Rsk and Returns of Commercal Real Estate: A Property Level Analyss Lang Peng Leeds School of Busness Unversty of Colorado at Boulder 419 UCB, Boulder, CO 80309-0419 Emal: lang.peng@colorado.edu Phone: (303)4928215 Abstract Ths paper analyzes the rsk and returns of drect commercal real estate nvestments at the property level. A novel regresson s developed to use property level cash flows nstead of ndex returns to estmate the senstvty of real estate returns to economc varables. Monte Carlo smulatons suggest that ths regresson s more accurate than the conventonal ndex approach. Applyng ths regresson to 3,125 commercal propertes held between 1978 and 2009, ths paper fnds that commercal real estate rsk premum s postvely related to GDP growth and the change n the credt spread, and negatvely related to nflaton, the stock market rsk premum, and the change n the term spread. The senstvtes vary across property types and tme. Ths paper also fnds that the rsk characterstcs of commercal real estate, such as loadngs on Fama French factors, vary across property types and tme. JEL classfcaton: C51, E30, G11, G12 ey words: drect commercal real estate nvestments, rsk and returns, Monte Carlo smulatons I thank the Real Estate Research Insttute for a research grant, and NCREIF for provdng the data. I am grateful for the constructve comments and suggestons provded by Jm Clayton, Jeffrey Fsher, Davd Geltner, Gal Haynes, Greg Macnnon, Aseh Mansour, Martha Peyton, and Doug Poutasse and semnar partcpants at Unversty of Colorado at Boulder. All errors are mne.
Rsk and Returns of Commercal Real Estate: A Property Level Analyss I. Introducton Drect commercal real estate nvestments consttute a large porton of the total wealth n the Unted States, wth the estmated value beng about $2 trllon. 1 However, comparatvely lttle s known about ther rsk and return characterstcs. The scarcty of emprcal evdence s mostly due to the lack of sutable data and methods. Snce property level data are generally not accessble to academc researchers, the lterature mostly uses real estate ndexes or comngled real estate funds to analyze the rsk and returns of drect commercal real estate nvestments. Such research typcally runs tme seres regressons of ndex or fund returns on economc condtons to analyze ther relatonshps. Whle helpng provde useful nsghts, the ndex (fund) approach has a few serous lmtatons. Frst, real estate ndexes and funds may have dfferent rsk and return characterstcs than ndvdual propertes. As Plazz, Torous and Valkanov (2008) and many others suggest, the commercal real estate market s characterzed by the buyng and sellng of ndvdual assets that often represent a non-trval share of nvestors portfolos. Therefore, the volatlty of real estate ndexes may not accurately reflect the rsk exposure of real estate nvestors. Emprcally, Fsher and Goetzmann (2005) show that the medan commercal real estate nvestment IRR across propertes sgnfcantly dffers from the average return of the natonal councl of real estate nvestment fducares (NCREIF) commercal real estate ndex across tme. Second, the ndex approach has econometrc weaknesses and lmtatons. Frst, real estate ndexes are not observed but estmated. The estmaton s not trval (see Baley, Muth and Nourse (1963), Geltner (1989), Shller (1991), Goetzmann (1992), Goetzmann and Spegel 1 2005 value, data source s Make Room for Real Estate, New York, Freeman and Company, LLC.
(1997), among many others), and ndexes can be estmated wth not only noses but also bases (see e.g. Gatzlaff and Haurn (1997), Fsher, Gartzlaff, Geltner and Haurn (2003), Goetzmann and Peng (2006), among others), whch may lead to the measurement error problem. Second, the ndex approach typcally uses tme seres regressons to analyze the relatonshps between ndex returns and economc condtons, n whch the degree of freedom s lmted by the number of sample perods. As a result, when the number of explanatory varables ncreases, the power of tme seres regressons quckly dmnshes. Thrd, the ndex approach often mples that propertes comprsed n the same ndex are homogeneous (see, e.g. Peng (2010)), and thus not sutable to test heterogenety n the rsk and return characterstcs across propertes, though such heterogenety may be economcally mportant (see, Peng and Thbodeau (2010) for evdence from the housng market). Ths paper ams to make two contrbutons to the lterature on the rsk and returns of drect commercal real estate nvestments. Frst, ths paper develops a novel econometrc method to analyze the relatonshps between commercal real estate returns and economc condtons at the property level. Ths method does not estmate ndexes, has large degrees of freedom, and allows a varety of drect tests on heterogenety of rsk and returns across propertes and tme. Ths paper uses Monte Carlo smulatons to provde strong evdence that the new method more accurately estmates the relatonshps than the ndex approach. Second, ths paper apples the novel method to an unusually rch data set provded by the natonal councl of real estate nvestment fducares (NCREIF). The data set contans detaled and complete actual cash flow nformaton from acquston to dsposton for 3,125 commercal propertes (estmated value beng about $147 bllon n 2009:3) nvested by nsttutonal nvestors, whch allows accurate measurement of nvestment performance. The hgh qualty data enable
ths paper to provde relable emprcal evdence on the rsk and returns of commercal real estate at the property level. Ths paper provdes two lnes of emprcal evdence. Frst, ths paper estmates the senstvtes of commercal real estate returns to economc condtons. Ths paper fnds that the commercal real estate rsk premum (.e., return mnus the rsk free rate) s postvely related to the GDP growth rate and the change n the credt spread, and negatvely related to the nflaton rate, the stock market rsk premum, and the change n the term spread. The negatve relatonshp between real estate and stock market rsk premum corroborates the conventonal wsdom that real estate nvestments help dversfy the rsk of stocks. The negatve senstvty to the term spread seems to ndcate that property values declne n busness cycle downturns. What seems counterntutve n the result, however, s the postve senstvty to the changes n the credt spread. The postve senstvty mples that when the credt spread becomes wder, whch may ndcate a decrease n external fnancng, commercal property returns are hgher. Ths paper conjectures that ths result s possbly due to the endogenety of the credt spread and the heterogenety n the commercal real estate market, but leaves further exploraton of ths result for future research. In estmatng the senstvtes, ths paper tests the heterogenety n the senstvtes across four property types: apartments, offces, ndustral propertes, and retal propertes. Ths paper fnds consstent sgns but varyng magntude of the senstvtes. For example, returns of apartments and ndustral propertes are less senstve to the nflaton rate than returns of offces; returns of retal propertes are more negatvely related to the stock market rsk premum than returns of offces. Ths paper also tests and substantates the tme varaton of the senstvtes. Specfcally, n an economc expanson (hgher stock market rsk premum), returns of ndustral and retal propertes are more strongly related to the GDP growth rate; returns of all property types are more negatvely related to the nflaton rate; returns of apartments and offces are more negatvely
related to the stock market rsk premum; returns of offces and ndustral propertes are more negatvely related to the term spread changes. These results have mportant mplcatons on the dversfcaton benefts of dfferent commercal property types n dfferent economc condtons. The second lne of emprcal evdence pertans to the rsk characterstcs of commercal real estate. Usng the same emprcal method, ths paper estmates the loadngs of commercal real estate returns on the conventonal Fama-French factors, the momentum factor, and some real estate specfc factors proposed by Pa and Geltner (2007). The results suggest sgnfcant heterogenety n the factor loadngs across property types. Partcularly, apartments drastcally dffer from the other three types. Whle apartments have low but postve loadngs on the stock market rsk premum and the SMB factors, other propertes have nsgnfcant loadngs on the stock market rsk premum, and hgh loadngs on the SMB factor. Further, whle apartments have a postve loadng on the HML factor, other propertes have sgnfcantly negatve loadngs. Ths paper also fnds strong evdence for the tme varaton n the factor loadngs. Specfcally, the loadngs for all the stock market factors are sgnfcantly lower n an economc expanson (hgher stock market rsk premum). Ths seems to ndcate that commercal real estate provde more dversfcaton benefts when the stock market does well. Fnally, ths paper fnds that, once the real estate specfc factors are ncluded, the loadngs on all factors become mostly nsgnfcant. Ths s lkely due to correlatons among the real estate factors and the smaller sample sze due to the lmted sample perod n whch the real estate factors are avalable. Ths paper s the frst, to our knowledge, that uses property level cash flows nstead of ndex returns to analyze the relatonshps between drect commercal real estate nvestments returns and economc condtons. The contrbuton of ths paper s twofold. Frst, the emprcal results provde orgnal and lkely more relable evdence regardng the rsk and returns of commercal
real estate. Second, the novel emprcal method developed n ths paper shows mportant mprovements to the conventonal ndex approach n analyzng the rsk and returns of real estate. The rest of ths paper s organzed as follows. Secton II revews the lterature. Secton III descrbes the data set. Secton IV dscusses the new emprcal method, and uses smulatons to substantate ts mprovements to the conventonal ndex approach. Secton V presents and nterprets the emprcal results. Conclusons are presented n Secton VI. II. Lterature Revew Ths secton provdes a bref revew for the lterature on the drect commercal real estate nvestments. Compared wth other real estate lteratures, such as the lterature of Real Estate Investment Trusts (REITs) (see e.g. Boudry, Coulson, allberg and Lu (2010) among many others) and the housng lterature (see e.g. Case, Cotter and Gabrel (2010) among many others), the lterature of drect commercal real estate nvestments s much smaller. Ths s not because drect commercal real estate nvestments are less mportant, but because of the dffculty n acqurng hgh qualty data. In fact, almost all papers n the lterature use fund/ndex level data or apprased values of propertes. For example, Brueggeman, Chen and Thhodeau (1984) use quarterly data from two comngled real estate funds (CREFs) from 1972 to 1983 to analyze the rsk of commercal real estate n the CAPM framework. They fnd real estate nvestment returns have an nsgnfcant market beta and a sgnfcant and postve correlaton wth the nflaton rate. Hartzell, Hekman and Mles (1986) use quarterly property-specfc ncome and apprecaton (apprased values) for up to 403 propertes from 1973 to 1983 to analyze the dversfcaton beneft of commercal real estate. They fnd an nsgnfcant correlaton wth the S&P returns, a negatve correlaton wth bond returns, and a postve correlaton wth the nflaton rate. Geltner (1989) un-smoothes the quarterly Frank Russell Company (FRC) and Prudental Property Investment Separate Account (PRISA) apprasal-based ndexes to study the rsk of commercal
real estate n the framework of CAPM, and fnds a zero stock market beta and a postve correlaton wth natonal consumpton. Gyourko and Lnneman (1988) analyze the correlaton between the nflaton rate and the returns of REITs, owner-occuped homes, and drect commercal real estate nvestments, whch s measured wth the FRC and PRISA ndexes. They fnd that returns of drect commercal real estate nvestments are mostly postvely related to nflaton, whle REIT returns are negatvely related to nflaton. Goetzmann and Ibbotson (1990) use apprasal-based returns of CREFs to fnd that commercal real estate returns are not related to stock returns, and postvely related to nterest rates. Lng and Naranjo (1997) analyze the senstvty of drect commercal real estate nvestments returns to economc varables, ncludng consumpton growth, the T-bll rate, and the term structure of nterest rates. They use the apprasal-based NCREIF natonal and regonal ndexes and other measurements to measure drect commercal real estate nvestments returns. They fnd a postve loadng on consumpton growth, and negatve loadngs on the real T-bll rate, the term spread, and the unantcpated nflaton. Ths paper dstngushes tself from the above papers n usng actual property level cash flow nformaton for a large number of propertes, whch allows accurate performance measurement and possbly leads to more relable results. A few recent papers use property level data provded by NCREIF, but am to answer dfferent research questons. Fsher and Goetzmann (2005) bootstrap the cash flows of about 4,000 ndvdual propertes n the NCREIF database over the perod 1977:4 to 2004:2, and analyze the dstrbuton of IRRs. They fnd that the medan IRR dffers sgnfcantly from the compound tme-weghted rate of return from the quarterly NCREIF ndex, and dversfcaton requres substantal captal. Pa and Geltner (2007) use apprased property values from the NCREIF database to construct and sort ndexes, whch are then used to construct Fama-French style real estate factors. They fnd that the real estate factors well explan the cross-secton of the ndex returns.
Another related paper s Plazz, Torous and Valkanov (2008). They use bannual and quarterly apprased values of commercal property types over the perod 1986 to 2002 from Global Real Analytcs to construct the cross-sectonal dsperson of returns across 20 to 60 Metropoltan Statstc Ares (MSAs), and then analyze the temporal varaton of the dsperson. They fnd that macroeconomc varables help explan the tme-seres fluctuaton of the dsperson, and a postve correlaton between returns and the cross-sectonal dsperson. However, ther results do not seem to drectly comparable wth the results n ths paper, because the two papers ask dfferent the research questons. Whle Plazz, Torous and Valkanov (2008) focus on the cross-sectonal dsperson of returns, whch s a mportant and novel rsk measurement, ths paper focuses on nvestment returns at the property level. III. Data III.1 Real Estate Data Ths paper analyzes commercal propertes n the natonal councl of real estate nvestment fducares (NCREIF) database. The NCREIF s a not-for-proft nsttutonal real estate ndustry assocaton. Establshed n 1982, t serves the real estate nvestment ndustry by collectng, processng, valdatng and then dssemnatng nformaton on the rsk/return characterstcs of commercal real estate assets. The NCREIF database comprses nsttutonal-qualty commercal real estate, as the observatons are populated by nvestment managers and plan sponsors who own or manage real estate n a fducary settng. The well dssemnated commercal real estate ndex (NPI) s constructed usng apprased values n the database. The NCREIF database contans quarter/property observatons from 1978:1 to 2009:3. Each observaton contans two types of nformaton. The frst type pertans to physcal attrbutes of the property, ncludng the property type (e.g. apartments, offces, ndustral propertes, retal
propertes, hosptalty propertes, etc), age, locaton, etc. The second type pertans to the nvestment and operaton of the property, ncludng the net operatng ncome (NOI), the captal expendture (CapEx), as well as the acquston cost or the net sale proceeds f applcable. All fnancal and operatonal nformaton s on an unlevered bass. The 3,125 sample propertes n ths paper are selected from about 24,000 propertes n the NCREIF database. Ths paper excludes about 64% of the 24,000 propertes n the database because they have not been dsposed n the market by the end of the sample perod and thus have unknown returns, about 21% propertes because of possble data errors, and about 1.5% propertes due to ther IRRs beng outlers. The specfc data cleanng procedure s below. Frst, ths paper focuses on the four major property types n the database: apartments, offces, ndustral, and retal propertes, whch consttute about 94% of the entre NCREIF sample. Second, ths paper only uses propertes that have been dsposed on or before 2009:3 and wth the fnal dspostons marked as true sales. Ths paper further cleans the sample to mtgate data errors. Propertes are excluded f they have mssng nformaton (e.g. mssng acquston quarter, acquston cost, NOI, CapEx, net sale proceeds) or problematc nformaton (e.g. NOI or CapEx s 0 for all quarters, or NOI or CapEx remans constant for at least 10 consecutve quarters). Further, propertes are excluded f ther maxmum NOI s greater than 20% of the acquston cost, f the sum of quarterly captal mprovements s greater than the acquston cost, f ts rato of average quarterly NOI to the acquston cost s n the top and bottom 2% of all propertes, and f ts rato of average quarterly captal mprovement to ntal purchase cost s among the top 2% of all propertes. The resulted sample comprses 3,587 propertes.
Ths paper then calculates the quarterly total return IRR r for each of the 3,587 propertes by solvng the followng present value equaton: where buy and V buy, and, sell V P + I E P + I E + V, (1) sell 1 t, t, t, sell, sell, sell, sell, buy, = + t= buy + 1 t buy sell buy r r sell are the quarters when property s acqured and dsposed respectvely; V are the acquston cost and the net sale proceeds respectvely; P t, s the net sale proceeds from a possble partal sale (e.g. the sale of one of two buldngs acqured as a bundle) n quarter t ; I t, and E t, are the NOI and CapEx n quarter t respectvely. 2 Note that ths paper analyzes realzed IRRs nstead of expected IRRs, n contrast to Plazz, Torous and Valkanov (2007) and others. For propertes wth multple IRR solutons, the solutons wth the smallest absolutely values are selected as the IRRs. After the IRR calculaton, propertes wth mssng IRRs or the top and bottom 1.5% of the IRRs are excluded. 3 The sample sze becomes 3,231. Fnally, snce an analyss n ths paper s to compare the conventonal ndex approach wth the property level approach n estmatng senstvty of real estate returns to economc varables usng exactly the same samples, to ensure that ndexes can be estmated wth reasonable accuracy, ths paper exclude early quarters n whch the sample ncludes few than 30 propertes. The resulted sample sze s 3,125. 4 Fgure 1 vsualzes the hstogram of the log IRRs of the fnal sample. 2 Snce the R functon ths paper uses to solve equaton (1) caps the number of perods at 48, a couple of propertes wth nvestment duraton longer than 48 quarters (12 years) are excluded from the sample. 3 IRR outlers tend to have short nvestment duratons and thus lkely correspond to flpped propertes and opportunstc nvestments. The mean of the bottom 1.5% IRRs s about -8% per quarter (-28% per annum), wth the mean nvestment duraton beng 9 quarters. The mean of the top 1.5% IRRs s 18% per quarter (94% per annum), wth the mean nvestment duraton beng 5 quarters. The mean nvestment duraton of the mddle 97% IRRs s about 20 quarters. 4 The estmated senstvty of real estate returns to economc varables and the estmated factor loadngs n ths paper are robust to the last round of sample cleanng.
Table 1 reports summary statstcs for the fnal 3,125 propertes by property types. Industral propertes have the most samples (1,084), followed by offces (834), apartments (758), and then retal propertes (449). Note that about 4% of the propertes are sold partally before ther fnal dspostons, and results n ths paper are robust wth these propertes excluded. The table also summarzes property values, whch equal property acquston costs adjusted to 2009:3 values wth estmated total return ndexes of the correspondng property types, whch wll be dscussed n next secton. 5 It s apparent that property values have wde ranges. For example, the maxmum value s about 2,000 tmes greater than the mnmum value for offces. The table further reports the dstrbuton of quarterly IRRs. Retal propertes have the hghest average quarterly IRR (2.95%), followed by apartments (2.66%), ndustral propertes (2.49%), and offces (2.36%). Fnally, Table 1 reports the dstrbuton of nvestment duraton (number of quarters from acquston to dsposton): 18 for apartments, 20 for offces, 19 for ndustral and 20 for retal propertes. Note that propertes that have not been dsposed are not n the fnal sample. Therefore, the duraton of the sample should not be nterpreted as the average duraton for all propertes n the NCREIF data set (see, e.g., Collett, Lzer and Ward (2000) for evdence for longer duraton of U commercal real estate). Fgure 2 plots the tme seres of propertes n the sample for the four property types. The sample perod vares across property types: the startng quarter s 1988:1 for apartments, 1980:2 for offces, 1978:4 for ndustral, and 1980:2 for retal propertes; the endng quarter s 2009:3 for all types. The tme seres have an obvous pattern: there are fewer samples n earler quarters and later quarters than n mddle quarters. The maxmum number of propertes s 1,199, whch s on 2004:4. The pattern s partly due to the fact that ths paper only analyzes propertes that have 5 For example, f the acquston cost s $1 mllon n 2008:1, and the total return ndex ncreases by 30% from 2008:1 to 2009:3, the property value reported s $1.3 mllon.
been dsposed by 2009:3, and propertes acqured n later perods are less lkely dsposed and thus less lkely n the sample. It s mportant to note that propertes n ths paper are not an unbased sample of all drect commercal real estate nvestments n the economy. Frst, propertes n ths paper are nsttutonal qualty propertes - they may have hgher values and more stable cash flows than other commercal propertes. Second, the fnal sample may systematcally dffer from propertes n the NCREIF database that have not been dsposed, partcularly f the reasons why the propertes n the sample were dsposed pertans to ther rsk and returns. Therefore, all the results n ths paper are condtonal on propertes beng nsttutonal qualty and beng actvely traded. Nonetheless, gven the large sze of the fnal sample (about $147 bllon), the emprcal results n ths paper have mportant mplcatons. III.2 Economc and Captal Market Data Ths paper uses the 5-year treasury constant maturty rate as the rsk free rate to construct the real estate return rsk premum, because ts term matches the nvestment duraton of the sample. Ths paper uses the GDP growth rate, the nflaton rate, and the stock market rsk premum to measure macroeconomc condtons, and uses the change n term spread (10-year treasury annual yeld mnus 1-year treasury annual yeld) and the change n the credt spread (BAA corporate bond annual yeld mnus AAA corporate bond annual yeld) to characterze the captal market. All the varables, except the stock market rsk premum, are taken from the Federal Reserve Economc Data (FRED). The stock market rsk premum s obtaned from enneth French s webste. Note that the fve varables are wdely used n the fnance lterature to summarze the state of the economy and to model the tme varaton of aggregate stock market expected returns (see, e.g. Campbell and Shller (1988), Fama and French (1989), and Torous, Valkanov and Yan (2005))
and n the real estate lterature to analyze the prcng of propertes (see, e.g. Clayton, Lng and Naranjo (2009), Peyton (2009), among others). GDP and CPI relate to current economc actvtes, and the stock market rsk premum contans nformaton on future economc actvtes. Therefore, they relate to demand for commercal real estate space and thus rental ncome and property values. The term spread s closely related to shorter-term busness cycles (see, e.g. Fama and French (1989)), and helps capture nvestors expectaton of long term economc rsk. The credt spread seems to proxy for external debt fnancng (see, e.g. Plazz, Torous and Valkanov (2008)), wth narrow credt spreads correspondng to an abundance of ths fnancng. Table 2 provdes summary statstcs for the economc varables. The rsk free rate s n log quarterly gross rates; the GDP growth rate and the nflaton rate are log frst order dfferences of quarterly GDP level and CPI level respectvely; the stock market rsk premum s log of 1 plus the quarterly rsk premum (rsk premum n percentage ponts); the change n the term spread and the change n the credt spread are log dfferences of 1 plus the spreads (spreads calculated wth annual rates n percentage ponts). Panel A shows that the rsk free rate, the GDP growth rate, and the nflaton rate are postvely autocorrelated, the stock market rsk premum and the change n the credt spread have low autocorrelaton, and the change n the term spread has negatve autocorrelaton. Panel B presents the correlatons among the varables. Note that the GDP growth rate s postvely related to the nflaton rate, the stock market rsk premum, but negatvely related to the changes n the term spread and the credt spread. Ths s consstent wth the noton that the term spread and the credt spread often wden n economc recessons. To estmate the rsk characterstcs of commercal real estate returns, ths paper uses the three Fama-French factors and the momentum factor, all of whch are standard rsk factors n the fnance lterature. All four factors are downloaded from enneth French s webste. Among the three Fama-French factors, the stock market rsk premum s the total return on the stock market
portfolo mnus the correspondng quarterly return on U.S. Treasury securtes from the CRSP. Note that the stock market rsk premum s also used n ths paper as a varable to measure economc condtons, and s summarzed n Table 2. SMB s the total return on a portfolo of small-cap stocks n excess of the return on a portfolo of large-cap stocks. HML s the total return on stocks wth hgh ratos of book-to-market value n excess of the returns on a portfolo of stocks wth low book-to-market ratos. The momentum factor s the average return on the two hgh pror return portfolos mnus the average return on the two low pror return portfolos. In addton to the standard rsk factors n the fnance lterature, ths paper also uses some real estate factors and estmates the loadngs of commercal real estate returns on them. Pa and Geltner (2007) use assessed property values n the NCREIF data to construct Fama-French-lke factors based on property sze (value) and the ter of metropoltan statstc areas (MSA) n whch propertes are located that s upper, mddle and tertary from an nsttutonal nvestment perspectve. They also nclude a NCREIF commercal real estate prce ndex (NPI) n excess of the rsk free rate as the thrd factor the real estate market factor. Table 3 summarzes quarterly tme seres of the four stock market rsk factors from 1979:1 to 2009:3 and tme seres of three real estate rsk factors (annual seres of the ter factor and the sze factor from 1984 to 2003, and quarterly seres of real estate market excess returns from 1979:1 to 2009:3). All stock market and real estate factors are n log of 1 plus the factors n percentage ponts. The real estate market excess returns are calculated as the NPI quarterly returns n excess of the 5 year treasury yeld quarterly rates. All correlatons between the real estate ter and sze factors and other varables are calculated usng annual seres from 1984 to 2003. It s worth notng that the three real estate factors are hghly correlated, whch actually causes multcollnearty and s lkely a reason for nsgnfcant factor loadngs.
IV. Research Desgn IV.1 The Property Level Model Ths secton descrbes the model that estmates the relatonshps between real estate nvestment returns and economc varables at the property level. Defne the total gross return of property from quarter t to quarter t + 1, R t, + 1, as R P + I E + V t, + 1 t, + 1 t, + 1 t, + 1 t, + 1 =, (2) Vt, where V t, s the value of property n quarter t, whch equals the acquston cost f the property s acqured n quarter t, or otherwse the net sale proceeds the nvestor would receve f she would sell the property (or the remanng part of the property f there s a partal sale before); P t, + 1 s the net sale proceeds from a possble partal sale (e.g. the sale of one of two buldngs acqured as a bundle) n quarter t + 1; I t, + 1 and E t, + 1 are the NOI and CapEx n quarter t + 1 respectvely. Ths paper assumes that the NOI s receved, the CapEx s spent, and the possble partal sale takes place at the end of quarter. It s mportant to note that V t, s only observed n the acquston and the dsposton quarters. Assume the rsk premum of log ( R t, ) s a lnear functon of varables { } where t log ( ) log ( ) F kt k = :, 1 t, t = α+ β k 1 tk,, kt, + ε, (3) = t, R T F β tk,, k= 1 T s the rsk free rate n quarter t ; { } are coeffcents of the varables for property n quarter t ; ε t, s an error term that s orthogonal to the explanatory varables. Note that equaton (3) can be used to acheve dfferent research goals. Frst, t can be used to analyze the F kt, k = 1 senstvty of real estate nvestment returns to economc condtons, n whch case { }
β tk,, k= 1 measure economc condtons and { } measure the senstvty. Second, equaton (3) can be F kt, k = 1 used to understand the rsk characterstcs of real estate nvestments, n whch case { } are rsk factors and { } β are factor loadngs. Note that the ntercept term tk α k= captures the,, 1 F kt, k = 1 tme nvarant component of the rsk premum that s not related to { }. If (3) s nterpreted as a lnear factor model and f the model s correctly specfed and ncludes all factors, α measures the rsk adjusted return. If property values were always observed, equaton (3) mples a tme seres regresson for each β tk,, k= 1 property f { } F kt, k = 1 are dentfable (e.g. beng tme nvarant). If { } are rsk factors, such tme seres regressons are essentally the same wth the frst step of the Fama MacBeth approach (see Fama and MacBeth (1973)) that estmates factor loadngs of ndvdual propertes. However, property values are only observed n the acquston and the dsposton quarters; therefore, (3) cannot be estmated as a tme seres regresson. To derve an estmable model from (3), for each property, addng both sdes of equaton (3) from the acquston quarter, buy, to the dsposton quarter, sell, leads to sell log sell ( Rt, ) log( Tt) t= buy + 1 t= buy + 1 ( sell buy ) ( F ) sell sell = α + β + ε. t= buy + 1 k = 1,, t k k, t t= buy + 1, t (4) log on the left sde of the equaton s the gross total return (n log) of t= buy + 1 sell Note that ( Rt, ) nvestng n property from the acquston quarter to the dsposton quarter. The man sell explanatory varable on the rght sde, 1( β 1 tk,, F t= buy + k= kt, ), represents the aggregate effects
F kt, k = 1 of varables { } over the same perod. Therefore, the tme subscrpts of both the dependent and explanatory varables are essentally ntegrated out, and both sdes of the equaton are functons of. To smplfy the notatons, denote by R the gross return from acquston to dsposton: R sell R, (5) t= buy 1, t + and rewrte equaton (4) as log sell ( R ) log( T ) t= buy + 1 ( sell buy ) ( F ) t sell sell = α + β + ε. t= buy + 1 k = 1,, t k k, t t= buy + 1, t (6) It s mportant to note that return, r, usng the followng equaton, R can be drectly calculated from the quarterly nternal rate of total R sell buy = r. (7) Snce both sdes of equaton (6) are functons of, the equaton mples a cross-sectonal β tk,, k= 1 regresson f { } are dentfable (e.g. under the assumpton of tme nvarant parameters that are dentcal across propertes). It s mportant not to confuse the cross-sectonal regresson n (6) wth the second step of the Fama MacBeth approach or any tests of factor asset prcng theores. (6) s used to estmate { β tk }, whch are factor loadngs f { } k=,, 1 F kt, k = 1 are rsk factors, whle the second step of the Fama MacBeth approach, treats factor loadngs as gven, and estmates the rsk premum of the loadngs. In terms of research purposes, the cross-sectonal regresson mpled by (6), f used to estmate factor loadngs, s actually smlar wth the frst step of the Fama MacBeth approach.
IV.2 Smulatons: the Property Level Approach vs. the Index Approach Ths secton uses Monte Carlo smulatons to analyze f the property level regresson mpled by β tk,, k= 1 (6) provdes more accurate estmators of { } than the conventonal ndex approach. The smulaton focuses on the performance dfference between the two approaches due to dfferences n ther estmaton strateges nstead of possble bases n ndex estmaton; therefore, to make the comparson more far to the ndex approach, n the smulaton, the ndex estmaton model s always correctly specfed and the ndex s estmated effcently. The smulaton analyzes sxteen scenaros over a perod of 80 quarters. The sxteen scenaros are the combnatons of four market types small (500 propertes) and large (1,500 propertes) markets wth homogeneous and heterogeneous propertes respectvely wth four levels of market lqudty: each property s traded wth 10%, 8%, 5%, and 2% probablty n each quarter. In a homogeneous market, the coeffcent of each economc varable s dentcal across propertes. In a heterogeneous market, the coeffcents vary across propertes; therefore, n heterogeneous markets, both approaches estmate the across property average coeffcents. Each of the sxteen scenaros s smulated for 200 rounds. Each round conssts of three steps. The frst step generates a panel of property values usng the followng equaton. log ( R ) t, = α+ β k 1 k, Fkt, + ε (8) = t, Note that equaton (8) s essentally equaton (3) wth the rsk free rate omtted, whch does not F kt, k = 1 affect the smulaton results. For the smulaton to be realstc, the economc varables { } n (8) take on hstorcal values (endng n 2009:3) of the U.S. GDP growth rate, nflaton rate, the stock market rsk premum, and changes n the term spread and the credt spread. The true
β tk,, k= 1 coeffcents { } are selected so that they are consstent wth emprcal evdence presented n next secton. Specfcally, n homogeneous market, the ntercept term α s 0.0125, and the coeffcents of the fve macroeconomc varables are 2.907, -5.33, -0.414, -6.934, and 13.216 respectvely. In heterogeneous markets, the ntercept and the coeffcents of each property are generated from a multvarate Normal dstrbuton wth the mean vector beng the above numbers, and the standard devatons beng the correspondng average standard devatons of coeffcent estmators across property types n Table 5. The error term ε t, s generated from a Normal dstrbuton wth zero mean and a standard devaton beng 0.059, whch s the average estmated standard devaton of the errors n regressons n Table 5. Usng ntal value $1 for all propertes and tme seres of value apprecaton rates generated from (8), tme seres of property values are generated. Ths paper then randomly selects some of the property values as observed sales based on the market lqudty assumpton. The second step uses the ndex approach and the property regresson respectvely to estmate coeffcents of explanatory varables. The ndex approach conssts of two steps. It frst estmates a return ndex usng repeat sales (pared sales of the same propertes) constructed from the sparse property sales generated from the prevous steps. The followng standard repeat sales regresson (RSR) s used to estmate real estate return ndexes: where property ; log, (9) ( R sell sell ) = log( M t) + υ, t t= buy + 1 t= buy + 1 R s the gross return from the acquston quarter buy to the dsposton quarter sell for M s the ndex return from quarter t t 1 to t ; υ t, s an error term. It s apparent that (9) s correctly specfed. The smulaton estmates (9) usng GLS (see, e.g. Case and Shller (1989) and Goetzmann (1992)). After the return ndex s estmated, the smulaton runs a tme seres regresson of ndex returns on economc varables:
log The property level regresson n ths step s log = α + β + ε. (10) ( M ) F, t k= 1 k k t t ( R ) ( sell buy sell ) t buy 1( F = + k= 1, ), (11) = α + β + ε k k t whch s estmated wth OLS. It s mportant to note that both approaches are correctly specfed. The thrd step measures and compares the accuracy of the two approaches n estmatng { k} k 1 β =. The accuracy of each approach s measured wth the mean squared error (MSE) of the coeffcent estmators. Table 4 summarzes the smulaton results. For each scenaro, ths table reports the average (across the 200 rounds) MSEs of the ndex approach and the property level regresson, and tests the dfference between the MSEs usng a pared t-test, wth the null hypothess beng that the MSE of the property regresson s greater than the MSE of the ndex approach. Three results are obvous. Frst, the property level regresson s sgnfcantly more accurate than the ndex approach n all sxteen scenaros. The mprovement n accuracy s also economcally sgnfcant the rato of the MSE of the property regresson to the MSE of the ndex approach ranges from about 1/3 to about 20%. Second, both approaches are more accurate n large markets, n markets wth more lqudty, and n markets wth homogenous propertes. Thrd, the mprovement n accuracy of the property level regresson over the ndex approach s more sgnfcant n markets wth heterogeneous propertes and low lqudty. Overall, the Monte Carlo smulaton provdes strong evdence that the property regresson provdes more accurate estmators than the conventonal ndex approach. V. Emprcal Results
V.1 Senstvty to Economc Condtons Ths secton frst uses both the ndex approach and the property regresson to estmate the average senstvty of commercal real estate rsk premum to the fve economc varables for each of the four property types. The property level regresson s based on equaton (6). A constrant, α = α and β,, tk = β, s mposed so that the regresson estmates the average ntercept term k and the senstvty wthn the same type and across tme. Whle ths constrant s strct, t defnes a useful benchmark case. When usng the ndex approach, ths paper uses the generalzed repeat sales regresson (GRSR) proposed by Peng (2010) to estmate a real estate total return ndex for each property type: log, (12) sell sell ( R) = θl log( Mt) + υ, t t= buy + 1 t= buy + 1 where R s the gross total return from the acquston quarter buy to the dsposton quarter sell for property ; M s the gross total return of the ndex from quarter t t 1 to t ; measures the senstvty of gross returns of propertes n the metropoltan statstcal area (MSA) l, n whch property s located, to the ndex returns; υ t, s an error term. θ l Note that ths paper does not ntend to estmate the best ndexes. The model n (12) s relatvely smple, yet more accurate than the standard RSR, and more transparent than many varatons of the RSR; however, t does not control for a varety of known problems that mght affect the accuracy of repeat sales ndexes. Ths paper prefers smple ndexes because the purpose of ndex estmaton s to llustrate the dfferences n results due to applyng dfferent approaches on exactly the same data.
Further note that the GRSR n (12) generalzes the standard repeat sales regresson n two ways. Frst, the dependent varable s not the log dfference between the sale prce and the purchase prce, but the log gross total return. Second, ths approach allows propertes n dfferent MSAs to have dfferent senstvty to the ndex. Peng (2010) shows that ths leads to more accurate ndexes n the presence of heterogeneous value apprecaton process across MSAs. 6 Note that mposng the constrant θ l = 1 wll reduce (12) to the standard RSR. (12) s estmated wth the two step EM algorthm proposed by Peng (2010). Fgure 3 plots the four ndexes. Usng the estmated ndexes, ths paper estmates (10) for the senstvty coeffcents. Two emprcal ssues n the ndex estmaton are worth mentonng. Frst, n estmatng (12), ths paper lets θ reman 1 for MSAs wth fewer than 10 propertes, 7 and use the error term to capture the devaton of θ from 1 for these MSAs. Second, multcollnearty sometmes presents, and some consecutve quarters cannot be dstngushed from each other. Ths paper follows the conventonal procedure that smply dvdes the estmated aggregate ndex log returns over these quarters wth the number of the quarters, and assgns the average to each quarter. The problems of multcollnearty and the smoothng procedure further llustrate the weakness of the ndex approach the estmated ndex returns may contan errors or bases. Table 5 reports the average senstvty coeffcents estmated wth the ndex approach and the property level regresson usng exactly the same data, for apartments, offces, ndustral and retal propertes. The two approaches provde dstnctve results. For the ndex approach, all senstvty estmators are nsgnfcant for all property types, and the adjusted R2s are all near 0. The property regressons, on the other hand, provde statstcally sgnfcant estmators, and have much hgher adjusted R2s: 0.54 for apartments, 0.43 for offces, 0.31 for ndustral propertes, and 6 Usng the conventonal RSR does not change any results or conclusons n ths paper. 7 All results are robust f we ncrease the number of observatons requred for us to estmate θ.
0.48 for retal propertes. Overall, the property level regresson seems much more powerful than the ndex approach. Table 5 provdes emprcal evdence regardng the senstvty of commercal real estate rsk premum to economc condtons. Frst, the senstvty to the GDP growth rate s sgnfcantly postve for all four property types. For example, the coeffcent s 3.428 for offces, whch mples that f the GDP growth rate ncreases by 1%, the rsk premum of offces ncreases by roughly 3%. The postve senstvtes are consstent wth the noton that property values are hgher when the economy grows. Second, the coeffcent of the senstvty to the nflaton s sgnfcantly negatve for all property types. The senstvty s also economcally sgnfcant. For example, the coeffcent s -7.819 for offces, whch suggests that f the nflaton rate decreases by 1%, the total return rsk premum of offces ncreases by about 8%. Ths result challenges the postve correlaton between real estate returns and the nflaton rate found by the lterature, and seems to suggest that drect commercal real estate nvestments are smlar wth securtzed real estate n the sense that both have postve correlatons wth nflaton. Thrd, the senstvty to the stock market rsk premum s statstcally negatve for all property types. If the stock market rsk premum decreases by 1%, the real estate rsk premum ncreases by about 0.3% for apartments and offces, 0.4% for ndustral propertes, and 0.7% for retal propertes. The negatve senstvty to the stock market rsk premum s consstent wth the lterature, and ndcates that commercal real estate nvestments provde valuable dversfcaton benefts to stock nvestments.
Fourth, the senstvty to the change n the term spread s negatve for all property types, whch seems sensble. An ncreasng term spread ndcates a busness cycle downturn and hgher requred returns, both of whch would decrease property values and thus total returns. The negatve senstvty to the term spread s consstent wth the lterature (see, e.g. Lng and Naranjo (1997)). Fnally, the senstvty to the change n the credt spread s postve and statstcally sgnfcant for all property types. Ths result does not necessarly contradct the lterature hgher credt spread s lkely postvely related to hgher nterest rates, and Goetzmann and Ibbotson (1990) fnd a postve correlaton between commercal real estate returns and nterest rates. However, ths result seems counterntutve when a wder credt spread s nterpreted as a contracton n external fnancng, whch should decrease real estate values and thus the total returns. A few thngs may help nterpret the result. Frst, the senstvty does not necessarly capture causaton, and both the real estate returns and the change n the credt spread are endogenous, whch makes the nterpretaton of the coeffcent challengng. Second, the result mght relate to the heterogenety wthn the real estate market. For nstance, when external fnancng decreases, whle the demand for real estate decreases on average, the demand for safer propertes mght ncrease, whch leads to hgher values of nsttutonal qualty propertes. However, ths paper ams to establsh the stylzed facts regardng the senstvty, and thus leaves the nterpretaton for future research. V.2 Heterogenety and Temporal Varaton of the Senstvty β = Ths secton formally tests the heterogenety n the senstvty coeffcents { k} k 1 and the ntercept term across property types. The senstvty coeffcents may depend on not only property types but also other property attrbutes (see, e.g. Fuerst and Marcato (2009), among others). However, ths paper does not ntend to explore the heterogenety n all dmensons.
Usng offces as the default property type, ths secton runs regressons based on equaton (6), ncludng not only the ntercept term and the fve economc varables, but also nteracton terms between them and dummes for apartments, ndustral, and retal propertes. The nteracton terms capture the dfferences n the ntercept term and the senstvty coeffcents between the three property types and offces. Specfcally, the regresson s log sell ( ) log( ) = ( ) α + ( ) R T sell buy sell buy α D A t= buy + 1 t 1 2 I ( ) α ( ) + sell buy D + sell buy α D R 3 4 sell A sell β 1 1, k( F 1 k, t) β 1 2, kd ( F k = t= buy 1 k, t) + k = t= buy+ I sell R sell β k 1 3, kd ( F t buy 1 k, t) β4, kd F = = + = 1 ( t= buy + 1 k, t) + + + + k ε +, (13) where R s the total gross return for property from the acquston quarter buy to the dsposton quarter sell ; T t s the rsk free rate; { F kt, } k = 1 are quarterly macroeconomc varables, and A D, I D, and R D are dummes for apartments, ndustral propertes, and retal propertes respectvely. Table 6 reports the results of sx specfcatons of the regresson (13). The frst fve specfcatons nclude each of the fve economc varables and ther correspondng nteracton terms respectvely, and the last specfcaton ncludes all fve varables and nteracton terms. The table provdes strong evdence for the heterogenety n the senstvty coeffcents across property types. Partcularly, n the sxth specfcaton, whch ncludes all fve economc varables, a varety of nteracton terms are statstcally sgnfcant. Frst, apartments and ndustral propertes have sgnfcant lower ntercept terms than offces. Second, apartments and ndustral propertes have less negatve senstvtes to the nflaton rate than offces. Thrd, retal propertes have more negatve senstvtes to the stock market rsk premum than offces. Fourth, apartments
have less negatve senstvtes to the change n the term spread than offces. Fnally, apartments and retal propertes have lower senstvtes to the change n the credt spread than offces. The senstvty coeffcents lkely vary not only across property types but also across tme. To make the senstvty coeffcents tme varant yet dentfable, ths paper needs to mpose constrants to equaton (6). Two types of constrants are often mposed to study tme varyng parameters. The frst allows the parameters to dffer before and after certan break ponts n tme. The second allows the parameters to be functons of tme varyng varables. Ths paper uses the second approach to avod possble ad hoc defntons of breakng ponts, and to analyze f the senstvty coeffcents depend on economc condtons. All fve economc varables used n ths paper are natural canddates for varables that mght affect the senstvty coeffcents. Ths paper assumes that the senstvty s a functon of stock market rsk premum, for two reasons. Frst, the stock market rsk premum s a catch-all varable that reflects the change n the expectaton of all future economc condtons. Second, the relatonshp between the stock market rsk premum and the senstvty coeffcents helps nvestors better understand how the dversfcaton benefts of real estate nvestments may change wth the stock market performance. Ths paper uses the followng regresson for the each property type to test f the senstvty coeffcents depend on the stock market rsk premum: log sell sell ( R) log ( T ) ( ) 1 t = sell buy α + β 1 1, k( F t= buy 1 k, t) + k= t= buy+ sell + β 1 2, k( ST 1 t Fk, t) + ε, k= t= buy + (14)
where R s the total gross return for property from the acquston quarter buy to the dsposton quarter sell ; T t s the rsk free rate; { F kt, } k = 1 are quarterly economc varables; ST s the stock market rsk premum n quarter t t. (14) mples that the senstvty of the commercal real estate total return rsk premum to economc varable β + β ST, F k s 1, k 2, k t whch s a functon of the stock market rsk premum. A postve (negatve) β 2,k ndcates a hgher (lower) senstvty when the stock market rsk premum s hgher. Table 7 reports strong evdence for the relatonshp between the senstvty coeffcents and the stock market rsk premum. Specfcally, when the stock market rsk premum s hgher, the senstvty to GDP growth s sgnfcantly hgher for ndustral and retal propertes; the senstvty to the nflaton rate s sgnfcantly lower for all property types; the senstvty to the stock market rsk premum s sgnfcantly lower for apartments and offces, whch also ndcates that the relatonshp between real estate returns and the stock rsk premum s non-lnear; the senstvty to the term spread s sgnfcantly lower for offces and ndustral propertes. These results substantate the tme varyng dversfcaton benefts of commercal real estate nvestments. V.3 Rsk Characterstcs of Commercal Real Estate Ths paper uses the regresson n (6) to estmate the rsk characterstcs of commercal real estate nvestments, and the regresson n (14) to analyze the tme varaton of the rsk. The explanatory varables are now rsk factors nstead of economc varables; as a result, the coeffcents are factor loadngs. Table 8 reports the results of the regresson n (6) wth the factors beng the Fama- French and the momentum factor. Frst, apartments and retal propertes have postve ntercept terms, about 0.5% per quarter for apartments and 0.8% per quarter for retal propertes, whch means they have postve rsk adjusted returns n the sample perod f the factor model s correctly