Rsk Reducton and Real Estate Portfolo Sze Stephen L. Lee and Peter J. Byrne Department of Land Management and Development, The Unversty of Readng, Whteknghts, Readng, RG6 6AW, UK. A Paper Presented at the Sxth PRRES Conference Sydney, Australa January 000 Phone: +44 (0) 118 931 6338: Fax: +44 (0) 118 931 817: E-mal: S.L.Lee@readng.ac.uk Abstract Despte a number of papers that dscuss the advantages of ncreased sze on rsk levels n real estate portfolos there s remarkably lttle emprcal evdence based on actual portfolos. The objectve of ths paper s to remedy ths defcency by examnng the portfolo rsk of a large sample of actual property data over the perod 1981 to 1996. The results show that all that can be sad s that portfolos of propertes of a large sze, on the average, tend to have lower rsks than small szed portfolos. More mportantly portfolos of a few propertes can have very hgh or very low rsk. Keywords: Rsk Reducton, Portfolo Sze. 1
Rsk Reducton and Real Estate Portfolo Sze 1. Introducton The nvestgaton of the mpact that portfolo sze has on rsk (volatlty) s of contnung nterest n real estate markets (see Byrne and Lee (1999) for a revew). The general approach uses the returns from a sample of propertes and then smulates portfolos of varous szes, usually wth equal-weghtng, and then calculates the average level of rsk for each portfolo sze. The averaged results usually ndcate that an ncrease n portfolo sze s accompaned by a reducton n portfolo volatlty and that most of the reducton occurs wthn the frst 0-40 propertes, after whch any fall n rsk level s margnal. The advce to an nvestor portrayed n these averaged smulaton results s to hold a portfolo contanng relatvely few propertes. It can be argued that ths general approach s defcent because an ndvdual nvestor owns only one portfolo and results based on the average are not really relevant to hs/her partcular case, whch may be substantally dfferent from the average. Indeed a few studes have alluded to the fact that the smulatons themselves dsplay a good deal of varablty around the mean portfolo rsk level, Barber (1991), Cullen (1991) and Byrne and Lee (1999). Ths s especally so for portfolos of a small sze. Thus nvestors who have reled on the prevous studes based on average portfolo results can have lttle confdence that ther portfolo wll dsplay the same level of portfolo rsk as that suggested by averaged results. In addton, studes based on equal-weghted smulatons may be felt to be rrelevant to property portfolos whch are typcally value-weghted. Indeed the work of Morrell (1993b), Schuck and Brown (1997) and Byrne and Lee (1999) suggests that value-weghted portfolo are sub-optmal because the portfolos have a hgher total rsk n comparson to equal-weghted portfolos. Smulatons, even value-weghted, probably seem unrealstc to most practtoners. Results from actual data would be desrable therefore and yet there s remarkably lttle emprcal evdence based on actual property portfolos. Ths s n spte of the fact that the few studes n the UK whch have used the returns from actual portfolos, Cullen (1991) and Morrell (1993a, 1997), suggest that the amount of rsk reducton n real estate portfolos s lmted and that a large level of varablty exsts around the mean portfolo rsk level, especally for small szed portfolos. The objectve of ths paper s to extend ths analyss further by studyng the affect of portfolo sze on rsk reducton usng actual property data over the perod 1981 to 1996.. Rsk Reducton Markowtz (195) showed that the varance of a portfolo of N assets s gven by: where: σ σ p = portfolo varance N N N p = w σ + w w j = 1 = 1j= 1 j σ = the varance of asset ; ρ j, = the correlaton between assets and j; N = the number of assets. σ σ ρ j j (1)
Equaton 1, n the specal case where σ equals the average standard devaton σ and ρ j equals the average correlaton coeffcent ρ for all, becomes: N σ p = w σ + w w = 1 N N = 1j= 1 j It wll be noted that for any gven w, the sum of all w for Substtutng nto the last term of equaton produces: j σ ρ () j must equal (1- ). w N w p = 1 σ = σ ρ + σ ( 1 ρ) (3) In addton f we assume equal weghtng equaton 3 smplfes to: σ 1 = σ ρ + σ (1 ) (4) N p ρ Equaton 4 shows that the total rsk (varance) of a portfolo can be broken down nto two components. The frst component, represented by the frst term on the RHS of equaton 4, cannot be elmnated by ncreasng the number of nvestments n a portfolo. Ths component of rsk s therefore common to all nvestments and s called systematc or market rsk, see Elton and Gruber (1977). In contrast the second term on the RHS of equaton 4, can be effectvely elmnated by ncreasng the number of nvestments n a portfolo. The elmnaton of ths part of total rsk wll be acheved rapdly, snce as N ncreases 1/N approaches zero very quckly. Ths component of rsk s labelled non-market or resdual rsk. The level of rsk reducton that can be acheved n a portfolo s lmted, or bounded by, the rsk of the market. Hence the reducton n rsk wthn a portfolo of ncreasng sze can only come about by the elmnaton of the non-market or resdual varance nherent n the nvestment. Two basc methods have been suggested n the lterature to measure the mpact of sze on portfolo rsk, the frst graphcal and the second statstcal. In the graphcal approach researchers usually smulate portfolos of ncreasng sze (typcally equally-weghted), based on ndvdual data, and calculate the level of rsk (standard devaton or varance of returns) for each portfolo. The ndvdual portfolo rsks are then averaged and plotted aganst portfolo sze. The resultant graphs typcally show an ntal rapd declne n average portfolo rsk whch then tapers away towards some market level 1. The statstcal approach follows much the same procedure wth a large number of portfolos of ncreasng sze smulated from ndvdual data from whch some measures of the rsk are calculated for each portfolo and the resultant values for each portfolo sze averaged. The researchers may then dsplay the results graphcally and/or more usually employ regresson methodology to derve the relatonshp between the measure of rsk and the portfolo sze. 1 See for example Jones Lang Wootton (1986); Barber (1991); Cullen (1991); Myer, Webb and Young (1997) and Byrne and Lee (1999) for studes n the property market and Evans and Archer (1968): and Wagner and Lau (1971); Johnson and Shannon (1974); Tole (198) and Lloyd, Hand and Modan (1981) for studes n equty and bond markets. 3
The frst regresson approach adopted n the lterature was suggested by Evans and Archer (E&A) (1968) and smply relates the standard devaton (total rsk) of a portfolo to the number of nvestments held usng the followng equaton: σ = α + β(1/ N) (5) E&A argue that the regresson of total rsk (standard devaton) on 1/N shows the mpact of portfolo sze on the non-market rsk wthn the portfolo because any fall n the value of total rsk must be a consequence the elmnaton of non-market rsk wthn the portfolo. E&A found that ths model explaned 98.6% of the varablty of the mean standard devaton for US stock market securtes. Ther analyss also showed that the reducton n total rsk was substantal up to portfolos of eght to ten securtes, after whch the standard devaton of the portfolo became asymptotc to the rsk of the market. The second method, suggested by Wagner and Lau (W&L) (1971), uses the proporton of market rsk n a portfolo to ndcate the reducton n rsk acheved by ncreasng portfolo sze. W&L use the Sngle Index Model (SIM) to determne how much of the varablty n returns of a portfolo can be explaned by some market ndex: R = α + β R + e (6) m where: R s the return of the portfolo ; R m s the return on the market portfolo; β s the ndex of systematc rsk of portfolo α, s the ntercept coeffcent and e s a random error term, whch has an expected value of zero. The coeffcent of determnaton ( R ) of such a regresson ndcates the proporton of varablty n returns that can be explaned by the market. The amount that s unque or specfc to the portfolo tself, the non-market rsk, s gven by (1 R ). A regresson of R on 1/N usng equaton (7) ndcates the number of nvestments to hold to reduce the amount of non-market rsk to an acceptable level: R = α + β(1/ N) (7) W&L usng ths approach agan found that the ncrease n R was substantal up to eght or ten securtes after whch the gan s margnal. Based on the E&A and W&L approaches the ntal mpresson s that securty portfolos need have only a few nvestments to be fully dversfed down to the market level. In the real estate market, usng the above approaches, Brown (1988, 1991) fnds that for equal-weghted portfolos after about ten propertes have been ncluded wthn a portfolo the reducton n rsk whch can be acheved by holdng more propertes dmnshes dramatcally. Ths supports the fndngs of E&A and W&L. However Brown also acknowledges that ths reducton n portfolo rsk s lkely to be hampered by the ndvsblty of ndvdual propertes and the preference of fund managers to follow value-weghtng schemes n developng ther portfolos. Brown fnds that value-weghted portfolos are less dversfed 4
than equal-weghted portfolos and so would requre more propertes to brng rsk down to the systematc (market) rsk level. Usng the regresson approach of W&L, Brown fnds that even assumng an equal-weghtng scheme t would be necessary hold more than 00 propertes to acheve a R of 95 per cent. Only 45 shares are requred to acheve the same level n the UK stock market. The effect of value-weghtng would be to requre an even greater number of propertes (Byrne and Lee, 1999). However, Tole (198) suggests that the results of E&A and W&L and by assocaton those of Brown can be msleadng for nvestors as they are based on averagng technques essentally desgned to obtan satsfactory regressons coeffcents. Such averagng, by ts nature, reduces the varablty of the data and so magnfes the statstcal ft of the regressons. It can be argued that prevous approaches are potentally flawed because of the fact that an ndvdual nvestor owns only one portfolo and results based on the average are not really relevant to hs/her partcular case, whch may be substantally dfferent from that average (Newbould and Poon, 1993). Tole (198) presents a dagram showng that the orgnal data used by E&A based on 60 smulatons for each portfolo sze from 1 to 40 securtes dsplay a wde varaton around the average standard devaton level. The smulaton results of Byrne and Lee (1999) suggest a smlar pcture n the UK property market. Byrne and Lee fnd that for the 0 asset level there s stll a 5% chance of havng a rsk level approxmately 15-5 percent above the average, dependng on the sector or regon chosen and the weghtng scheme employed. At the 40 asset level the devaton from the average s stll 11 to 18 percent. Only at the 00+ asset portfolo s the devaton small enough to be gnored. When Tole (198) appled the approach of E&A to 55 smulated portfolos, wthout averagng the ndvdual standard devatons, the resultng R was only 14%, rather than the 98.6% found from the averaged regressons. Such a low level of statstcal ft mples that the confdence an nvestor can have that ther portfolo wll behave n the same way as the average s lkely to be weak to say the least. Consequence an ndvdual nvestor who follows the advce contaned n prevous studes whch are based on the results of average portfolo rsks may be exposng themselves to potentally much greater rsk than they ntend. Tole argues that the true measure of rsk reducton n a portfolo should not be the average but the worst poston. Ths s smlar to the argument of McDonald (1975) who suggests most nvestors see dversfcaton as desgned to reduce the probablty of ex post returns beng an adverse surprse. Investors who wsh to avod such adverse surprses from an unfortunate selecton, would be better off lookng at the worst case rather than the average standard devaton or varance when consderng the rsk reducton effect of ncreasng sample szes. Ths s a vew shared by Fung (1979). In the approach of E&A ths wll be the upper bound of the spread around the average. In the case of the W&L approach t wll be the lower bound. Usng ths defnton of rsk reducton Tole fnds that 5-40 securtes are requred to acheve a level of rsk reducton wthn the US stock market rather than the 8-10 suggested prevously. In any case property professonals may feel that the results of smulatons, even when valueweghted, are not really representatve of the dversfcaton strateges actually followed by fund managers. It may be felt that the results based on the performance of actual funds may be markedly dfferent from the output of smulatons. Indeed ths seems to be the case. In partcular Cullen (1991) fnds that when portfolo rsk, measured by standard devaton, s plotted aganst the number of propertes wthn a portfolo, volatlty s not reduced as fund sze ncreases. However when specfc rsk s plotted aganst portfolo sze Cullen fnds that ths measure of rsk does declne as fund sze ncreases, although agan the graphs dsplay a wde varaton around the average level. Cullen concludes that although large scale dversfcaton does appear to preclude the hghest standard devaton levels ths s only acheved for portfolos of 50 propertes or above. Small portfolos, wth less than 100 propertes, exhbt very hgh volatlty levels as well as very low ones. Morrell (1993a, 5
1997) draws smlar conclusons, fndng that although there s a general tendency for the largest funds to acheve hgh levels of rsk reducton many also dsplay hgh levels of specfc rsk. Small funds n contrast can show remarkably hgh levels of rsk reducton even wth relatvely few propertes n ther portfolos. Morrell (1997) also fnds that the average systematc rsk ( R ) n the 16 portfolos analysed was only 81%, wth a quarter of the funds havng R values less than 76%. Thus work on actual property portfolos shows that the theoretcal benefts to portfolo rsk of ncreasng portfolo sze are dffcult to acheve n practce. In the lght of ths work and the crtcsms of Tole (198) any analyss needs f possble to be based on the rsk levels of actual portfolos rather than averaged smulated results n order to obtan a better representaton of the mpact of portfolo sze on portfolo rsk levels. Ths study nvestgates whether t s possble to acheve a reducton n portfolo rsk down to that of the market and the number of propertes needed to obtan ths level usng actual property portfolos over the perod 1981-1996. 3. Data The data used n ths paper come from two sources. Frst the IPD Annual Dgest and second the Local Markets Report (Investment Property Databank (IPD), 1998). These sources offer dfferent levels of aggregaton of the ndvdual property data upon whch the results are based, to protect confdentalty. The IPD database, at the end of 1998, contaned 13,933 propertes wth an aggregate value of 75.3bn. The data n the Local Markets Report provde the lowest level of publshed aggregaton wthn the IPD database. The data consst of the total returns on propertes n the three sectors, Retal, Offce and Industral at varous locatons, gvng a total of 39 property portfolos. The locatons are based for the most part on local authorty boundares drawn up n the 199 Local Government Act. These ndvdual local authorty portfolos were combned nto mxed-town level property portfolos on a value-weghted bass to form 111 portfolos. In contrast the Annual Dgest presents the results of the UK real estate market n a number of aggregatons. Frst by the three property types; Offces, Retal and Industral, across the standard regons of the UK, wth further dvsons for the London area to account for the domnance of ths regon n UK property funds. These are 41 dfferent property portfolos. These ndvdual property types were combned nto 1 mxed-property portfolos. Secondly by 8 market segments, as used by IPD to analyss portfolo performance. The hghest level of aggregaton s nto the three property types, Retal, Offce and Industral. In total therefore the analyss presented below s based on 587 property portfolos varyng n sze from 6 to 6806 ndvdual propertes. The summary statstcs are presented n Table 1. Ths table prompts the followng comments. Frst as the level of aggregaton ncreases the data do show a fall n total rsk (varance) towards the market level, but the declne s small and depressngly slow. So for example even at the hghest levels of aggregaton there s stll some way to go to reach the market rsk level, mplyng that property funds managers are lkely to requre very large numbers of propertes to attan the level of rsk of the market. Although the spread of the data, as measured by the range (max-mn), around the average level of total rsk declnes wth the ncrease n aggregaton, agan the data stll shows a large amount of varablty at even the hghest levels of aggregaton. Even on ths bass there can be lttle confdence on the part of property fund managers that ther portfolo wll behave lke the average, as suggested by Tole (198). The level of market rsk (R-squared) wthn the lowest aggregated or Local Market data s very varable from almost zero to over 90 per cent. Ths ndcates that the market explans very lttle the varablty n property returns at an ndvdual level, hence the varablty of ndvdual property returns s manly due to ther unque or specfc factors: locaton, locaton and locaton. Even so as portfolo sze ncreases average R-squared values also ncrease as the nfluence of the market on portfolo returns 6
begns to bte. Nonetheless the mpact of the market even on the hghest aggregated portfolos s stll low compared wth the mpact of a stock market ndex on equty portfolos. Ths beng so, property portfolos are unlkely to be able to track the returns of the market, especally f they are small szed portfolos of less than say, 100 propertes. Fnally t wll be notced that the amount of specfc rsk n the portfolos tends to declne wth ncreased portfolo sze but agan the effect s slow and the data stll dsplays large levels of varablty n even the largest aggregated data. The followng secton analyses these effects n more detal. 7
Table 1: Summary Statstcs for the Portfolo Sub-dvsons Number of Number of Propertes Total Rsk R-squared Specfc Rsk Sub-Dvsons Portfolos Max Mn Average Max Mn Average Max Mn Average Max Mn Average Local Market Data Retal 06 85 6 4 6.90 3.65 4.59 88.54 16.87 58.94 6.6.41 3.6 Offce 93 403 6 3 6.31 3.9 4.99 91.1 0.31 67.51 5.3.08 3.74 Industral 93 60 6 17 5.96 4.16 5.07 9.97 0.7 64.6 5.54.9 3.90 Mxed 111 300 19 64 5.34 3.55 4.60 94.76 1.08 75.93 4.4 1.74 3.04 Annual Data Standard Regons Retal 14 1570 5 465 5.34 3.88 4.9 86.76 48.55 75.75 3.61.14.79 Offce 16 90 3 65 5.61 3.13 4.79 9.98 19.45 64.44 4..5 3.51 Industral 11 754 3 19 5. 3.89 4.84 83.11 1.4 50.51 4.73 3.11 4.01 Mxed 1 318 48 895 5.05 3.7 4.31 96.71 44.81 73.46 3.49 1.64.75 Segments 8 5510 5 914 5.40 3.81 4.53 97.51 4.54 74.46 4.16 1.34 3.01 Sector Data Number of Propertes Total Rsk R-squared Specfc Rsk Retal 1 6806 4.17 88.0.05 Offce 1 436 5.0 97.66 1.6 Industral 1 174 4.84 75.67 3.43 8
4. Analyss and Results The average number of propertes n each portfolo was calculated over the whole perod from 1981 to 1996. Ths portfolo sze data was compared wth three measures of rsk. The frst of these was total rsk (varance n log form). Secondly a measure of market rsk, the coeffcent of determnaton ( R ), of each portfolo was calculated relatve to the IPD Annual Index. Fnally non-market rsk, or resdual varance (n log form), was calculated usng the followng equaton: RVar = Var(R ) β Var(R ) (8) m where: RVar s the resdual or unsystematc varance of portfolo ; Var(R ) s the varance of returns for portfolo ; Var(R m ) s the varance of market returns and β s the slope of the regresson of return of portfolo on the returns of the market usng equaton (6). A regresson of RVar on the number of propertes was then made, as n equaton (9), to measure the rsk reducton as portfolo sze ncreases: RVar = α + β(1/ N) (9) Usng the data for the 587 portfolos, Fgure 1 shows the mpact of portfolo sze on total rsk (varance n log form). As wll be readly apprecated there s a great deal of varablty n the varance especally at low portfolo szes,.e. less than 100 propertes. Also, as the number of propertes wthn the portfolos ncreases, there s only a mnor reducton n portfolo rsk. Indeed there are a number of portfolos wth portfolo szes n the hundreds that show hgher levels of rsk than for portfolos of less than 50 propertes. Ths supports the conclusons of Cullen (1991) and Morrell (1993a, 1997) that portfolo rsk has lttle to do wth the number of propertes n the portfolo. Fgures and 3 present much the same pcture. Although on average t may be true, portfolo sze does not necessarly lead to a reducton n portfolo rsk n all crcumstances. Ths has mportant ramfcatons for fund management as t mples that two funds wth the same number of propertes are more than lkely to have wdely dfferng levels of rsks (varance) even for portfolos of hundreds of propertes. Even so, ncreasng the number of propertes wthn a portfolo nto the thousands s unlkely to do much to ncrease ther level of confdence. Ths s confrmed n Table by the regressons of the three measures of portfolo rsk on the average number of propertes wthn the 587 portfolos. The regressons progress from the lowest level data sets, the ndvdual Local Authorty (LA) data to the hghest levels of aggregaton, the property type data, where the Overall LA1 data s the combnaton of the ndvdual LA and the Overall LA data also ncludes the mxed-town data. The Overall data regresson ncludes all the data sets. In order to smplfy the presentaton of the data Fgures 1-3 only show the data up to the 400 property level, even though the data contans portfolo szes up to more than 6000 propertes. Graphs showng the full data are avalable on request. 9
The results n Table show the coeffcents of the regressons n equatons 5, 7, and 9, together wth the coeffcent of determnaton ( R ) and the standard error of the regresson. Table 1 shows that the sgns of the beta coeffcents are all the correct and n all but one case are sgnfcant at the 5% level. The level of sgnfcance s partcularly strong for the resdual varance regressons, as suggested by portfolo theory. Rsk does on average declne sgnfcantly as the number of assets n the portfolo ncreases. However, as wll be apprecated the amount of varablty explaned (adjusted R ) by all the regressons s small and consderably below that produced by prevous studes usng averaged data. Panel A of Table shows the regresson results for total rsk on number of propertes. The coeffcent of determnaton (adjusted R ) s small, never more than 7.5% and can be as low as 1.3%. As a result the standard errors around the regresson results are very hgh. It s ths whch leaves the nvestor wth lttle confdence that ther portfolo wll behave lke the average. The number of propertes wthn a portfolo has lttle or no mpact on the level of total rsk of the portfolo, confrmng the results of Cullen (1991) and Morrell (1993a, 1997). Table : Results of Regresson of Rsk on the Number of Propertes Rsk T-stat. T-stat. Adjusted Standard Measure Alpha Beta Alpha Beta R-Squared Error % Panel A: Log. Varance LA Retal 4.43.65 70.60.99 3.73 0.45 LA Offce 4.87.0 53.61 1.47 1.7 0.45 LA Industral 4.88.43 5.44.6 4.8 0.38 Overall LA1 4.60 3.04 93.11 4.55 4.80 0.48 Overall LA 4.57 3.36 17.68 6. 6.99 0.45 Overall 4.56 3.40 151.54 6.94 7.45 0.46 Panel B: R-Squared LA Retal 0.71-1.95 35.1-6.87 18.38 0.15 LA Offce 0.73-1.00 1.7-1.93.91 0.17 LA Industral 0.70-0.71 15.70-1.37 0.93 0.18 Overall LA1 0.71-1.33 41.63-5.77 7.65 0.17 Overall LA 0.75-1.76 57.93-9.00 13.78 0.16 Overall 0.74-1.69 67.37-9.45 13.1 0.17 Panel C: Resdual or Specfc Rsk LA Retal 3.17 7.37 41.0 6.76 17.9 0.56 LA Offce 3.49 4.43 5.11.11 3.67 0.68 LA Industral 3.51 5.05.14.76 6.70 0.64 Overall LA1 3.30 6.40 5.35 7.50 1.41 0.61 Overall LA 3.09 8.56 6.97 11.54 0.86 0.6 Overall 3.08 8.80 73.50 1.90.06 0.63 10
The results for the measure of systematc rsk, n Panel B, are only slghtly better, wth the goodness of ft coeffcent reachng a maxmum of 14% but the lowest s less than 1%, for the Industral property data. The average R, as ndcated by the Alpha, s only 74%, slghtly less than that reported by Morrell (1997). As can be seen n Fgure, there s a great deal of varablty around the regresson lne, especally at the lower portfolo szes. For example, at the 0 property level the R-squared values range from 0 to 9 percent. However, at approxmately the 300 property level the spread s less, rangng from 56 to 95 per cent. There s a tendency for the amount of systematc rsk n any portfolo to ncrease as the number of propertes ncreases, but the effect s only margnal and even very small portfolos can show much hgher levels of market rsk than the largest portfolos. Ths suggests that most f not all portfolos wll dsplay hgh levels of trackng error, that s the varablty of ther portfolo returns relatve to some benchmark of performance. Ths s lkely to be the case even for portfolos of thousands of propertes. The trackng errors of small portfolos are lkely to be huge, even for value-weghted portfolos. Fund managers may fool themselves nto thnkng that they must be trackng the market f they dsplay the same value-weghtng as the market across property types and regons, when n fact they should have very lttle confdence that ths s really the case. In contrast the fgures n Panel C for specfc rsk (resdual varance n log form) show generally much stronger results, the adjusted R-squared values reachng a hgh of per cent. Even so the results are stll weak n comparson wth those reported n prevous work based on averaged smulatons. Agan, hundreds f not thousands of propertes wll be needed for fund managers to feel confdent that the man nfluence on ther portfolos returns s that of the market rather than the unque or specfc factors n the property returns. The hgh levels of non-market rsk wthn even the largest portfolos suggest that the performance of a property portfolo s due to some unque or specfc features (of ts component parts). Ths has mportant mplcatons for performance measurement servces that try to attrbute the fund manger s contrbuton to property portfolo performance. If the rsk level of even the largest funds s a consequence of ther unque characterstcs, rather than the nfluences of the market, t becomes dffcult to solate those features of fund performance whch are due to structure or polcy (sector and regonal weghtng relatve to the benchmark) and the selecton or property component (the manager s skll n choosng the rght property). The regresson results confrm the mages presented n Fgures 1 to 3. Increasng portfolo sze leads on average to a reducton n rsk, however measured. But the one area where the effect s greatest s n the reducton of the specfc or resdual rsk n the portfolo, as suggested by portfolo theory. Nonetheless the results even for the specfc rsk regressons are weak, confrmng the fndngs of Tole (198) that wthout the averagng effect typcally found n smulaton studes the regressons generally lack power and dsplay large standard errors. 11
5. Concluson Ths paper has re-evaluated the potental for rsk reducton n the UK real estate market for property portfolo across the whole spectrum of portfolo szes n numerous regons and types usng actual data over the perod 1981-1996. When the full data set s used the statstcal sgnfcance of the regressons of three standard measures of portfolo rsk on sze s greatly reduced. The results confrm the fndngs of Cullen (1990) and Morrell (1993a, 1997). Property portfolos of a large sze, tend on average, to have lower rsks than small szed portfolos, but portfolos wth relatvely few propertes can have very hgh or very low rsk. An ndvdual nvestor who uses the advce contaned n prevous studes whch are based on the results of average portfolos may be exposed to greater rsk than they antcpate. Fund managers can have lttle confdence that ther portfolo wll dsplay the same level of rsk as the average. Ther portfolo could be sgnfcantly hgher or lower than they antcpated, especally at small szes. The results suggest that for fund managers to be confdent that ther portfolo wll have a rsk level more lke the average they need to hold portfolos of a consderably greater sze than they mght expect, or can sensbly hold. The results of prevous studes whch suggest that only 0-40 propertes are needed to reduce the rsk of a property portfolo down to the market level are a sgnfcant underestmate. The actual fgure s more lkely to be around 400-500 propertes, a portfolo sze well above that of even the largest fund n the UK. Sze alone does not necessarly lead to a reducton n portfolo rsk. Clearly other factors are of greater mportance. 1
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Fgure 1: Average Number of Propertes and Portfolo Varance 6 5 Predcted Regresson Lne Based on All the Data Total Rsk 4 3 Number of Propertes 0 100 00 300 400 15
Fgure Average Number of Propertes and R-Squared 1.0 0.8 R-Squared 0.6 0.4 Predcted Regresson Lne Based on All the Data 0. 0.0 Number of Propertes 0 100 00 300 400 16
Fgure 3 Average Number of Propertes and Specfc Rsk 6 5 Predcted Regresson Lne Based on All the Data 4 Specfc Rsk 3 Number of Propertes 1 0 100 00 300 400 17