Risk Reduction and Diversification in UK Commercial Property Portfolios. Steven Devaney

Transcription

1 ISSN Rsk Reducton and Dversfcaton n UK Commercal Property Portfolos By Steven Devaney Dscusson Paper August 007 Edtor: Dr W Davd McCausland

2 Rsk Reducton and Dversfcaton n UK Commercal Property Portfolos Mark Callender 1, Steven Devaney, Angela Sheahan 3, Tony Key 4 June 5 th 007 Abstract The ssue of dversfcaton n drect real estate nvestment portfolos has been one of the most wdely studed topcs n academc and practtoner lterature. Most work, however, has been done usng mean returns and rsks for broad market segments as nputs to asset allocaton models, or n a few cases usng data from small sets of ndvdual propertes. Ths paper reports results from a comprehensve testng of asset allocaton modellng drawng on records of 10,000+ UK propertes tracked by Investment Property Databank. It provdes for the frst tme robust estmates of the dversfcaton gans attanable gven return, rsk and cross-correlatons across ndvdual propertes actually avalable to fund managers. The dscusson of results covers mplcatons for the number of assets and amount of money needed to construct balanced portfolos by drect nvestment, or va ndrect specalst vehcles. Acknowledgement Ths paper s drawn from a wder study commssoned by the Investment Property Forum (IPF) Research Programme. The full report was publshed by the IPF n May 007, and s avalable from The authors are grateful for the IPF s support for the research, and the nvaluable advce of the members of the IPF project steerng group: Nel Turner (Schroders), John Gellatly (BlackRock), Guy Morrell (HSBC), Nck Tyrell (J P Morgan) and Charles Follows (IPF). 1. Mark Callender, Schroders Property Investment Management, 31 Gresham Street, London ECV 7QA e: [email protected]. Steven Devaney, Unversty of Aberdeen Busness School, Edward Wrght Buldng, Dunbar Street, Aberdeen AB4 3QY e: [email protected] 3. Angela Sheahan, IPD, 1 St. John's Lane London EC1M 4BL e: [email protected] 4. Tony Key, Cass Busness School 106 Bunhll Row, London EC1Y 8TZ e: [email protected] Page 1

3 1 Introducton Ths paper nvestgates the potental for rsk reducton and dversfcaton n portfolos of drect nvestments n UK commercal property, drawng on Investment Property Databank (IPD) records of thousands of ndvdual propertes. Its prmary objectve s to establsh the specfc rsk and trackng error of portfolos contanng varyng numbers of assets. In the course of that nvestgaton, t provdes full nformaton on the return, rsk and correlaton characterstcs of ndvdual propertes, and ther varaton across market segments. Standard analytcal and smulaton methods are appled to determne the varaton n rsk wth number of assets for balanced funds seekng to track the overall market ndex, and also for specalst funds offerng nvestors exposure to specfc segments of the market. There s an extensve lterature on the ssue of portfolo rsk and the number of assets held n both equty nvestment and property nvestment. Prevous work on property, however, has mostly been lmted to exercses based on small samples of ndvdual assets, or takng aggregate results for sub-segments of the market, to measure the potental rsk reducton. The approach used here s the frst, to our knowledge, whch apples all the man avalable methods to the full dataset whch s the best representaton of the full unverse of assets actually avalable to UK fund managers. It therefore gves the most realstc pcture of the choces avalable to managers seekng to construct portfolos wth a specfc rsk tolerance aganst ndex benchmarks. Prevous studes on UK property data have estmated the number of propertes requred to acheve a dversfed portfolo anywhere between 0 (Jones Lang Wootton, 1986) and,000 (Young et al, 006). Such wde spreads reflect dfferences n the defnton of dversfed as much as fundamental dfferences n the data sets and technques used. There s a broad consensus among academcs and practtoners that portfolos of 30 to 60 propertes can dversfy away a large part of the rsk of ndvdual assets, whle a portfolo of around 00 propertes acheves around 90% of the theoretcal maxmum dversfcaton. Our results are broadly confrm the establshed consensus, but provde a more robust quantfcaton of feasble rsk reducton over a longer perod of tme, and for a wder range of nvestment objectves. Followng ths ntroducton, Secton establshes the prmary theoretcal framework for the analyss, and revews prevous work on the subject n both equtes and property markets,. Secton 3 brefly descrbes the IPD data set used, and the detals of the portfolo smulaton methodology. Secton 4 sets out the characterstcs of property performance at the asset level, and out man results. Secton 5 concludes wth a dscusson of practcal mplcatons of the work, and areas for further development. Lterature revew The standard measures of portfolo rsk and dversfcaton can be derved drectly from the basc theores of Modern Portfolo Theory and the Captal Asset Prcng Model. Ths secton frst derves and defnes these standard measures, and then revews ther applcaton n prevous work on both equtes and property markets..1 The measurement of rsk and dversfcaton Followng the fnance lterature, we apply two dstnct measures of portfolo rsk. The frst s total portfolo rsk the standard devaton of a portfolo of n assets. The rsk reducton avalable from portfolos of dfferent szes can be measured ether by the extent to whch an n asset portfolo reduces rsk from the most rsky portfolo a sngle asset or approaches that of the least rsky portfolo the market ndex. The second measure of rsk s dversfcaton the closeness wth whch a portfolo of n assets tracks movements n a Page

4 market Index year by year, or the extent to whch the specfc rsk of ndvdual assets has been dversfed away, leavng only the systematc rsk of the market ndex. The basc prncples of the rsk reducton measure are famlar from the orgnal formulatons of Modern Portfolo Theory (Markowtz, 195, 1959). In the standard form of presentaton, the expected return on a portfolo s the captal weghted average returns on each asset: where n E( r ) = w E( r ) EQUATION 1 p E( r p ) = 1 s the expected portfolo return w s the proporton of funds nvested n asset E r ) ( and s the expected return from the ndvdual asset. Expected portfolo rsk s a functon of both the weghted varance of the ndvdual assets, and a double summaton of the weghts and covarances between ndvdual assets: where n = 1 n n σ = w σ + w w Cov EQUATION σ p p = 1 j= 1 j s the varance (rsk) of portfolo returns w s the proporton of funds nvested n asset σ s the varance of returns from asset, w s the proporton of funds nvested n asset j j Covj s the covarance n the returns of assets and j. Whle covarance between any par of assets s found by: where Covj j j = ρjσ σ j EQUATION 3 ρj s the correlaton between the returns of assets and j σ s the standard devaton of the returns of asset σ j s the standard devaton of the returns of asset j. Whle t s not mmedately obvous that there s a relatonshp between the portfolo rsk and number of assets held, a general formula can be derved on the assumpton that assets are equally weghted. If n assets each carry a weghtng of 1/n, Equaton can be restated as: σ σ p 1 n p = σ + n 1 cov n where s the varance (rsk) of portfolo returns n s the number of assets n the portfolo σ s the average asset varance covj s the average covarance between portfolo assets. j EQUATION 4 Page 3

5 Clearly, for a gven average varance of assets, as n ncreases, the frst term of the total portfolo rsk decreases, whle the second term ncreases as a proporton of total rsk. For small number of very rsky assets, therefore, addng addtonal asset to the portfolo wll always acheve a large measure of rsk reducton. Wth a large number of assets, the mpact on rsk on addng further assets at the margn wll depend prmarly on the average level of covarance. Equaton 4 provdes a specfcaton of rsk wthn a smple Mean Varance Portfolo framework, and the mpact of number of assets on the expected spread of portfolo returns around a market average. It s an expresson of rsk reducton wth ncreasng portfolo sze. Rsk reducton can be measured ether as the standard devaton of expected portfolo return around the market average taken drectly from Equaton 4. If s often expressed as a percentage rsk reducton, the percentage reducton n standard devaton around the market average produced by a portfolo of n propertes aganst the standard devaton of a sngle property portfolo around that average. Thus f the standard devaton n returns for a sngle property about the market average s 10% and a 0 property portfolo reduces that standard devaton to %, an 80% rsk reducton has been acheved. Rsk reducton measures only the standard devaton n returns for a portfolo aganst a market ndex n a sngle perod, or a mult-perod holdng perod. When appled over a holdng perod, t does not measure how closely, over several of years, a portfolo can be expected to move n lne wth the market average the concept commonly known n performance measurement as trackng error. The approach of the Captal Asset Prcng Model (CAPM) (Sharpe, 1963) splts overall rsk nto systematc rsk, volatlty caused by factors common to all assets, and specfc rsk, volatlty caused by factors whch affect only a sngle asset. Snce systematc rsk cannot be dversfed away, a rgorous defnton of dversfcaton s the reducton of specfc rsk n a portfolo, and not the reducton n total rsk. In the standard CAPM formulaton, the expected return on a sngle asset s: where r r = α + βrm + ε EQUATION 5 s the return from ndvdual asset r m s the return on the market of all nvestble assets α s a constant and and ε β s a random error term. By dervaton, the rsk on a sngle asset s: where σ + σ s the senstvty of the returns of asset to the market = β σ m σ ε EQUATION 6 s the total varance of returns from asset σ m s the varance of market returns β (together) s the varablty of asset attrbutable to market (systematc) factors σ m σ ε represents the varablty of asset attrbutable to specfc factors. In Equaton 6, the rsk of an asset s a combnaton of systematc rsk (the frst term) and specfc rsk (the second term). For an ndvdual asset, therefore, the proporton of total rsk accounted for by systematc rsk s: Page 4

6 R β σ = σ m EQUATION 7 where R s the rato of systematc varance to total varance A general relatonshp between portfolo rsk and the number of assets held s not mmedately apparent from Equaton 7. However, Brown and Matysak (000: ) derve the relatonshp shown n Equaton 8, agan on the assumpton that all n assets are equally weghted, and that all assets share common characterstcs n terms of specfc rsk and covarance. Usng ther notaton: R na = na + B where n s the number of assets held A represents systematc rsk of a sngle asset B s the specfc rsk of a sngle asset. A can be computed as ether the average covarance of all assets or as the varance of the market snce, for the whole market, the average β = 1. B n turn can be found by subtractng the A from the average varance of all assets. EQUATION 8 Hence, as n ncreases, systematc rsk becomes a larger component of total rsk and the R rato rses. Ths formula can be used to fnd the typcal dversfcaton of a portfolo of any sze, or be rearranged to fnd the number of assets needed for a gven level of rsk reducton. Under the CAPM formulaton (Sharpe, 1964), n an effcent market, the expected return on an asset would reflect only the extent to whch t vared wth the market, snce that was the motvaton for ts purchase. Its return would not reflect ts specfc rsk, on the assumpton that rsk could be dversfed away n a mult-asset portfolo. On ths vew, dversfcaton s seen as the removal of rsk for whch the nvestor s not compensated and not smply as the reducton of overall rsk. From ths theoretcal bass, the analyss apples two separate measures of portfolo rsk. Frst, the reducton n standard devaton n portfolo returns compared wth the standard devaton n a market ndex over a perod, s termed rsk reducton, and can be calculated from Equaton 4. Second, a full measure of the extent to whch systematc rsk has been reduced, and total portfolo rsk approaches the systematc rsk of the market ndex, termed dversfcaton, can be calculated from Equaton 8. Both rsk reducton and dversfcaton can be estmated n two ways. Gven averages of the standard devatons of ndvdual assets, the correlaton between ndvdual assets (or ntercorrelaton), and the correlaton between ndvdual assets and a market ndex, they can be calculated by analytcal methods e drectly from summary statstcs usng Equatons 4 and 8. These methods are, however, n ther smple form restrcted to an assumpton of equal portfolo weghts. The alternatve s smulaton methods, whch construct hypothetcal portfolos by samplng from a unverse of ndvdual assets. Smulaton methods can assume ether an equally weghted portfolo, or a value weghted portfolo n whch each asset contrbutes to total return n proporton to ts captal value. Page 5

7 . Prevous studes on equty and property portfolos Work on the ssue of dversfcaton and portfolo sze was orgnally conducted on equty markets. Here we brefly revew those early foundatons, and then consder n more detal the body of work on property markets. For equty markets, Evans and Archer (1968) s the earlest emprcal study usually cted, and t provdes the basc methodology for subsequent work. They constructed portfolos of between 1 and 40 stocks through random selecton from the S&P 500, repeatng the selecton for each portfolo sze 60 tmes, and measurng average standard devaton from the 60 trals. The results suggested that most rsk reducton was acheved wth a portfolo of only 8 stocks and that the benefts of addng stocks beyond ten were not very great. Elton and Gruber (1977) added analytcal solutons to the rsk reducton queston e devsng general formulae from the average varance and covarance of stocks quoted on the NYSE and ASE, rather than smulatng portfolos from seres of returns on ndvdual stocks. Agan, t was observed that most of the avalable rsk reducton could be acheved wth 10-0 stocks n the portfolo, although Elton and Gruber argued that very large portfolos could stll acheve sgnfcant mprovements n rsk. These early studes gnored varaton n management and transactons costs wth sze of portfolo. Statman (1987) measured the gan from holdng a large portfolo set aganst the ncrease n portfolo costs. He found that the benefts of holdng a larger portfolo outweghed the added costs only for portfolos of up to stocks. Despte dfferences n emphass resultng from the use of dfferent tme perods and methods, studes of equty markets have reached the same general conclusons; that most rsk reducton and, also, a hgh degree of dversfcaton can be acheved wth a surprsngly small number of stocks. In the real estate feld, the development of research on ths topc awated the creaton of large-scale data sets by frms of valuers n the 1980s. Usng the basc smulaton approach establshed by Evans and Archer (1968) and small sets of ndvdual property records, Jones Lang Wootton (1986) concluded that a portfolo of 0 propertes acheved most of the potental rsk reducton. Barber (1991) put that threshold at propertes. These studes dd not formally measure the extent of full dversfcaton, or reducton n trackng error. The frst larger-scale and more rgorous exercse was conducted by Brown (1988). Takng base data on monthly returns for 135 propertes, Brown appled analytcal methods backed up by some smulatons. He found that market returns represented by the average for the whole sample of propertes explaned, on average, only 10% of the varaton n return on ndvdual propertes, compared to 30% n the case of UK equtes. Gven that hgh degree of specfc rsk, therefore, a large amount of rsk reducton could be acheved wth a portfolo of only 10 propertes. But, due to the low nter-correlaton between assets, an extremely large number of propertes 00 would be needed for the market to explan more than 95% of the portfolo return. Brown s analytcal results were produced usng an assumpton of equal portfolo weghts for each of the 135 ndvdual assets. Hs accompanyng smulaton exercses, however, allowed ths assumpton to be relaxed, and suggested that the wde varatons n lot szes between property assets could have an mportant nfluence on the results. As Brown (1988:146) noted, hs results mean that t s very dffcult for all but the very largest property portfolos to track a market ndex such as IPD, and that two medum szed funds whch are smlar n structure may perform very dfferently. Brown and Schuck (1996) suggest that ths barrer to dversfcaton s one of the factors that explans why property Page 6

8 nvestors generally hold much lower weghts than ndcated by portfolo optmsaton models. The mplcatons of value weghtng of property assets were taken further by Morrell (1993), who stressed that equal weghtng s not a realstc choce for nvestors constructng a balanced portfolo ncludng (say) low value ndustral unts and hgh value shoppng centres. To gve a fuller account of the nevtable mpact of value weghtng on rsk, Morrell used full cash flow data on 56 assets held from 1984 to 1987 to construct portfolos of to 50 propertes, on both equal weghtng and value weghtng assumptons. Estmates of rsk for were taken from 100 samplng trals for each portfolo sze. The results showed that the dsperson of returns for the value weghted portfolos was sgnfcantly greater than that for the equally weghted portfolos of the same total value, because ndvdual assets wth large lot szes can domnate the portfolo return. Thus, Morrell concluded, prevous estmates of rsk reducton wth portfolo sze underestmated the number of propertes requred to acheve a gven level of dversfcaton. In a dscusson of these results, Schuck and Brown (1997) observed that the relatonshps between number of assets, ther specfc and systematc rsk, and uneven lot szes are complex. Whle uneven lot szes mght, on average, ncrease the rsk found n value weghted portfolos, the precse mpact depends on an nterplay between ndvdual asset rsks, the spread n lot szes and the correlatons between assets. In some cases, value weghted portfolos could show lower rsk than equally weghted portfolos. Overall, Schuck and Brown suggested that value weghted portfolos were more lkely to show ncreased rsk when nter-asset correlatons are low, as n UK commercal property. A further development n Morrell (1997) noted that, because property assets are ndvsble, property portfolos contan unque sets of assets, unlke equty portfolos of varyng sze whch wll be largely constructed from shares n the same companes. Ths adds a further level of varance between actual property portfolos and an ndex, on top of the low level of correlaton between assets. Morrell consdered that, as a substtute for the ablty to crossnvest n dfferent propertes, property fund managers attempt to dentfy market segments wth greater homogenety whch can then be used to structure portfolos. The key queston for such managers then becomes how many assets n each segment are requred to provde a reasonable approxmaton of ther rsk and return characterstcs. The constructon of portfolos usng market segments has been nvestgated n most detal by Byrne and Lee (000). They appled both analytcal and smulaton methods to a dataset of returns for dfferent UK local authorty dstrcts, splt by sector, coverng the perod 1981 to These data ponts were then aggregated nto 4 regons and portfolos were constructed selectng from the whole dataset and from partcular sector/regon combnatons. The authors observed that prevous studes whch reported only the average results from many tral sets of portfolos were msleadng. Whle ncreasng portfolo sze may reduce sgnfcantly reduce average rsk by the tme portfolos rse to (say) 0 propertes, the ndvdual outcomes of the trals may stll show a wde dsperson. In other words, some of the randomly selected portfolos stll show hgh levels of specfc rsk. Byrne and Lee found that, addng ths further dmenson, t took another step up on portfolo sze, to assets, to produce sets of portfolos wth a reasonable degree of confdence that the average level of rsk reducton would be acheved by all ndvdual portfolos. The most recent nvestgaton of the ssue usng ndvdual property data s reported n Brown and Matysak (000), whch revsted the work of Brown (1988). Ths used IPD monthly returns for 100 propertes over the perod 1987 to 1997, splt nto two fve-year subperods, and annual returns for 750 propertes over the perod 1987 to Overall, on the monthly fgures the analyss found rsk reducton results very smlar to those n Brown s 1988 study (also based on monthly returns). The results also suggested that market states Page 7

9 may mpact on rsk reducton, wth rather hgher nter-correlatons between propertes and therefore less potental rsk reducton n the hghly volatle boom and bust market from 1987 to 199. Brown and Matysak s results based on the annual returns, however, were sgnfcantly dfferent, fndng a much hgher average correlaton between assets (0.4) than on the monthly fgures (0.10). Ths suggests that the frequency at whch returns are measured may mply very dfferent dversfcaton characterstcs. At a monthly frequency, correlatons may be based downward by the large proporton of propertes around 60% - for whch captal values reman unchanged n any one month. Gven the length of tme necessary to adjust portfolo structures, measurement at an annual frequency mght well be consdered more approprate. In that case, the potental for rsk reducton may be lower than suggested by many papers based on hgher frequency results. There have been few attempts to match up the results predcted from analytcal methods or smulatons based on small samples to the range of returns and rsks acheved by actual nvestment funds. Funds covered by IPD, as reported n Cullen (1991), do not appear to show a systematc relatonshp between portfolo sze and rsk. Indeed, some very small portfolos record very low levels of rsk aganst theoretcal predctons based on the number of propertes held. Whle there may be several explanatons for ths counter-ntutve result, Byrne and Lee (003) consder t may be due to the attrbuton of fund rsk to systematc and specfc factors. In partcular, both total volatlty as measured by the smple varance on total returns, and dversfcaton as measured on the CAPM model, may rse wth the sze of portfolos. Thus large funds are more lkely to track the market, and therefore pck more systematc rsk, whle at the same tme reducng specfc rsk through ther wder access to the full range of market segments and lot szes. Smaller portfolos, by contrast, may show low overall varance due to fortutous combnatons of assets, but ther returns are much more weakly lnked to the market ndex. To take hypothetcal extreme cases, a two-property portfolo of assets whch are negatvely correlated wth each other but weakly correlated wth the market ndex would show very low rsk coupled wth very poor dversfcaton measured by ts ablty to track the market. At the other extreme, two propertes hghly correlated wth each other and wth the market ndex would show a hgh level of rsk, but hgh dversfcaton, trackng close to the market. Prevous work, n summary, provdes a well-establshed theoretcal base. Studes based on analytcal methods or smulatons run on small sets of ndvdual property data show a large measure of consstency, n that ncreasng the number of propertes n a portfolo at the low end of the sze range up to 30 to 50 propertes - produces rapd reductons n rsk due to the combnaton of hgh asset specfc rsk and low asset nter-correlatons. Very hgh levels of dversfcaton, removng say 90% of specfc rsk from portfolos, can be acheved only wth very large holdngs of 00 or more assets. There remans a queston mark, however, on how these theoretcal predctons marry up wth observed performance of real portfolos. And no prevous research has used complete ndvdual property hstores taken from IPD s largest avalable record of nvestble propertes. Brdgng these gaps sets the agenda for the present study. 3 Objectves, data and methods Followng from prevous work, ths study has used the full range of establshed methods the analytcal approach and the smulaton approach and the largest avalable data set of ndvdual property records, where possble over 4 years from 1981 to 004. It therefore ams to clearly up some of the uncertanty surroundng the results of earler studes assocated wth lmted sample szes and specfc tme perods. Page 8

10 Furthermore, access to a large set of ndvdual propertes enables us to undertake more dsaggregaton of the characterstcs of returns and portfolos. Prevous work has been almost exclusvely concerned wth the all-property level n other words wth dversfcaton ssues relevant to the constructon of balanced funds benchmarked aganst an All Property ndex. Wth a larger data set, we can also nvestgate relatonshps between portfolo sze and dversfcaton for specalst funds wth a one-segment focus (such as London offces or shoppng centres) whch seek to replcate segment-specfc returns. Ths type of fund has, n recent years, become one of the most favoured ndrect nvestment vehcles. Fnally, hstores of return for all the actual nvestment funds tracked by IPD can be generated from the same data set used n the theoretcal analyss. Ths means t s possble to cast more lght on the lnkages between the predctons about portfolo performance generated by theory to the emprcal results acheved n practce. The wde coverage of the IPD system, agan, makes t possble to separate out portfolos wth specfc characterstcs such as balanced funds from the overall sample. The ndvdual property data that are the foundaton of the analyss are taken from IPD s annual databank. At the end of 004, the databank covered around 11,000 propertes wth a total value close to 10 bllon. IPD estmates ths s equvalent to approxmately 50% of all commercal property held by large-scale professonal nvestors, and a much hgher fracton of that held by the largest domestc nsttutonal nvestors, lsted property companes and nvestment funds. IPD data, and the prncples of ts constructon, are wdely used and understood n both ndustry and academa. Detals on the databank and the underlyng prncples of measurement are avalable from The theoretcal analyss cuts nto the ndvdual property data n two ways: annual crosssectonal samples from 1981 to 004, and longtudnal tme seres samples from 1994 to 004. In both cases, the propertes selected are standng nvestments as defned by IPD e propertes held between two year-end valuaton dates, and thus excludng all propertes transacted or under development n the course of the year. Meanwhle, the comparson ndces for the market and for dfferent market segments were also obtaned from the IPD databank. The cross-sectonal analyss draws on the full set of propertes avalable each year, to measure the dsperson of ndvdual propertes returns around the all-property and segment averages. Ths s the bass for analytcal methods to determne the dversfcaton mpacts of dfferent portfolo szes n any one year, and also for parallel smulaton methods constructng randomly selected portfolos wth varyng numbers of propertes. The sample szes avalable for ths part of the research were at a mnmum of 11,000 n 004, and up to 15,000 n earler years. Our longtudnal analyss replcates the constructon of portfolos over the perod 1994 to 004. To brng ths as close as possble to a realstc representaton of portfolos actually avalable to medum-long term nvestors, the tme seres analyss was based only on propertes contnuously held by nvestors covered by IPD throughout the assumed holdng perod. Ths restrcton cuts the avalable sample sze to 1,70 propertes for the ten year perod. Agan, ths sample served as the bass for both analytcal methods based on summary statstcs, and for smulaton exercses. Lmtng the longtudnal analyss to the relatvely small sub-set of IPD propertes contnuously recorded for ten years rased possble problems of survvor bas - that the characterstcs of these long-held assets are n some way dfferent from the whole populaton of avalable propertes. However, tests for consstency n the annual returns and annual standard devatons wth a larger set of propertes, held over the fve years 1999 to 004, suggested there was no assocaton between length of holdng perod and these key characterstcs for the purposes of ths analyss. Page 9

11 Well establshed Monte Carlo smulaton methods have been used n both cross secton and tme seres to construct hypothetcal portfolos of varyng szes. For each smulaton tral, portfolos of from 1 to 500 propertes (n steps of 1 up to 0 propertes, then steps of 10 up to 100 propertes, and steps of 50 from 100 to 500 propertes) were obtaned by random selecton wthout replacement from the avalable unverse of ndvdual propertes. For each portfolo sze, the random selecton process was repeated 0,000 tmes n the case of the cross sectons and 5,000 tmes for the tme seres returns. Average returns, standard devatons and ranges n standard devatons were then calculated from the sets of trals at each portfolo sze. 4 Results Ths secton frst descrbes the key characterstcs of ndvdual property returns n annual cross secton, whch underle all the results that follow. We then take n turn the results produced from cross-sectonal analyss and from longtudnal analyss of the ndvdual property data. The fnal part of ths secton brefly compares the theoretcal results wth the rsk characterstcs of actual nvestment funds tracked by IPD. 4.1 Indvdual Property Rsk Across all propertes n the sample, the standard devaton n returns about the ndex average for ndvdual years has ranged between 35.1% and 16.9% (Table 1 the years selected represent the man turnng ponts n the property cycle). The standard devaton n return across propertes wthn the IPD n 004 was 16.9% wth an nterquartle spread of 11.5 pp. By way of comparson, the standard devaton n returns across all equtes lsted on the FTSE n 004 was 4.5% wth an nterquartle spread of 3.5%. Table 1 Dsperson n ndvdual property total returns, selected years Standard Devaton % Average Std. Retal South East Std. Retal Rest UK Shoppng Centres Retal Warehouses Cty Offces West-End Offces Rest of S.E. Offces Rest of UK Offces Industral South East Industral Rest UK All Property Table 1 splts the summary statstcs nto 10 prmary market segments, whch are extensvely used n IPD s portfolo reportng servce, and therefore stand as the splt of the market most commonly used by fund managers n asset allocaton. There are large and persstent dfferences n the spread of returns wthn segments. Averaged across years, Cty and West End offces show the greatest spreads n return. Shoppng centres, retal warehouses and Rest of UK ndustrals all show standard devatons less than half those found n the central London offce segments. The larger return spreads seen n Central London segments may appear surprsng gven that they are the most geographcally compact of all the segments. Page 10

12 There appears to have been a downward trend n one-year dsperson at the all-property level, and wthn each of the market segments though agan ths s less marked n the Central London offce segments. A number of factors may have contrbuted to ths fall n return spreads. Wthn segments, the two most mportant factors are lkely to have been a long term ncrease n average lot szes and a decreasng varablty n the spread of valuatons. Snce 1981, the average lot sze n the IPD has rsen four-fold after adjustment for rsng captal values. Snce hgh valued propertes show much tghter spreads of returns, ths effect has probably accounted for the bulk of the narrowng. Prevous work by IPD (RICS, 006) has also shown that the spread of valuatons around transactons prces has narrowed over tme, accountng for a further substantal proporton of the narrowng wthn segments. At the all-property level, a further narrowng s lkely to have resulted from a fall n the weghtng of offces, where return spreads are greatest, and also a narrowng n the range of returns across segments. 4. Cross Sectonal Analyss As a frst step n the analyss, portfolos were been constructed from annual cross-sectonal data by samplng portfolos from the records for 11,000 15,000 propertes each year. The portfolo returns were value-weghted. Ths exercse was carred out at the all property level each year from 1981 to 004. For market segments, to lmt computng tme to a manageable level, smulated portfolos were constructed for the years 1988, 1991, 1997, 001 and 004, selected to represent a range of market states through the perod. Fgures 1 and summarse the results of the all property portfolo smulatons for a sngle year, Fgure 1 shows the mean standard devaton from 0,000 smulatons at each portfolo sze. Fgure shows the same results n the form of spreads n total returns across the 0,000 smulatons at each portfolo sze. (Note that n these charts and those whch follow, the gaps n the lnes show changes n the steps at whch portfolo szes were ncreased.) In 004, the IPD all property return was 18.3% and the standard devaton n return of ndvdual propertes around that mean was 16.9%. Addng a second property to a 1 property portfolo yelded the largest sngle reducton n expected standard devaton, to 9.1%, removng nearly 60% of the rsk of nvestment n a sngle property. A portfolo of 40 propertes would have an expected standard devaton of.6%, removng 75% of the rsk of an ndvdual property a fndng consstent wth prevous studes whch suggested the bulk of specfc rsk could be removed wth portfolos around that sze. Cuttng the expected standard devaton n return around the IPD average to less than 1%, however, would requre a portfolo of 350 propertes. Repeatng ths procedure for every year from 1981 to 004 yelds the results summarsed n Fgure 3, whch shows the expected standard devaton n returns for a range of smulated portfolo szes. Page 11

13 Fgure 1 Cross-secton: average standard devaton of smulated portfolos 004 Mean Standard Dev Average Std Dev n Portfolo Returns Number of Propertes Fgure Cross-secton: spreads n returns of 0,000 smulated portfolos 004 Percentle Range n Returns th percentle 5th percentle 50th percentle 75th percentle 95th percentle Number of Propertes Fgure 3 Cross-secton: average standard devaton of smulated portfolos Percentle Range n Returns property 100 propertes 0 propertes 350 Propertes Number of Propertes Page 1

14 Table Cross-sectonal analyss: dsperson of smulated portfolo returns Number of Propertes n Hypothetcal Portfolo Standard Devaton n Returns on Hypothetcal Portfolos Std. Retal South East Std. Retal Rest UK Shoppng Centres Retal Warehouses Cty Offces West-End Offces Rest of S.E. Offces Rest of UK Offces Industral South East Industral Rest UK All Property Average of Fve Years Standard Devaton n Returns on Hypothetcal Portfolos Std. Retal South East Std. Retal Rest UK Shoppng Centres Retal Warehouses Cty Offces West-End Offces Rest of S.E. Offces Rest of UK Offces Industral South East Industral Rest UK All Property There has been a clear down-trend n both the standard devaton of all propertes around the IPD average wthn each year (e the 1 property portfolo), and n the expected standard devaton of portfolos n all sze ranges. In the frst fve years of the seres, standard devaton across all propertes averaged 8.5%, and the expected standard devaton for a 0 property portfolo averaged 4.6%. In the last fve years of the seres, those fgures dropped to a standard devaton of 19.8% for ndvdual propertes, and an expected standard devaton of.8% for a 0 property portfolo. Annual outcomes have broken away from the downtrend only n 1988 / 1989, perhaps due to the large swng n the market and wde spread between segment returns n those years, but also n 1999 / 000 where there s no such mmedately obvous explanaton. The same procedure may be used to create smulated portfolos n each of the market segments. Table condenses results for segments to show rsk reducton across a range of portfolo szes for 004, and results averaged over the fve years When expressed as a percentage rsk reducton from a 1 property portfolo, most segments show smlar results n both the 004 results and the averaged results over fve years. Page 13

15 Table 3 Summary Statstcs for Longtudnal Samples of Contnuously Held Propertes Std. Retal -South East Std. Retal - Rest UK Shoppng Centres Retal Warehous es Cty Offces West-End Offces Rest S.E. Offces of Rest of UK Offces Industral South East Industral Rest UK Other Property All Property Number of Propertes ,78 Number of Propertes ,719 Average Std Dev Average Std Dev Intercorrelaton between Propertes Average Standard Devaton Correlaton between Propertes and Index Average Standard Devaton Page 14

16 Generally, a 10 property portfolo acheves a rsk-reducton of 65% to 75%, and a 100 property portfolo a rsk reducton of 85% to 90%. The notable exceptons are the Cty and West End offce markets, where the base rsk of a 1 property portfolo s much hgher, but lower ntercorrelatons between propertes mean that the rsk reducton benefts of added propertes are much greater. So for these markets a 10 property portfolo acheves a rsk reducton of 80% to 85%. It would appear that, for large-scale nvestors n the Central London offces, hgh market and specfc rsk may be offset by hgher rsk reducton benefts. In general, the range n returns for specalst segment portfolo s smaller than the range n balanced fund returns (.e. the all property level results), because the range n balanced fund returns s stretched by varatons n performance across dfferent sectors of the property market. 4.3 Longtudnal analyss Ths secton constructs portfolos usng tme seres data for 1,78 propertes contnuously recorded by IPD over the ten years from 1994 to 004. Table 3 gves summary statstcs for ndvdual propertes over ths perod and the fve year perod 1999 to 004. At the all property level, t would appear that standard devaton n returns for ndvdual assets converges to a long run fgure around 10%-11%. Volatlty s a lttle hgher on the longer-run fgures because they nclude years of hgher year-on-year varaton n the market ndex. On ths measure, the average rsk of a sngle property held over ten years at 11% s.5 tmes the standard devaton on market ndex returns over the same perod at 4.4%. Results at the segment level are not wholly consstent over the two perods, or wth the cross sectonal data dscussed n the last secton. On the ten year fgures, there are farly small varatons n ndvdual property rsk across segments. Despte the large dsperson n returns shown by the annual cross secton results, the Central London offce segments are at the lower end of the rsk range. Measured over fve years, however, there s a wder spread n property rsks across segments, and the Central London offce segments agan appear as the most rsky. At the all property level, the average ntercorrelaton between ndvdual buldngs s low, at 0.18, but wth a wde spread around that average ndcated by a standard devaton more than double the mean. Wthn segments, average ntercorrelatons between propertes are not much greater than across all propertes ndcatng the low proporton of property level varance explaned by segment attrbutes. Industral propertes and offce propertes outsde the South East show lower ntercorrelatons than the other segments, perhaps due to a wder spread of locatons and lower average lot szes. On average, ndvdual property returns over ten years are moderately correlated wth returns on the all property ndex, showng a correlaton of Perhaps surprsngly, the correlatons between ndvdual propertes and ther respectve segment averages are at most lttle hgher, and usually a lot lower, than the correlatons wth the all property average. Correlatons wth the segment average are partcularly low n offce segments, wth the excepton of the Rest of the South East. Agan, ths s a reflecton of the weak explanatory power of the segmentaton n explanng property returns (on ths, see also Devaney and Lzer, 005). Smulated portfolos were constructed from the ten year sample of data by the samplng methods descrbed n the last secton. As n the cross-sectonal analyss, portfolos are value-weghted. The results are summarsed n Fgures 4 and 5. Over the ten year perod, the standard devaton n the market Index was 4.5%, and the expected rsk of a sngle property portfolo was 11.0% - a dfference of 5.5 pp. The extent of Page 15

17 smple rsk reducton wth ncreasng portfolo sze s rather greater than found n the crosssectonal varaton n annual returns. Thus a 1 property portfolo s enough to reduce the total rsk by 80% from that of a sngle property, and a portfolo of 30 propertes reduces that rsk by 90% - gvng an expected standard devaton n portfolo return of 5.1%, only 0.60 pp above the standard devaton of the ndex. A portfolo of 150 propertes shows an expected standard devaton of only 4.6%, cuttng out 99% of the rsk of a sngle property portfolo. Fgure 4 Longtudnal: average standard devaton of smulated portfolos Mean Standard Dev Portfolo Standard Devaton IPD Market Index Standard Devaton Number of Propertes Fgure 5 Longtudnal: spreads n returns of 0,000 smulated portfolos Percentle Range n Returns th percentle 5th percentle 50th percentle 75th percentle 95th percentle Number of Propertes Overall, because ndvdual propertes are weakly correlated wth each other, and mldly correlated wth the market ndex, the expected rsk of portfolos falls qute sharply wth ncreasng sze. Fgure 5, however, demonstrates that smaller portfolos stll show a hgh probablty of departng from the expected (average) rsk by large margns. A 1 property portfolo may cut the expected excess rsk by 80% but 5% of 1 property portfolos would have rsk more than.6 pp above the market ndex. To cut the probablty of rsk less than 1% above the market ndex to less than 5% requres a portfolo of 30 propertes Page 16

18 Fgure 6 Longtudnal: standard devatons smulated vs analytcal results Mean Standard Dev Portfolo Smulatons Analytcal Method (Eqn 4) Number of Propertes Fgure 7 Longtudnal: Dversfcaton (R-squared) smulated vs analytcal results R-squared Portfolo smulatons Analytcal Methods (Eqn 8) Number of Propertes Fgure 7 Longtudnal: dversfcaton (trackng error) of smulated portfolos Mean Trackng Error pp Number of Propertes Page 17

19 Fgure 6 demonstrates that results from the smulaton exercse (whch are value weghted) are very close to those whch would be produced more drectly by analytcal methods (whch assume equal weghtng). The analytcal result apples Equaton 4 from Secton.1, calbrated wth the average property standard devaton of 11.0% and average ntercorrelaton of 0.18 from Table 3. Smulated rsk s between 1.07 and 0.94 tmes that predcted by analytcal methods throughout the range of portfolo szes. Smulated portfolos tend to show hgher than predcted rsk at the lower end of the sze range, and slghtly lower rsk for larger portfolos. Though the dfferences between the two methods are small, they are most lkely to reflect rather lower correlatons between large lot sze propertes than between small lot szes. In contrast to the results for smple rsk reducton, the extent of dversfcaton shown as feasble by the smulaton method dffers a lot from the predctons of a smple analytcal method (Fgure 7). Dversfcaton by the analytcal method s predcted by Equaton 8 from Secton.1, wth average standard devaton for ndvdual propertes at 11% and the average correlaton between propertes and the IPD market ndex at As before, the dfference between the two sets of results are that the smulatons are value-weghted, whle the analytcal method assumes equal weghts. The smulated portfolos show much lower dversfcaton potental than the analytcal predcton, especally n the md-range of portfolo szes between 3 and 50 propertes. The dfference suggests that large hgh value propertes are less strongly correlated wth the benchmark ndex than those wth small lot szes. Whle ths mplcaton holds true at the all property level, takng n varaton n lot sze across segments, t does not mean that the same s necessarly true wthn market segments. Fgure 8, meanwhle, presents estmates of trackng error (the standard devaton of the annual dfferences n standard returns between the portfolo and the market ndex), a measure of dversfcaton and portfolo rsk more wdely used n fund analyss. The expected trackng error for a property portfolo s 7.6%, fallng to 4.1% for a 10 property portfolo, and.6% for a 30 property portfolo. Trackng error falls below 1% only for portfolos of nearly 300 propertes. These, fuller, measures of dversfcaton are less comfortable than the smpler rsk reducton results. Because the average correlatons between ndvdual propertes and the market ndex are only 0.41, a farly large portfolo (say 50 propertes) may approach qute close to the same rsk as the market ndex over a perod of years, but stll vary substantally from the ndex returns year by year. Whch measure s most approprate depends, ultmately, on the nvestment objectve. An nvestor seekng only property s return and rsk characterstcs over a holdng perod would be prmarly concerned wth rsk reducton. An nvestor seekng the addtonal dversfcaton beneft of property nvestment relatve to other assets would also be concerned wth full dversfcaton and trackng error. The former, f the rsk reducton target s set at (say) avodng 90% of the specfc rsk of an ndvdual property, can be acheved wth farly small portfolos of 0 propertes. The latter, f the dversfcaton target s set at an expected trackng error of less than % requres 60 propertes, and 300 propertes f that target s set at a trackng error under 1%. Thus far, the longtudnal analyss has been carred out at the all property level, replcatng the task of constructng a UK balanced fund. On those results, at average lot szes n 005, creatng a 60 property balanced fund wth an expected trackng error of % (and R-squared of 0.84) would cost a total of 833 mllon. Exactly the same smulaton technques have been used to estmate the number of propertes and portfolo value needed to create specalst funds amng to track an IPD segment benchmark wth varyng levels of rsk tolerance (Table 4). In these cases, the benchmark ndex s the approprate segment ndex over the perod. For Cty offces and shoppng centres, the small sample szes of Page 18

20 contnuously held propertes mean t s not possble to generate portfolos wth hgh levels of dversfcaton, and also that results for all portfolo szes should be taken as ndcatve. In terms of the number of propertes, n most segments propertes are needed to construct a moderately dversfed portfolo (taken as R-squared of 0.75, consstent wth a trackng error around.5%) settng apparently low thresholds for specalst funds. The man excepton s Rest of UK offces, where the large spread of locatons s reflected n a low correlaton between ndvdual propertes and the segment benchmark. The amount of captal needed to construct those segment-trackng specalst portfolos, however, vares over a much wder range. Average lot szes n the IPD at the end of 005 ran from 7 mllon for Standard Retals through mllon for Cty offces, and 84 mllon for shoppng centres. Accordngly, the sze of fund needed for a moderately dversfed shoppng centre fund runs to over 1 bllon, whle equally well dversfed standard retal and ndustral funds could be held wth only 100 mllon. To construct a balanced portfolo va a funds of funds approach requres partcpaton n funds wth a total value of.5 bllon. Table 4 Longtudnal smulatons: portfolo szes requred to acheve gven dversfcaton Number of Propertes Total Portfolo Value m Extent of Dversfcaton R Std. Retal S East Std. Retal Rest UK Shoppng Centres ,018 - Retal Warehouses ,494 Cty Offces West-End Offces Rest of S.E. Offces Rest of UK Offces Industral South East Industral Rest UK All Property , Emprcal evdence on portfolo rsk Havng establshed theoretcal estmates of rsk reducton and dversfcaton potental, ths secton brefly revews the evdence on portfolo sze and rsk shown by the actual nvestment funds covered by IPD over from 1981 to 004. In 004, IPD separately recorded 31 dfferent funds, whch allows some parttonng of the sample nto balanced portfolos (e coverng a broad spread of market segments) and specalst funds wth a narrower concentraton. Over tme, the structure of portfolos appears to have run n the face of the prncples of dversfcaton. The average number of propertes per fund has fallen steadly from 93 n 1981 to 45 n 004. A number of factors have drven ths halvng n average portfolo sze. Fund managers have, typcally, weeded smaller propertes out of ther portfolos, wth an especally large sell-off of unt shops, and concentrated ther holdngs n large lot sze shoppng centres and retal parks. Ths trend has been drven manly by a desre to cut management costs. Page 19

21 Table 5 The Dsperson n Portfolo Total Returns from Balanced Funds, Average Number of Propertes Lower Quartle Medan Upper Quartle Inter-Quartle Range Note. Fgures are portfolo returns, not managed standng nvestment returns. The returns n ths table reflect the mpact of ndrect nvestments, developments and tradng. Returns are un-geared. Over the last decade, there has also been a prolferaton of new pooled nvestment vehcles such as lmted partnershps, many of them set up to gve specalst focus, and often seeded out of the drect portfolos of large nsttutons and property companes. Snce, on average, IPD funds now hold 1% of ther property exposure through ndrect pooled vehcles an n many cases over 0% ndrect many nvestors are seekng to dversfy through holdngs n pooled vehcles rather than wthn ther own portfolos. Although the average number of propertes n the drect portfolos of balanced funds has shrunk from 97 to 48 propertes snce 1981, those wth substantal ndrect holdngs are lkely to be exposed to a larger number of underlyng assets than before. In any event, despte a fall n portfolo szes, the spread of returns across balanced funds has shrunk over the last twenty years (Table 5). The nterquartle range has narrowed steadly over the last decade, from an average of over 8 pp n the last fve years of the 1980s to less than 4 pp average over the frst fve years of the 000s. A number of factors may account for ths convergence n returns. Frst and foremost, the dsperson of fund returns wll have narrowed as a result of the decreased ranges n ndvdual property returns dscussed n Secton 4. Our cross-sectonal smulatons showed that, for a 50 property portfolo, expected standard devaton would also have halved, from 5.5% over the last fve years of the 1980s to.5% over the frst fve years of the 000s. In addton, the fgures n Table 5 show the number of assets drectly held n funds, whle the returns also nclude the mpact of holdng ndrect nvestments whch, as noted above, may have provded a balancng ncrease n dversfcaton as drect portfolos have shrunk. The returns fgures also nclude the mpact on performance of development actvty, whch s a Page 0

22 large rsk factor for ndvdual funds, and the typcal exposure to development has fallen substantally snce the early 1990s. To strp out some of those factors, the summary statstcs on spreads of returns n Table 6 are based only on drect portfolos of standng nvestments. Funds have been splt nto specalsts, wth a sngle sector focus, and balanced funds nvestng across a range of sze bands. The actual performance of funds n ths sngle year s broadly consstent wth the results from our cross sectonal smulatons. For balanced funds, these suggested an expected standard devaton of 4.7% for a 10 property fund, 3.4% for a 0 property fund, and.1% for a 60 property fund. Table 6 Number of Propertes and the Range n Fund Returns n 004 Number of Propertes Number of Funds Standard Devaton n Returns 1 Average Total Return Specalst Funds < Balanced Funds < Standard devaton across ndvdual fund returns n Unweghted average. Specalst funds, on average, held 3 propertes n 004. The average s heavly skewed by a few very large portfolos, so the medan number of propertes for specalst funds was only 10 propertes. Aganst the cross sectonal and longtudnal results for hypothetcal portfolos, the majorty of specalst funds would appear to be poorly dversfed. At a medan sze of 10 propertes, our cross sectonal results suggest specalst funds wll show standard devatons around ther segment benchmarks of 3% to 4% n any one year. From the longtudnal smulatons, t requres propertes to acheve a moderate degree of dversfcaton (defned as an R-squared of 75%) wthn most segments, whch s half the number requred to acheve the same dversfcaton n a balanced fund. These fndngs suggest that nvestors seekng dversfcaton through ndrect nvestment should spread ther segment exposure across several vehcles. That strategy mght, however, be traded off aganst the potental gans from concentratng exposure n selected funds expected to out-perform segment benchmarks. Unfortunately, even wth a total of 31 fund records, the sample of funds s not large enough, and the varaton of fund structures wthn the broad categores of balanced and specalst s too large, to gve a more precse comparson of hypothetcal predcton and emprcal results at ths stage. Page 1

23 5 Conclusons The analyss has revsted the ssues of rsk reducton and dversfcaton usng the fullest possble property data set, and a full range of the methods appled n prevous work. In the man, the results provde confrmaton of prevous work, beneftng from a larger number of ndvdual propertes, and a longer tme perod, thus allowng a more robust quantfcaton for segments of the market, for sub-sets of fund types, and of trends over tme. Overall, the results confrm prevous studes, that a large measure of rsk reducton can be acheved wth portfolos of propertes, but that full dversfcaton of systematc rsk can only be acheved n very large portfolos of 00 and more propertes. At 005 average lot szes values, the captal value of a property portfolo would be mllon, and the value of a 00 property portfolo would be.8 bllon. The large span between those two sets of fgures demonstrates the crtcal mportance of careful defnton of terms, and of quantfed nvestment objectves, n any dscusson of rsk management n property portfolos. Hgh property-specfc rsks and low nter-correlatons between ndvdual propertes mean that rsk reducton gans are easly obtaned for both balanced all property funds, and specalst segment-focussed funds. On results for recent years, expressed as the extent to whch the rsk of an ndvdual property s reduced n a sngle year or over a holdng perod, the attanable rsk reducton of 75%-80% wth only 10-1 propertes sounds mpressve. But that stll leaves an expected standard devaton n expected portfolo returns around the market ndex of 4.5% n any one year, and ncrease n standard devaton over the market ndex through a ten year holdng perod of 1.5 pp. Because the results do not seem senstve to value weghtng, analytcal methods based on summary statstcs appear to provde a satsfactory method of estmatng rsk reducton. Full dversfcaton gans, the probablty of trackng the market ndex year-by-year through a holdng perod, s much harder to acheve. Ths reflects the moderate correlatons between ndvdual property returns and benchmark returns at both all property and segment level, and the mpact of value weghtng. Our results demonstrate that value weghted portfolos show much weaker dversfcaton gans wth ncreasng sze, because propertes at larger lot szes tend to be more weakly correlated wth ther benchmarks. So, over a ten year holdng perod, dversfcaton n terms of an mpressve soundng R-squared at 0.75 to 0.80 can be acheved wth balanced portfolos of propertes, but that equates to a less comfortable annual trackng error of.5% to.0% per year. Very full dversfcaton, set at an R-squared of 0.90 and a trackng error under 1.5% per year requres portfolos of more than 100 propertes, or a portfolo value of 1.4 bllon. Because of the value weghtng mpact, full dversfcaton cannot be measured by smple analytcal methods. We hope these fndngs provde a framework for a wder understandng of the defntonal and measurement ssues essental to the dscusson of dversfcaton ssues n the ndustry, and n reportng to nvestment clents. There are potental areas of further development from the methods used n ths study. One possble qualfcaton to the results s that they have been based on samplng from the entre unverse of propertes recorded by IPD, wth no restrctons on lot szes, buldng qualty, leasng status or other determnants of volatlty. It may be that fund managers seekng to construct benchmark trackng portfolos wthn a total portfolo value lmt would select only stablsed propertes wth less lkelhood of dsturbance from (say) requred captal spendng, tenant defaults, or nterrupted cash flows. If ths s the case, our results Page

24 may overstate the number of propertes needed to acheve gven rsk targets for delberately constructed balanced or specalst portfolos. On a related but tangental pont, our work has constructed portfolos purely by random selecton, an underlyng assumpton of zero manager skll n asset selecton and management. Smulatons allowng for specfed degrees of manager skll n selectng propertes wth (say) returns above the medan would cast more lght on the actual levels of skll attaned by real world managers. Page 3

25 References Barber, C Modern Portfolo Theory; Fact and Fantasy. Paper presented as part of the semnar seres Property n a Portfolo Context organsed by the Socety of Property Researchers and the RICS. Brown, G. R Reducng the Dsperson of Returns n UK Real Estate Portfolos. Journal of Valuaton. 6 (): Brown, G. R Property Investment and the Captal Markets. London: Chapman & Hall. Brown, G. R. and Matysak, G. A Real Estate Investment: A Captal Market Approach. Harlow: FT Prentce Hall. Brown, G. R. and Schuck, E. J Optmal Portfolo Allocatons to Real Estate. The Journal of Real Estate Portfolo Management. (1): Byrne, P. and Lee, S Rsk Reducton n the Unted Kngdom Property Market. Journal of Property Research. 17 (1): Byrne, P. and Lee, S An Exploraton of the Relatonshp Between Sze, Dversfcaton and Rsk n UK Real Estate Portfolos: Journal of Property Research. 0 (): Cullen, I Rsk Management n Investment Property Portfolos, Paper presented as part of the semnar seres Property n a Portfolo Context organsed by the Socety of Property Researchers and the RICS. Devaney, S. and Lzer, C Indvdual Assets, Market Structure and the Drvers of Return. Journal of Property Research. (4): Elton, E. J. and Gruber, M. J Rsk Reducton and Portfolo Sze: An Analytcal Soluton. Journal of Busness. 50 (4): Evans, J. L. and Archer, S. H Dversfcaton and the Reducton of Dsperson: An Emprcal Analyss. The Journal of Fnance. 3 (5): JLW Rsk and Asset Allocaton: Implcatons of Portfolo Strategy. London: Jones Lang Wootton. Markowtz, H. M Portfolo Selecton. The Journal of Fnance. 1: Markowtz, H. M Portfolo Selecton: Effcent Dversfcaton of Investments. Yale CT: Yale Unversty Press. Morrell, G. D Value Weghtng and the Varablty of Real Estate Returns: Implcatons for Portfolo Constructon and Performance Evaluaton. Journal of Property Research. 10: Morrell, G. D Property Rsk and Portfolo Constructon. Paper Presented to the Sxth IPD Investment Strateges Conference, Brghton, 7-8 November Schuck, E. J. and Brown, G. R Value Weghtng and Real Estate Portfolo Rsk. Journal of Property Research. 14 (3): Sharpe, W. F A Smplfed Model for Portfolo Analyss. Management Scence. 9 (): Sharpe, W. F Captal Asset Prces: A Theory of Market Equlbrum under Condtons of Rsk. The Journal of Fnance. 19: Statman, M How Many Stocks Make a Dversfed Portfolo? Journal of Fnancal and Quanttatve Analyss. : Young, M. S., Lee, S. L. and Devaney, S. P Non-Normal Real Estate Return Dstrbutons by Property Type n the U.K. Journal of Property Research. 3(): Page 4