Searching for a Common Factor. in Public and Private Real Estate Returns

Transcription

1 Searchng for a Common Facor n Publc and Prvae Real Esae Reurns Andrew Ang, * Nel Nabar, and Samuel Wald Absrac We nroduce a mehodology o esmae common real esae reurns and cycles across publc and prvae real esae markes. We frs place REIT ndces and drec real esae NCREIF apprasal-based and ransacon-based ndces (NPI and NTBI) on a comparable bass by adjusng for leverage and secor. We exrac a common real esae facor, whch s allowed o be perssen, from all hese markes. Indvdual real esae ndces load on hs common facor and hey also are drven by perssen, dosyncrac shocks. The common real esae facor s procyclcal and has low correlaons wh sandard sysemac facors. Shor-run dosyncrac devaons from he common real esae facor load on several capal marke facors for REITs and on lqudy facors for drec real esae. Ths Verson: * Ann F. Kaplan Professor of Busness, Columba Busness School, New York, NY Research Analys, Fdely Invesmens, Boson, MA, Correspondng auhor, Nel.Nabar@fmr.com Porfolo Manager, Fdely Invesmens, Boson MA Elecronc copy avalable a: hp://ssrn.com/absrac=

2 1. INTRODUCTION Are real esae nvesmen russ (REITs) and drec real esae ownershp smlar or dfferen? On he one hand, boh nvolve nvesng n physcal buldngs and land, whch generae cash flows. Paglar, Scherer, and Monopol [2003, 2005] sugges ha afer adjusng REITs and drec real esae ndces for leverage and secor composon, and also adjusng drec real esae reurns for apprasal smoohng, REITs and drec ownershp have smlar rsk and reurn characerscs. Oher auhors have shown here are mporan dfferences beween REITs and drec real esae reurns. For example, drec real esae ransacons lead drec real esae apprasals, and here are sgnfcan lead-lag paerns beween REITs and drec real esae reurns. 1 Some of hese dfferences perss even afer akng no accoun he dfferen secor and leverage composon of REITs and drec real esae reurns. We sudy he long-run commonaly and shor-run dfferences beween REITs and drec real esae reurns. Alhough REITs are securzed, REITs and drec real esae reurns should be drven by common fundamenals n he long run snce boh nvolve ownershp of real esae. Carlson, Tman, and Tu [2010] develop a model based on dfferen coss of capal n whch publc and prvae real esae markes move ogeher n he long run, bu n he shor run, REITs and drec real esae prce movemens can dverge. In he shor run, REITs and drec real esae reurns dverge hrough vehcle-specfc shocks. Snce REITs provde mmedae lqudy and rade on cenralzed exchanges where oher eques rade, hey are exposed o sysemac equy marke facors. Clayon and MacKnnon [2001], for example, argue ha REITs have sgnfcan exposure o value and small-cap facors. REITs are wdely held and so may be buffeed by nvesor senmen and nose raders, whch DeLong, Shlefer, Summers, and Waldmann [1990], Hong, Schenkman, and Xong [2006], and ohers argue are sgnfcan nfluences on publcly raded sock markes. By conras, drec real esae nvesng nvolves less frequen ransacons and apprasal-based prcng ends o smooh reurns over me. Drec real esae s hen exposed o lqudy smoohng effecs whch do no affec REITs. Over he long run, hese effecs could cancel ou, so ha boh REITs and drec real esae reurns are exposed o he same common drvers and hus move ogeher. Our analyss proceeds n hree pars. Frs, we follow Paglar, Scherer, and Monopol [2005] and L, Mooradan, and Yang [2009], among ohers, and place REIT and drec real esae reurns on a comparable bass so ha hey have he same leverage and secor composon. We refer o he raw REIT 1 See, for example, Gyourko and Kem [1992], Barkham and Gelner [1995], and Okarnen, Hoesl, and Serrano [2011]. Elecronc copy avalable a: hp://ssrn.com/absrac=

3 and drec real esae reurns adjused hs way as comparable reurns. Unlke Paglar, Scherer, and Monopol [2005], we do no adjus for auocorrelaons or volaly nduced by he apprasal process. Raher, we preserve hese dosyncrac properes because hey are specfc o a parcular ndex, and we wsh o characerze how each ndex dffers from he componens ha are common across REIT and drec real esae markes. Second, we esmae a common facor across REIT and drec real esae reurns usng a laen componens model. We fler he common real esae facor from he observed comparable REIT and drec real esae reurns. The model arbues some poron of he movemens of a parcular real esae ndex as shared across all ndexes, bu some poron s specfc o ha ndex. Boh he common and dosyncrac componens are allowed o be auocorrelaed. Our esmaon mehodology handles dfferen sarng daes of each ndex. Fnally, we characerze he dynamcs of he common real esae facor and examne how he ndexspecfc componens move relave o he common facor. Ths allows us o explcly lnk he sources of dfference beween he common real esae facor and he underlyng characerscs of he varous real esae nvesmen vehcles. Our approach s relaed o a number of papers whch nvesgae he lead-lag relaonshps beween REITs and drec real esae, especally whn conegraed sysems. 2 Our approach s dfferen because we work drecly wh reurns, whch are I(0), raher han wh a oal reurn ndex, whch s I(1). Ths makes our work comparable wh he majory of fnance sudes whch drecly model reurns. By assumng a facor model, we also mpose economc resrcons on he sources of he shocks o each real esae marke ha hey mus come from common sources or dosyncrac sources. Thus, he man advanage s ha our model hghlghs he common real esae facor and reas each real esae marke as drecly exposed o he common facor. Conegraon models, n conras, employ an unconsraned covarance marx and esmae a common rend by fndng a lnear combnaon of he I(1) seres ha s saonary raher han decomposng common and dosyncrac shocks. Workng drecly wh reurns raher han I(1) varables also makes our work smlar o sandard facor models such as he CAPM or APT and makes our model comparable o he earler leraure by Goezmann and Ibboson [1990], Glbero [1990], and Lng and Naranjo [1999]. However, hese auhors do no allow for any perssence. In our model boh he sysemac and dosyncrac componens can be auocorrelaed, and we emprcally fnd ha perssence s hgh for he common real esae facor and 2 See, among ohers, Meyer and Webb [1994]; Gelner and Kluger [1998]; Paglar, Scherer, and Monopol [2005]; Hoesl and Serrano [2007]; Fuss, Morawsk, and Rehkugler [2008]); L, Mooradan, and Yang [2009]; Okarnen, Hoesl, and Serrano [2011]; and Sefek and Suryanarayanan [2011] 2

4 he drec real esae dosyncrac componens. Thus, our model also capures he smoohng effecs of Gelner [1991] and Ross and Zsler [1991], bu allows he common and dosyncrac smoohng effecs o be esmaed raher han needng o be drecly observed. 2. DATA We adjus he REIT reurns o be comparable o drec real esae on he bass of secor and leverage adjusmens followng Paglar, Scherer, and Monopol [2003, 2005]. For publcly raded real esae, we ake REITs from he CRSP/Zman Real Esae Daa Seres. The CRSP/Zman socks are lnked wh CRSP for reurns and wh Compusa for fnancal saemen daa. As a sarng pon for publcly lsed real esae reurns, we consruc a value-weghed ndex of REIT reurns from hs combned daase. For prvaely held real esae reurns, we use wo ndces based on daa from he Naonal Councl of Real Esae Fducares (NCREIF). The frs s he apprasal-based Propery Index (NPI). Apprasals are calculaed based on facors ha are already n place and are no nsananeous and are herefore laggng. The second s he NCREIF Transacon Based Index (NTBI), whch s based on properes n he NPI ha were sold. 3 As of December 1980, here were 54 REITs wh an aggregae marke capalzaon of $1.8 bllon n he CRSP/Zman equy-only seres, compared o $1.9 bllon n prvaely held properes n he NCREIF daabase. In he early 1990s, he number and marke value of REITs as well as he marke value of prvae marke ransacons ncreased dramacally. Durng he recovery from he savngs and loan crss of he lae 1980s and early 1990s, he real esae ndusry recapalzed and nvesmen n boh REITs and drec real esae ncreased. The number of REITs peaked around 200 n 1998, and REIT capalzaon reached a maxmum above $430 bllon n The marke value of he NPI posed a hgh close o $340 bllon n Snce hen, he number of REITs has fallen o 133 wh a $370 bllon capalzaon n December 2011, compared o $280 bllon n prvaely held real esae n he NPI and NTBI seres. 4 3 The NTBI s calculaed n wo sages. Frs, for all properes sold n he quarer, NCREIF calculaes he average rao of he sales prce dvded by he apprasal, lagged wo quarers. Second, hs rao s mulpled by he NPI level, also lagged wo quarers, o conver he resul no he NTBI ransacon-based prce ndex. The lagged apprasal s used nsead of he curren apprasal because he apprasal prce may be nfluenced by a subsequen sale whn wo quarers. 4 Source: Auhors based on CRSP/Zman and NCREIF daa. 3

5 2.1 Leverage Adjusmens Alhough ndvdual properes whn he NPI and NTBI have leverage assocaed wh hem, NPI and NTBI reurns are repored on an unlevered bass. REIT reurns, on he oher hand, represen he equy reurn of leveraged properes. Durng he pas 30 years, REIT leverage deb and preferred equy dvded by enerprse value has averaged 43%, and annual neres expenses have ranged from jus under 6% o almos 9%. 5 We delever he REIT reurns o make hem comparable o he NCREIF reurns followng Paglar, Scherer, and Monopol [2003, 2005]. Usng he mos recen balance shee daa on a monhly bass, we compue a leverage rao for each REIT: Deb + Preferred Equy Leverage Rao =, Deb + Preferred Equy + Equy Marke Capalzaon (1) where he equy marke capalzaon s compued usng common equy, and we ake book values for he preferred sock and deb. We compue an annualzed neres cos per monh for each REIT usng he formula: Ineres & Preferred Cos LTM Ineres Expense + LTM Preferred Dvdends =, (Deb + Preferred Equy ) + (Deb + Preferred Equy ) (2) whch akes he neres and preferred dvdends pad over he las 12 monhs dvded by he average amoun of preferred equy and deb over he las 12 monhs. We use a one-year wndow o esmae he neres rae of deb o conrol for he effecs of refnancng. Usng he leverage rao and neres cos n equaons (1) and (2), respecvely, we compue a monhly delevered REIT reurn: Delevered REIT Reurn = REIT Reurn (1- Leverage Rao) Ineres Expense + Leverage Rao, 12 (3) The delevered monhly REIT reurns are convered o he quarerly frequency o mach he quarerly frequency of he NPI and NTBI seres. 5 Source: Auhors based on CRSP/Zman daa. 4

6 Exhb 1 shows ha from January 1994 o December 2011, he raw REIT average reurn per quarer s 2.53%, wh a sandard devaon of 13.07%. Takng leverage no accoun lowers he average quarerly reurn o 1.14%, wh a sandard devaon of 5.15%. Thus, adjusng for leverage has a subsanal effec on average reurns and volaly a crucal dsncon beween REITs and repored drec real esae reurns. EXHIBIT 1 Quarerly Reurns, Sandard Devaons, and Seral Correlaons of Publc and Prvae Real Esae Average Quarerly Reurns Source: Auhors based on CRSP/Zman and NCREIF daa. Quarerly Sandard Devaon Seral Correlaon 5 year 10 year Snce 1994 Avalable Hsory Snce 1994 Avalable Hsory Avalable Hsory REIT 2.53% 3.96% 3.40% 3.46% 13.07% 11.51% 0.14 NPI 0.84% 2.01% 2.25% 2.06% 2.43% 2.22% 0.78 NTBI 0.62% 2.34% 2.74% 2.74% 5.74% 5.74% REIT (leverage adjused only) 1.14% 2.37% 2.36% 2.71% 5.15% 4.79% 0.07 Comparable REIT 1.16% 2.38% 2.41% 2.78% 4.99% 4.51% 0.06 Comparable NPI 0.98% 2.19% 2.31% 2.28% 2.24% 1.98% 0.77 Comparable NTBI 0.47% 2.41% 2.64% 2.64% 5.49% 5.49% Noe: Avalable hsory sars n Q for NTBI and Q for oher seres. All seres end n Q Secor Adjusmens REIT and NCREIF reurns have dfferen secor composons. REITs prmarly fall no he four core real esae secors of aparmen, real, offce, and ndusral, alhough oher secors are ganng represenaon. 6 By conras, gven NCREIF s nsuonal focus, NPI and NTBI nclude only he four core real esae secors plus hoels. To place REITs, NPI, and NTBI on he same secor bass, we consder he four core real esae secors whou hoels. 7 Real REITs have he larges wegh n he CRSP/Zman REIT seres. Aparmen, offce, and ndusral REITs have sayed n 5% 10% bands around her curren weghs. Hsorcally, offce and real have been he larges weghs n he NCREIF ndces. Real 6 Hsorcally a leas 80% of he oal REIT capalzaon was n hese secors, bu ha weghng has fallen o abou 60% n recen years as new secors ncludng healhcare, daa cener, sorage, mber, and ohers have convered o REIT saus and/or ganed nvesor aenon. 7 We also exclude hoels because of her small wegh n he NPI less han 5% a any me and her relavely nfrequen ransacons. 5

7 gradually moved from he 40% n 1994 o 22% oday as he supply of oher propery ypes grew much faser han real, whle some real ypes especally malls moved no he REIT forma. 8 Exhb 2 shows he secor composon of our core REIT and NPI/NTBI seres as of December REITs are much more heavly weghed owards real, a 46%, whle he NPI/NTBI propery-ype mx s more balanced, wh a 22% wegh n real. Offces, a 36%, accoun for a larger proporon of he drec propery ndex, compared o he REITs wegh of 18%. EXHIBIT 2 REIT and NPI/NTBI Core Propery-Type Weghs as of 12/31/2011 REITs Core Propery Type Secor Mx NPI/NTBI Core Propery Type Mx Real 46% Aparmen 25% Indusral 11% Offce 18% Real 22% Offce 36% Aparmen 27% Indusral 15% Source: Auhors based on CRSP/Zman and NCREIF daa. To consruc a comparable REIT reurn seres, we wegh monhly reurns of REITs n he four core propery ypes (aparmen, real, offce, and ndusral) by oal capalzaon (deb plus preferred sock plus equy). To consruc he comparable NPI and comparable NTBI reurns, we wegh he quarerly NPI and NTBI reurns for each propery ype and by he weghs of each propery ype n he comparable REIT ndex. Exhb 1 also repors summary sascs of he comparable REIT, NPI, and NTBI seres. Takng secor composon no accoun does no sgnfcanly change he reurns from he delevered REIT seres or he raw NPI and NTBI seres. For example, he mean and sandard devaon per quarer of he delevered REIT reurns are 2.36% and 5.15%, respecvely, from 1994 o Allocang he REIT seres no he core propery ypes changes he mean and sandard devaon per quarer o 2.41% and 4.99%, respecvely. Smlarly, weghng he NPI and NTBI wh he same secor weghs as he core propery 8 Source: Auhors based on CRSP/Zman and NCREIF daa. 6

8 ypes n he REIT ndex has mnor effecs. For he NPI, he mean and sandard devaon per quarer are 2.25% and 2.43%, respecvely, n he raw seres and 2.31% and 2.24% afer accounng for secor weghs. For he NTBI, he mean and sandard devaon s 2.74% and 5.74% n he raw seres and 2.64% and 5.49% afer accounng for secor weghs. Even hough he REIT and he NCREIF seres have dfferen secor composons, adjusng for secors has a relavely small effec on hese uncondonal momens because all he seres are dversfed across several secors. All hese secors are exposed o he same underlyng economc drvers n he economy n he long run. Exhb 3 plos rollng wo-year averages of he quarerly reurns for all hree comparable seres and shows ha hey exhb a large degree of comovemen. Ye here are salen dfferences. The comparable REIT and NTBI seres are sgnfcanly more volale han he comparable NPI seres due o dfferences n ndex consrucon, namely equy and ransacon-based reurns raher han apprasals (see also Exhb 1). There are addonal dfferences due o he mng of he real esae cycle and he economc envronmen. Generally speakng, he comparable REIT seres seems o lead he comparable NTBI reurns, whch leads he comparable NPI reurns. Because of nsananeous lqudy, he publc markes are he mos forward lookng, followed by drec ransacon markes, followed by apprasals. Ths s conssen wh he fndngs of Gyourko and Kem [1992], Barkham and Gelner [1995], and ohers. EXHIBIT 3 Reurns o he Comparable Real Esae Seres 8% 6% 4% 2% 0% -2% -4% -6% Two Year Average Quarerly Reurns Comparable REIT Comparable NPI Comparable NTBI 1982Q1 1983Q1 1984Q1 1985Q1 1986Q1 1987Q1 1988Q1 1989Q1 1990Q1 1991Q1 1992Q1 1993Q1 1994Q1 1995Q1 1996Q1 1997Q1 1998Q1 1999Q1 2000Q1 2001Q1 2002Q1 2003Q1 2004Q1 2005Q1 2006Q1 2007Q1 2008Q1 2009Q1 2010Q1 2011Q1 Source: Auhors based on CRSP/Zman and NCREIF daa. 7

9 Exhb 3 shows ha durng he early 1990s, real esae fundamenals were poor and recoverng from an oversupply of underlyng properes. Very lle capal was avalable o he real esae ndusry, and he publc markes provded capal for he ndusry o recapalze. The ably o buy asses n he publc markes a favorable prcng helped REITs ouperform he underlyng propery markes. Durng he lae 1990s echnology bubble, sock marke nvesors were generally more focused on faser growng companes, whle seady ndusres lke real esae were ou of favor. Despe moderae fundamenals a he underlyng propery level, he comparable REIT ndex underperformed he comparable NPI and NTBI ndces. In , he lack of lqudy mpaced all forms of capal-nensve real esae as avalable fundng dred up. The overall message n Exhb 3 s ha he hree seres represenng publc and prvae real esae markes have large underlyng comovemens reflecng common exposure o he underlyng economy. There are also mporan vehcle-specfc dosyncrac componens. Esmang he relaonshps beween our hree seres o exrac a common, underlyng real esae facor s he focus of he nex secon. 3. MODEL We decompose a class of real esae, r, no exposure o a common real esae facor, ndex-specfc componen, g : where esae facor, esae facor, f, and an r = β f + g, (4) β represens he loadng of he real esae class, or nvesmen vehcle, on he sysemac real f. We specfy ha he dosyncrac componen, f. g, s orhogonal o he common real The common real esae facor, f, follows: f = c + f + (5) f φ f 1 σ fε, where ε ~ N(0,1). The auocorrelaon, φ f, allows for perssence n he common real esae facor. The dynamcs of he real esae ndex componen, g, follow: g = c + g + u (6) φ, 1 σ, whch also allows perssence hrough ϕ. We se u ~ IID N(0,1) o be ndependen of ε a all leads 8

10 and lags and also ndependen across seres. Exhb 4 llusraes he relaon beween he common real esae facor and he varous real esae seres. Snce we model reurns n equaons (4) (6), he ndex level can be nerpreed as he cumulaed reurn seres. Movemens n he real esae cycle correspond o he common real esae facor, f. As he model allows reurns o be auocorrelaed, can capure he long swngs n real esae markes documened by many auhors (see, for example, Wheaon [1999]). The ndvdual real esae markes, boh publc and prvae, follow he real esae cycle because hey have exposure o he common real esae facor hrough he facor loadngs, β. The larger he facor loadng, he more ha real esae marke moves n sync wh he real esae cycle, all oher hngs beng equal. The real esae ndces do no exacly follow he real esae cycle due o shocks ha are specfc o he marke segmen. These shocks, g, can hemselves follow her own cycles, whch are capured hrough he φ erms. Snce he perssence of he dosyncrac real esae marke movemens may no be he same as he common real esae facor, he dosyncrac cycles can parally offse, exacerbae, or somemes compleely cancel he effec of he common real esae cycle. EXHIBIT 4 Common Real Esae Facor and Real Esae Seres For llusrave purposes only. 9

11 The model allows for rch paerns n machng lead-lag paerns hrough mpled cross- and auocorrelaons. For example, he cross-covarances of real esae marke and real esae marke j are gven by cov( rr ) = ββφ var( f ), (7) k, j, k j f where 2 2 var( f) σ f / (1 φ f ) =. The cross-covarances of a gven real esae class are gven by 2 k k cov( rr,, k ) βφ f var( f ) φf var( g ), = + (8) where 2 2 var( g ) σ / (1 φ ) =. The model can be nerpreed as a facor model where f s he common facor and g are dosyncrac shocks specfc o each real esae seres. Ths makes our model smlar o a CAPM or an APT as well as he models esmaed by Goezmann and Ibboson [1990], Glbero [1990], and ohers. However, here are wo mporan dfferences: We allow for perssen common and dosyncrac facors, and our common facor s laen. Gelner [1991], Ross and Zsler [1991], and many ohers develop mehods o unsmooh drec real esae reurns. These mehods mplcly nvolve modelng he prvae real esae reurn, whch s he llqud asse, wh loadngs on conemporaneous and lagged asse reurns ha are assumed o be lqud and have auocorrelaons close o zero (see also Sefek and Suryanarayan [2011]). Sandard smoohng flers assume ha he loadngs decrease n absolue value as he lags ncrease. A smlar formulaon s mpled by our model. Snce he common real esae facor, f, s perssen, we have: r = k + φβσε+ φβσε 1+ φβσε , (9) 2 3 f f f f f f where he ε shocks are..d. nnovaons o he common real esae facor n equaon (5). Thus, he exposure o a perssen real esae facor also nduces smoohng n a parcular real esae marke. And he model also allows he possbly of auocorrelaed marke-specfc devaons away from he common real esae facor. We esmae he common real esae componen, f, by a Bayesan Gbbs samplng algorhm, whch we deal n he Appendx. The algorhm jonly esmaes he common real esae facor and he parameers of he model. 10

12 4. EMPIRICAL RESULTS 4.1 Parameer Esmaes Exhb 5 repors parameer esmaes of he model. The common real esae facor has an average reurn of 1.89% per quarer. The common facor s hgh quarerly auocorrelaon (φ f = 0.69) ndcaes he srong nfluence of pas observaons and reflecs he cyclcal, rendng naure of real esae. Facorloadng beas above 1.0 for REIT and NTBI sugges ha he marke ransacon-based vehcles have greaer exposure o he real esae facor, whle he apprasal-based NPI has much lower exposure (β = 0.37) o he real esae facor. Thus, marke-based real esae ransacons have greaer exposure o underlyng real esae rends. EXHIBIT 5 Parameer Esmaes Common Real Esae Facor Poseror Poseror Idosyncrac Reurns Mean Sd Dev Mean Sd Dev c f REIT c φ f REIT φ σ f REIT σ NPI c Facor Loadngs Poseror NPI φ Mean Sd Dev NPI σ REIT β NTBI c NPI β NTBI φ NTBI β NTBI σ Source: Auhors based on CRSP/Zman and NCREIF daa. The oher model parameers reflec he seres-specfc dosyncrac reurns afer subracng he common real esae facor from he hree seres. Afer hs adjusmen, REIT reurns have no auocorrelaon (φ 0), whch s expeced for a publc, forward-lookng secury, bu he dosyncrac sandard devaon s relavely hgh a 4.51% per quarer. In conras, he NTBI reurns are negavely auocorrelaed (φ = 0.34). Ths may reflec he nose and samplng bas nheren n he seres, as only a small fracon of properes rade durng any gven perod (see commens by Goezmann [1992]). We fnd ha he auocorrelaon of he NPI s sll hgh (φ = 0.59), even afer adjusng for he common real esae facor, whch s also posvely auocorrelaed. Such predcable and perssen auocorrelaon reflecs he smoohng nheren n reurns ha resuls from he apprasal process. Ths suggess a lnk o Cannon and Cole [2011], who fnd ha apprasals are off by 12% on average from ransaced prces and 11

13 lag prces n boh rsng and fallng markes. Accordng o Cannon and Cole, NPI apprasal error s sysemac and has a macro nfluence. Our resuls show ha he perssence nduced by hs process s even larger han he perssence from he general real esae cycle. 4.2 Common Real Esae Facor Exhb 6 plos he four-quarer movng average of he common real esae facor and he comparable seres. By consrucon, he real esae facor s a compose of he hree underlyng seres, ye s no smply an equal-weghed combnaon of hem. Raher, he algorhm allows each real esae marke o have dfferen facor loadngs and places more wegh on he REIT and NTBI seres (see Exhb 5). Our esmaon s also able o exrac he real esae facor n he early par of he sample even when he NTBI seres s no avalable. The common real esae facor capures he underlyng rend of generally posve quarerly reurns n he real esae marke durng he pas 30 years, wh a slowdown n he lae 1980s and early 1990s, exremely srong reurns n he md-2000s, and a seep declne n EXHIBIT 6 Reurns o he Common Real Esae Facor and Comparable Real Esae Seres 10% 8% 6% 4% 2% 0% -2% -4% -6% -8% 1yr Quarerly Movng Average Reurns of Real Esae Seres Common Real Esae Facor Comparable NPI 1981Q1 1982Q1 1983Q1 1984Q1 1985Q1 1986Q1 1987Q1 1988Q1 1989Q1 1990Q1 1991Q1 1992Q1 1993Q1 1994Q1 1995Q1 1996Q1 1997Q1 1998Q1 1999Q1 2000Q1 2001Q1 2002Q1 2003Q1 2004Q1 2005Q1 2006Q1 2007Q1 2008Q1 2009Q1 2010Q1 2011Q1 Source: Auhors based on CRSP/Zman and NCREIF daa. Comparable REIT Comparable NTBI 12

14 4.3 Common Real Esae Facor Innovaons We characerze how nnovaons o he common real esae facor move wh macro, syle, and lqudy facors, all a he quarerly frequency. We sar wh he reurns of he equy and bond markes, proxed by he S&P 500 and Barclays Aggregae ndces, o es for relaons wh he capal markes. Snce he demand for real esae s also relaed o aggregae acvy n he real economy, we nclude real GDP growh and he change n he Consumer Prce Index (CPI). Fnally, because real esae s a capal-nensve busness, we also nclude a cred spread varable, he dfference beween he yeld on BAA-raed corporae bonds and he yeld on he 10-year Treasury. To characerze he real esae marke from an nvesmen-syle perspecve, we look a several sandard syle facors: SMB, HML, and MOM, respecvely, whch are he reurns o small mnus large cap socks, value versus growh socks, and momenum consruced by Fama and French [1993] and Carhar [1997]. We also consder wo lqudy varables. The frs lqudy varable measures lqudy n sock markes. Ibboson, Chen, and Hu [2011] documen ha socks sored by urnover exhb dfferences n reurns. Smlarly, we rank socks n he Russell 1000 Index monhly by urnover defned as shares raded dvded by shares ousandng durng he pas 12 monhs and hen calculae he spread beween he one-monh forward reurns of he lowes qunle mnus he reurns of he hghes qunle. Ths low mnus hgh urnover facor s he reurn o sock-level llqudy. To measure he level of lqudy specfc o he real esae marke more drecly usng NCREIF daa, we calculae he percenage of properes n he NPI ha sold durng a gven quarer. These wo facors have a cross-seconal correlaon of only 0.02, suggesng ha sock marke lqudy and real esae lqudy are very dfferen. We regress nnovaons of he common real esae facor, whch s defned as he nnovaon n equaon (5) above, and repor he resuls n Exhb 7. 9 In he mulvarae regresson, he common real esae facor loads posvely and sgnfcanly on he S&P 500, ndcang ha s procyclcal. There s also a large negave coeffcen on he cred spread, whch s no surprsng gven ha real esae s a capalnensve asse class, and wdenng spreads are deleerous for he real esae ndusry. Real esae reurn nnovaons are lnked o sock marke and real esae lqudy, bu n dfferen ways. Real esae reurns are negavely correlaed wh sock marke lqudy. Conssen wh Cannon and Cole [2011] and ohers, here s a srong posve relaon beween real esae reurns and real esae lqudy. 9 In he unvarae regressons, he common real esae facor also loads sgnfcanly and posvely on SMB, bu negavely on sock marke lqudy. 13

15 EXHIBIT 7 Regresson Resuls: Common Real Esae Facor Common Real Esae Facor Innovaons Bea P Value S&P 500 Index Barclays Aggregae Change n Real GDP Growh Change n CPI Change n BAA Treasury Spread MOM SMB HML Low Turnover Hgh Turnover NPI Turnover Noe: Coeffcens n bold are sgnfcan a 5% level. Source: Auhors based on Haver Analycs and Bloomberg daa. 4.4 Specfc Real Esae Marke Innovaons We consruc specfc real esae marke nnovaons akng he resduals n equaon (6). Exhb 8 plos he wo-year quarerly movng average of he nnovaons for each seres. REIT nnovaons show he greaes varably around he common real esae facor, and end o lead he nnovaons n he NPI and he NTBI. A urnng pons n he real esae cycle, REIT nnovaons move n oppose drecons from NPI nnovaons, rendng sgnfcanly hgher or lower durng real esae booms and buss n , , , and Exhb 9 characerzes how real esae marke nnovaons away from he common real esae marke cycle move. We run mulvarae regressons on he nnovaons n he real esae seres usng he same facors we used o analyze he common real esae facor. We fnd ha REIT nnovaons have several sgnfcan relaonshps wh hese exogenous facors, loadng posvely on he S&P 500 and Barclays Aggregae ndces as well as SMB and HML. Based on hs analyss, REITs provde nvesors wh exposure o real esae hrough he common facor, as well as o oher macroeconomc and capal marke especally sock marke facors. Our resuls refne he commonly held belef ha REITs provde real esae exposure plus equy marke exposure. These equy 14

16 marke exposures are a poenal source of opporuny for acve managers of REIT porfolos n he shor erm. EXHIBIT 8 Real Esae Seres Innovaons 2yr Quarerly Movng Average of Innovaons REIT Innovaons NPI Innovaons NTBI Innovaons 6% 5% 4% 3% 2% 1% 0% -1% -2% -3% -4% 1982Q1 1983Q1 1984Q1 1985Q1 1986Q1 1987Q1 1988Q1 1989Q1 1990Q1 1991Q1 1992Q1 1993Q1 1994Q1 1995Q1 1996Q1 1997Q1 1998Q1 1999Q1 2000Q1 2001Q1 2002Q1 2003Q1 2004Q1 2005Q1 2006Q1 2007Q1 2008Q1 2009Q1 2010Q1 2011Q1 Source: Auhors. EXHIBIT 9 Regresson Resuls: REIT, NPI, and NTBI Innovaons Facors REIT Innovaons NPI Innovaons NTBI Innovaons Bea P Value Bea P Value Bea P Value S&P 500 Index Barclays Aggregae Change n Real GDP Growh Change n CPI Change n BAA Treasury Spread MOM SMB HML Low Turnover Hgh Turnover NPI Turnover Noe: Coeffcens n bold are sgnfcan a 5% level. Source: Auhors based on Haver Analycs and Bloomberg daa. 15

17 NPI nnovaons load on wo facors, cred spreads and real esae marke urnover. We beleve hs offers several nsghs no he performance of he NPI: Increased acvy n he physcal real esae marke leads o hgher reurns n he NPI, whch suggess ha he apprasal process s revsed hgher by ransacon acvy. And conrary o he sandard belef ha he NPI does no have srong correlaons wh he capal marke, NPI nnovaons are affeced by cred spreads, a capal marke lqudy facor. However, NTBI nnovaons have no sgnfcan lnks wh any of our facors, possbly because supermposng a lmed number of ransacons n any gven perod over apprased values nroduces samplng nose ha may be obscurng he resuls. Ye s noable ha NTBI has weak negave correlaons wh all he facors excep SMB and lqudy n boh sock and real esae markes. The posve assocaon wh real esae marke lqudy conrass wh hs facor s negave albe nsgnfcan relaon o REITs. Whle he sascal relaon s nsgnfcan, he coeffcen on he cred spread s economcally very large. Ths s nuve. As fnancng becomes harder o oban, apprasals should be lowered, whch affecs NTBI valuaons. 5. CONCLUSIONS Invesors can ge exposure o real esae hrough publcly raded REITs or prvae equy funds. Whle some assume ha publc and prvae real esae are separae asse classes and have dfferen reurn and rsk properes, we esmae a common real esae cycle across publc (REIT) and prvae (NPI and NTBI) real esae markes. We fnd ha hs common real esae facor s hghly perssen, reflecng he cyclcal naure of real esae, and broadly exposed o procyclcal marke facors. Our model s able o capure dosyncrac movemens n vehcle-specfc real esae markes away from he common facor. These nnovaons can also be perssen. Innovaons n publcly raded real esae reurns away from he common rend are correlaed wh equy and bond marke reurns, as well as capalzaon and valuaon mercs, mplyng ha nvesng n publc secures furher ncreases exposure o oher marke facors. These capal marke dslocaons are a poenal source of opporuny for managers of REIT porfolos n he shor erm. Innovaons n prvae real esae reurns away from common rend are posvely correlaed wh capal and real esae marke lqudy. Over he full real esae cycle, however, he effecs of hese dfferen exposures largely dsappear. 16

18 APPENDIX The esmaon s done by a Bayesan Gbbs samplng algorhm. The esmaon allows for mssng observaons, snce he NTBI sample s shorer han he NPI and REIT samples. The algorhm nvolves eravely drawng he parameers and he laen facor from a seres of condonal dsrbuons, whch n seady sae yelds he dsrbuons of he parameers, he sysemac facor, and he laen seresspecfc dosyncrac facors. Mssng observaons are reaed as laen facors and are also drawn n each eraon. A exbook reamen of Gbbs samplng procedures s presened by Rober and Casella [1999]. Smlar esmaons o equaons (4) (6) are done by Sock and Wason [2002] for a prncpal componens model and by Ang and Chen [2007] for a sochasc bea and volaly model, among ohers. {r unobs We denoe he parameer vecor as θ = ( c, φ, σ, β, c, φ, σ ). We use he noaon θ o denoe f f f he full se of parameers, less he parameers of neres. We denoe he se of mssng reurns as unobs { r }, he laen common real esae facor as { f }, and he full se of daa by Y. We erae over he followng condonal draws: Sysemac Facor We draw p({ f } θ,{ r }, Y} usng he forward-backward algorhm of Carer and Kohn [1994]. unobs Equaon (4) represens a sae equaon and he reurns n equaon (5) represen a seres of measuremen equaons n a Kalman fler sysem. We use he forward-backward algorhm of Carer and Kohn [1994] o draw he sysemac facor. Noe ha when he mssng reurns are known, he measuremen equaons consue a sandard me-seres panel. Sysemac Facor Parameers Gven he seres of { f }, he condonal draw p( cf, φ f, σ f θ,{ f}) s a sandard regresson and we draw hese parameers usng a sandard conjugae normal-nverse gamma dsrbuon. We assume a dffuse normal pror for φ f whch yelds a normal poseror and an unnformave nverse gamma pror for σ whch yelds an nverse gamma poseror. f The full se of consans c f and he real esae marke-specfc c parameers are undenfed. For denfcaon, we assume ha he laen facor mean s gven by he weghed means of each real esae marke reurn, where he weghs are he facor exposures, β. We ake he weghed averages only for he daa whch are observable a each pon n me. Then, we use he AR(1) n equaon (5) o nfer ou he parameer c f from he uncondonal mean of he laen facor. 17

19 Sysemac Facor Loadngs We draw p( β θ,{ f },{ r }, Y). Equaon (4) s a regresson of ndex reurns on he observable unobs sysemac facor { f }. Ths s a conjugae normal-nverse gamma draw. We requre addonal assumpons for denfcaon gven he small number of real esae seres. Frs, we ake an emprcal Bayes approach usng an nal esmae of he laen facor from an equally weghed average of he hree real esae seres. Inal esmaes of he sysemac facor loadngs are obaned by sandard regressons usng equaon (4). We se he pror mean, μ, o be he esmaed coeffcens and he p pror sandard devaon, σ, o be he Newey Wes [1987] sandard error esmae usng four lags. β The esmaes are scaled so ha he cross-seconal sandard devaon across he beas s equal o 0.5, and hs s mananed n all draws. Second, o ensure ha no one seres domnaes and ha he Kalman fler s well defned when he laen facor s exraced, we rejec all draws fallng ousde a range gven by four mes he pror sandard devaon around he pror mean, [ μ p 4 σ p, μ p + 4 σ p ]. We use only daa ha are observable n drawng he beas. p β β β β β β β Idosyncrac Parameers To draw p( c,,,{ },{ unobs φ σ θ f r }, Y}), we noe ha gven { f } and reurns, we can nver he dosyncrac reurn, { g }, from equaon (6). Then, equaon (6) s a sandard regresson and we use a conjugae normal-nverse gamma draw. We ake an emprcal Bayes approach o esmang φ. Usng he nal esmae of he laen facor, we can form an nal esmae of{ g } and esmae he parameers n regresson (6). We specfy he esmaed coeffcen and Newey Wes [1987] sandard error compued usng four lags o be he pror mean and pror sandard devaon, respecvely. Occasonally, here are very large values of φ drawn for he REIT seres hs s no a problem for he oher seres and we do no updae hese values when hs occurs. Specfcally, we rejec all values fallng ousde plus or mnus four pror sandard devaons away from he pror mean for he REIT seres. To denfy he consans, c, we repor hem as marke-specfc consans around he common facor mean. Ths s done as follows. We draw he consan n he regresson (5) and compue he real esae marke uncondonal mean. We calculae he marke-specfc mean by subracng he mean of he laen facor. Usng he AR(1) process n regresson (5), we conver hs back o a consan erm, whch s repored as c. Thus, all consan erms for he dosyncrac real esae seres parameers represen condonal mean movemens around he common real esae facor. 18

20 Mssng Reurns The {g unobs mssng reurn draw, ( unobs unobs p r θ,{ f }, ) Y nvolves smulang he dosyncrac reurn,{ g }, whch follows an AR(1) process from equaon (6). Noe ha { f } n hs sep s observable, so he smulaed dosyncrac reurns can be added o he sysemac facors n equaon (5). 19

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24 Vews expressed are as of he dae ndcaed, based on he nformaon avalable a ha me, and may change based on marke and oher condons. Unless oherwse noed, he opnons provded are hose of he auhors and no necessarly hose of Fdely Invesmens. Fdely does no assume any duy o updae any of he nformaon. Pas performance s no guaranee of fuure resuls FMR LLC & Andrew Ang. All rghs reserved. 23