Heterogeneous Information and Appraisal Smoothing

Transcription

1 Heerogeneous Informaion and Appraisal Smoohing Ping Cheng Deparmen of Finance, College of Business Florida Alanic Universiy 777 Glades Road, Boca Raon, FL Zhenguo Lin Deparmen of Finance and Economics Mississippi Sae Universiy Mississippi Sae, MS 3976 Yingchun Liu Deparmen of Finance, Insurance and Real Esae Laval Universiy Quebec, G1V 0A6, Canada Absrac This sudy examines he heerogeneous appraiser behavior and is implicaion on he radiional appraisal smoohing heory. We sho ha he parial adjusmen model is consisen ih he radiional appraisal smoohing argumen only hen all he appraisers choose he same smoohing echnique. Hoever, if appraiser behavior is heerogeneous and exhibis crosssecional variaion due o he difference in heir access o, and inerpreaion of informaion, he model acually leads o a mixed oucome: The variance of he appraisal-based reurns can be higher or loer han he variance of ransacion-based reurn depending on he degree of such heerogeneiy. Using daa from he residenial marke, e find ha, conrary o ha he radiional appraisal smoohing heory ould predic, appraisal-based indices may no suffer any smoohing bias. These findings sugges ha he radiional appraisal smoohing heory, hich fails o consider he heerogeneiy of appraiser behaviors, exaggeraes he effec of appraisal smoohing. January 11, 011

2 Heerogeneous Informaion and Appraisal Smoohing [Absrac] This sudy examines he heerogeneous appraiser behavior and is implicaion on he radiional appraisal smoohing heory. We sho ha he parial adjusmen model is consisen ih he radiional appraisal smoohing argumen only hen all he appraisers choose he same smoohing echnique. Hoever, if appraiser behavior is heerogeneous and exhibis cross-secional variaion due o he difference in heir access o, and inerpreaion of informaion, he model acually leads o a mixed oucome: The variance of he appraisal-based reurns can be higher or loer han he variance of ransacion-based reurn depending on he degree of such heerogeneiy. Using daa from he residenial marke, e find ha, conrary o ha he radiional appraisal smoohing heory ould predic, appraisal-based indices may no suffer any smoohing bias. These findings sugges ha he radiional appraisal smoohing heory, hich fails o consider he heerogeneiy of appraiser behaviors, exaggeraes he effec of appraisal smoohing. 1. Inroducion One of he mos exensively documened observaions in he real esae lieraure is ha appraisal-based reurn series (as exemplified by he NCREIF Propery Indices) exhibi comparable reurns o common socks, bu ih much loer volailiy. Tha is, he risk-adjused reurns of commercial real esae are significanly higher han hose of common socks. This is ofen referred o as he real esae risk premium puzzle, (Lusch (1988), Shilling (003)) as i suggess ha real esae reards invesors ih addiional premium for he same risk. The consisenly repeaed such observaion over ime and he desire o solve he puzzle have promped one of he leading heories in real esae he appraisal smoohing heory. As ariculaed in Gelner (1989, 1991) and many ohers, he appraisal smoohing heory argues ha he seemingly superior performance of real esae is essenially caused by he raional

3 behavior ha appraisers exhibi in heir pracices. Paricularly, i is believed ha, in forming an appraisal esimae on a given propery, he appraiser ends o no only analyze he curren marke informaion, bu also give some consideraion o he pas marke informaion of he same or similar properies. This is called parial adjusmen behavior, as he curren marke informaion is no given 100% consideraion. This behavior effecively implies ha he appraisers end o eighed-average he pas and presen informaion o form heir appraisal opinion. An appraisalbased reurn series such as he NCREIF Propery Index, herefore, is essenially some sor of moving average of he underlying asse performance. As such, i is expeced o be smoohed and exhibi donard-biased volailiy over ime. Correcion of such smoohing bias, he heory argues, ill lead o increased variance and reduced risk-adjused reurns for real esae o he levels comparable o ha of common socks, hus solving he real esae risk premium puzzle. Based on he assumed appraiser behavior, Gelner (1989, 1991) exended he ork of Blundell and Ward (1987) o propose a formal model knon as he parial adjusmen model, in hich he curren appraisal reurn is expressed as a eighed average of he pas rue propery reurns (or rue propery appreciaion raes). This model formalizes he smoohing argumen and provides he normaive foundaion for he heory. Over he pas eny years, he parial adjusmen model has gained ide populariy among academics, and is ofen aken as he heoreical launch pad for many sudies se ou o quanify smoohing effec or develop de-smoohing mehodologies. Despie repeaed and ofen sophisicaed elaboraions by many sudies from various angles, i is orh noing ha he hole idea of appraisal smoohing heory is almos enirely moivaed o explain one simple fac he excepionally lo volailiy in he only indusry sandard 3

4 benchmark of commercial real esae a he ime, he NCREIF Propery Index. In rerospec, as e ill presen in his paper, i appears ha e migh have leaped o find he cause of a phenomenon before making sure o ha exen ha phenomenon is acually real. In his sudy, e go back and ake anoher look a he roo of he appraisal smoohing heory, re-examine he facs and logic behind he parial adjusmen model, and presen ne empirical evidence o verify he key predicions of he appraisal smoohing heory. Afer a brief revie of relevan lieraure in he nex secion, he res of he paper proceeds o presen hree invesigaions on he appraisal smoohing heory: Firs, e examine he iniial facs ha moivaed he appraisal smoohing heory - he reurn volailiy of he NCREIF Propery Index (NPI) in relaion o invesmen horizons. We find ha he idespread belief of NPI exhibiing exremely lo volailiy urns ou o be a biased observaion ha is valid only under he implici assumpion ha commercial propery are o be held for very shor period of ime (i.e. a quarer or a year). Under longer and more pracical holding periods, hoever, he volailiy of NPI is no nearly as lo as previously believed. In oher ords, had he variance of NPI been examined over more realisic invesmen horizon, i migh no have appeared so lo as o promp he idea of he appraisal smoohing heory. The iniial facual ground of he appraisal smoohing argumen is hus quesionable. Second, e reexamine he logic behind he normaive foundaion of he appraisal smoohing argumen he parial adjusmen model. Taking a formal approach, e demonsrae ha he model suppors he radiional appraisal smoohing heory only under he assumpion of homogeneous appraiser behavior all appraisers exhibi exacly he same parial adjusmen 4

5 behavior in erms of eighing pas vs. presen informaion. Previous lieraure generally discusses appraisal heerogeneiy in he conex of appraisal errors in he reurn or value esimaes. The curren sudy analyzes he impac of he oher heerogeneiy in he model he differen choices appraisers make in eighing pas versus presen informaion. When such heerogeneiy is considered, e sho ha he model leads o a mixed oucome: The variance of he appraisal-based reurns is no alays loer han he rue variance, raher i could be eiher higher or loer han he variance of ransacion-based reurn depending on he degree of such heerogeneiy. Third, e empirically verify he cenral predicion of he appraisal smoohing heory ha appraisal-based reurns are expeced o exhibi lo volailiy and ha, in he absence of appraisal influence, ransacion-based reurns should exhibi significanly higher volailiy. Using o ell-respeced housing price indices, e find ha he appraisal-based reurns acually exhibi moderaely higher (no loer) volailiy han he ransacion-based reurns. This finding conradics ha he smoohing heory ould predic, bu i is more consisen ih our heoreical invesigaion, hich suggess appraisal-based reurns may no suffer any smoohing bias.. Relaed Lieraure Afer o decades of developmen, he noion ha appraisal causes smoohing has become so enrenched in he lieraure ha here is rarely any formal invesigaion ino he validiy of he facs or logic upon hich he appraisal smoohing argumen is based. Much of he appraisal smoohing lieraure simply sars ih he presumpion ha smoohing does exis, and proceeds 5

6 in idenifying he magniude of he appraisal smoohing effec and developing de-smoohing mehods for recovering he rue volailiy. Alhough he size of he lieraure is oo large o be revieed here in deail, a comprehensive discussion on he evoluion of he appraisal smoohing heory and de-smoohing mehodology can be found in Gelner, MacGregor and Schann (003), in hich many prominen sudies on he subjec are revieed. In his secion, e mainly discuss he sudies on he oher side of he lieraure hose presened conflicing evidences and argumens o he radiional appraisal smoohing heory. Empirical evidence conradicing he appraisal smoohing argumen are fe and far in beeen. Webb, Miles and Guilkey (199) consruced a reurn index using only sold properies, and repored ha ransacion-based porfolio reurns have approximaely he same volailiy as he appraisal-based porfolios. De Wi (1993) compares in-house versus ouside appraisals and find ha independen ouside appraisals sugges no significan smoohing bias. Hendersho and Kane (1995) develop a benchmark of propery fundamenal values and repor he change of fundamenal (marke) values exhibis less volailiy han normally observed from appraisal-based reurns. Brueggeman, Chan and Thibodeau (199) use a non-appraisal-based index o sho ha commercial real esae exhibi much higher risk-adjused reurns han financial asses during he period of , suggesing ha he good daa (i.e. ransacion-based index) do no exhibi volailiy near he level of socks. Cho and Megbolugbe (1996) compared appraisal-based index ih a ransacion-based index and found no evidence of significanly loer volailiy in he appraisal-based index. Similar finding is also repored by Chinloy, Cho and Megbolugbe (1997) ho compared he volailiy of separae purchase and appraisal daa samples obained from Fannie Mae and Freddie Mac during , and found he appraisal daa o be more 6

7 volaile han he purchase daa. These anecdoal evidences, hough imporan, are no direc challenges o he appraisal smoohing heory, and hey are ofen regarded as he excepions of ha he appraisal smoohing heory predics. The only direc challenge o he appraisal smoohing heory so far is a sudy by Lai and Wang (1998), in hich he auhors ake a heoreical approach o examine he condiions and assumpions for he appraisal smoohing heory o hold. Lai and Wang (1998) poined ou a suble inconsisency in Gelner (1989, 1991) in hich he parial adjusmen model is expressed as appraisal reurn being a moving average of pas rue reurn, bu is inerpreed as appraisal value being a moving average as pas rue values (no reurns). They believe ha his disincion is imporan. They argue ha he reurn-averaging assumpion, hough consisen ih a loer appraisal variance, is inconsisen ih appraisers acual behavior, because he rue marke reurns are never observable. On he oher hand, he value-averaging assumpion, hough someha more realisic, is more likely o require pas rue values be approximaed by pas appraisal values in pracice. And hey sho ha, hen boh he appraisal value and he rue value of a propery are assumed o be sochasic, he resuled appraisal variance ill be higher raher han loer. In a comprehensive revie of he appraisal smoohing lieraure, Gelner, MacGregor and Schann (003) couner he criicism of Lai and Wang (1998) by insising ha he moving average process reasonably capures he manner by hich appraisers ypically use he comps in pracice. In he discussion of a general version of he parial adjusmen model (page 105, Eq. (0)), hey coninue o disregard he disincion beeen he reurn-averaging and valueaveraging assumpion ha Lai and Wang (1998) deemed imporan. 7

8 The sudy of Lai and Wang (1998) is idely acknoledged in he subsequen lieraure, bu fe have joined he debae on he issues hey raised. Insead, majoriy of he research coninues o press ahead under he assumpion ha appraisal smoohing exiss, and proposiions for various de-smoohing mehods keep publishing in leading academic journals. To menion a fe of he more prominen ones, in a sudy of real esae allocaion in mixed-asse porfolios, Corgel and deroos (1999) compared several de-smoohing models proposed by oher sudies and find ha hey all achieve he objecive of inflaing real esae volailiy and reduce real esae allocaions. Bu he allocaions seem o be raher sensiive o hich de-smoohing model used. By raionalizing he appraisal process in a so-called sicky value frameork, Bron and Maysiak (000) argue ha, despie appraisal errors being small a individual propery levels, i is sill necessary o de-smooh he aggregaed index, hough hey concede ha i is unclear hich desmoohing procedure produces he bes resul. Clayon, Gelner, and Hamilon (001) noe he lack of empirical suppor and calibraion of he parial adjusmen model, and aemp o provide such suppor by conducing a direc empirical es using a sample of Canadian commercial propery ha conains boh appraisal and ransacion informaion. They find srong evidence ha appraisers end o anchor on heir previous appraisals o form he curren esimaes a behavior ha he parial adjusmen model is based upon. Their finding confirms he resul of Diaz and Wolveron (1998) hich finds he anchoring behavior of he appraisers o be significan, a conclusion ha as only eakly suppored by an earlier similar experimen of Diaz (1997). While Cho, Kaaguchi and Shilling (003) coninue o refine he Fisher-Gelner-Webb desmoohing echnique (Fisher, Gelner and Webb (1994)) and apply boh he original and revised procedures o U.S., U.K. and Japanese commercial propery reurn indexes, Pagliari, Scherer and Monopoli (005) simply use an earlier mehod proposed by Gelner (1993) o de-smooh he 8

9 NCREIF index for performance comparison beeen privae and public real esae. Edelsein and Quan (006), hoever, sugges ha de-smoohing may no be necessary because, hey argue, even if smoohing bias exiss a individual propery levels, he individual errors may offse each oher a he aggregaed index level. On he oher hand, Wang (006) coninues o argue for he necessiy of de-smoohing and proposes a mulivariae approach o uncover he rue real esae volailiy ihou he assumpion of a eak form marke efficiency ha as implicily made in some early sudies. His mehod suggess he rue real esae volailiy in he U.K. is abou 1.5 imes ha of appraisal-based series. Ineresingly, also using commercial propery daa from U.K., Bond and Hang (007) find ha he level of smoohing in appraisal-based real esae indices is far less han assumed in many academic sudies. (page 378) I is perhaps fair o say ha, despie years of remendous research effor, lile consensus has been esablished among academics beyond he general belief ha appraisal causes smoohed reurn series. There is lile agreemen ih regard o ho much smoohing here is in he NCREIF Index and ha model produces he bes de-smoohing oucome. In fac, i is no even clear heher researchers agree on ha he bes oucome should be. While a marke efficiency argumen suggess he de-smoohed real esae reurn should exhibi similar volailiy as socks, Fisher, Gelner and Webb (1994) argue he reasonable real esae volailiy should only be abou half ha of socks, considering oher risk facors of real esae. The findings of Cho, Kaaguchi and Shilling (003) furher sugges ha he objecive of de-smoohing should a leas vary across differen counries and differen propery ypes. As he objecive of de-smoohing remains ad hoc and largely subjecive, i is no obvious ha a consensus ill ever be reached on he degree of smoohing bias in he NCREIF Index (or any appraisal-based real esae index), le alone a 9

10 pracical and generally applicable de-smoohing mehod. Given his, i is perhaps ime o sep back and reflec on ho e go here in he firs place before e move forard. 3. The Iniial Fac ha Moivaed he Appraisal Smoohing Theory Despie is raher complex evoluion over o decades, he appraisal smoohing heory is mainly moivaed by a simple observaion he NCREIF Propery Index (NPI) exhibis excepionally lo volailiy (variance) compared o socks, so lo ha i canno be explained by classical pricing models. This observaion can be easily confirmed ih he publically available NPI oday. For demonsraion purpose, e obain he quarerly NPI for he period of 1978Q1-008Q4. During his period, he average quarerly reurn and sandard deviaion of he NPI are.45% and 1.70%, respecively. On a per-uni-of-reurn basis, he risk-o-reurn raio is 1.7% /.45% = For comparison, he same raio for he quarerly S&P500 Index during he same period is Clearly, he volailiy of he NPI is indeed very lo, approximaely less han onefifh ha of he S&P500 on a per-uni-of-reurn basis. Fe people have doubed his fac because, firs, his is more han a NCREIF-only phenomenon. Similar resuls have been consisenly repored from various daa sources and over differen ime periods, some of hich dae back o he pos-world War II era (e.g. Zerbs and Cambon (1984), Sirmans and Sirmans (1987)). Second, he calculaion of mean and variance (or sandard deviaion) is so simple and sraighforard ha nobody ould doub anyhing can go rong ih heir compuaions. One hing ha fe people have paid aenion o, hough, is he implici invesmen horizon assumed behind he calculaions. Specifically, he mean and sandard deviaion direcly compued from a quarerly (or annual) index of NCREIF implies a holding period of one-quarer 10

11 (or one year). Since real properies are ypically held for muliple quarers or years, does he single-period performance represen he average periodic performance of a muli-period invesmen? In he finance lieraure, e are used o assuming he anser is yes, because an efficien marke implies ha sock reurns are reasonably independen and idenically-disribued (i.i.d.) and holding period is irrelevan. Bu for real esae, his is no he case and he holding period may acually maer. To find ou heher he real esae performance appears differenly under differen holding periods, e apply he folloing simulaion approach o he quarerly NPI over he period of 1978Q1 008Q4. Firs, since he NPI is repored in quarerly reurns, e conver he enire series ino an index ih 1977Q4 being 100. Taking he index as he original sample, e hen run he simulaion in he folloing seps: for a given holding-period, say one year, e randomly pick any quarer o buy he porfolio a he index level, hen e sell a he index level a he end of he holding period (i.e. four quarers laer), and compue he reurn of his invesmen. By repeaing his process and randomly buy he marke a any ime for 100,000 imes hrough re-sampling (ih replacemen), e obain 100,000 simulaed annual reurns. We hen compue he average quarerly reurn and sandard deviaion for hese simulaed reurns and compue he risk-o-reurn raio (or risk per uni of reurn). The raios are hen obained for a differen holding period, ranging from 1 o 36 quarers (9 years) by repeaing he hole simulaion process. For comparison purpose, e also replicae he exac same process o he quarerly S&P500 Index over he same period as he NPI. The simulaion resuls are summarized in Figure 1. 11

12 Risk-o-reurn raios Figure 1. Simulaed Risk-o-reurn Raios of NCREIF vs. S&P500 (1978Q1 008Q4) NCREIF S&P Invesmen Horizon (in number of quarers) I is immediaely obvious ha he paern of he risk per uni of average reurn for he NCREIF Index is quie differen from ha of he S&P500. The raio of he S&P500 essenially moves horizonally ih modes flucuaion, suggesing i is basically independen of he invesmen horizon. In sharp conras, he raio for he NCREIF Index is highly horizon-dependen and consisenly increases ih he holding period. A shor horizons, he raio is consisen ih he excepionally lo volailiy or significan risk premium ha is so idely documened in he lieraure. Hoever, as he holding period becomes more realisic and longer, he difference beeen NCREIF and he S&P500 quickly narros, and evenually disappears as he holding period approaches 9 years (36 quarers) and beyond (hich is no uncommon for commercial real esae a all). This finding suggess ha he conclusion ha NCREIF exhibis exremely lo volailiy, hich is ha moivaed he original idea of he appraisal smoohing heory, urns ou o be a parial ruh and valid only hen he holding period is unrealisically shor. Had he 1

13 NCREIF performance been examined under more realisic invesmen horizons (e.g. 5 years or longer), e migh have a very differen percepion abou he volailiy of he Index, or commercial real esae in general. Bu ha abou he fac ha, in Figure 1, he risk-o-reurn raio of NCREIF remains belo ha of he S&P500 hroughou he 36 quarers? Does i sugges appraisal smoohing bias? If in heory he risk-o-reard raios of socks and real esae should be abou he same, here are o compeing explanaions. One is ha he volailiy gap in Figure 1 is caused by ha Lush (1988) called he non-variance risk facors illiquidiy, lumpiness, high ransacion coss, ec. ha are unique o real esae. Since hese facors mus be priced in he markeplace by raional invesors, i is possible ha hen he risks associaed ih hese facors are properly accouned for, he oal real esae risk ould be close o ha of socks on a per-uni-of-reurn basis. Essenially, ha Lush (1988) implies is ha he real esae pricing model (or he convenional performance merics) are deficien in ha hey fail o price he non-variance facors, and he calls for he developmen of ne performance measures and pricing models ha are more consisen ih he real esae fundamenals. The oher explanaion ould be he appraisal smoohing argumen. This explanaion basically aribues he volailiy gap in Figure 1 o a bad daa problem ha is caused by a supposed appraiser behavior. De-smoohing is essenially an effor of inferring good informaion from he bad daa. Alhough boh explanaions can be rue o cerain exen, recen sudies by Lin and Vandell (007), Lin and Liu (008) and Cheng, Lin, and Liu (010a) have proposed a ne real esae risk meric ha explicily inegraes illiquidiy risk (ime-on-marke risk) ih price 13

14 volailiy. This risk meric, hen applied o NCREIF index, sugges ha he risk-adjused reurn is almos idenical o ha of socks, leaving virually no room for he appraisal smoohing argumen o explain he gap. These recen sudies aside, for hose ho believe ha he volailiy gap in Figure 1 is enirely caused by appraisal smoohing, i is a leas obvious ha, since he volailiy gap is horizondependen, so mus be he objecive of de-smoohing. This is an imporan observaion as i quesions much of de-smoohing lieraure ha disregard holding period and aemp o inflae he appraisal-based reurn volailiy by a presumed proporion. Assumpion such as ha real esae volailiy should be abou half ha of socks (Fisher, Gelner and Webb (1994)) has o be reconsidered because, as shon in Figure 1, he NPI s volailiy is already more han half ha of socks as soon as he holding period exceeds 3 years (1 quarers). In realiy, mos real properies are held far longer han 3 years (see Cheng, Lin and Liu (010b)). Had he NPI been examined accordingly, e migh have a differen percepion as o ho lo he NCREIF volailiy really is. I is orh noing ha he imporance of he horizon-dependence of real esae performance should no be underesimaed. If he highly liquid and informaion-efficien financial marke is characerized by securiy reurns being independen and idenically-disribued (i.i.d.), he illiquid and inefficien privae real esae marke is hen characerized by propery reurns being horizondependen. The real esae lieraure has exensively and repeaedly documened ha propery prices do no follo he random alk and ha he reurns over ime exhibi serial persisence 14

15 (non-i.i.d.). 1 This is a significan disincion beeen he o markes and i quesions he validiy of applying classical heories such as Modern Porfolio Theory (MPT) and Capial Asse Pricing Model (CAPM) o real esae invesmen analysis. As e kno, models such as he MPT and CAPM are essenially single-period models in hich hey assume all asses are o be held for one period, and he opimal porfolio is one ha maximizes he invesor s objecive over such a single-period horizon. The realiy, hoever, is ha asses are ofen held for muliple periods of ime. The validiy of single-period model o muli-period invesmen is largely based on he sudies by Meron (1969), Samuelson (1969), and Fama (1970), among ohers, hich sho ha an invesor s uiliy maximizaion over muliple holding periods is essenially indisinguishable from ha over a single-period if asse reurns are independen and idenically-disribued (i.i.d.) over ime. Wihou he i.i.d. condiion, hese classical models are no applicable o real esae. In oher ords, he real esae risk premium puzzle can very ell be caused by inappropriae applicaion of hese single-period pricing models and he radiional performance merics. This issue, of course, should be invesigaed more rigorously in separae sudies. 4. Examinaion of he Parial Adjusmen Model We no urn o he normaive foundaion of he appraisal smoohing heory he parial adjusmen model. Firs, e demonsrae ha he model only suppors he appraisal smoohing argumen under he implici assumpion of homogeneous appraiser behavior. Second, e sho ha, once he implici assumpion is relaxed o recognize heerogeneous appraisal behavior, he model ill be inconsisen ih he appraisal smoohing argumen and may even suppor he opposie conclusion. 1 The lieraure on he subjec is oo large o be revieed here fully. A fe examples include Case and Shiller (1989), Englund, Young and Graff (1995), Gordon and Quigley (1999) and Gao, Lin and Na (009), among ohers. 15

16 As proposed in Gelner (1989, 1991), he formal parial adjusmen model expresses he appraisal reurn as a eighed average of he curren and pas rue marke reurns: ~* ~ i r i i 0 i 0 r and 1 (1) i Where ~ r i is he rue marke reurn disribuion in period i ( i 0,1,,... ), and i is he corresponding eigh he appraiser places based on his/her knoledge. i is also knon as he smoohing parameer. Unlike Lai and Wang (1998), hich challenges he empirical jusificaion of he model in he firs place, e sar by aking he parial adjusmen model as given. Tha is, e do no argue heher he model reasonably capures he fundamenal appraiser behavior in real life; e are no concerned abou heher rue marke reurns are obainable; and e are no considering he inconsisency discerned by Lai and Wang (1998) ha he model is expressed as he average of pas reurns bu ofen inerpreed as he average of pas values. Obviously, hese are all criical issues ha quesion he validiy of he model. Bu he curren sudy focuses on a differen quesion: le s assume he model is valid, is i really consisen ih he appraisal smoohing argumen ha i is inended o suppor? Ho does he model suppor he appraisal smoohing argumen? The smoohing effec (loer appraisal volailiy) can be easily demonsraed if e consider here are only o periods in he model for mahemaical simpliciy. In pracice, a o-period model is no necessarily unrealisic as mos appraisers ypically only look back o consider he mos recen sales informaion on he same or comparable properies (marke comps). Thus, he appraisal reurn in period of Equaion (1) can be rerien as 16

17 ~ r () * ~ (1 ) ~ r r 1 Where is he eigh placed on he curren marke informaion. I ends o be higher if he appraiser is more confiden abou he curren marke informaion, and vice versa. For simpliciy, suppose ha r~ and ~ r 1 share he same disribuion ih mean u and variance and he correlaion beeen ~ r 1 and r~ is assumed o be. This assumpion ill be relaxed laer in he paper. For no, he volailiy of he appraisal reurn Var ~ ~ ~* r can be expressed as: * ( r ) Var ( r (1 r 1] [ (1 ) (1 ) ] (3) ) ~ Given ha 1 and 0 1, e have [ (1 ) (1 ) ] [ (1 ) (1 )] 1. As a resul, e can conclude ha ~* Var ( r ) (4) The equaliy holds only if 1. Therefore, hen reurns over ime is no perfecly correlaed, Equaion (4) suggess ha he variance of he appraisal reurn ~* r is alays less han he variance of he rue marke reurn r~. In oher ords, appraisal reurns alays undersae (or smooh ou) he volailiy of rue real esae reurns, as long as Equaion () is a reasonable represenaion of he parial adjusmen behavior for all appraisers. This is essenially he normaive foundaion for he radiional appraisal smoohing heory. I demonsraes ha appraisal causes smoohing. Ho does he model FAIL o suppor he smoohing argumen? An issue ha has been given lile consideraion by he previous lieraure, hoever, is he choice of he eighs, or he smoohing parameers. In one of he model s original presenaions, 17

18 Gelner (1991) sugges ha, alhough he parial adjusmen is an individual behavior, he only difference beeen he models he presened a he aggregaed index level and he disaggregaed individual level (Eq. (1) and (1a) of ha paper) is ha he individual appraisal errors are diversified aay a he aggregaed level, bu he eighing parameers remained same a boh levels. This implies an implici assumpion all appraisers, despie heir heerogeneous access o and inerpreaion of informaion from various sources, ould eigh he pas versus presen informaion in exacly he same ay. Tha is, appraisers exhibi homogeneous parial adjusmen behavior. Subsequen lieraure using he parial adjusmen model has generally adoped he assumpion and reas he parameers as invarian across appraisers. I is under his assumpion ha he parial adjusmen model, as demonsraed above, suppors he argumen ha he appraisal variance o be less han ha of he rue variance. The realiy, hough, is ha even if he parial adjusmen is consisen ih he appraisers behaviors in using pas informaion such as idenifying he comps, here is no precise rule on ho such adjusmen should be done. Therefore, i is no hard o imagine ha, cerain degree of professional consensus noihsanding, heerogeneous parial adjusmen exiss even hen here is no apparen incompeence, negligence, or impropriey on he par of he appraisers. Such heerogeneiy implies ha he smoohing parameer, alhough specific o each individual appraiser a he disaggregaed level, mus exhibi cross-secional dispersion and hus inroduce anoher source of variaion ino he parial adjusmen model a he aggregaed index or porfolio level. The resuled appraisal reurn index, herefore, is likely o exhibi larger variance han if he parameer is reaed as invarian. 18

19 I is necessary o noe ha his addiional variaion due o heerogeneous smoohing parameer is no caused by some kind of random behavior of he appraisers. I is due o he fac ha all appraisers canno, and indeed should no eigh he pas versus presen informaion in exacly he same ay because of heir differences in access o, and inerpreaion of informaion. The differen choice of smoohing parameer, herefore, is a resul of raional appraiser behavior. Each appraiser chooses he mos appropriae eighing parameer based on his/her professional judgmen. A he aggregae level, he eighs vary across appraisers ih cerain dispersion. Ignoring such heerogeneiy in he pas may have led us o exaggerae he smoohing effec on appraisal-based reurn indices. Belo, e conduc a formal analysis o invesigae he impac of heerogeneous parial adjusmen behavior on he resuled appraisal variance. In he conex of he model in Equaion (), his analysis begins by recognizing he cross-secional variaion of he smoohing parameer. Suppose ha follos a disribuion ih mean and variance. The variance essenially capures he variaion of he smoohing parameer among appraisers. Based on he condiional variance formula, he variance of he appraisal reurn ( 1 1 ~ r * can be expressed as, ~ * Var r ) E[ Var ( r ~ (1 ) ~ r )] Var[ E[ r ~ (1 ) ~ r ]] (5) Since E[ r ~ (1 ) ~ r 1 ] u, hence Var[ E[ r ~ (1 ) ~ 1 r ]] 0. Simplifying Equaion (5) yields, ( ~ * Var r ) E[ (1 ) (1 ) ] (6) Our analysis does no require he assumpion of a specific disribuion for. I only assumes ha he mean and variance of can be esimaed. 19

20 Noe ha varies among differen appraisers and i is disribued ih mean and variance. Given ha E[ E( )] E[ ], e have E [ ]. Equaion (6) can hen be simplified as Var ~ * ( r ) (1 ) [ (1 ) (1 ) ] (7) Comparing Equaion (7) ih Equaion (3), e can readily see ha he second erm of Equaion (7) is exacly he righ-hand side of Equaion (3). In oher ords, Equaion (7) shos ha he radiional appraisal smoohing argumen (Equaion (3)) undersaes he volailiy of appraisal reurn r by an amoun of (1 ). Given ha his amoun is alays posiive hen 1, ~* depending on he magniude of, i is possible ha he firs erm (1 ) in Equaion (7) could be large enough o reverse Equaion (4) such ha Var ( ~* ). Tha is, he variance of appraisal reurns may acually oversae he rue volailiy of. In any even, he posiive firs erm in equaion (7) suggess ha he smoohing effec should be less han previously believed under he radiional appraisal smoohing heory, hich assumes is invarian and 0. Therefore, once he assumpion of homogeneous parial adjusmen behavior is relaxed o accoun for appraisal heerogeneiy, he parial adjusmen model no longer necessarily suppors he appraisal smoohing argumen. r To see his poin ih an example, suppose ha here are o ypes of appraisers ih equal numbers in he marke and he correlaion is assumed o be zero for simpliciy. The firs ype of appraisers has no confidence in he curren marke informaion and hus gives 100% eigh o he reurn of las period and 0% eigh o he curren informaion. Hoever, he second ype of appraisers is 100% confiden in he curren informaion and hus ill no consider he pas 0

21 informaion in heir valuaion process. Wih his example, e can deduce ha he eigh is disribued ih mean of 1 and variance of 1 4. Insering hese numbers in Equaion (7) ih he assumpion of 0, e have Var ~ * ( r ) [( ) (1 ) ] This suggess ha afer considering cross-secional variaion among appraisers, he variance of he appraisal reurn may no be reduced a all. Hoever, based on he radiional appraisal smoohing heory (ignoring he heerogeneiy of appraisal behaviors and assuming 0), he variance of appraisal reurn is only. 5. Heerogeneous Appraisal under Changing Marke Condiions No e exend our analysis o anoher aspec of he heerogeneous appraisal he ime-varying naure of he smoohing parameer. A fe sudies have recognized ha, in eighing pas versus presen informaion, same appraisers may choose differen eigh () in differen imes, or under differen marke condiions. Maysiak and Wang (1995) sugges ha he appraisal smoohing parameer is likely o be ime-varying as appraisers ould adap heir valuaion process according o marke condiions. Bron and Maysiak (1998) applied he Kalman filer approach o sudy he issue and found ha he smoohing parameer varied across marke condiions. Their finding as confirmed by Clayon, Gelner and Hamilon (001) hich examined his issue using a sample of Canadian properies. Clayon e al. also found ha greaer smoohing effec (more emporal lag bias) as correlaed ih periods of slo real esae marke hen feer ransacions and less curren informaion are available. While i is an empirical maer as o ho 1

22 much he smoohing parameer varies over marke condiions, he fac ha i varies arrans an exension of our analysis o he seing of changing marke condiions. In he las secion, e assume ha r~ and ~ r 1 share he same mean. In realiy, he housing marke may experience a good or bad ime in he nex period hen marke condiions change. In oher ords, he expeced reurn in period may become higher or loer han ha of he previous period. Suppose ha u. When 0, he marke improves over he las period. u 1 When 0, he opposie is rue. The magniude of reflecs he degree of ho much he marke condiions change. Inuiively, since appraisers are less agreeable on ho o respond o dramaic marke movemens, hey end o eiher over- or under-reac o available informaion. Therefore, a dramaic change of he marke condiions is likely o be associaed ih a large dispersion of, ha is, is a funcion of, i.e. ( ). When marke condiions change, i.e. 0, he nd erm of Equaion (5) becomes, Var ( E[ r ~ (1 ) ~ r 1 ]) Var ( u 1 ( ) ) (8) As a resul, hen 0 Equaion (5) can be furher simplified as Var ~ * ( r ) ( ) (1 ) ( ) [ (1 ) (1 ) ] (9) From Equaions (7) and (9), e can obain Var ( ~ r ( ~ * 0) Var 0) ( ) (1 ) [ ( ) ] (10) * r Since a larger dispersion of is ofen associaed ih he change of marke condiions, i.e. ( ), Equaion (10) implies ha hen he real esae marke experiences donurn or upurn, he appraisal reurns are likely o become more volaile.

23 No e relax anoher assumpion ha he variances of reurns in periods and 1 are equal. In realiy, he variances may differ, especially hen marke condiions change. Suppose ha r~ i is disribued ih mean u i and variance ( i, 1), Equaion (9) hen becomes i ( ~ * Var r ) ( ) ( [ 1 (1 ) 1 1 ) ( ) (1 ) 1 ] (11) Equaion (11) is a general represenaion of he variance in appraisal-based reurns under changing marke condiions and heerogeneous appraiser behaviors. In he radiional appraisal smoohing argumens, hich implicily assume ha all appraisals share he same smoohing parameer (i.e. ( ) 0), Equaion (11) becomes Var ~ * ( r ( ) 0) (1 ) 1 (1 ) 1 (1) The difference beeen Equaions (11) and (1) is ( ~ * ( ~ * Var r ) Var ( ) 0) ( ) ( ) (13) r essenially capures he effec of heerogeneiy of appraisal. Since is alays posiive, 3 i implies ha ignoring he heerogeneiy of undersaes he volailiy of appraisal-based reurns and oversaes he effec of smoohing. Furhermore, hen Equaion (11) ha, Var ~* ( r ) 1 1 1, e can readily sho from. Tha is, he appraisal-based reurns may exhibi higher, raher han loer, volailiy han ha of he rue reurns. Furhermore, given ha 0, ( ) 0 and 0, he smoohing effec suggesed by he radiional appraisal smoohing 3 I can be shon ha ( ) ( ) [ ( ) ] ( )

24 heory is exaggeraed, o he larger exan hen he dispersion of smoohing parameer among appraisals is higher and/or hen marke condiions change dramaically. The above heoreical analysis can be summarized in hree conclusions: Firs, he radiional appraisal smoohing argumen ha appraisal mus resul in smoohed reurns - is only valid under he implici assumpion ha all appraisers exhibi exacly he same parial adjusmen behavior and eigh he pas vs. curren informaion in he same ay. Second, hoever, if one agrees ha in realiy he appraisers eighing of pas vs. curren informaion varies boh crosssecional and over ime, e conclude ha he appraisal variance ill be higher han ha is indicaed under he homogeneous assumpion. This suggess ha he smoohing effec is no as srong as previously believed. Third, and more imporanly, e sho ha i is possible ha, hen he appraisal heerogeneiy is high enough, he resuled appraisal variance can acually exceed he rue variance. In oher ords, he parial adjusmen model does no definiively suppor he appraisal smoohing argumen, ha is, even if e do no quesion is validiy in he firs place. From a cerain angle, our findings echo some of he earlier findings by Lai and Wang (1998), in hich he auhors demonsrae he appraisal variance is higher han he rue variance if appraisers rely on pas appraisal values (no pas rue reurns in Equaion (1)). Our conclusions are dran in a differen ay. Tha is, e ake he model in Equaion (1) as given and sho ha appraisal variance can be eiher higher or loer han he rue variance depending on he degree of he appraisal heerogeneiy. In oher ords, here is no definiive connecion beeen appraisal and smoohing. 4

25 6. A Realiy Check on Wha he Appraisal Smoohing Theory Predics The above heoreical conclusions sugges ha, depending on he degree of appraisal heerogeneiy, he parial adjusmen model can resul in appraisal variance ha is eiher higher or loer han he rue variance (or no much differen from each oher). This conradics he radiional appraisal smoohing argumen, hich predics ha appraisal-based reurns necessarily exhibi lo volailiy and ha, in he absence of appraisal influence, ransacion-based reurns should exhibi significanly higher volailiy. We no use empirical daa o examine hich of hese predicions is more consisen ih he realiy. According o he appraisal smoohing heory, appraisal bias is defined as he deviaion of appraisal-based reurns from he unobservable rue marke reurns. In pracice, he appraisal bias can be measured as he difference beeen he volailiies of appraisal-based and ransacionbased reurns. The presumpion is ha he volailiy of ransacion-based real esae reurns should no be as lo as ha is observed from appraisal-based reurns such as he NCREIF index. Hoever, as surprising as i may be o some readers, here is virually no compelling evidence as o ha he ransacion-based volailiy should be. The difficuly is undersandable here is simply no a ransacion-based index ha is oherise comparable ih he appraisal-based NCREIF index. 4 Therefore, sudies ha aemped o sho he exisence of smoohing bias ofen mus make criical assumpions abou he ransacion-based reurns and appraiser behavior ha causes he bias. This approach effecively implies ha he smoohing bias has o be demonsraed based on assumpion as oppose o facs. As Edelsein and 4 Recenly, hoever, NCREIF has adoped he MIT ransacion-based index. Bu his ne index is consruced ih a very differen mehodology and is no, in our vie, oherise comparable ih he radiional NCREIF Propery Index in erms of index mehodology. 5

26 Quan (006) characerize he problem: Smoohing is defined as he deviaion of an index from one hich is never observed; and since i is his deviaion beeen series hich gives rise o he problem, i is no surprising smoohing is ofen demonsraed based on assumpions made abou he rue series and appraiser mehodology and pracice. Frequenly, in he absence of empirical suppor, he exisence of smoohing is largely assumed and unsmoohing echniques amouns o a conrived soluion o an assumed problem (page 43). Recenly available daa in he residenial marke has made i possible for us o direcly measure he degree of appraisal bias a he aggregae level. Alhough smoohing has been mainly discussed in he conex of commercial real esae, he parial adjusmen behavior, he alleged cause for smoohing, is common among boh commercial and residenial appraisers. In fac, residenial appraisers are knon o rely more on he so-called marke comparable approach, hich suggess hey end o give more eigh o he pas price informaion. Therefore, if he parial adjusmen causes smoohing, he phenomenon should be observed from he housing marke daa. In lae 004, he hen Office of Federal Housing Enerprise Oversigh (OFHEO), hich laer merged ino he Federal Housing Finance Agency (FHFA) in Ocober 008, released a ne purchase-only Home Price Index (HPI) o supplemen is original all-ransacion index. Unlike he original index hich uses a large sample mixed ih housing sales and refinancing deals (here he propery value is he appraisal value insead of sales price), he purchase-only index excludes refinances from he hole sample, hus i is based on he par of he sample ha is free of appraisal bias. The porion of he purchase sub-sample averages abou 4% of he 6

27 hole sample over he period of , hich implies ha he appraisal daa (from refinance deals) averages abou 58% of he sample during he same period. Such proporion is high enough for appraisal effec o be noiceable in he all-ransacion index. Given ha boh indexes are consruced ih he same repeaed sales mehodology and differ only in heher heir samples include appraisal-based values, he difference in he volailiies of he o indexes offers good indicaion of he appraisal effec. A quick realiy check of he appraisal effec can be found in he official FHFA Quarerly Nes Release. Figure is copied from he 009Q1 issue. Figure. Hisoric Housing Price Changes Repored by he FHFA (formerly OFHEO) Source: The Federal Housing Finance Agency (FHFA) Nes Release, 009Q1. 7

28 The above figure displays he annualized hisoric reurns of he o U.S. naional indexes. If he predicions of he appraisal smoohing argumen is rue, one ould expec ha he appraisalbased index is more smoohed and he beer daa (i.e. he ransacion-based Purchase-only Index) should exhibi significanly higher volailiy. Clearly, neiher expecaion is suppored by Figure. In fac, he opposie seems o be rue he Purchase-only Index is consisenly less volaile and more smoohed han he appraisal-based All-ransacion HPI during he 18-year period, excep perhaps in more recen quarers afer 007Q3 hen he financial crisis sared, during hich ime he marke is disored by disproporionally large number of abnormal sales such as foreclosure and shor sales ih depressed prices. The simple fac presened in Figure challenges he basic predicions of he radiional appraisal smoohing heory. Hoever, inerpreaion of Figure should be made ih cauion, because here is anoher source of noise in he all-ransacion index besides heerogeneous appraisal behavior he mix raio beeen he purchase vs. refinance ransacions in he sample, hich may vary over ime. 5 When he raio is relaively sable, he difference in Figure can be aribued mainly o he appraisal effec. Bu hen he raio varies dramaically, he variaion may become a significan source of noise. While i is no easy o disenangle he o effecs (heerogeneous appraisal and varian mix raio) in he All-ransacion Index, a leas one poin is clear: The o indices do no differ significanly suggesing beer daa (i.e. he Purchase-only index) does no exhibi significanly higher volailiy han he appraisal-based index. To he 5 In his regard, he NCREIF Index also includes sales hen he propery is sold. So, like he All-ransacion HPI, he NCREIF is an appraisal-based, bu no appraisal-only index, alhough is mix raio may be quie differen. 8

29 conrary, he paerns of he o indices are more consisen ih he argumen ha appraisalbased index do no suffer any smoohing bias a all. Given he geographic diversiy of he housing marke, e exend he invesigaion shon in Figure o he regional sub-index level. The FHFA repors sub-indices a he nine census regions (see Appendix for a map of hese regions). Taking he All-ransacion and Purchase-only indices for each region over he period of 1991Q1 008Q4, e replicae Figure for all nine regions and display he resuls in Figure 3. The regional comparison beeen he o indices exhibi raher a consisen paern ih he naional resuls (Figure ) in a leas o aspecs: Firs, he appraisal effec, as indicaed by he discrepancy beeen he All-ransacion and he Purchaseonly indices, seems o be raher modes in mos of he years excep he laes marke peak and he subsequen donfall. Second, ihou excepions, he volailiy of he appraisal-based Allransacion index seems higher (or less smoohed) han he Purchase-only index over ime and across mos of he regions. While here is some room for inerpreaion, he case for appraisal causing smoohing is raher difficul o make in ligh of hese facs. 9

30 Figure 3. Comparison beeen Appraisal-based and Transacion Based FHFA Index by Regions (199Q1 008Q4) Eas-Souh Cenral Mid-Alanic Wes-Souh Cenral 10.0% 0.0% 10.0% 8.0% Pruchase-only All-ransacion Purchase-only All-ransacion Pruchase-only All-ransacion 15.0% 8.0% 6.0% 6.0% 4.0% 10.0% 4.0%.0% 5.0% 0.0%.0% 199Q1 1995Q1 1998Q1 001Q1 004Q1 007Q1 0.0% -.0% 0.0% 199Q1 1995Q1 1998Q1 001Q1 004Q1 007Q1 199Q1 1995Q1 1998Q1 001Q1 004Q1 007Q1-4.0% -5.0% -.0% Eas-Norh Cenral 8.0% 6.0% 4.0%.0% 0.0% 199Q1 -.0% 1995Q1 1998Q1 001Q1 004Q1 007Q1-4.0% -6.0% Purchase-only -8.0% All-ransacion Ne England 0.0% 15.0% 10.0% 5.0% 0.0% 199Q1 1995Q1 1998Q1 001Q1 004Q1 007Q1-5.0% Pruchase-only All-ransacion -10.0% Wes-Norh Cenral 10.0% 8.0% 6.0% 4.0%.0% 0.0% 199Q1 -.0% 1995Q1 1998Q1 001Q1 004Q1 007Q1-4.0% Pruchase-only All-ransacion -6.0% 0.0% Mounain Region 0.0% Souh-Alanic 30.0% Pacific Region 15.0% 10.0% 5.0% 0.0% % Purchase-only All-ransacion -10.0% 15.0% 10.0% 5.0% 0.0% 199Q1-5.0% 1995Q1 1998Q1 001Q1 004Q1 007Q1-10.0% -15.0% Pruchase-only All-ransacion 0.0% 10.0% 0.0% 199Q1 1995Q1 1998Q1 001Q1 004Q1 007Q1-10.0% -0.0% -30.0% Pruchase-only All-ransacion Noe: This figure displays he hisoric annual housing price changes for he nine census regions over he period of 199Q1 008Q4. I shos ha (1) he appraisal effec only causes modes deviaion beeen he o indexes; and () he appraisal-based all ransacion index seems more (no less) volaile over ime and across all regions.

31 The hisoric rends repored in Figures and 3 are annual changes of he housing indices. As e kno, hese rends are consisen ih he expecaion of invesors ih a one-year invesmen horizon. In realiy, properies are held for various lenghs of imes. Given he horizondependence of he NCREIF Index indicaed in Figure 1, here is good reason o believe residenial real esae ill exhibi he same characerisics. Therefore, e an o use he FHFA naional home price index o examine he appraisal effec over various invesmen horizons. Since he Purchase-only index covers only he period of 1991Q1 008Q4, e limi he range of hypoheical holding periods o be 1 0 quarers (or up o five years). Then e apply he same simulaion approach ha produced Figure 1 o he o FHFA indices. Afer e obain he simulaed sandard deviaions of each index for each holding period, e compue he appraisal bias, hich is measured as he percenage by hich he sandard deviaion of he All-ransacion index differs from ha of he Purchase-only index for a given holding period. The resuls are shon in Figure 4. Figure 4. Appraisal Effec across Invesmen Horizons Holding Purchase-only All-ransacion Appraisal Period (qr) (S. Dev.) (S. Dev.) Bias 1 1.3% 1.01% -17.9%.1% 1.90% -10.% 3.81%.68% -4.7% % 3.41% -4.1% 5 4.3% 4.13% -4.3% % 4.83% -.% % 5.48% 0.8% % 6.09% 1.7% % 6.65% 1.6% % 7.1%.1% % 7.73% 3.4% % 8.0% 3.8% % 8.63% 3.5% % 9.07% 3.4% % 9.5% 3.9% % 9.95% 3.7% % 10.36% 3.1% % 10.80% 3.0% % 11.31% 3.6% % 11.8% 4.1% 10.0% 5.0% 0.0% -5.0% -10.0% -15.0% -0.0% Appraisal Bias Holding Period (number of quarers) Noe: S. Dev. is he holding period (oal) sandard deviaion. The appraisal bias is measured as he percenage by hich he sandard deviaion of he all-ransacion index differs from ha of he purchase-only index.

32 Figure 4 clearly indicaes ha appraisal bias is also horizon-dependen. Smoohing can only be observed under shor holding periods (less han 1.5 years). For example, a holding period of one quarer, he sandard deviaions of he o indexes (1.3% and 1.01%, respecively), hich are he convenional esimaes of reurn volailiies from quarerly indexes, indicae he quarerly all-ransacion index undersaes he volailiy of he purchase-only index by 17.9% - a significan smoohing bias. Hoever, e mus keep in mind ha quarerly reurn and risk implicily assume ha an invesor only holds he index porfolio for a single quarer and sell i immediaely, hich is no possible in realiy. As holding periods becomes more pracical (say, o years or longer), he appraisal bias quickly shrinks and urns o posiive. Tha is, he Allransacion index acually oversaes he sandard deviaions of he Purchase-only index, albei by a modes margin of abou ~ 4%. These resuls are consisen ih Figure and 3 in ha hey furher sugges ha i is a mispercepion ha appraisal-based real esae reurns exhibi lo volailiy. Had he reurn volailiy been examined under more pracical holding periods, he radiional appraisal smoohing argumen ould have appeared ill-suppored empirically o begin ih. Some readers may noice ha, a holding period of 4 quarers (one year), he appraisal bias is sill negaive in Figure 4, hich seems o conradic he annual index changes shon in Figures and 3. This is because e included in our calculaion he mos recen several quarers during hich he marke is disored by rampan foreclosure and shor sales, hich causes he Purchase-only index o exhibi significanly higher volailiy. Hoever, hen e selec he daa period prior o he recen financial crisis (i.e. 1991Q1-006Q4), e find he sandard deviaion of he annual 3

33 Purchase-only index o be.4%, versus.8% for he All-ransacion index. These resuls are herefore consisen ih Figures and 3, suggesing he Purchase-only index o be more smoohed. In addiion, e find ha he serial correlaion for he annual reurns of Purchaseonly index is 0.73, versus 0.64 for he All-ransacion index during he same period. This finding conradics ye anoher radiional appraisal smoohing argumen ha predics he appraisal-based index is supposed o exhibi higher serial correlaion han ransacion-based index. 6 We acknoledge ha residenial daa may no be ideal for examining he radiional appraisal smoohing heory, as he heory is mainly developed for commercial real esae. Hoever, if using pas marke and appraisal informaion is a common behavior among residenial and commercial appraisers, he impac of parial adjusmen should be observable in boh residenial and commercial real esae daa. Furhermore, recen sudy suggess ha he difference beeen commercial and residenial real esae markes should no be overly exaggeraed. For example, Gyourko (009) has presened raher comprehensive evidence shoing he inexricable connecions beeen he economic and financial fundamenals of he commercial and residenial real esae. I finds ha, among oher hings, he propery value appreciaion in oner-occupied houses and commercial properies move ogeher conemporaneously and over ime, despie he o markes are driven by demand from o groups of buyers ha differ grealy in heir moivaions, preferences, and decision crieria. Finally, i is necessary o poin ou ha our heoreical analysis does no depend on any daa. So he imperfecion of he daa should no affec he main conclusions of our analysis. 6 We hank an anonymous referee for suggesing he comparison of serial correlaions for he o indices. 33

34 7. Conclusions This sudy examines he empirical moivaion and normaive foundaion of radiional appraisal smoohing argumen. We begin by examining he idely repored fac ha moivaed he appraisal smoohing argumen in he firs place he excepionally lo volailiy of he appraisal-based NCREIF Index. We sho ha he fac is based on an incomplee observaion, hich is valid only for unrealisically shor holding periods (a year or a quarer). When more realisic and longer holding periods are considered, he NPI s volailiy (per uni of reurn) is no as lo as previously believed compared o ha of socks. The fac ha he volailiy gap beeen socks and real esae in Figure 1 is horizon-dependen furher suggess ha i is inappropriae o de-smooh he NCREIF Index by inflaing is volailiy by a presumed percenage. Second, e conduc a heoreical analysis o demonsrae ha he appraisal smoohing heory is suppored by he parial adjusmen model only under he assumpion of homogeneous appraiser behavior - all he appraisers eigh he pas vs. curren informaion in exacly he same ay. By relaxing he homogenous assumpion, e sho ha heerogeneous appraisal behavior ill resul in appraisal variance o be higher han under he homogeneous condiion, implying ha he appraisal smoohing effec, if i exiss, is no as srong as he radiional appraisal smoohing heory previously suggess. Furhermore, e sho ha i is possible ha he heerogeneiy may be o such a degree ha he resuled appraisal variance acually exceeds he rue variance. Tha is, appraisal may exaggerae, raher han undersae he rue variance of real esae reurns. Third, e presen empirical evidence from he residenial marke, hich consisenly suggess, hisorically, he appraisal-based FHFA All-ransacion Index in fac appears o be slighly less 34

35 (no more) smoohed han he Purchase-only index. These evidences are consisen ih our heoreical findings, as hey sugges ha he appraisal heerogeneiy may indeed be such ha an appraisal-based index acually exceeds (albei moderaely) he variance of an oherise comparable ransacion-based index. The facs conradic he cenral predicion of he radiional appraisal smoohing heory he ransacion-based index should have significanly higher volailiy han he appraisal-based index. The findings of his sudy have hree implicaions. Firs, if real esae performance is horizondependen and appraiser behaviors are heerogeneous, inferring rue marke volailiy from an appraisal-based index is even more complex han ha he de-smoohing lieraure has aemped before. Given he appraisers heerogeneous reamen of informaion in aggregae, and smoohing bias ha may exis a he individual propery level, he ulimae volailiy of he index depends on hich influence dominaes he oher. De-smoohing may be he rong hing o do because he appraisal-based index may already oversae he rue volailiy, as he FHFA indices sugges in his paper. To infer he rue marke volailiy from an appraisal-based index, herefore, boh influences should be undersood and properly conrolled. This suggess an ineresing empirical research: Ho differen are appraisers in choosing heir smoohing echniques, boh cross-secionally and over ime? Second, if he FHFA indices are indicaive of he commercial real esae marke, as Gyourko (009) suggess, he NCREIF index may no suffer much smoohing bias afer all. As he longes and mos observed marke index for commercial real esae, he credibiliy of he Index, and o some exen, he credibiliy of he appraisal indusry in general, has been severely undermined by 35

36 he appraisal smoohing heory in recen years. While many sudies ofen blame he smoohing bias for heir nonsensical findings, some researchers have dismissed he NCREIF Index as compleely useless. This kind of criicisms appears premaure in ligh of he findings of his sudy. Smoohing bias may exis a individual propery level, bu is impac o he aggregaed index is likely o be largely offse by he influence of he appraisal heerogeneiy. 7 A he end, he index ill no be as smoohed as many had believed, especially hen i is vieed under more realisic invesmen horizons. Finally, ho are e going o explain he long sanding real esae risk premium puzzle? The radiional appraisal smoohing heory can no longer provide a credible explanaion, as he heory does no seem o sand up ell agains simple logic and facs. Therefore, in order o undersand hy real esae exhibis higher risk-adjused reurns han financial asses (i.e. he real esae risk premium puzzle), i is perhaps useful o reconsider he alernaive explanaion suggesed by Lush (1988). In his presidenial address o he American Real Esae and Urban Economics Associaion in 1988, Lush poins ou he fac ha in real esae markes more han variance affecs price. Tha being he case, he argued: less variance is no an uncomforing finding, bu raher precisely ha e ould expec in markes here more han variance is priced. These non-variance facors include illiquidiy, heerogeneiy, high ransacion coss, ec. His vie is concurred by Lai and Wang (1998), in hich he auhors roe: a poenially more fruiful ay o sudy hy 7 For insance, based on an analysis of housing daa from Fannie Mae and Freddie Mac over he period of , Chinloy, Cho and Megbolugbe (1997) conclude ha smoohing is less of a problem han he volailiy induced by small sample size and heerogeneous beliefs among appraisers (page 97). 36

37 he variance of propery reurns is loer han ha of sock marke afer adjusing for risk is o examine he unique characerisics of propery markes. (page 53) Unil he unique characerisics of real esae is properly capured and priced in a ne real esae risk meric, fair comparison of he performances beeen real esae and socks, as ell as he proper role of real esae in mixed-asse porfolios, ill remain a major challenge facing academics and praciioners alike. Appendix. The Nine Census Regions used by OFHEO 37