RISK AND RETURN ANALYSIS OF REAL ESTATE SECURITIES: AN APT

APPROACH

DISSERTATION

Presented in Partial Fulfillment ofthe Requirements for the Degree Doctor of

Philosophy in the Graduate School ofThe Ohio State University

By

Deborah A. Pozsonyi, B.S., M.S.

*****

The Ohio State University

1994

Dissertation Committee: Approved by

Anthony Sanders, Ph.D. Ronald L. Racster, Ph.D. %~ AdVisor Paul Schultz, Ph.D. Business Administration Graduate Program Copyrightby Deborah A. Pozsonyi 1994 Dedicated to the Loving Memory of

Bertalan "Apu" Pozsonyi

who dearly loved this country and me. I knew him as "Apu" which means father in Hungarian. Apu exhibited an extraordinary degree ofbravery in the face ofdeath and had an immense degree of appreciation for the freedom and opportunities America offered. He taught me the meaning ofcourage, perseverance, patience, understanding, acceptance, forgiveness, compassion, honesty and love --- by example.

God Bless America

Koszonom Apu

11 ACKNOWLEDGMENTS

The formidable and monumental journeyto thisjuncture has not been a solitary sojourn. I humbly acknowledge each of you who havegreatlyinfluenced, supported and encouraged me to complete this dissertation

First and foremost, I singmy praises and thanksto Thee '0 Lord. A sincere thank you to my advisor and chairman, Anthony Sanders, who sometimes saw more ability in me than I, myself, believe existed. Thankyou for expanding my abilities and understanding. To Tony Sanders and the rest of my committee, Paul Schultz and Ron Racster: thank you for your guidance, patience, and assistance. Thankyou to mymother, MargitPozsonyi, and my siblings Annie, Julie, Linda and Bobbyfor their love and support. A heartfelt thanksto mydearest friends and supporters, Dr. Lisa Osberg, and SteveNaber,Ph.D. Lisa and Stevetirelessly shared their experience, wisdom and love. Steve deserves special thanks for helping with SAS programming and spending timeto help checkmywork. A very special thanksto K.C. Chanfor generously giving timeto review myresults on a briefpass-through from Hong Kong. I would also liketo thankthose who each, in their own way, gave me support me during mytenure as a graduate student. Thankyou Joe Damico, Phylis and Zoltan Koczor, DarrellLee, Juan Bowen,Bruce Reitz, Scott Wilson, Betty Bell, Gita

ill DeSouza, GeorgeKalbouss, Michael Dehlendorf, Dennis Golko, Joan Patton, Craig Stevens, DaveLambert, Willard McIntosh, Ph.D., MaryMeredith and the memory of Aaron Supowit. Time and spacecannot accommodate allto whomI am enormously grateful.

IV VITA

June 1987 B.S.B.A., The Ohio State University Columbus, Ohio

1988-1992 Graduate Teaching Associate Dept. of Finance The Ohio State University

1989-1992 Economics & Research Consultant Ohio Association of Realtors Columbus, Ohio

1992 Master of Arts Department of Finance The Ohio State University

1993-1994 Graduate Research Associate College of Medicine The Ohio State University

1994-Present Assistant Professor Department of Real Estate Georgia State University Atlanta, Georgia

FIELDS OF STUDY

Major Field: Business Administration Studies in Real Estate & Urban Economics and Finance

v TABLE OF CONTENTS

DEDICATION ii

ACKNOWLEDGMENTS iii

VITA v

LIST OF TABLES viii

LIST OF FIGURES x

CHAPTER PAGE

I. INTRODUCTION 1

II. LITERATURE SURVEY OF RECENT EMPIRICAL RESEARCH ANALYZING EQUITY REITS AND CONSTRUCTION SECURITIES ...... 10

III. THEORY OF ASSET PRICING, ARBITRAGE PRICING AND MIMICKING PORTFOLIOS 25

Introduction to Modem Asset Pricing 25 Capital Asset Pricing Model. 27 Arbitrage Pricing Theory 31 CAPM as Special Case ofAPT 36 Arbitrage Pricing and Mimicking Portfolios 37

IV ESTIMATION AND FORMATION OF DATA SERIES .44

Introduction 44 Real Estate Security Portfolios: HBCs and EREITs .45 Market Indices 49 Macroeconomic Factors 52

VI Security Portfolios Grouped by Capitalization 60

V. METHODOLOGY AND EMPIRICAL RESULTS 62

Single Factor Model 64 Results and Discussion 65 Multifactor Macroeconomic ModeL 68 Results and Discussion 69 Multifactor Mimicking Portfolio Model 71 Formation of Mimicking Positions 74 Results 77 Concluding Remarks 80

VI. TESTING REAL ESTATE FOR THE SMALL FIRM EFFECT 83

Introduction 83 Literature Review 85 Data 88 Methods and Empirical Results 89 Conclusion 91

VII. CONCLUSION 93

BIBLIOGRAPHY 120

VIl LIST OF TABLES

TABLE PAGE

1. Glossary and Definitions ofVariables 97

2. Monthly Means and Standard Deviations ofReturn Series 98

3. Correlations for Return Series 99

4. Derivation ofData Series 100

5. Means and Standard Deviations of Macroeconomic Factors l0l

6. Correlations of Macroeconomic Factors l02

7. SingleFactor Model: 1973-90 103

8. SingleFactor Model: Subsample 104

9 Direct Impacts ofthe Macro Factors on EHBC, EREIT, and EWNYSE ...... 105

10. Subperiod Direct Impacts ofMacro Factors on EHBC, EREIT and EWNYSE 106

11. MimickingPortfolio Returns l 07

12. Impacts ofMimicking Portfolios on EHBC, EREIT, and EWNYSE: 1973-1990 108

13. Subperiod Impacts ofMimicking Portfolios on EHBC, EREIT, and EWNYSE 109

14. Excess Mean Returns of Portfolios of Securities Grouped by Capitalization and Month: 1973-1990 110

Vl11 LIST OF TABLES

15. TBILL and Excess Mean Returns ofEREITs, HBCs, and EWNYSE Grouped by Month: 1973-1990 111

16. Regression ofJanuary Real Estate Returns on SmallCapitalization Finns' January Returns 112

17. Regression ofReal Estate Returns on Small CapitalizationFinns' and VWNYSE Index: 1973-1990 113

18. Regression ofReal Estate Returns on Finn Returns in the 4th Decile by Capitalization: 1973-90 114

IX LIST OF FIGURES

FIGURE PAGE

1. Cumulative Monthly Returns 115

2. January Excess Mean Returns Grouped by Market Capitalization: 1973-1990 116

3. Excess Mean Returns Grouped by Market Capitalization and Month: 1973-1990 117

4. Excess Mean Returns Grouped by Month: 1973-1990 118

5. October Excess Mean Returns Grouped by Market Capitalization: 1973-1990 119

x CHAPTER I INTRODUCTION

Within the broad sector ofreal estate are several types ofasset classes

influenced by various local and regional geographic factors. These include single­

family homes in Spokane, Washington; the Rockefeller Center in New York City; and

the Hong Kong and Shanghai Bank in Hong Kong. In additionto geographicfactors

are financial and macroeconomic factors which systematically affect all asset returns.

The purpose ofthis dissertation is to identify financial and macroeconomic factors which influence real estate returns and investigate the following: (1) examine

the sensitivity ofreal estate to these pervasive market factors, (2) compare the risk and

return relationship of production-oriented real estate securities and equityREIT returns

with a portfolio ofmarket securities, (3) use performance measuresto test whether real

estate earns positiveexcessrisk-adjusted returns, and (4) examine real estate securities

for return characteristics generally associated with small capitalization firms.

Investors considering the inclusion of real estate in their asset portfolio need

estimates ofrisk and expected return. This studyprovidesthese estimates for the

1 2

sample period January 1973 through December 1990 and an analysis of the extent to whichreal estate securities maybehave like small capitalization firms. Two distinct portfoliosof real estate securities analyzed here include (1) a portfolio of production­ orientedhomebuilding securities (HBC), and (2) a portfolio of equityreal estate investment trusts (BREIT). The securities in these portfolio are traded on the New

York Stock Exchange (NYSE), American Stock Exchange (AMEX), and National

Association of Security Dealers Automated Quotations System (NASDAQ).

Employing transactions-based price data from real estate securities which trade on major stock exchanges as opposedto appraisal-based data mitigates distortions which mayarise as a result of smoothed appraisal-based returns (GeItner, 1989).

Whenthe Chairman of the Federal Reserve Bank, AlanGreenspan, announces

an increase in interestrates, new homes sales fall and construction activity slows

down. Consequently, homebuilding securities are expected to fall and be sensitive to changes in interest rates. In addition to changes in interestrates, it is ofinterestto

analyze how changes in other financial and macroeconomic factors mayinfluence the

returns of a portfolio of production-oriented homebuilding securities (HBC) in

relationship to a portfolio of equity-based real estate investment trusts (BREIT). Given

the nature of construction activity, the volatility of a portfolio of homebuilding

securities should be greater than that of equityrealestate investment trusts which 3 generally manage and own existing real estate assets with underlying lease contracts.

And, in fact, this is what we find. Since EREITs primarily manage and hold existing real estate assets backed by leases, cash flows ofEREITs are analogous to bonds and should have a risk structure that is intermediate between stocks and bonds.

Real estate constitutes a considerable proportion ofthe national wealth.

Ibbotson and Fall (1979) estimate that over 50% ofinvestible wealth in the United

States consists ofreal estate. Furthermore, approximately 33% ofthe world's wealth is in real estate (Ibbotson, Siegel, & Love, 1985). Since, real estate is the single largest asset class and investment category, investors recognize the importance ofincluding it in their investment portfolios.

Equity REITs, in particular, are becoming an important real estate investment vehicle for institutional investors and others wanting to participate in real estate. In fact, REITs raised an unprecedented $14 billion of capital in 19931 and are the "hottest sector for stock offerings on Wall Street" today.'

The importance ofreal estate in a well-diversified portfolio can be evidenced by the increased attention granted this asset class by large pension funds. In 1993, for example, the Ohio Legislative changed the Ohio Revised Code, Chapter 3307, to grant

1 Kenneth Leventhal & Company 2 The New York Times,August4, 1994. 4 all Ohio public employee pension funds the right to invest in real estate investment trusts (REITs). One ofthese pension funds, State Teachers Retirement System, has reevaluated its investment portfolio and may increase its real estate investment allocation to approximately 12% ofits total assets.'

California Public Employees Retirement System (CalPERS), the largest public pension fund in the United States with total assets exceeding $70 billion, is another pension fund which has reevaluated the relative importance ofits real estate portfolio.

CalPERS recently allocated $250 million, or 2% ofits real estate portfolio, to be invested in real estate investment trusts". In addition to increasing its investment in

REITs, CalPERS also initiated a homebuilding investment program in 1992. Its homebuilding program provides capital to the homebuilding industry in the form of both debt and equity.' In 1992 CalPERS invested approximately $75 million in single- family housing construction activities. While CalPERS is not mandated to restrict its homebuilding investments, it currently has 66 different projects with small, nonsecuritized homebuilding companies which operate in California." "The goal ofits

3June 10, 1994 conversation with Bonnie Roberts, Director of Research, STRS 4REIT Advisory Services Group at Kenneth Leventhal and Company. S Abby, D. andNeff, D. "Attracting Pension FundCapitalto the Homebuilding Industry". UrbanLand, UrbanLand Institute. June 1994 6 June23, 1994conversation with AIFerdandez, CalPERS 5 homebuilding investment program is to achieve high risk-adjusted rates ofreturn and increase portfolio diversification" (Abby & Neff, 1994).

Clearly, institutional investors have increased their attention to diversifying their portfolios with real estate investments. Accompanying this heightened institutional real estate investment activity and increased securitization is a decrease in traditional sources offinancing. The savings and loan crisis and numerous defaults on commercial mortgages largely resulting from overbuilt markets have resulted in a shortfall ofloans to many residential and commercial real estate developers. Banks and savings and loans have reduced their level oflending to construction activities by $63 billion, from

$186 billion to $123 billion between 1989 and 1992 (peiser & Beigel, 1992). This is approximately a 34% reduction. A contributing factor in this decrease in lending activity is the Financial Institutions Reform, Recovery and Enforcement Act of 1989

(FIRREA). FIRREA limits lenders in the number ofloans they can make to anyone borrower in addition to increasing risk-based capital requirements. Thus, banks, insurance companies, and savings and loans, which have historically been the primary source offinancing for the real estate industry, now face more stringent risk-based capital requirements and issue fewer development loans or commercial real estate financing. 6

As traditional sources of financing reducetheir commitment ofcapital to single­ family housing construction and real estate investment activities, developers look to other sources to provide needed debt and equity. One sourceis securitized capital markets. The reluctance of traditional lenders and investors combined with legislative changes, suchas FIRREA, haveinduced many investors requiring acquisition, development, and construction loans to go public and issueinitial public offerings

(IPOs), bonds, and marketable equity securities.

Increased securitization of real estate has createda needto systematically

analyze the risk and returncharacteristics of real estate securities since the extentto

which real estate should be included in a well-diversified portfolio is determined by these estimates of risk and expected return.

Following the theoretical work of Ross (1976) and Huberman, Kandel, and

Stambaugh (1987), this studyuses real-estate based securities to estimate the risk and

return characteristics of real estate as an asset class. Building on the empirical work of

Chan, Chen, and Hsieh (1985), Chen, Roll, and Ross (1986), and Chan, Hendershott,

and Sanders (1990), this paper estimates factor indices offive important financial and

macroeconomic factors. It also examines the extentto which innovations in these financial and macroeconomic factors mayexplain assetreturn variation. Thesefive factors include (1) growth in industrial production, (2) change in expected inflation, (3) 7 unexpected inflation, (4) default risk, and (5) change in the slope ofthe term structure of interest rates.

Using methods employed in Chan, Hendershott, and Sanders (1990), this study also estimates returns ofmimicking portfolios which have a one-to-one correspondence to the innovations ofthe financial and macroeconomic factors under consideration.

The extent to which real estate returns are influenced by changes in these factors, as well as portfolio performance measures may be obtained through the use ofmimicking portfolios.

In their study, Titman and Warga (1986) show that estimates ofREIT risk are dependent on the type of asset pricing model used. They find that the investment performance measures of a sample ofREITs, using a five-factor model, are typically lower than performance measures derived from a single factor market model. Although explanations or models should be as simple as possible, if a simple single-factor model cannot capture the important risk characteristics of assets returns, then a multifactor model should be used. Sweeney and Warga (1986), for example, show that the Capital

Asset Pricing Model (CAPM) is insensitive to changes in interest rates. Since real estate is sensitive to changes in interest rates, the arbitrage pricing theory (APT) may be more appropriate in explaining asset prices and real estate returns. (Sweeney &

Warga, 1986; Chan, Hendershott, & Sanders, 1990; Gyourko & Keirn, 1992). 8

APT is more robust than CAPM. It does not makestrong assumptions about the distribution of asset returns, the existence and efficiency of a market portfolio or the ability to borrow at the risk free rate. Also, APT can be extended to a multiperiod framework. Finally, unlike CAPM, APT allows more than one systematic factor to explain asset returns.

Using macroeconomic factor indices rather than return-based factor series does not easily lenditselfto return and risk analysis. Thisis because indices do not have a return-based interpretation. Therefore, this studyestimates a set of mimicking portfolioreturns to be used in placeof the macroeconomic indices. Ifexact arbitrage pricing holds, then positions represented in these mimicking portfolios can be used to estimate the risk premiums associated with each of the macroeconomic factors under consideration. That is, since the macroeconomic factorsthemselves are not priced, the mimicking positions can be used to derive mimicking portfolio returns. Consequently, mimicking portfolio returns provide a foundation upon which we can estimate the sensitivity of real estate returns to innovations in these macroeconomic factors and derive a type ofperformance measurement.

The remainder of this dissertation is organized as follows: Chapter2 providesa

survey ofrecent empirical research whichanalyzes real estate risk and return. A

summary ofthe data, data sources, statistical properties, real estate portfolio 9 construction, size-based security portfolios, marketindices and macroeconomic indices is presentedin Chapter3. Chapter4 presentsthe methodology and empirical results of the hypotheses tested. Three models are used in the hypothesis tests. They are a single-factor model, multivariate macroeconomic model, and multifactor model using mimicking portfolio returns in place of the factors. Chapter 5 provides a definition and discussion of the small firm effect and examines the real estate portfolios under consideration for the existence of small capitalization firm characteristics. Finally,

Chapter 6 concludes this dissertation by providing a summary of the empirical results and suggested areas for future research. CHAPTER II

LITERATURE SURVEY OF RECENT EMPIRICAL RESEARCH ANALYZING EQUITY REITS AND CONSTRUCTION SECURITIES

This chapter focuses on recent empirical research which studies real estate and investigates the extent to which real estate securities may be used appropriately to proxy for real estate. A review ofexisting research on the risk and return characteristics and the possible relationship between equity REITs and appraisal-based return series is presented first. In contrast to equity REITs, this chapter also surveys empirical research which investigates real estate construction-related securities.

Real Estate Investment Trusts (REITs) are securitized financial assets which largely invest in real estate-related assets. Currently, REITs constitute approximately one to two percent oftotal real estate wealth in the United States, or $48 billion.'

Even though REITs are legally required to hold high percentages ofreal estate-related

1 NAREIT [1993] reporton the net assetvalueof 206 REITs 10 11 assets in order to avoiddoubletaxations, researchers questionwhether we can derive efficient estimates on real estate by using REITs. Furthermore, since real estate assets are infrequently traded and have relatively hightransactions costs associated with the trade, some argue that REITs reflectthe volatility ofthe secondary securities market rather than real estate, per se. (Ross & Zisler, 1987a, 1987b, 1991). That is, much of the existing literature questions the extentto whichequityREITs reflectthe true nature ofreal estate or underlying income-producing propertiesofREITs. Can real estate­ related securities traded on the national exchanges be used to study the characteristics and nature of the real estate sector, in general? In other words, do equityREITs or securitized real estate-related securities reflectthe true nature ofthe underlying income producing properties?

Should equityREITs be used to characterize the true nature ofthe underlying assets? Furthermore, do these securities merely reflectthe volatility characteristic of the stock market? These questions are particularly compelling since real estate-related

REITs trade much more frequently than durable real estate assets on the central stock exchanges.

2 To qualify for tax exemptions, REITs must (1) invest 75% of their total assets in mortgagees, real estate equities, cash or government securities, (2) distribute 75% of their taxable income to shareholders, (3) derive 75% of their gross income from mortgages, rents, and capital gains from the sale of realty, and (4) not act as dealers whose ordinary line of business is to hold real estate primarily for the purpose of selling it. 12

The answer to these questions first requires a distinction between the types of

REITs that exist. REITs may be categorized into three groups: (1) mortgage REITs,

(2) equity REITs, and (3) hybrid REITs. Mortgage REITs predominately hold mortgages on real estate properties, equity REITs primarily hold real estate properties, and hybrid REITs hold a combination ofmortgages and properties.

Although equity REITs are often referred to as "real estate investments," there exists debate in the literature as to whether REITs may be called "real estate assets."

That is, although equity REITs exhibit some fundamental economic characteristics associated with the real estate sector, there is debate in the literature about whether it is appropriate to use transactions-based REIT security prices to estimate unsecuritized real estate returns and volatility parameters. The question is, do equity REITs serve as a good proxy to estimate the risk and return parameters of real estate? Are the risk characteristics of equity REITs indicative ofthe true nature ofthe real estate market?

Ross and Zisler (1987a, 1987b, 1991) analyze the extent to which equity REITs may reflect the true nature ofthe real assets market by employing two sources ofdata:

(1) securitized REIT data series and (2) unsecuritized appraisal-based data series. They conclude that the securitized index overstates real estate's 'true' volatility, whereas the appraisal-based return series underestimates it. They conclude that real estate's 'true' 13 risk and return lie somewhere between the estimates obtained from each ofthese two data sources.

Goetzmann and Ibbotson (1990) use Granger causality tests to determine whether there exists autocorrelation between real estate security returns and appraisal­ based returns. Using lagged values ofsecuritized REITs and unsecuritized appraisal­ based real estate returns during the 1972-1987 sample period to test the hypothesis that the securitized REIT market contains information which leads the appraisal-based series, they reject this hypothesis and suggest that securitized REIT returns are too volatile to reflect underlying real asset values. Furthermore, they imply that appraisal­ based indices provide more reliable estimates ofrisk and return than equity REIT ones.

In a Salomon Brothers report, Mengden and Hartzell (1986) use a portfolio of

19 equity REITs for the 1973-1986 sample period and provide evidence that REITs may not be a good portfolio substitute for investors wanting to invest in unsecuritized real estate. Their research suggests that their sample of equity REITs exhibit "hybrid" qualities. That is, equity REITs exhibit characteristics which are exhibited in both the unsecuritized real estate market and the stock market in general.

Corgel and Rogers (1991) also test the 'hybrid hypothesis' using firm-level data of 52 REITs during the 1981-1986 sample period. Their research reveals that some of these REITs have a strong correlation with market returns, some REITs are correlated 14 with a proxy for real estate returns, and others exhibit hybrid security characteristics.

They conclude that REITs are hybrid securities and that there exists an aggregation bias in the indices.

Although it is not entirely clear whether the price of REITs reflects underlying real asset values, real estate professionals do not believe that appraisal-based estimates of real estate accurately reflect the volatility ofreal estate. Hartzell (1989) asks academicians, institutional investors, real estate professionals, and pension fund managers whether they believe appraisal-based estimates ofreal estate having "one-fifth ofstock risk" accurately reflect real estate risk. Only 18% ofthe 116 respondents believed this to be the case and as a group estimated the volatility to be 57% ofthat exhibited by stocks in general. In fact, Firstenberg, Ross, and Zisler (1987) demonstrate that equity REITs have approximately six times the amount of variability as appraisal-based returns.

While appraisal-based returns may be biased and tend to smooth estimates of volatility, several studies do support the hypothesis that REITs are efficiently priced, including those of Giliberto (1990), Chan, Hendershott, and Sanders (1990), Ennis and

Burik (1991), and Gyourko and Keirn (1992). Each ofthese studies will examine whether there exists an efficient market for REITs. 15

Giliberto (1990) uses a sample of equity REITs during the 1987 to 1989 sample period and demonstrate that there exists a factor or set of common factors present in both an REIT sample and an unsecuritized real estate index of returns. They also find evidence that changes in REIT returns lead changes found in the unsecuritized real estate index.

Chan, Hendershott, and Sanders (1990) use both a single-factor and multifactor model to analyze a sample ofequity REITs over the 1973-1986 sample period.

Although they do not find any evidence that equity REITs are a hedge against inflation, their research suggests that three factors have a statistically significant effect on real estate security returns: (1)changes in unexpected inflation, (2) default risk, and (3) slope ofthe term structure. When regressing equity REITs on a single-factor market model, they do find evidence that real estate earns positive excess risk adjusted returns; however, this evidence dissipates when they use mimicking portfolio returns in a multifactor model. In the multifactor model, they estimate that equity REITs exhibit approximately 60% ofthe variability compared to an equally-weighted basket of securities as proxied by the EWNYSE. This estimate may vary, however, depending upon the degree to which each equity REIT may be leveraged since they find, not surprisingly, that greater leverage leads to greater risk. 16

Ennis and Burik (1991) employ a NAREIT index coupled with empirical evidence presented by other researchers' to argue that equity REITs are efficiently priced and that the volatility observed in the REIT index is consistent with real estate's

"true" volatility. They further conclude that equity REITs provide more reliable estimates ofreal estate's true return and volatility then do appraisal-based return series.

Another approach used to examine market efficiency is to test for the existence ofmarket segmentation. Ambrose, Ancel and Griffiths (1992), for example, use fractal geometry methods to test for market segmentation across return series for REITs and stocks. They conclude that these markets are not segmented since returns for both

REITs and stocks follow a random walk. They also argue and provide some evidence that REITs are not a good proxy for actual real estate returns.

Liu, Hartzell, Greig, and Grissom (1990) also look for evidence of market efficiency by examining whether the real estate market is segmented from the stock market. Using a sample of equity REITs over the 1978-1986 sample period, they find evidence that real estate securities are integrated with the stock market but that the underlying commercial properties in these equity REITs, using FRC and ACLI data, are segmented from the stock market. They attribute their evidence of segmentation to

3 Allen and Sirmans (1987), Shilling, Do, and Sirmans (1989), Giliberto (1990), Chan, Hendershott, and Sanders (1990), and Gyourko and Keirn (1992). 17 such real estate market barriers as information and transaction costs. They recognize, however, that other factors may have contributed to these findings such as misspecification ofthe market index or the type real estate data used (i.e., appraisal­ based, imputed value, or actual sales price).

Another set of empirical studies which investigates the relationship between equity REITs traded on central exchanges and appraisal-based return series includes

Granger casualty tests. These are tests ofthe existence ofautocorrelation between equity REIT returns and appraisal-based returns. Studies which employ Granger casualty tests and confirm the hypothesis that REIT returns lead appraisal-based returns include Giliberto (1990, 1993), Goetzmann and Ibbotson (1990), and Myer and Webb

(1993a).

Other empirical studies which provide evidence on the relationship between

REITs, real estate, and stocks include Giliberto (1990, 1993), Barkham and Geitner

(1993), Chan, Hendershott and Sanders (1990), Liu and Mei (1992a), Gyourko and

Keirn (1992), and Han (1991). These researchers find a common factor or common set offactors which link the securitized REITs and unsecuritized appraisal-based return indices, or find a factor(s) between securitized REITs and stocks, in general. 18

Giliberto (1990) analyzes, compares, and contrastsfour return series data: (1) appraisal-based, Russell-NCRElf4, real estate returns, (2) transaction-based, NAREIT, equityREITs, (3) the S&P500 stock index, and (4) an investment-grade bond index developed by Salomon Brothers during the 1978-1989 sample period. Usingthe correlations of the residuals, Giliberto finds evidence of a common factor or set of factors whichis presentin both sets of the real estate-based return series. He terms this common factor or set offactors "pure real estate." Giliberto also provides empirical evidence that the appraisal-based return series are lagged by usinglagged residual values of the NAREIT index to explain contemporaneous variations in the residuals in the appraisal-based return regression.

Giliberto (1993) builds on his studyin 1990 to provide further evidence of the existence of "pure real estate" in both the Russell-NCREIF and REIT samples. They find empirical evidence to support"pure real estate" factorsby creating a "hedged"

REIT indexthat relates andthe unsecuritized real estate returnswith securitized equity

REITs.

Other empirical research which provides evidence on the relationship between

REITs and appraisal-based real estate returns includes Barkham and GeItner (1993).

4 NCREIF standsfor the National Council of RealEstateInvestment Fiduciaries. Before 1990, this was known as the Frank Russell Company (FRC) Property Index. 19

They provide evidence that price changes in securitized REITs lead changes observed in the appraisal-based real estate return series and find that REIT price movements predict price changes in real property. In addition, this research indicates that a link exists in the fundamental pricing of both the securitized and unsecuritized real estate markets and provides further evidence to support the hypotheses tested by Geitner

(1992).

Geitner (1990, 1992) adjusts the appraisal-based Russell-NCREIF Index for smoothing and then performs a comparative analysis between the "noise" found in the

Russell-NCREIF Index and the noise found in a transaction-based, unlevered NAREIT index. They define this noise as the market return component, or "excess volatility," which is not based on market fundamentals. That is, he hypothesizes that this noise contains information about future dividends and expected returns. In his analysis he finds that both the unsecuritized (Russell-NCREIF) and securitized (REITs) are equally noisy and concludes that these indices are not driven by identical, contemporaneous noises. Furthermore, he finds that market fundamentals present in each ofthese two indices are more highly correlated than the individual unsystematic noises ofthe indices. In short, Geltner shows that while transaction-based REIT and appraisal-based returns differ at discrete points in time, a long-run comparative analysis ofthe REIT 20 and "desmoothed" appraisal-based data series reveals that these two data series are quite similar, if not the same.

Liu and Mei (1992a) analyze the extent to which transactions-based real estate capitalization rates may provide information about securitized REIT expected excess returns. In their empirical analysis, they find that capitalization rates contain information which is useful for analyzing and, to some degree, predicting REIT returns.

Additionally, they argue that since REITs have a strong statistical relationship with small capitalization stocks and capitalization rates of real estate transactions, REITs may be termed "hybrid" securities.

Gyourko and Keim (1992) illustrate how the transaction-based REIT stock market is an important source ofinformation about the dynamic nature of real estate sector over the 1978-1990 sample period. They demonstrate this by showing how information imbedded in REIT security prices is later reflected in The Russell-NCREIF appraisal-based return series. More specifically, they provide evidence that real estate­ related securities, which include equity REITs, general contractors, subdividers and developers, provide economically important and timely information about changing real estate market fundamentals. The results oftheir empirical research "implies that the stock market signals changes in real estate values" one year prior to the release of the appraisal-based Russell-NCREIF returns. Their conclusion is further reinforced by 21 their finding that their REIT sample is contemporaneously correlated with the National

Association ofRealtors' transaction-based home price index. In addition, they find a sharp contrast between the betas ofthe various real estate-based securities such as

REITs and present evidence that construction-based real estate securities exhibit a greater degree ofvolatility than equity REITs.

Han (1991), however, questions the efficiency ofthe market for REITs by demonstrating how smoothed appraisal-based returns may have a statistically significant influence on REIT returns. That is, he argues that REIT returns lag the appraisal-based return series.

Few empirical studies analyze the risk and return parameters ofbuilding contractors or single-family home builders listed on.the major stock exchanges. The empirical studies that do exist include Davidson and Palmer (1978), Sagalyn (1990) and

Gyourko and Keirn (1992).

Davidson and Palmer (1978) use a sample of 11 equity REITs and 10 homebuilding firms over the 1972 to 1977 sample period to analyze the returns and volatility ofthese securities. In their analysis they perform a comparative analysis of the investment performance of these real estate-related securities with the Standard &

Poor's Index. They find that their sample of equity REITs has a beta of .87, whereas 22 their homebuilding firms have an average beta of approximately 2.57. Using a Jensen performance measure, they conclude that both equity REITs and homebuilding securities perform better on an average, on a risk-adjusted basis, than the market index.

In addition, they use a Treynor measure to compare the equity REITs with the homebuilding firms. They find that REITs outperform the sample ofbuilding firms and conclude that equity REITs appear to offer a greater return than homebuilding firms and stock market on a risk-adjusted basis.

Using distinct economic cycles as defined by the National Bureau ofEconomic

Research (NBER), Sagalyn (1990) studies cyclicality in the performance of real estate securities, using four sample groups against the overall market and the S&P500 as a proxy over the 1974-1987 period. The four groups ofreal estate securities include a portfolio ofall survivor REITs, equity REITs, homebuilders real estate companies, and commercial real estate companies. "Survivors" are defined as securities that have data on share prices and dividends over the entire sample period. In addition to these real estate security portfolios, Sagalyn uses the NAREIT and the appraisal-based Prudential

Realty Investment Separate Account (pRISA) indices for comparison. She demonstrates that the volatility ofreal estate securities is much higher than that of

PRISA. During periods ofhigh growth in real GNP, she finds, equity REITs exhibited lower variance, higher returns, and a lower beta than the overall stock market and 23 argues that appraisal-based data underestimate real estates true volatility during periods oflow economic growth. In addition, she finds that the homebuilders and commercial real estate companies have a much greater degree ofvolatility than the portfolios of

REITs and market proxy, particularly over periods oflow economic growth and recessionary business cycles.

By defining economic cycles, Sagalyn (1990) reaches a fuller understanding of real estate risk and its cyclical nature. Exploring real estate over long sample periods reveals important information, but by analyzing its return characteristics over well­ defined subperiods, Sagalyn is able to reveal subtleties which a more simple model might miss.

A simple model like the single-factor CAPM, for example, is useful in explaning an assets systematic risk and its sensitivity to the market portfolio. As an alternative, the arbitrage pricing theory (APT) holds that several factors may systematically explain variability in asset returns. The question then becomes, which model should be employed? Is the CAPM sufficient to explain real estate risk and returns? Can the single-factor model be used to derive reliable performance measures?

Titman and Warga (1986) show that estimates ofREIT risk are dependent on the type ofasset pricing model used. They find that the investment performance 24 measures ofa sample ofREITs, using a five factor APT-based model, are typically lower than performance measures derived from a CAPM-type single factor model.

William ofOckham, a philosopher ofthe fourteenth century, argued that

"entities are not to be multiplied beyond necessity." Necessity, however, sometimes dictates and supersedes simplicity. Although explanations or models should be as simple as possible, if a simple single-factor model is not able to capture the important risk characteristics of assets returns, then perhaps a multifactor model is a better choice. Sweeney and Warga (1986), for example, show that the Capital Asset Pricing

Model (CAPM) is insensitive to changes in interest rates. If, in fact, real estate is sensitive to changes in interest rates, then it may be argued that the arbitrage pricing theory (APT) is more appropriate to explain asset prices and real estate returns. The next chapter surveys both the CAPM and the APT. CHAPTER III

THEORY OF ASSET PRICING, ARBITRAGE PRICING AND MIMICKING PORTFOLIOS

Introduction to Modern Asset Pricing Theory

In this chapter, theories ofasset pricing, arbitrage pricing, and mimicking portfolios are reviewed. The asset pricing theories under consideration include the capital asset pricing theory (CAPM) and arbitrage pricing theory (APT). To better understand these asset pricing theories, the law ofone price, modem portfolio theory and systematic versus unsystematic risk will be discussed briefly.

Asset pricing theories hold that capital markets are or will be driven to equilibrium by market forces. That is, the value ofan asset is determined by investors buying and selling until prices reach equilibrium. Since new information is continuously and randomly generated, change in security prices are continuous and random as well.

25 26

At the heart of market equilibrium and the asset pricing theories explored in this paper is the law ofone price and modem portfolio theory. According to the law ofone price, the same good cannot sell for two different prices. Assuming frictionless markets, ifthese goods did sell for different prices, investors would drive their prices to the same price. If, for example, a security is "overvalued," investors will sell this security, thereby exerting pressure to drive down the price until the price of a security is at equilibrium. Conversely, investors would go long and bid on an "undervalued" securities, thereby exerting pressure to drive up the security's price.

Another theory used to establish both the CAPM and APT is the modem portfolio theory developed by Markowitz (1952). This theory holds that by combining assets which are not perfectly correlated, a portfolio's risk may be reduced without sacrificing expected returns. That is, diversifying portfolios with uncorrelated assets can eliminate unsystematic (diversifiable) risk. Ifwe assume that we can costlessly diversify investment portfolios, then the market will not reward investors for bearing unsystematic risk. It is for this reason that only systematic (market) risk will be priced since unsystematic risk can be costlessly diversified. Diversification can lead to efficient portfolios.

An efficient portfolio is an asset or combination of assets which has only systematic risk. More specifically, an efficient portfolio has the maximum expected 27 return for a given level of risk, or equivalently, the minimum level of risk for a given level of expectedreturn.

Both the capital asset pricing model and arbitrage pricing model price assets by each asset's degree of exposureto systematic risk.

The remainder of this chapter reviews the capital asset pricing model (CAPM) and the arbitrage pricing theory (APT). To showhow both theories are based on similar intuition, the derivation of the CAPMwithin the APT framework will be reviewed. The theory of arbitrage pricing and mimicking portfolios concludes the chapter.

Capital Asset Pricing Model

The capital asset pricing model (CAPM) was developed by Sharpe(1963, 1964) and Treynor(1961) with additional contributions madeby Mossin(1966), Lintner

(1965), and Black (1972). CAPMis a theory of how assets are pricedin relationto their risk. Thistheory assumes that if allinvestors employed Markowitz's portfolio theory to find portfolios in the efficient set, then eachinvestorwould choose one of the portfolios in the efficient set, based on their aversion to risk. 28

Assumptions used to develop the CAPM include the following: (1) frictionless asset markets and costless information are available to all investors, (2) all assets are marketable, perfectly divisible, and fixed, (3) a risk-free asset exists in which investors may borrow and lend in unlimited amounts, (4) investors have homogeneous expectations about asset returns that have a joint normal distribution, (5) investors are risk averse and maximize the expected utility oftheir end ofperiod wealth, and (6) there is an absence of such market imperfections as taxes and restrictions on short selling.

In a frictionless market, the borrowing rate equals the lending rate and leads to the development ofthe Capital Market Line whose slope is as follows:

(1)

Ifall assets are marketable and divisible, then components of human capital

(e.g. ability to program computers or cook) can be sold, not rented for wages, at market prices. Homogeneous expectations means that all investors choose from the same identical opportunity set since they possess the same information. 29

The mathematical proofofthe CAPM requires that in equilibrium, the market portfolio must be an efficient portfolio on the top half ofthe minimum variance opportunity set. The market portfolio consists of all assets held according to their market value weights'.

In equilibrium, the prices ofassets must adjust until all are held by all investors.

The market portfolio will consist ofall assets held in proportion to their value weights and the proportion of each asset must be as follows:

market value of the individual asset w = (2) i market value of all assets

A portfolio with investments ofx% in risk asset j and (l-x%) in the market portfolio will have the following mean and variance:

(3)

1 The efficiency of the marketportfolio and the CAPMarejoint hypotheses since it is impossible to test the validityof one withouttestingthe other. Roll (1977) arguesthat even ifthe CAPMholdsand marketsare efficient, it is impossible to testbecause of the difficulty in measuringthe true market portfolio. 30

) ) Where E(Rp is the expected return on the portfolio, E(Rj is the expected return on the jth asset, E(it) is the expected return on the market portfolio, CT~ is the variance

ofthe jth asset, and CT jm is the covariance between asset j and the market portfolio.

Given this measurement ofexpected return and risk, the CAPM holds that the expected return ofasset j is a linear function ofthat asset's exposure to systematic risk,

hj • The following the is the CAPM:

(5)

where rf is the risk free return or return on a zero-beta portfolio. The resultant expected return can then be used, for example, as a discount rate or cost of capital, given the assets, exposure to systematic risk. In equilibrium, all assets will be efficiently priced in terms of systematic risk since unsystematic risk can be eliminated through diversification. 31

Arbitrage Pricing Theory

Traditional arbitrage pricing theory (APT) introduced by Ross (1976) has fewer restrictive assumptions than the capital asset pricing model. APT assumes that asset markets are perfectly competitive and frictionless, and investors have homogeneous expectations that single-period random asset returns are governed by the following k­ factor linear stochastic model:

t =1,... ,n (7)

Using vector notation, equation (6) can be expressed as:

R=E+Bf+e (8)

where E is the N x 1 vector ofmean expected returns, B is the N x k matrix offactor loadings or scores, f is a kx 1 vector offactor realizations, and e is the Nx 1 vector of error terms which represent residuals or asset-specific, idiosyncratic risk. It is assumed 32

that the means of f and 8 are zero, that individual factors, f, are uncorrelated with each other and with 8, and that the unexpected residuals between all assets must be independent as follows:

E(1; ) = 0 (9)

E(8j )=0

E(1;~) = 0

E(~h )=0

E(8j 8; ) = 0

These assumptions lead to diversified portfolios that have several desirable properties.

First, portfolio returns are the weighted average of the returns of the assets included in the portfolio:

N

rp =LX/; (10) j=!

N where Xi represents assets i's weight in portfolio p and L x j = 1. Second, the i=1 portfolio's betas are a linear weighted average ofthe assets' betas: 33

(11)

for each of the k risk factors. Since the portfolio variance lacks covariance terms and the risk factors are statistically independent, the portfolio variance can be partitioned into its systematic and unsystematic risk components:

where (52 ( ep) represents unsystematic risk.

Unsystematic risk, however, can easily be diversified away and is therefore not priced. That is, consider an equally-weighted portfolio in which the weight of all n

1 assets are equal, Xi = -, The portfolio's unsystematic risk component can then be n written as follows: 34

(13)

As the number of asset n grows infinitely larger, the equation above asymptotically approached zero:

liml.!.1 (12(8) =0 (14) n--+oo n n

Therefore, APT holds that the market will not reward investors for needlessly bearing diversifiable risk. Furthermore, modern financial theory holds that asset returns will be a function of undiversifiable (i.e. systematic) risk alone since diversifiable (i.e. idiosyncratic) risk can be eliminated through diversification in a large asset market.

That is, since it is possible to costlessly diversify all idiosyncratic risk the market will not reward investors for holding this idiosyncratic risk. 35

As a result, Ross' asset pricing model states that when the number of securities is infinite the following model will hold exactly:

where Ao represents the return on a riskless asset or zero-beta portfolio and Ai is the risk premium on factor j.

The law of one price is at the foundation of APT. The law of one price holds that the same good cannot sell for two different prices. If the same good sells for different prices, the first arbitrageur who discovers this will attempt to sell the good at the higher price, thereby exerting downward price pressure, and bid on the lower priced good to exert upward pressure on the low price. Arbitrageurs will continue this type of trading until all prices are in equilibrium. The existence of riskless arbitrage is incompatible with equilibrium and therefore a key ingredient ofAPT.2

2 APTdoes, however, assume that arbitrageurs faceno restrictions or short sellingand may, therefore, receive 100%of the proceeds from their short saleto finance their longpositions in other assets. At first glance, somearguethat this is too restrictive. Miller (1989), however, arguesthat even ifonlya few large professional investors can exercise this the abilityto financelong positions with 100%of the proceeds from a short sale, this is sufficient to support the law of one price and the existence of "true" arbitrageopportunities. 36

CAPM as a Special Case of the Single-Factor APT

Ifwe define Ao ' in equation (15) as the return on a zero beta asset, then it follows that Ao =rf in the CAPM, equation (5), and by rewriting equation (15),

E(1\)-Ao =bnA 1+bi2A2+···· (16)

E(1\)-rl =bnA1 +bi2A2+····

where Aj measures investors' expected return for assuming one unit increase in hij risk.

Ifwe assume only one systematic factor prices asset returns and hif=l.O , then

hi2 =hi3 =... =O.

E(1\)-rf =bnA1 (17)

E(1\) =rl +bilA 1 37

By assuming that this one factor is the market price of risk, i.e. Al =E(rm) -rf , then the following is true:

QED

This demonstrates that the one-factor APT may be shown to accommodate CAPM with fewer restrictive assumptions. This also demonstrates that although the APT and

CAPM were derived using different economic logic, both models complement one another and may be shown to price assets similarly.

Given this APT framework, there will now be a discussion ofthe theory and creation ofmimicking portfolios.

Arbitrage Pricing and Mimicking Portfolios

The motivation ofusing mimicking portfolio returns in place ofthe macroeconomic factors under consideration and a survey ofthe theory and development of mimicking positions that may be used in place ofthe factors in APT 38 are now explored. For convenience, exact arbitrage pricing as presented in equation

(15) is rewritten in vector notation as follows:

E=irf+Bu (19) where i is a vector of ones, and U is a kxl vector ofthe factors' risk premiums. By combining the APT model, equation (8), and exact arbitrage pricing, equation (19), and rearranging terms, the following is obtained:

R-rf =Bu+Bf +e (20)

Since APT does not specify the number offactors or their identities, two approaches used to apply the APT are the factor analytic method and the multivariate factor model.

This dissertation employs a multivariate factor model and prespecifies the factors to be a set of macroeconomic factors empirically tested in Chen, Roll, and Ross

(1986) and Chan, Chen, and Hsieh (1985).

The problem with using equation (20) for empirical exploration is that the risk premiums, u, are inextricably linked with B as a constant. That is, ifwe regress asset returns in excess ofthe risk-free rate on a set ofmacroeconomic factors presumed 39 to drive asset returns, we can obtain estimates ofthe factor sensitivities, B, but we cannot obtain estimates ofthe risk premiums associated with each ofthe factors, U.

Huberman, Kandel, and Stambaugh (1987) set forth the theory which characterizes sets of mimicking portfolios and the relationship between mimicking portfolios and the minimum variance frontier. The elegance with which they present and summarize the theory ofmimicking portfolios, provides the foundation upon which this review of mimicking portfolio theory and our empirical research are based.

The beauty ofusing mimicking portfolios is that their returns can be substituted in place ofthe factors in an exact arbitrage pricing relation. Researchers can then test additional implications of arbitrage pricing theory. By using mimicking portfolios, researchers can obtain a performance measure like the CAPM Jensen to analyze security or portfolio performance. Furthermore, by using mimicking portfolios in place of the factors, risk premiums may be estimated and associated with the expected payoffs ofthese mimicking positions.

By definition, mimicking portfolios are sets ofassets whose returns mimic or mirror fluctuations in the factors under consideration. To illustrate, assume that

APT holds that there are five factors that systematically explain asset returns. Five corresponding mimicking portfolios could then be constructed so that the movements in each ofthese portfolios' returns would have a one-to-one correspondence with its 40 associated factor's movements and be uncorrelated with movements in the other four factors.

Consider a set of N assetsand let v represent an Nx1 investment positionin these assets. Since the cost of this position is v'i, and its payoffis v'r, then its return is v'r /v'i. Systematic risk of this position is v'BB'v and unsystematic risk is v'Zv, where b, is the kth column of the matrix B and Z is the covariance matrixof E(ee') the residuals e in equations (8) and (20).

Assuming k factors systematically drive asset returns, let A represent an Nxk

matrix ofmimicking positions. Each column of A, a k , is linearly independent. The cost of the position in the kth column of A is a~i and its payoffis a~r.

Let M represent the kxI vector of mimicking portfolios' returns,

M=A'r (21)

where r is an NxI vector of assetsor portfolio of assets used to createthe mimicking positions. Let C represent the Nxk covariance matrix,

C =cov(R,M) =VA (22) 41 where V is the covariance matrix of r .

Ifexact arbitrage pricing holds and the payoffs to the positions in matrix A can be used in place of the factors for pricing assets, the matrix A can be defined as factor-mimicking positions. These factor-mimicking positions can then be used to estimate the risk premiums associated with the factors. More formally, the expected returns may be stated in relation to the mimicking portfolios' return sensitivities as follows:

E=irr +Cv (23)

where v is a vector of constants.

Huberman, Kandel, and Stambaugh (1987) offer the proofs and conditions that support (1) when positions in A represent factor mimicking positions, and (2) that ifthe global minimum-variance portfolio has positive systematic risk, then mimicking portfolios can exist.

The relationship between exact arbitrage pricing and mean-variance efficiency are demonstrated in Chamberlain (1983), Grinblatt and Titman (1987), and

Jobson and Korkie (1985). Chamberlain (1983) explores this relationship when the number of assets is assumed to be infinite, whereas Grinblatt and Titman (1987) and 42

Jobson and Korkie (1985) consider this relationship when there are a finite set of assets. More specifically, Grinblatt and Titman (1987) propose and show that exact linear arbitrage pricing with respect to the k reference portfolios exists if and only if these reference portfolios are on the mean-variance frontier.

Jobson and Korkie (1985) show that in a special case, where the k factors are traded assets (or positions) and the risk-free asset exists with a return that differs from the minimum variance portfolio's expected return, exact arbitrage pricing implies that the tangent (Sharpe-Lintner) portfolio is a portfolio ofthe k factors.

Huberman, Kandel, and Stambaugh (1987) go on to show that if exact arbitrage pricing holds and i is in the column space of B, then every portfolio on the minimum-variance frontier is a portfolio ofmimicking positions. Furthermore, they also offer a proofofthe proposition that ifthe global minimum-variance portfolio is the only portfolio ofmimicking portfolios on the minimum-variance frontier, then exact arbitrage pricing does not hold.

Given these proofs, Huberman, Kandel, and Stambaugh (1987) show that there are numerous sets ofmimicking portfolios for a given set offactors. Huberman,

Kandel, and Stambaugh (1987) also provide three examples to illustrate how mimicking positions can be constructed. One ofthe examples is employed in this dissertation where, 43

Substituting this into equation (21), the mimicking portfolio returns are equivalent to weighted least squares:

where the elements of A are the coefficients of vector r used in computing the factor scores.

It is these mimicking portfolio returnsin equation (25) that are used in place ofthe factors themselves when performing an analysis of risk-adjusted performance.

This methodology will be discussed in further detail in the empirical presentation in

Chapter 5 after the source and nature of data employed are presented. CHAPTER IV

ESTIMATION AND FORMATION OF DATA SERIES

Introduction

This chapter develops the source of data employed and provides a description ofhow the return series or indices are formulated. The data gathered and developed for this dissertation span 216 months from January 1973 to December 1990 and encompass a complete business cycle which includes recessions, recoveries and economic expansions as well as high and low inflationary periods. Monthly data is employed or constructed, unless otherwise noted.

Two real estate security portfolios are used in this dissertation: (1) an equally­ weighted portfolio of homebuilding securities and (2) an equally-weighted portfolio of equity real estate investment trusts. In addition to these equally-weighted real estate return portfolios are two separate sets ofequally-weighted portfolios ofsecurities

44 45 grouped by capitalization. The first is a set of portfolios of securities grouped into deciles by capitalization. The second set includes portfolios of securities grouped into

"semideciles" or twenty capitalization groups. Details are provided on the source and construction of these "size-based" portfolio returns.

Also included in this chapter are a statistical summary of the data employed and a sectionon how the macroeconomic indices are constructed. Table 1 provides a glossary and summary of the data and abbreviations used.

Real Estate Security Portfolios: HBCs and EREITs

Empirical analysis is presented on two portfolios of real estate securities. One is an equally-weighted portfolio ofhomebuilding securities (HBCs). The other is an equally-weighted portfolio of equity real estate investment trusts (EREITs).

Both the HBC andEREIT portfolio returnsare computed by using individual

monthly security data over the 216 month sample period. By using equally weighted

returns, as opposedto value-weighted returns, portfolio returnswill not be skewedby a few large firms. 46

Anyqualifying homebuilding or equity REIT security that did not have any

missing data is included in the monthly sample to reducethe impact of sample selection bias. That is, each of the real estate portfolios includes homebuilding or equityREIT

securities that mayhavefailed or beendelisted over the estimation period. The sample

of homebuilding firms includes publicly traded securities on the New York Stock

Exchange (NYSE), American Stock Exchange (AMEX) or the National Association of

Securities Dealers and QuotationSystem (NASDAQ).

The searchfor qualifying homebuilding securities beganby identifying real

estate firms, using a set offour-digit Standard Industry Classification (SIC) codes in

the Centerfor Researchin Security Prices(CRSP) database. Firmsfalling into SIC

codes 1521-1542 and 6552 were identified. Thenthe sample of construction firms

obtained were narrowed to homebuilding securities that predominately build single­ family detached homesas opposedto income producing properties such as apartment

or commercial buildings or multifamily housing units such as condominiums and

townhouses. Value LineInvestment Survey andStandard and Poor's Security

Owner'sStock Guide were also consulted to identify additional homebuilding company

securities and narrow the sample to firms which predominately build single-family

residential housing. The HBC portfolio return series is estimated by calculating an

equally weighted meanreturn from monthly observations. 47

The total sample ofhomebuilding securities includes 46 firms whichwere listed on the NYSE, AMEX, or NASDAQ over the sample period. The minimum number of homebuilding firms in HBC in anyone month was 19 and the maximum number was

31. Only 7 of the firmshad return data for every month in the estimationperiod. On an average, there were 24 firms per monthin the homebuilding sample.

In addition to the HBC sample is a sample of equity real estate investment trust securities (BREIT)l. Equity real estate investment trusts are publicly traded corporations which pool capital and primarily investin income-producing properties.

In addition,REITs are a closed-endinvestment company which meansthat after the initial offering, it cannot acquire additional investments. As a result, future earnings willbe function of the profitability ofa REITs existing assets and the ways these assets are managed.

In order to be exemptfrom doubletaxation and qualify as an REIT under the rules ofthe InternalRevenue Service, REITs must distribute 95% oftheir cash flows in the form ofdividends. The types ofequityREITs included in the sampleprimarily invest in commercial officebuildings, warehouses, industrial parks, multifamily housing, and shopping centers. Sincehealth care REITs primarily participate in sale-leaseback

1 The returns to the HBCportfolio was createdby the author while returns to EREITwas providedby Darrell Lee. 48 arrangements with such healthcare providers as nursing homes, assisted living centers, hospitals, and medical buildings, they are not considered 'typical' equity REITs. That is, health care REITs generally purchase properties from health-care providers and then lease them back. Consequently, these health care REITs are not included in the EREIT sample.

Equity real estate investment trust securities are first identified by surveying the

CRSP database for firms in the 6799 standard industry classification (SIC) code. Since

SIC 6799 also includes mortgage REITs and hybrid REITs, in addition to health care

REITs, such additional sources as the REIT FactBook and Standardand Poor's

SecurityOwner'sStock Guide are referenced to isolate qualifying equity REITs.

The total sample ofqualifying equity REITs thirty-one (31) firms which were listed on the NYSE, AMEX, or NASDAQ over the sample period. The minimum number of equity REITs anyone month was 10 and the maximum number was 30.

Only 4 ofthese EREITs firms had return data for every month in the estimation period.

On an average, there were 21 EREITs per month in the equity REIT sample. 49

Market Indices

In order to conduct risk and return analyses on a comparative basis, four stock indices are employed. These indices include an equally weighted index (EWNYSE), a value-weighted index (VWNYSE), Standard and Poor's 500 (SP500) and a portfolio ofsmall capitalization stocks (Small). Each ofthese indices was downloaded from the

CRSP tapes and includes all capital gains and dividends generated by the underlying securities.

The EWNYSE contains monthly returns on an equally weighted portfolio of securities listed on the major exchanges, whereas the VWNYSE includes the monthly returns of a value-weighted portfolio of securities. Another market index used is the

SP500 index.

A size-based portfolio referred to as SMALL or SMI was also obtained from

CRSP by the following methodology. At the end of each year, CRSP ranks all securities according to its market capitalization at the end ofthe previous year. CRSP then partitions all securities into ten groups or deciles. SMALL is a return series, which includes capital gains and distributions offirms ranked in the lowest decile by market capitalization. Ifthe market capitalization ofa security is not available at the 50

end of the previous year, then the earliest available price and number of shares are used

to rank all listed securities.

Figure 1 exhibits the cumulative monthly returns estimated from the following

four return indices: HBC, SP500, EREIT, and SMALL. The HBC return series

exhibits the greatest degreeof variability, with particularly highpeaks during

expansionary economic periods(1983 and 1986) and low troughs during times of

recessions (1974-75 and 1981-1982). The EREIT also exhibits a degree of variability,

but it is not as pronounced as the HBC series.

In addition to the marketindices is a total return series on a portfolio of 30 day treasury bills from Ibbotsonand Associates. Table2 reports the monthly means and

standard deviations of the return series in excess of treasury bill rates. The results in

Table2 indicate that Small returns in excess of treasury bill rates exhibited the highest

monthly meanreturn of 0.65% over the entire sample period. Thiswas followed by

EWNYSE (0.53%), HBC (0.52%), EREIT (0.5%), SP500 (0.31%), and VWNYSE

(0.31 %). The order of variability, however, differs, with HBC having the highest

variance and followed by the Small Index, EWNYSE, EREIT, VWNYSE, and SP500,

respectively. The variability ofHBC leads all the return series with a standard

deviation of 0.116 and 0.126 in the full sample period and the first subsample period

(1973-1981), respectively. To some extentHBC'shighdegree of volatility maybe a 51

result ofthe relatively small number ofsecurities in the HBC portfolio in relation to the

number of securities in EWNYSE, VWNYSE, Small and the SP500.

Excess HBC returns had a highermonthly mean return during 1973-81 than

during the 1982·90 period. In fact, excess returns were almost four times greater in the first subperiod. Whilereturns were almost 400% greater during the first subperiod, the variability ofHBC returns in the second subperiodwere only 84% ofthe variability

reported during the first subperiod. Excess EREIT returns also exhibited a higher

mean return and variability during the first subperiod as did the EWNYSE and Small

Index. VWNYSE and SP500, on the other hand, had a lower mean return during the first subperiod than the second subperiod.

Table 3 reports the correlationbetween the return seriesunder consideration.

As expected, the highest correlation for the sample period existed between the market indiceswhere VWNYSE and SP500 had a correlationcoefficient of 0.995. The

relationship between the SP500 and EREIT, however, were not as highly correlated

and, in fact, had the smallest correlation coefficient of .59. When examining the

relationship between the two real estate portfolios, it is clear that they are not perfectly

correlated and, in fact, exhibit a correlation coefficient of .725. This supports the

contention that although these two real estate portfolios mayface many ofthe same 52 risk factors, they may differ by the degreeto which their returns are affected by changes in marketforces (Gyourko and Keirn, 1992).

Macroeconomic Factors

While the arbitrage pricing theory does not indicate how many factors systematically influence asset returns or what they might be, Chen, Roll and Ross

(1986) and Chan, Chen and Hsieh (1985) provide evidence that multivariate factor pricing equationhelps explain asset returns. Chen, Roll andRoss (1986) associate price changes in the stock marketto innovations in macroeconomic show how five macroeconomic variables systematically explain stock market returns. Since APT holds that there are only a few systematic risk factors inherent in asset returns, it is arguable that these factors would be relatedto innovations in majormacroeconomic variables such as interest rates and gross national production. Chen, Roll and Ross (1986) explore this hypothesis and provide evidence that assetreturns are governedby changes in the following five macroeconomic factors: 1) growth in industrial production, 2) change in expected inflation, 3) unexpected inflation, 4) default risk, and

5) the slope ofthe term structure. That is,these factors seemto be "priced" or associated with non-zerorisk premia in the APT-basedmacroeconomic model so that 53 investors are compensated for the systematic risk present in the assets. These same macroeconomic variables are the dependent variables used in the multivariate factor pricing equation presented in the next chapter.

Chan, Chen and Hsieh (1985) build on the work of Chen, Roll and Ross by examining the firm size effect in a multivariate factor model. Their empirical results show that the default risk premium is largely responsible for the risk-adjusted differential between returns to firms in the top five percent and the bottom five percent oftheNYSE.

This study, in turn, builds on the work of Chen, Roll and Ross (1986) and

Chan, Chen and Hsieh (1985) by estimating the same macroeconomic variables used in their studies. The following is a presentation ofhow each ofthese indices and expected inflation are estimated. Table 4 provides a summary ofhow each macroeconomic variable is defined.

Growth in Industrial Production

Empirical research by Peek and Rosengren (1976) shows that returns to stocks, in general, lead changes in GNP growth by approximately two quarters. Chen, Roll, 54 and Ross (1986) argue that since assets are related to changes in industrial production in the long run, monthly asset returns may reflect anticipated changes in this variable.

By following their argument a time series of growth in industrial production from t to t+ 1 was derived from data obtained from Citibase database and the Surveyof

Current Business. The monthly growth rate ofindustrial production, MP, in month t is computed as follows:

(26)

where IP is industrial production.

As shown in Table 5, the monthly growth rate for industrial production averaged 0.22% during the entire sample period, 0.12% during 1973-81, and 0.31% during 1982-1990.

Inflation

Two ofthe macroeconomic variables are a variant ofan inflation variable. One ofthese is change in expected inflation, DEI, and the other is unexpected inflation, ill. 55

Both of these variables incorporate an estimate of expected inflation in their calculation. The reason whytwo inflation-related variables are included in the analyses is that if future inflation forecasts are influenced by factors other than past economic forecast errors, then change in expected inflation, DEI, mayprovide current information not present in unexpected inflation, ill.

The following is a description of how expected inflation (EI), a component in the estimation of change in expected inflation (DEI) and unexpected (UI), is estimated.

Since there is no generally accepted theory on the construction of expected inflation, it is estimated by using an ad hoc model. After estimating inflation with the consumer price index(CPIU) from Citibase, expected inflation is calculated usingan autoregressive model with six lags:

where I t-n is the observed inflation in n periodsago, cn is the correlation coefficient assigned to the nth laggedinflation variable, and &t is the disturbance term which is assumed to be stationary and uncorrelated with all I t -n. Conditions for stationarity 56

include that G( havemeanzero, constant variance, andzero autocovariance. To support the use of this model, the error term of this model was tested and found have meanzero.

Using estimates of expected inflation obtained from equation (27), change in expectedinflation, DEI, fromt-l to t is estimated by subtracting current expected inflation from expectations about next month's expected inflation:

(28)

The meanmonthly value of the change in expected inflation is 0.0 for the sample period and both subsample periods.

The other macroeconomic inflation-related variable that may affect asset prices and provideinformation not presentin change in expected inflation is unexpected inflation, UI. Unexpected inflation in period t is measured as the difference between the realized rate of inflation, I in periodt, as reportedin the Consumer Price Index, and the expectedinflation in the sametimeperiod. More formally, unexpected inflation was measured as follows: 57

(29)

As shown in Table 5, unexpected inflation has a mean rate of 0.02% per month over the entire sample period, 0.04% over 1973-81, and 0.01% over 1982-90.

Default Premium

The default premium is hypothesized to capture changes in financial risk and bankruptcy risk. Since the discount rate used in the discounted cash flow model is a function of the priceof risk, changes in the default premium affect security prices in general and may signal a change in the business cycle. The default premium is measured as follows:

Default, = Portfolio return (Baa and under), - LGBt (30)

wherethe first term in the equation represents the return on a portfolio of highyield bondswhichreceived a rating of Baa and belowand the second term, LGB, is the 58 return on a portfolio oflong-term government bonds. Returns for both ofthese bond portfolio return series are obtained from Ibbotson and Associates.

Table 5 shows that there is a 0.0% monthly default premium over the full sample period and subsample rates of 0.19% and -0.19% over the 1973-81 and 1982­

90 subsample periods, respectively.

Change in the Slope of the Term Structure

The last macroeconomic factor used to explore return and risk characteristics of real estate securities is the change in the slope of the term structure. The importance of this factor in pricing assets is apparent since the price of an asset is estimated by discounting expected future cash flows. Cash flows to be received further into the future may require a discount rate that differs from the discount rate used to convert short-term cash flows investors expect to receive. By using the term structure variable, researchers can isolate changes in asset returns which are related to actual changes in the slope ofthe term structure as opposed to the default premium which reflects changes in risk aversion (Chen, Roll, and Ross, 1986). 59

The changein the slopeof the term structure in periodt was formulated as follows:

(31)

whereLGB t is a portfolio oflong-term government bonds and TB t is the return on

Treasurybills obtained fromIbbotsonand Associates.

Table5 reports that the change in the slopeof the term structure exhibited a monthly average of 0.10% over the entire sample periodand -0.40% and 0.60 over the subsample periods 1973-81 and 1973-1990, respectively.

Table6 reports descriptive statistics for the macroeconomic factors. Although most indices show a negligible amount of correlation, there is a negative correlation betweenthe default premium, DEF, andthe slopeof the term structure, TERM, with a correlation coefficient of -0.62. This is not unexpected since treasurybonds are a common component in both the default risk premium andthe slope ofthe term structure index. That is, returnsto long-term treasurybonds are subtracted in DEF, while beingadded in TERM. Another important feature ofTable6 is that although these macroeconomic factors are not entirely uncorrelated, they do show very low to 60 no correlation which is consistent with the requirement that these independent factors be uncorrelated.

Security Portfolios Grouped by Capitalization

Two separate sets of size-based portfolios contain securities grouped by market capitalization. The first set includes securities grouped into deciles by capitalization, and the second set includes securities grouped into 'semideciles' or twenty capitalization groups. The size-based group oftwenty portfolios is used to construct mimicking portfolio returns, whereas the decile group is used to test the real estate portfolios for the existence ofthe anomalous small firm effect.

Each ofthe size-based security portfolios is an equally-weighted return series, which includes capital gains and distributions ofall firms ranked in the lowest decile by capitalization. At the end of each year, CRSP ranks all securities according to its market capitalization at the end ofthe previous year. CRSP partitions all securities into ten groups or deciles. Ifa security's capitalization was not available at the end of the 61 previous year, then the earliest available price and number of shares were used to rank all listed securities.'

The set of20 size-based portfolios were constructed in a way similar to the

CRSP rankings. These size-ranked portfolios were formed by ranking all common stocks listed for at least five years on the NYSE. At the end of each year from 1972 to

1989, securities are ordered by their market capitalization and grouped by size into 20 asset portfolios from which an equally-weighted portfolio return is estimated.. This resulted in a series of216 monthly returns for each ofthe twenty size-ranked portfolios.

2 The returns to the set of 10 size-based portfolios was createdby the author while returns to the set of 20 wasprovided byKC Chan. CHAPTER V

METHODOLOGY AND EMPIRICAL RESULTS

This chapter contains a presentation of three models used to investigate the sensitivity of real estate returnsto changes in systematic factors. The three modelsare

(1) a single-factor model, (2) a multifactor macroeconomic model, and (3) a multifactor modelusing mimicking portfolio returns in placeofthe macroeconomic factors. After each of the models and the method of estimation are discussed, the empirical results are presented.

Ifis of interestto derive estimates from each of the three models since empirical evidence suggests that a single-factor CAPM-type model may be inappropriate for studying the risk-returnrelationship of real estate assets (Brueggman, Chen, &

Thibodeau, 1984, Brueggman, Chen, & Thibodeau, 1992, and Chen& Tsang, 1988).

Returns to real estate have been shownto be particularly sensitive to changes in interest rates and unexpected inflation (Titman & Warga, 1986, Chan, Hendershott, &

Sanders, 1990, Brueggman, Chen, & Thibodeau, 1984, and Gyourko & Keirn, 1992).

Consequently, the multifactor model may provide a more useful framework than a

62 63 single-factor model for analyzing the risk and return relationship of real estate

securities. Sweeney andWarga (1986) provide additional supportusingthe multifactor modelby showing that the single-factor CAPM is very insensitive to changes in interest rates.

Other systematic factors in addition to changes in interestrates maydriveasset returns. Chan, Chen andHsieh (1985)buildon the work of Chen, Roll, and Ross

(1986) analyzing the firms sizeeffect whereby returnsseemto be relatedto the market

capitalization of a firm. By usingmacroeconomic factors as prespecified in CRR,

CCH provide evidence that the firm sizeeffect is capturedby the factor loadings of the

APT. Theirresearchsupportsthe existence of efficient markets and provides evidence that the firm size effectis a result of risk factorswhichthe single-factor modelcannot

capture. More specifically, they find that the default risk premium is largely responsible

for the risk-adjusted differential whichexists betweenreturnsto NYSE firms in the top

five percent and firms in bottom five percentaccording to marketcapitalization.

Building on this research and usingmethods set forth in Chan, Hendershott, and

Sanders (1990), this research uses the same factors prespecified in Chen, Roll, and

Ross (1986) and estimates a set of portfolios which mimic each of these five factors usingtheory set forth in Huberman, Kandel, and Stambaugh (1987). 64

The remainder ofthis chapter is divided into three major sections. In the first section, a single-factor model is presented and used to regress real estate security returns on a market proxy. The second section presents how a multifactor model is used to examine the relationship of real estate returns to changes in five macroeconomic factors. The third section contains a multifactor model using estimates a set ofportfolios which mimic each ofthe macroeconomic factors under consideration. This model is used to analyze the investment performance ofreal estate in an APT framework. In each ofthese sections, the method is presented and then followed by a presentation and discussion ofthe empirical results.

Single Factor Model

In the case ofthe single-factor model, a regression similar to the market model is assumed to be a well specified model, meaning that the joint distribution between the

, return on the portfolio and the single-factor, rm , is such that the disturbance term, Bj in

the regression has mean zero and is orthogonal (uncorrelated) with rm . 65

The alpha(a) in equation(32) is a Jensen performance measure. A statistically significant positive alpha indicates superiorperformance or positive excess risk­ adjusted returns, and a negative alpha signifies negative excessrisk-adjusted returns.

The returns for each ofthe real estate portfolios, HBC and EREIT, in excessof the one monthtreasurybill rate, are regressed on the excess returns to the market proxy. Table7 presents the resultsfrom the full 216 month sample period.

Results and Discussion

PanelA in Table 7 showsthe resultsfrom equation(32) usingHBC as the independent variable. Regardless of whichmarketproxyis used as the dependent variable, the Jensen performance measure is not statistically different from zero. The beta, p, however, is statistically significant andis estimated to be 1.6 usingboth the equally weighted and valueweighted marketproxies. 66

PanelB in Table7 showsthe results fromequation (32) usingEREIT as the independent variable. Here, too, there is no evidence of superior or inferior risk­ adjusted performance, and the estimates of beta are statistically significant at the .05 level of confidence. The coefficient estimate, P, showslittle sensitivity to the choiceof

market proxyand averages 0.74 usingboth EWNYSE and VWNYSE, in tum.

The resultsin Table7 indicate that returnsto the HBC portfolio are over two times more sensitive to changes in the market indexthan returnsto the EREIT portfolio.

Table8 displays the regression results obtained for the single factor model when the sample period is divided into two subsample periods: 1973-81 and 1982-90. The results obtained, again, suggest that the portfolio ofHBC securities are over 200% riskier than our portfolio of equityREITs. Furthermore, we find no evidence of excess expected returns in either subperiod examined. Comparing the coefficients over the two subperiods, it appearsthat the coefficient estimates for EREIT declined by more than 50% from the 1973-81 to 1982-90 periods. The beta estimates on the HBC portfolio, however, do not exhibit signs of nonstationarity.

Using a single factor model, no evidence of abnormal returns to real estate is found. Thisis consistent with evidence presented by Chan, Hendershott, and Sanders

(1990), Smith and Shulman (1976), Han (1990), and Glascock (1991). Hartzell and 67

Mengden (1987), however, do present evidence that a portfolio ofREITs provides a positive abnormal return offour percent during the 1972 through 1987 sample period.

The results from tests offinancial performance, however, are a function ofthe sample period, the return data employed, and the model used to analyze investment performance. When Chan, Hendershott, and Sanders (1990), for example, use a single­ factor model, they find evidence for excess risk-adjusted returns for the 1973-1987 sample period using the value-weighted NYSE as a market proxy, but find no evidence for excess returns usingthe same sample period and an equally-weighted NYSE proxy.

In addition, they find that during the 1980-1987 period, equity REITs exhibit positive excess returns irrespective ofwhich index is used to proxy the market.

The beta coefficients estimated using EREIT as the independent variable are also consistent with existing literature which finds REIT returns to be less risky than the market portfolio i.e. f3 < 1. (Chan, Hendershott, & Sanders, 1990, Ross & Zisler

1987a, 1987b, 1991, Gyourko & Keirn, 1992, and Mengden & Hartzell, 1986). In addition, the empirical results presented here which reveal that the P-coefficient of

EREIT declined by more than 50% from the 1973-1981 to 1982-1990 periods, are also consistent with the literature which finds that equity REITs exhibit a significantly lower degree ofvolatility during the 1980s (Chan, Hendershott, & Sanders, 1990, Giliberto,

1989). 68

Multifactor Macroeconomic Model

The empirical test of the relative sensitivity of real estate returns to five macroeconomic factors is based on the work of Chen, Roll, and Ross (1986) who associate marketreturns with changes in industrial production, expectedinflation, unexpected inflation, default risk, and the slope in the term structure. Chapter IV,

Estimation and Formation of Data Series, details the source of the data and how each of these factors is derived. For convenience, Table4 provides a summary of how each of the factor indices is derived.

To estimate the relative sensitivity of real estate returns to changes in macroeconomic variables, three indices (HBC, EREIT, and EWNYSE) are regressed, individually and directly onto each of the five factor indices over the 216 month sample period. 69

Results and Discussion

Coefficient estimates and the corresponding standard errors from equation (33) for each ofthe three portfolios are reported in Table 9. When HBC is used as the independent variable, the coefficients for changes in industrial production (MP), default risk (DEF), and slope ofthe term structure (TERM) are positive and statistically different from zero at the 10% or lower confidence levels. The unexpected inflation (VI) coefficient, however, is negative and significantly different from zero.

The results in Table 9 also show a significant positive influence for MP, DEF, and TERM when EREIT is used as the independent variable. Here, too, the results show a significant negative ill coefficient. This same pattern is repeated when regressing EWNYSE on the factor indices. Only one factor, change in expected inflation (DEI), shows no significant influence on security returns.

When comparing the results ofHBC to EREIT, it is interesting to note that each ofthe common significant coefficient estimates is a greater when HBC is the independent variable. This is expected and consistent with evidence presented by

Gyourko and Keirn (1992) and Sagalyn (1990) who find that construction firms exhibit greater volatility than equity REITs or a market index. 70

When EREIT is used as the independent variable in equation (33), the coefficient estimates for MP, DEF, and TERM are lower than those reported for the

EWNYSE. These coefficient estimates seem to indicate that EREITs are not as sensitive to changes in industrial production, default risk, or the slope ofthe term structure as the EWNYSE. However, the higher unexpected inflation (UI) coefficient in the EREIT regression suggests that EREIT returns may be more sensitive to changes in unexpected inflation than EWNYSE, but not as sensitive as EHBC.

Like Chan, Hendershott, and Sanders (1990), evidence from Table 9 shows that both EREIT and EWNYSE are significantly and positively related to default risk

(DEF), and the slope ofthe term structure (TERM), and negatively related to changes in unexpected inflation (VI). In contrast to Chan, Hendershott, and Sanders (1990), both the EREIT and EWNYSE indices are shown to be significantly positively related to changes in MP, industrial production, whereas CHS shows that only the equity

REIT portfolio is significantly and positively related to MP.

Table 10 reports the regressions from equation (33) during the 1973-1981 and

1982-1990 subperiods. The positive significant relation between each of the three indices under consideration and MP (change in industrial production) in the 1973-81 subperiod seems to disappear during the 1982-1990 subperiod. The coefficient to 71 default risk and term structure variables, however, are systematically positive over both subperiods for each ofthe three portfolios underconsideration.

Multifactor Mimicking Portfolio Model

This sectionpresentsthe multifactor mimicking portfolio model, constructionof the mimicking portfolio returns, methods, and empirical results. Before the methods used to construct mimicking portfolios are presented, though, it mayprove useful to first define mimicking portfolios and set forth the motivation for usingmimicking positions in place of the macroeconomic indices in equation(33).

Mimicking portfolio returns are defined to be a set of portfolios with returns that mimic, or have a one-to-onecorrespondence, with the movements of each macroeconomic factor under consideration. One advantage of using mimicking portfolio returns in place of factor indices is that mimicking portfolio returns, as opposed to the use of factor indices alone, can be used to explain asset returns and price assets when exact arbitrage pricing holds. Anotheradvantage is that by using portfolio returns in placeof the factors, a type of Jensenperformance measure maybe derived from empirical testing. 72

By regressing returnsin excess of the risk-free rate, or a zero beta portfolio, onto mimicking portfolio returns and a constant, the constantcan be interpreted as a type of performance measure. That is, ifthe constantis not significantly different from zero, then returns of the independent variable are commensurate with their risk. If, however, the constantis significantly negative, then there is evidence of inferior performance; a significantly positive constant, however, signifies that the independent variable is a superior investment. Thisresearchwill analyze the performance of real estate returns usingthis type of model.

The empirical model and method used to constructmimicking portfolios closely follows the work of Chan, Hendershott, and Sanders (1990). In order to establish the methodsused in CHS (1990) and makethis chapter as selfcontained as possible, the following is a briefreview of the APT modeland motivation for using a two-stage estimation procedureto estimate mimicking portfolios andtheir associated risk premiums.

In the APT asset returns are assumed to be generated by a linear factor model:

r=E+Bf+8 (34) 73

where r is a Nxl vector ofasset returns, E is an Nxl vector of expected returns, f is a Kxl vector ofcommon random factors with expected values ofzero, B is an NxK matrix of sensitivity coefficients (factor loadings), and e is an Nxl vector ofresiduals.

Assuming that an exact factor structure holds and the residuals are uncorrelated across securities

E =irF +Bu (35)

where rF is the risk-free rate if one exits, t is a vector of ones, and u is a Kxl vector offactor prices or risk premiums associated with each factor. It is these risk premiums which are estimated by mimicking portfolio returns.

By combining equations (34) and (35)

r - ir; = Bu + Bf + e (36) 74

Since the risk premiums, u, are imbedded in the constantin equation(36), a two-stage variantof the Farna-MacBeth method is employed to estimate these premia using a set of mimicking portfolios returnswhichmimic or are perfectly correlatedwith the realizations of the K factors (Fama& MacBeth, 1973).

Formation of Mimicking Positions

This sectiondescribes the two-stage processused to estimate mimicking portfolio returns that are used in place of the factors in a multifactor model.

First, a time-series regression usingequation(36) is used to estimate the factor sensitivities, B, and the residual covariance matrix, Z. A series of 216 monthly returns to twenty size-based portfolios of securities ranked by marketcapitalization, in excess of the one-month treasurybill rate, are regressed directly on the five factor indices.

From this time-series regression, a (20x5) matrix of B -coefficient estimates and a

(20x20) residual covariance matrix Z, are obtained.

Several studiespresent evidence whichsuggests that there existsa firm size effect, so that portfoliosof assets with different marketcapitalizations maypossess 75 different risk and return characteristics (Chen, 1981, 1983, Chan, Chen, & Hsieh,

1985). In view ofthis evidence, size-based portfolios are used in the analysis to reduce the incidence of estimation errors in the B -coefficients.

The second step in the two-step procedure used to estimate mimicking portfolios is to run a cross-sectional weighted least squares regression using the theory set forth in Huberman, Kandel and Stambaugh (1987) and the empirical methods used in Chan, Hendershott, and Sanders (1990). Theoretically, the set of mimicking portfolios employed in this study are assumed to have the minimum residual variance of all possible mimicking portfolios. These mimicking portfolios have the minimum residual variance of all potential mimicking portfolios subject to the condition that

(37) where a/c is a N x 1 vector that represents positions in the N assets that move one-for­ one with the movements in the k-th factor and is unrelated to the other factors and e/c is a K x 1 vector with the k -th row equals one and the other rows equal zero. Returns to the mimicking portfolios on the K mimicking positions are given by

R= Air (38) 76

where A is a N x k matrixwhose k -th column is at and A is givenby

(39)

where V is the covariance matrix of asset returns and Z is the covariance matrix of the assets residuals obtained in the time-series regressions.

By regressing a time series of real estate portfolio returns in excess of the one­ monthtreasury bill rate onto excess mimicking portfolio returnsand a constant, estimates of a performance measure and the sensitivity of the real estate portfolio returns are obtained. 77

Results

Table 11 summarizes the estimated returns to the mimicking portfolios constructed over the full sample period. The results show positive risk premiums associated with changes in industrial production, change in expected inflation, default risk, and slope ofthe term structure. Ofparticular interest is the negative risk premium associated with changes in unexpected inflation. This implies that investors may demand a lower discount rate when there is a rise in unexpected inflation, but the significantly negative p-coefficient presented in Table 12 indicates otherwise since the product oftwo negative numbers is a positive value.

Table 12 presents the results ofregressing HBC and EREIT returns onto the mimicking portfolio returns in excess ofthe one month treasury bill rate for the full sample period. The results show that each ofthe five dependent variables, on average, significantly explain price movements in homebuilding securities, HBC, and an equally­ weighted market index (BWNYSE). When the portfolio ofequity REITs (BREIT) is regressed on the mimicking returns, all but the mimicking returns related to changes in expected inflation (RRDEI) are statistically significant.

A comparison ofthe results shown in table 12 reveal that HBC is more sensitive to changes when compared to EREIT. On average, HBC is over twice as sensitive to mimicking positions related to changes in industrial production, unexpected inflation, 78 default risk and the slopeof the term structure as EREIT. Whencomparing the coefficient estimates of EREIT to EWNYSE, however, there is evidence that EREIT is not as sensitive as the marketproxyto changes in mimicking positions relatedto industrial production, unexpected inflation, default risk and the slope ofthe term structure.

Table 12 also reports an estimate of the constantfor each regression which serves as a type of Jensen performance measure. Each regression showsthat the a constant is not significantly different from zero. This implies that there is no evidence that real estate earns excess risk-adjusted returns. That is, returns to real estate are commensurate with its level of risk.

Table 13 repeatsthe regression performed abovefor each of the two subperiods examined. The resultsfrom 1973 through 1981 in Panel A show some differences from those reported in PanelB for 1982through 1990. More specifically, the coefficients relatedto industrial productionand unexpected inflation are significant in both HBC and EREIT regressions, but becomestatistically insignificant for both of these independent variables during the 1982through 1990 subsample. Anotherinteresting finding is that HBC returns appear to be more sensitive to changes in mimicking returns relating to the slopeof the term structure C!3RTERM =2.070) in the 1982-1990 subsample period than the 1973-1981 subsample period C!3RTERM=1.663). Another difference 79 across subsample periodsreveals that returnsto EREITs appearto be less sensitive to changes in default risk in the later subsample period as indicated by the lower p­ coefficient estimate. Finally, statistical significance for the variables relating to changes in industrial production, expectedinflation andunexpected inflation seems to evaporate from the first subsample periodto the second subsample period.

Estimates of the constanttermsreportedin Table 13 implies that there is some evidence of excessrisk-adjusted returns overthe subsample periods. More specifically, the estimates imply inferior performance for HBC andEWNYSE during the first subsample period, and superiorperformance for allthree portfolios (HBC, EREIT, and

EWNYSE)for the second subsample periods. Thesefindings, however, are inconclusive sincethe subsample results indicate that security pricesare not commensurate with their level of risk.

Anotherinteresting finding is obtained whenregressing the full sample of

EWNYSE on the mimicking portfolio returns. The adjusted R 2 is a remarkable 0.90.

While it is not the intent of this dissertation to verify the validity of the multifactor mimicking portfolio model, a discussion is warranted. Why is the adjusted R 2 so high?

Does the model fit the data this well? Are the subsample results which indicate excess risk adjustedreturns valid? 80

Several observations come to mind when comparing the results presented here and those reported in Chan, Hendershott, and Sanders (1990). First, comparing the subsample results with those reported in CHS show some similarities. For 1973-1981,

R 2=0.859, and CHS report R 2=.895 for 1973-1979. The results for 1982-1990 indicate R 2 =0.125 compared to the 1980~ 1987 CHS R 2 =0.196. Second, expected inflation is estimated over a longer sample period the 1973-1987 sample period analyzed in CHS. Differences in estimates ofexpected inflation effect estimates ofboth the DEI and ill variables. A final observation is that perhaps the R 2 is a result ofthe additional degrees offreedom derived from using a longer sample period and the fact that the mimicking portfolios were formed from NYSE stocks.

Concluding Remarks

Just how sensitive are real estate returns to changes in the market? As shown, a portfolio of homebuilding securities seems to be substantially and consistently more sensitive to changes in the market factors than the portfolio ofequity REITs and an equally weighted market proxy, EWNYSE. Also shown is evidence which indicates that EREITs are less sensitive to changing economic conditions than the stock market as a whole. These results hold for both the single-factor and multifactor models considered. 81

Resultsshow that changes in industrial production, default risk and the slope of the term structure of interestrates significantly explain pricemovements in portfolios of real estate and a broad index of stocks. It appearsthat increased inflationary expectations have a negative influence on both EREIT and the market index,

EWNYSE, but have an insignificant effect on a portfolio of single-family homebuilding securities.

When mimicking security investment positions are created to capture movements in observable macroeconomic factors and used in placeofthese factors in a multifactor model, results indicate that increases in unexpected inflation, default

(bankruptcy) risk, and the slope of the term structure of interest rates have a negative effecton real estate security prices. Thisnegative effectis particularly pronounced for the portfolio of single-family homebuilding securities.

The greater sensitivity of homebuilding securities as compared to equityREITs is not a surprising result whenthe source of revenue for each of these real estate-based portfoliosis considered. Single family homebuilders beingproducers of large fixed assets are in a highly cyclical industry. Given that construction of homes involve durable assetswith relatively long lead times, revenues to homebuilders are subjectto fluctuations in building, construction, and economic activity. Furthermore, in view of the fact that equityREITs primarily invest in income producing properties, EREIT 82 revenues are largely the product oflong term leases. It is these long term leases which make the revenues of equity REITs less volatile to changes in general economic conditions. During an economic conditions upturn, the tenant in the long term lease may have the option to increase the consumption of space, but is restricted in times of economic turmoil from reducing this consumption as set forth in the agreements in the contract.

Another finding is that EREIT is generally less sensitive to changing market conditions than a broad index of stocks. The nature of long term leases probably contributes to this observation. Long term leases usually include provisions which pass-through increases in maintenance or energy costs, overage rents and lease escalation clauses. These provisions in the long term leases and the long term leases themselves contribute to the stability ofequity REIT revenues and may also reduce the negative impact associated with increases in inflation. This is consistent with empirical evidence presented by Gyourko and Linneman (1990) which shows how long term leases may limit the degree to which returns to real estate reflect changes in the market and the empirical evidence presented in Chan, Hendershott and Sanders (1990). CHAPTER VI TESTING REAL ESTATE FOR THE SMALL FIRM EFFECT

Introduction

This chapterpresents a test of the hypothesis that real estate securities behave

like small capitalization firms and exhibit anomalous returnsin January. The January

effect (i.e. small firm effector firm size effect) refersthe paradoxical behavior ofsmall

capitalization stock returns in January. While this phenomenon is not premised on any

existing financial theory, it is ofinterest to researchers because ofits persistence and

strong association with small capitalization firms. (Keirn (1985), Reinganum (1981,

1983),Roll (1983a, 1983b).

Sincethe January effect is contraryto the efficient-markets or general

equilibrium theories, many researchers are interested in investigating this anomaly and

trying to solvethis mystery. Gultekin and Gultekin (1983) provide evidence that the

Januaryeffectis not restricted to the United States market alone and find that there

83 84 exists an international January effect by demonstrating its presence in 16 other countries!

Figure 2 provides an illustration of the small firm effect by isolating January returns of 10size-based return portfolios. The figure showsJanuary returns in excess of the treasurybill rate of all securities listed on NYSE and AMEXfromJanuary 1973 through January 1990. Each of these ten size-based portfolios contains securities grouped by market capitalization by Center for Researchin Security Prices (CRSP). At the end of eachyear, CRSPranks all securities according to its market capitalization at the end of the previous year and then assigns each security a decile ranking. Ifa security's capitalization at the end of the previous year was not available, the earliest available price and sharedata of a security is used to rank the security. After identifying the deciles and the returns of the securities each decile contains from 1973 through 1990, an equally weighted monthly return index which includes capital gains and distributions is calculated.

Table 14 presentsa numerical presentation of returnsto the 10 size-based portfolios of securities grouped by capitalization and month. The smallest decile portfolio, S1, has a January return of 15.69%, which is in excess of the treasurybill rate. This wouldtranslate into a return in excess of 150% per annum if the average

January return persisted throughthe year. By looking at Table 14, however, one can 85 see that this is not the case. The January effectlives up to its name and resides in the month ofJanuary alone.

. Do real estate securities behave like small capitalization firms and exhibit anomalous January returns? Thischapterpresents a test of this hypothesis. Sincethere is a growinginterestin equity REITs and homebuilding firms, it is important to investigate this issue.

Literature Review

Rozeffand Kinney (1976)were among the first researchers to present evidence of the January effect. Using returnsof stocksfromthe New York Stock Exchange from 1904to 1974, they group return data into monthly returns and find that the average rate of return is approximately 3.5%. What is this January effectand why is it so persistent? Possible explanations for the January effect include the price-pressure hypothesis and the risk-premium hypothesis.

The price-pressure hypothesis involves extraordinary trading-volume activity whichcan causethe priceof securities to rise or fall. Why would there be an extraordinary volume of trading activity in the beginning of the year? Potential explanation include year-end tax loss selling or bonuses obtained by investors which are 86 used to purchase securities in the new year. Studies whichsupporttax-loss selling include Branch (1977), Reinganum (1983), Givoly and Ovadia (1983), and Schultz

(1985).

Another possible explanation for the January effect is the risk premium hypothesis. Ifuninformed investors, for example, assume a greater degree ofrisk for trading against informed insider traders who try to camouflage their trades during high trading volume activity, these uninformed investors should be expected to earn compensation for assuming this greater risk.

Seyhun (1988) analyzes the effect that corporate insider traders may have on small capitalization firm returnsin January. He reports that some insiders do tend to accelerate their planned stock purchases of small firms and postpone stock salesin

December; small firms' insiders, however, havean increased number of net purchases in December whichcontrastswith an oppositepattern of tradingexhibited by large firms' insiders. He argues that since there is no evidence that insiders increase their stock purchases in January, accelerating stock pricesof small cap firms in January cannot be the result of additional purchases of stock by insiders. He concludes that sinceinsider trading activity in small firms does not increase significantly in January, there is no evidence that the January effect represents compensation to uninformed traders for the risk of trading against informed insider traders. 87

An extension to this researchis Chan, Chen and Hsieh (1985) which investigates the firm sizeeffectwhereby returns seemto be relatedto the market capitalization of a firm. Using macroeconomic factors as prespecified in Chen, Roll, and Ross (1986), CCH provideevidence that the firm sizeeffectis captured by the factor loadings of the APT. Their research supports the existence of efficient markets and providesevidence that the firm size effectis a result ofrisk factors whichthe single-factor modelcannot capture. Their empirical researchrevealsthat the default risk premium maybe largely responsible for the risk-adjusted differential which exists between returns to NYSE firms in the top five percent and firms in bottom five percent accordingto market capitalization.

Evidenceof the firm size effectis graphically providedin Figure 3 and numerically summarized in Table 14. Analyzing the figure and the table reveal two important return patterns. First, the existence of a January effectis supported by the extraordinarily large Januaryreturns in small capitalization firms. Also, Januaryreturns appear to be decreasing monitonically at a decreasing rate as firm size increases. The second pattern revealed is negative meanreturnsto allfirms in October. These negative October meanreturns are largely the result of unusually large declines in the marketin 1978and 1987. Figure 5 isolatesOctober meanreturns and revealsa pattern between firm size and a decline in meanreturns. As shown, October meanreturns to 88 each of the size-based portfolios is negative. More importantly, there evidence that the negative effect of October on security returns appears to decline as finn size increases.

The returns data used to test for a January effect are from the Center for

Research in Security Prices (CRSP). The sample includes monthly returns of all firms listed on the CRSP monthly returns file from January 1973 through December 1900.

At the end of each preceding year, CRSP assigns every finn to a decile group based on its market capitalization. Firms with the smallest market capitalization are assigned to portfolio 1, firms with the second smallest capitalization are assigned to portfolio 2, and so on. Ifthe market capitalization for a finn is not available from the previous year, the finn is assigned to a decile ranking based on its earliest available capitalization in the current year.

Using these ten size-based capitalization groupings, an equally weighted return series is estimated from the monthly returns of each finn. Since CRSP assigns each finn to a capitalization group based on its most current capitalization, the equally weighted size-based portfolios are rebalanced and updated on a yearly basis. The 89 resultant size-based portfolios are labeled S1 or SMI for the smallest capitalization portfolio to S10 or SMI0 for the largest capitalization group.

In addition to these size-based groupings ofdecile portfolios are two equally weighted real estate securities portfolios: EREITs and HBCs. A description on how each ofthese portfolios is constructed is included in Chapter IV, Estimation and

Formation ofData Series.

Figure 4 shows the excess mean returns ofHBC, EREIT, and the EWNYSE grouped by month. HBC exhibits the largest mean return in January, with a 12.4 percent mean excess return. Table 15 provides the numerical companion to Figure 4.

Methods and Empirical Results

To test ifthe real estate securities portfolios, HBC and EREIT, behave like small capitalization firms, a regression of January real estate portfolio returns in excess of the treasury bill rate is regressed on the January excess returns to the smallest market capitalization group:

rj(JAN) - rf = aO + p(rsml(JAN) - rf) + e j (41) 90

Ifthe P-coefficient equals one and is statistically significant, then the independent variable is highly correlated with the January effect associated with small capitalization firms.

Table 16 presents the results ofthis test. As shown, when EREIT excess returns are used as the independent variable, the p-coefficient is 0.57 and statistically significant. Using HBC as the independent variable results in a statistically significant p-coefficient of 1.30. This suggests that although both real estate portfolios do exhibit a form ofthe January effect, HBC more closely resembles, ifnot exceeds, the January effect associated with small capitalization firms.

Nine additional regressions that resemble the regression above are performed.

Each regression uses the January returns for each ofthe other nine size-based decile portfolios in tum. The results of these tests reveal that although HBC January returns exhibit behavior which is more closely associated with small capitalization January returns, EREIT January returns exhibit behavior which is more closely associated to mid-capitalization January returns.

In another test, the full sample of216 observations ofreal estate returns is regressed on both a small firm and large firm portfolio as proxied by SMI and

VWNYSE, respectively: 91

Ifthe PI-coefficient equals one, P2 equals zero and both are statistically significant, the independentvariableexhibits behavior similar to small capitalization firms and

dissimilar to the large capitalization index.

Table 17 presents the results ofthis test. As shown, when EREIT excess

returns are used as the independent variable, both coefficients are statistically

significant, with the PI-coefficientequal to 0.34 and P2 equaling0.35. Both

coefficients also statistically significant when the using the HBC as the independent variablewith the PI-coefficientequal to 0.87 and P2 equal to 0.58.

Conclusion

The empirical evidence presented shows that both of our real estate portfolios

earn a substantial portion oftheir annual returns in January. Althoughthere is evidence

that each ofthese portfolios exhibit some degree ofa January effect, when testing

these portfolios for the existence ofthe small firms effect, it appears that the portfolio

of single-family homebuilding securities (HBC) behaves much like small capitalization 92 firms, whereas the portfolio of equity REITs (EREIT) exhibits behavior that more closely resemble midcap stocks. CHAPTER VII

CONCLUSION

Empirical results provide evidence that homebuilding securities seem to be substantially and consistently more sensitive to changes in systematic forces than the portfolio ofequity REITs and an equally weighted market proxy, EWNYSE. In addition, evidence indicates that EREITs are less sensitive to changing economic conditions than the stock market as a whole. These results hold for both the single­ factor and multifactor models considered.

Results show that changes in industrial production, default risk and the slope of the term structure ofinterest rates significantly explain price movements in portfolios of real estate and a broad index of stocks. It appears that increased inflationary expectations have a negative influence on both EREIT and the market index,

EWNYSE, but have an insignificant effect on a portfolio ofsingle-family homebuilding securities.

When mimicking security investment positions are created to capture movements in observable macroeconomic factors and used in place ofthese factors in a multifactor model, results indicate that increases in unexpected inflation, default

93 94

(bankruptcy) risk, and the slope of the term structure of interest rates have a negative effect on real estate security prices. Thisnegative effect is particularly pronounced for the portfolio of single-family homebuilding securities.

The greater sensitivity ofhomebuilding securities as compared to equityREITs is not a surprising resultwhen the sourceof revenue for each of these real estate-based portfolios is considered.

Single family homebuilders being producers of large fixed assetsare in a highly cyclical industry. Returns to single family homebuilders are dependent upon both supply and demand conditions in local housing markets and systematic macroeconomic influences. Given that construction of homes involve durable assetswith relatively long lead times, revenues to homebuilders are very sensitive to fluctuations in building, construction, and economic activity.

Revenues of equityREITs are less riskythan homebuilding firms. This is expectedin viewof the fact that equityREITs primarily invest in income producing propertiesand earn revenues whichare largely the product of longterm leases. It is these longterm leases whichmakethe revenues of equity REITs less volatile to changes in general economic conditions. During an economic conditions upturn, the tenant in the longterm leasemayhavethe optionto increase the consumption of space, but is restrictedin timesof economic turmoil from reducing this consumption as set forth in the agreements in the contract. Furthermore, many of the longterm lease 95 agreements held by equity REITs usually provide for cost-pass throughs, overage rents and lease escalations. It is for these reasons that the revenues of equity REITs are less risky than both single-family homebuilders and the securities market in general.

Empirical results supports this by showing that EREIT returns are less sensitive to fluctuations in systematic factors than HBC and generally more sensitive to systematic forces than a broad market index.

It is believed that the nature oflong term leases also contributes to EREIT being less sensitive, in general, to changing market condition than a broad index of securities. Many ofthe equity REITs hold properties backed by long term leases which include provisions which pass-through increases in maintenance or energy costs, overage rents and lease escalation clauses. These provisions in the long term leases and the long term leases themselves contribute to the stability ofequity REIT revenues and may also reduce the negative impact associated with increases in inflation. The risk of individual Equity REITs, however, may vary and be dependent upon not only the assets held and the degree to which these assets have leases which insulate these firms from increases in operating costs, but also the degree to which equity REITs are leveraged.

This is consistent with empirical evidence presented by Gyourko and Linneman (1990) which shows how long term leases may limit the degree to which returns to real estate reflect changes in the market and the empirical evidence presented in Chan,

Hendershott and Sanders (1990). 96

Finally, the empirical evidence presented shows that both of our real estate portfolios earn a substantial portion oftheir annual returns in January. Although there is evidence that each ofthese portfolios exhibit some degree ofa January effect, when testing these portfolios for the existence ofthe small :firms effect, it appears that the portfolio of single-family homebuilding securities (HBC) behaves much like small capitalization firms, whereas the portfolio of equity REITs (BREIT) exhibits behavior that more closely resemble midcap stocks. 97 Table 1: Glossary and Definitions of Variables

Symbol Variable Source or Definition IP Industrial Production Industrial production during month (Survey a/Current Business) I Inflation Log relative of Consumer Price Index

EI Expected inflation Estimated by a univariate autoregressive model with six lags Baa Low grade bonds Return on portfolio ofhigh-yield corporate bonds rated Baa and under (Ibbotson and Associates) LGB Long-term government Return on portfolio of long-term bonds government bonds (Ibbotson and Associates) TBill Treasure bill Return on 1 month T-bills (Ibbotson and Associates) EWNYSE Equally-weighted equities Return on equally-weighted portfolio of NYSE and AMEX stocks (CRSP tape) VWNYSE Value-weighted equities Return on value-weighted portfolio of NYSE and AMEX stocks (CRSP tape) HBC Equally-weighted Return on equally-weighted portfolio of homebuilding equities homebuilding stocks listed on NYSE, AMEXandOTC EREIT Equally-weighted equity Return on equally-weighted portfolio of REIT securities equity REITs listed on NYSE and AMEX SP500 Standard and Poor's 500 Return on portfolio of equities Index (CRSP tape) Small Small Firm Portfolio Return on portfolio of small firms in the lowest decile by capitalization listed on NYSE, AMEX and OTC (CRSP Tape) 98 Table 2

Monthly Means and Standard Deviations of Return Series

1973-90 1973-81 1982-90

HBC-Thill Mean 0.0052 0.0084 0.002 Std. Dev. 0.116 0.126 0.106 T-stat (mean=O) 0.665 0.691 0.209

EREIT-Thill Mean 0.005 0.0064 0.0029 Std. Dev. 0.057 0.071 0.039 T-stat (mean=O) 1.185 0.931 0.764

EWNYSE-Thill Mean 0.0053 0.0069 0.0038 Std. Dev. 0.063 0.073 0.052 T-stat (mean=O) 1.243 0.988 0.750

VWNYSE-Thill Mean 0.0031 -0.0005 0.0066 Std. Dev. 0.049 0.050 0.049 T-stat (mean=O) 0.913 -0.095 1.427

SP500-Thill Mean 0.0031 -0.0014 0.0075 Std. Dev. 0.048 0.048 0.049 T-stat (mean=O) 0.936 -0.282 1.596

Small-Thill Mean 0.0065 0.0108 0.0023 Std. Dev. 0.066 0.077 0.054 T-stat (mean=O) 1.436 1.448 0.433

Treasury Bills Mean 0.0065 0.0066 0.0064 Std. Dev. 0.002 0.003 0.002 T-stat (mean=O) 44.472 26.335 42.863 99

Table 3

Correlations for Return Series

~IEWHBC EREIT EWNY VWNY SP500 Small EWHBC 1.000 0.725 0.853 0.677 0.640 0.809

EREIT 1.000 0.809 0.637 0.590 0.784

EWNY 1.000 0.879 0.839 0.977

VWNY 1.000 0.995 0.844

SP500 1.000 0.799

Small 1.000 100 Table 4

Derivation of Data Series

Symbol Variable Definition

:MPt +! Growth in Industrial Production

Change in Expected Inflation

Unexpected Inflation

Default Premium

Slope of Term Structure 101 Table 5

Means and Standard Deviations of Macroeconomic Factors Monthly Rates

1973-90 1973-81 1982-90

MPt+1 Mean 0.0022 0.0012 0.0031 Std. Dev. 0.345 0.032 0.026 t-stat (mean=O) 1.11 0.39 1.27

DEIt+ I Mean 0.0000 0.0000 0.0000 Std. Dev. 0.018 0.002 0.001 t-stat (mean=O) 0.05 0.12 -0.07

UIt Mean 0.0002 0.0004 0.0001 Std. Dev. 0.033 0.003 0.003 t-stat (mean=O) 1.31 1.29 0.51

DEFt Mean 0.0000 0.0019 -0.0019 Std. Dev. 0.357 0.030 0.030 t-stat (mean=O) 0.003 0.68 -0.67

TERMt Mean 0.0010 -0.0040 0.0060 Std. Dev. 0.408 0.034 0.033 t-stat (mean=O) 0.44 -1.21 1.89 102 Table 6

Correlations for Macroeconomic Factors

+ DEl + UI DEFt TERM ~I MPt 1 t 1 t t MPt+1 1.000 -0.02 0.15 0.24 -0.23 (-0.001) (-0.269) (-0.064) (-0.030)

DElt+1 1.000 -0.02 -0.01 -0.12 (-0.365) (0.168) (-0.341)

UIt 1.000 0.09 -0.20 (0.264) (-0.003)

DEFt 1.000 -0.62 (-0.803)

TERMt 1.000

Numbers refer to the macrofactors and the mimicking portfolios (in parentheses) 103 Table 7

Single Factor Model 1973-90

r. Panel A: J =HBC

Constant P R2 t-statistic for constant

EWNYSE-rj 0.0034 1.561** 0.725 0.82 (0.0041) (0.065)

VWNYSE-rj 0.0069 1.592** 0.456 1.18 (0.0058) (0.118)

Panel B: rj = REIT

Constant P R2 t-statistic for constant

EWNYSE-rj 0.0007 0.736** 0.656 0.301 (0.0023) (0.036)

VWNYSE-rj 0.0023 0.745** 0.406 0.779 (0.0030) (0.061)

Standard errors of regression coefficients are in parentheses 104 Table 8: Single Factor Model: Subsample

Panel A: 1973-81 r.1 =HBC

Constant P R2 t-statistic for constant

EWNYSE-rf -0.0024 1.557** 0.807 -0.448 (0.0053) (0.073)

VWNYSE-rt 0.0091 1.670** 0.461 1.030 (0.0089) (0.177)

r, =REIT

EWNYSE-rf 0.0006 0.830** 0.716 0.176 (0.0037) (0.051)

VWNYSE-rf 0.0068 0.951** 0.448 1.339 (0.0051) (0.101)

Panel B: 1982-90 r.1 =HBC

Constant P R2 t-statistic for constant

EWNYSE-rf -0.0039 1.580** 0.611 -0.607 (0.0064) (0.122)

VWNYSE-rf -0.0078 1.512** 0.465 -1.042 (0.0075) (0.159)

rj = REIT

EWNYSE-rt .0008 0.553** 0.549 0.305 (0.0025) (0.048)

VWNYSE-rf -0.0006 0.530** 0.419 -0.216 (0.0029) (0.060) Standard errors of regression coefficients are in parentheses Table 9

Direct Impacts of the Macro Factors on EHBC, EREIT, and EWNYSE 1973-1990

Dependent Variable Constant MP DEI VI DEF TERM R 2

EHBC 0.0033 0.513 2.003 -4.561 1.946 1.935 0.236 t-statistic 0.470 2.048 0.420 -1.765 6.479 7.215 Standard Error (0.0069) (0.250) (4.771) (2.583) (0.300) (0.268)

EREIT 0.0038 0.262 3.242 -3.047 0.984 0.953 0.251 t-statistic 1.120 2.141 1.386 -2.406 6.682 7.250 Standard Error (0.0034) (0.123) (2.338) (1.266) (0.147) (0.131)

EWNYSE 0.0042 0.321 0.734 -2.903 1.295 1.167 0.324 t-statistic 1.169 2.499 0.300 -2.191 8.405 8.488 Standard Error (0.00360 (0.128) (2.447) (1.325) (0.154) (0.138)

I-'o lJl Table 10: Subperiod Direct Impacts of the Macro Factors on EHBC, EREIT, and EWNYSE

Panel A: 1973-81 Dependent Variable Constant MP DEI ill DEF TERM R2 EHBC 0.0136 0.727 0.904 -7.618 1.791 1.655 0.221 t-statistic 1.238 2.059 0.128 -2.008 4.116 4.373 Standard Error (0.0108) (0.353) (7.058) (3.794) (0.435) (0.379) EREIT 0.0094 0.433 3.357 -4.163 0.992 1.001 0.236 t-statistic 1.547 2.185 0.847 -1.953 4.057 4.708 Standard Error (0.0061) (0.198) (3.964) (2.131) (0.244) (0.213) EWNYSE 0.0106 0.405 -0.798 -5.572 1.276 1.149 0.340 t-statistic 1.838 2.158 -0.212 -2.760 5.513 5.706 Standard Error (0.0058) (0.188) (3.755) (2.019) (0.232) (0.201)

Panel B: 1982-90 EHBC -0.0093 0.141 1.920 0.458 2.279 2.539 0.279 t-statistic -1.037 0.395 0.290 0.126 5.352 6.463 Standard Error (0.0089) (0.358) (6.621) (3.627) (0.426) (0.393) EREIT -0.0009 0.003 1.659 -1.060 0.948 0.956 0.318 t-statistic -0.291 0.021 0.698 -0.814 6.205 6.781 Standard Error (0.0032) (0.129) (2.376) (1.302) (0.153) (0.141) EWNYSE -0.0021 0.181 0.520 0.766 1.300 1.282 0.325 t-statistic -0.490 1.055 0.164 0.440 6.360 6.799 Standard Error (0.0043) (0.172) (3.178) (1.741) (0.204) (0.189)

f-' 0 Q\ 107 Table 11

Mimicking Portfolio Returns 1973-90

n=216

Variable Mean Standard Deviation MP 0.00262 0.073 DEI 0.00007 0.006 VI -0.00035 0.011 DEF 0.00499 0.076 TERM 0.00370 0.077 Table 12

Impacts of the Mimicking Portfolios on EHBC, EREIT, and EWNYSE 1973-1990

Dependent Variable Constant MP DEI ill DEF TERM R2

EHBC -0.0026 0.604 1.593 -4.138 2.068 1.726 0.667 t-statistic -0.325 9.361 2.041 -8.678 18.455 15.891 Standard Error (0.0081) (0.065) (0.780) (0.477) (0.112) (0.109)

EREIT -0.0001 0.280 0.609 -1.980 1.011 0.846 0.630 t-statistic -0.017 8.311 1.497 -7.958 17.279 14.925 Standard Error (0.0042) (0.034) (0.407) (0.249) (0.058) (0.057)

EWNYSE -0.0001 0.314 1.019 -2.711 1.340 1.219 0.904 t-statistic -0.025 16.586 4.446 -19.361 40.699 38.235 Standard Error (0.0024) (0.019) (0.229) (0.140) (0.033) (0.032)

...... o 00 Table 13: Subperiod Impacts of Mimicking Portfolios on EHBC, EREIT, and EWNYSE

Panel A: 1973-81 Dependent Variable Constant MP DEI VI DEF TERM R2 EHBC -0.038 0.950 -2.308 -6.712 2.000 1.663 0.684 t-statistic -2.292 6.793 -1.138 -5.890 11.196 7.947 Standard Error (0.0167) (0.140) (2.027) (1.140) (0.179) (0.209) EREIT -0.0142 0.511 -0.034 -3.690 1.002 1.004 0.634 t-statistic -1.698 7.158 -0.038 -6.894 10.500 10.121 Standard Error (0.0084) (0.071) (0.875) (0.535) (0.095) (0.099) EWNYSE -0.0173 0.414 0.467 -5.030 1.325 1.212 0.859 t-statistic -3.274 9.189 0.846 -14.883 22.009 19.348 Standard Error (0.0053) (0.045) (0.552) (0.338) (0.060) (0.063)

Panel B: 1982-90 EHBC 0.0366 0.100 1.998 1.333 1.974 2.070 .435 t-statistic 1.961 0.729 0.913 1.047 8.157 8.809 Standard Error (0.0187) (0.137) (2.188) (1.273) (0.242) (0.235) EREIT 0.0174 0.086 1.304 -0.407 0.867 0.792 .542 t-statistic 2.806 1.889 1.794 -0.963 10.781 10.149 Standard Error (0.0062) (0.045) (0.727) (0.423) (0.080) (0.078) EWNYSE 0.0369 0.178 3.120 0.936 0.488 0.291 .125 t-statistic 3.207 2.114 2.313 1.193 3.273 2.007 Standard Error (0.0115) (0.084) (1.349) (0.785) (0.149) (0.145)

...... 0 \D Table 14: Excess Mean Returns of Portfolios of Securities Grouped by Capitalization and Month 1973-1990

81 82 83 84 85 86 87 88 89 810 Jan 0.1569 0.0974 0.0792 0.0717 0.0589 0.0495 0.0440 0.0342 0.0285 0.0174 (0.142) (0.125) (0.115) (0.105) (0.102) (0.096) (0.087) (0.084) (0.079) (0.065) Feb 0.0336 0.0174 0.0103 0.0074 0.0059 0.0099 0.0064 0.0038 0.0001 -0.0021 (0.105) (0.067) (0.059) (0.053) (0.048) (0.051) (0.046) (0.045) (0.040) (0.037) Mar 0.0207 0.0178 0.0173 0.0178 0.0140 0.0125 0.0114 0.0096 0.0084 0.0064 (0.075) (0.070) (0.071) (0.064) (0.064) (0.058) (0.057) (0.052) (0.045) (0.038) Apr 0.0033 -0.0009 -0.0007 -0.0005 0.0022 0.0033 0.0036 0.0006 0.0008 0.0024 (0.047) (0.044) (0.044) (0.044) (0.045) (0.043) (0.042) (0.043) (0.043) (0.039) May 0.0028 0.0007 0.0022 0.0010 -0.0002 0.0046 0.0049 0.0054 0.0059 0.0059 (0.068) (0.060) (0.057) (0.050) (0.052) (0.053) (0.051) (0.047) (0.050) (0.042) Jun 0.0104 0.0131 0.0124 0.0150 0.0105 0.0141 0.0136 0.0132 0.0146 0.0122 (0.035) (0.037) (0.036) (0.038) (0.042) (0.036) (0.038) (0.036) (0.037) (0.031) Jul 0.0017 0.0033 0.0011 0.0030 0.0007 0.0025 0.001l 0.0002 -0.0021 -0.0021 (0.051) (0.053) (0.056) (0.056) (0.056) (0.057) (0.052) (0.049) (0.052) (0.047) Aug -0.0080 -0.0534 -0.0087 -0.0067 -0.0053 -0.0022 0.0007 0.0032 0.0041 0.0032 (0.082) (0.072) (0.068) (0.067) (0.069) (0.072) (0.068) (0.064) (0.065) (0.061) 8ep -0.0170 -0.0239 -0.0146 -0.0153 -0.0161 -0.0145 -0.0162 -0.0144 -0.0149 -0.0187 (0.048) (0.042) (0.045) (0.050) (0.047) (0.048) (0.049) (0.047) (0.048) (0.046) Oct -0.0483 -0.0412 -0.0335 -0.0334 -0.0319 -0.0269 -0.0263 -0.0198 -0.0111 -0.0023 (0.107) (0.107) (0.104) (0.102) (0.103) (0.097) (0.097) (0.090) (0.092) (0.086) Nov -0.0100 -0.0017 0.0007 0.0071 0.0123 0.0115 0.0136 0.0147 0.0137 0.0092 (0.078) (0.077) (0.071) (0.074) (0.071) (0.069) (0.065) (0.062) (0.061) (0.051) Dec -0.0219 -0.0119 -0.0066 -0.0012 -0.0010 0.0005 0.0067 0.0059 0.0073 0.0073 (0.062) (0.057) (0.047) (0.047) (0.048) (0.044) (0.039) (0.036) (0.034) (0.030) Numbers in the parentheses are the standard deviations ofthe return series...... o 111

Table 15

TBILL and Excess Mean Returns of EREITs, HBCs, and EWNYSE Grouped by Month

1973-1990

TBILL EREIT HBC EWNYSE Jan 0.0060 0.0468 0.1240 0.0635 (0.002) (0.088) (0.192) (0.097) Feb 0.0059 0.0048 0.0195 0.0083 (0.002) (0.035) (0.105) (0.049) Mar 0.0065 0.0163 0.0516 0.0134 (0.003) (0.066) (0.125) (0.058) Apr 0.0068 -0.0064 -0.0119 0.0015 (0.003) (0.039) (0.083) (0.042) May 0.0065 -0.0051 -0.0088 0.0035 (0.002) (0.044) (0.086) (0.050) Jun 0.0063 0.0140 0.0075 0.0130 (0.002) (0.037) (0.059) (0.035) Jui 0.0066 0.0104 -0.0125 0.0011 (0.002) (0.034) (0.066) (0.051) Aug 0.0065 -0.0119 -0.0255 -0.0029 (0.002) (0.065) (0.108) (0.066) Sep 0.0066 -0.0062 -0.0388 -0.0164 (0.002) (0.044) (0.071) (0.046) Oct 0.0069 -0.0228 -0.0356 -0.0271 (0.002) (0.070) (0.144) (0.097) Nov 0.0063 0.0144 0.0022 0.0073 (0.002) (0.061) (0.135) (0.065) Dec 0.0067 0.0011 -0.0088 -0.0012 (0.002) (0.061) (0.073) (0.041)

Numbersin the parentheses are the standarddeviations ofthe return series. 112 Table 16

Regression of January Real Estate Returns on Small Capitalization Firms' January Returns

1973-90

rj(JAN) - rf = ao + {3(rsml(JAN) - rf) + 8 j

Panel A: rj = REIT

2 Constant rsml(JAN) - rf R t-statistic for constant -0.0426* 0.5698** 0.829 -3.2720 (0.013) (0.062)

Panel B: rj = HBC

2 Constant rsml(JAN) - rf R t-statistic for constant -0.0803* 1.302 ** 0.920 -4.155 (0.019) (0.093)

Standard errors of regression coefficients are in parentheses * Significant at the 95% confidence level ** Significant at the 99% confidence level 113 Table 17

Regression of Real Estate Returns on Small Capitalization Firms' and VWNYSE Index

1973-90

Panel A: rj = EREIT

2 Constant rsml(full) - rf rvwny(full) - rf R t-statistic for constant 0.0000 0.3412** 0.3453** 0.590 0.014 (0.003) (0.035) (0.065)

Panel B: r. = HBC

Constant R2 t-statistic for constant -0.0055 0.8724 ** 0.5760** 0.754 0.160 (0.019) (0.054) (0.102)

Standard errors ofregression coefficients are in parentheses * Significant at the 95% confidence level ** SIgnificant at the 99% confidence level 114 Table 18

Regression of Real Estate Returns on Firm Returns in the 4th Decile by Capitalization

1973-90

r) - r/ =ao + p(rsm4(full) - r/) + &)

Panel A: rj = EREIT

2 Constant rsm4(full ) - r/ R t-statistic for constant 0.0008 0.6912** 0.6822 0.378 (0.002) (0.032)

Panel B: rj = HBC

2 Constant rsm4(full) - r/ R t-statistic for constant -0.0027 1.4423 ** 0.728 -0.646 (0.004) (0.060)

Standard errors of regression coefficients are in parentheses * Significant at the 95% confidence level ** Significant at the 99% confidence level ~ 115 W ii a:: E w U)

Z~/06 VOl06 BO/6B

Z~/BB "- \ vO/BB ". BOILB

Z~/9B vO/9B BO/SB

~} Z~/vB .... ~ ... vOlvB t ( BO/CB -7.':'""----_ \. Z~/ZB ) -, " ( vO/ZB i £e ( I ) o .­ BOILB ~ ( , '. Z~/OB ...... -­ vOIOB BO/6L ZL/BL vO/BL BOILL

Z~/9L vO/9L BO/SL ZL/vL VOlvL BO/CL -­CD -­N -­o o JANUARY EXCESS MEAN RETURNS GROUPED BY MARKET CAPITALIZATION

0.16 ..... 0.14 1m Jan I 0.12 0.1 0.08 0.06 0.04 0.02 o M l£) r--­ 00 o -~ :E ~ ~ ~ ~ ~ ~ ~ tn tn tn tn tn tn tn tn -~ tn

Figure 2: January Excess Mean Returns Grouped byMarket Capitalization: ...... 1973-1990 0' EXCESS MEAN RETURNS GROUPED BY MARKET CAPITALIZATION AND MONTH

0.2

III SMI 0.15 .SM2 DSM3 0.1 OSM4 .SM5 SMI0 8SM6 SM9 IISM7 SM8 SM7 II1 SM8 SM6 .SM9 SM5 IIIIISMIO SM4 SM3 SM2 SMI

;> 0 o Q) Z 0 ...... Figure 3: Excess Mean Returns Grouped by Market Capitalization and Month: ---J 1973-1990 EXCESS MEAN RETURNS GROUPED BY MONTH

O.]400

O. ]200

0.1000

Dec

...... Figure 4: Excess Mean Returns Grouped by Month: ]973-1990 OJ OCTOBER EXCESS MEAN RETURN"S GROUPED BY MARKET CAPITALIZATION

0

-0.005

-0.01

-0.015

-0.02 -0.025 Imactl -0.03 .

-0.035

-0.04 ­

-0.045

-0.05 ..­ r

I--' I--' Figure 5: October Excess Mean Returns Grouped by Market Capitalization: \0 1973-1990 BIBLIOGRAPHY

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