property sector returns in

a VAR system at time t; 1−tϑ is the CIV residual (disequilibrium) in the past at time t-1; ϖ is a binary dummy variable with 1

= declining market and 0 = rising market at time t; )*( 1 tt ϖϑ − is the interactive term with past disequilibrium and current

market condition; ∑

=−∆

k

i

iti Y4

*ρ is the sum of k number of one period lagged property sector returns in the VAR system and ψ

represents the error term of the system. ***, ** and * denote statistical significance at the 1%, 5%, and 10% levels, respectively.

)(tHEALY∆

)(tINDUY∆

)(tLODGY∆

)(tRETLY∆

)(tSELFY∆

32

Table 5 Determinants of Cointegration Disequilibrium

Panel A. Equity Market Common Factors

θ0 θEquityMkt θEquitySMB θEquityHML θEquityUMD θEquityLIQ R-Sqr

Coefficient 0.0134 -0.3486 -0.1213 -0.2083 -0.1955 0.1503 0.01

t-test (1.21) (-1.30) (-0.42) (-0.55) (-0.95) (0.45)

Panel B. Macroeconomic Factors

λ0 λMP λUI λDEI λUTS λUPR R-Sqr

Coefficient -0.15629 0.3069 18.8750 -33.8751 -1.3046 19.1280 0.21

t-test (-4.73)*** (0.20) (3.07)*** (-2.23)** (-1.55) (5.58)***

In Panel A, the cointegration residual is regressed against Fama-French-Carhart-Pastor-Stambaugh

equity market five factors:

= θ0+ θ1(REquityMkt – Rft) + θ2EquitySMBt + θ3EquityHMLt + θ4EquityUMDt + θ5EquityLIQ + εpt,

where is the CIV residual (disequilibrium) at time t. REquityMkt – Rft is the CRSP equity market index risk

premium, the EquitySMB is the equity size premium measured as the difference in returns of small cap and large cap equity portfolios, the EquityHML is the equity value premium calculated as the difference in returns of high book-to-market and low book-to-market equity portfolios, and the equity momentum factor, EquityUMD, is the difference between equity returns of last year high return and low return portfolios. EquityLIQ is the value-weighted Pastor-Stambaugh equity liquidity factor that long stocks with high liquidity betas and short stocks with low liquidity betas. Other than the liquidity factor, equity data is

downloaded from the website of Professor Kenneth French.In Panel B, the cointegration residual is

regressed against Chen, Roll, and Ross (1986) macroeconomic five factors:

= λ0+ λ1MPt+ λ2UIt + λ3DEIt + λ4UTSt + λ5UPRt + τpt,

where MPt is the industrial production growth rate, UIt is unexpected inflation rate, DEIt is the change in expected inflation, UTSt is the term structure and UPRt is the risk premium at time t. All five factors are on a monthly basis.T-stats are reported beneath each parameter estimate. *** and ** and * denote statistical significance at the 1%, 5%, and 10% levels, respectively.

tϑ

tϑ

tϑ

tϑ

tϑ

tϑ

tϑ

33

Table 6 Portfolio Constituents

Panel A Annual VWCOI portfolio constituents for the value-weighted cointegration-inspired portfolio (in percentage)

Country 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

UNCL 6.08 6.14 6.48 2.86 3.09 7.64 4.61 8.45 7.43 6.67 9.46 9.72 8.68 8.87 10.46 HEAL 14.85 18.20 16.35 14.83 12.67 9.06 7.71 8.69 9.57 9.60 9.36 8.92 10.17 14.16 19.24 RESI 31.07 30.57 32.19 35.91 34.78 36.17 42.30 37.50 33.35 30.46 29.04 28.18 29.16 21.42 23.81 RETL 42.51 38.18 36.13 38.47 41.12 39.56 37.95 36.85 43.15 46.19 44.96 44.80 43.00 46.58 33.03 SELF 5.49 6.91 8.84 7.93 8.34 7.57 7.42 8.51 6.49 7.07 7.19 8.39 8.99 8.97 13.47

Panel B Annual EWCOI portfolio constituents for the equal-weighted cointegration-inspired portfolio (in percentage)

Country 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

UNCL 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 HEAL 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 RESI 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 RETL 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 SELF 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20

Panel A reports the annual percentage (%) allocations of the value-weighted cointegration-based VWCOI portfolio. At the beginning of every year over the sample period, we construct the VWCOI based on five essential property type REITs’ prior December market value, the portfolio is also held for the next 12 months. Panel A reports the annual percentage (%) allocations of the equally-weighted cointegration-based EWCOI portfolio. At the beginning of every year over the sample period, we construct the EWCOI with 20% weight on each sector, the portfolio is also held for the next 12 months.

34

Table 7 Portfolio Performance01/1995-12/2009

Panel A. Summary Statistics

Portfolio RET(%) SD(%) SHP(%) J-K z-test (vs. MKT) T-test H0: (RET-Rf) = 0

MKT 0.93 5.90 10.78 1.44

VWCOI 1.02 5.75 12.72 1.67* 1.71*

EWCOI 1.05 5.45 13.95 1.73* 1.87*

3MTB (Rf) 0.38 0.19

Panel B. VWCOI Performance Summary

Portfolio a b1 b2 b3 b4 R-Sqr

VWCOI 0.0014 0.9699 0.0329 -0.1581 0.0820 0.97

(1.92)* (67.59)*** (1.02) (-4.68)*** (0.13)

VWCOIUp -0.0006 1.0278 0.1025 -0.2159 -0.4759 0.93

(-0.36) (26.61)*** (2.24)** (-4.49)*** (-0.57)

VWCOIDown 0.0023 0.9733 -0.0313 -0.1204 2.4491 0.97

(1.69)* (56.32)*** (-0.64) (-1.90)* (1.78)*

Panel C. EWCIM Performance Summary

Portfolio a b1 b2 b3 b4 R-Sqr

EWCOI 0.0020 0.9215 0.0995 -0.1831 0.7479 0.94

(1.85)* (37.32)*** 1.63 (-2.67)*** 0.69

EWCOIUp -0.0006 0.9090 0.1364 0.0919 -1.1144 0.83

(-0.34) (15.48)*** (1.20) (0.92) (-0.44)

EWCOIDown 0.0039 0.9266 0.0833 -0.2529 0.6356 0.97

(3.02)*** (30.83)*** 1.04 (-3.55)*** (0.56)

Panel A reports descriptive statistics for the benchmark and portfolios used in the study over the 180-month period October 01/1995-09/2009. RET is the monthly raw return and SD is the standard deviation of monthly returns, and SHP is the Sharpe ratio. MKT is the value-weighted CRSP/Ziman REIT Market Index. MPT is the Markowitz’s optimized portfolio from seven property type REIT indices. MPTESSE is the Markowitz’s optimized portfolio from five essential property type REIT indices. CM is the value-weighted cointegration-based five essential property type REITs portfolio. INDE is the value-weighted two non-cointegrated property type REITs portfolio. REDU is the value-weighted two redundant property type REITs portfolio. Panel B presents the results of the four-factor model regression:

Rt - Rft = a+ b1(RMKT – Rft) + b2SMBt + b3HMLt + b4UMDt + ept, where Rpt is the monthly portfolio return, Rft is the monthly Citigroup 3-month Treasury bill return, RMKT is the value-weighted CRSP/Ziman REIT Market Index, SMB (small minus big) is the REIT size factor, HML (high minus low) is the REIT style factor and UMD (up minus down) is the REIT momentum factor. T-stats are reported beneath each parameter estimate. We report the model R-sqr and MSE for the explainable and unexplainable portion of the variation of REIT market return. ***, ** and * denote statistical significance at the 1%, 5%, and 10% levels, respectively.

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