ABSTRACT TRADING RULES IN HOUSING MARKETS WHAT CAN WE LEARN? GREG COSTELLO Curtn Unversty of Technology Ths paper examnes the applcaton of tradng rules n testng nformatonal effcency n housng markets. The paper revews and extends the work of Lnneman (1986) and Londervlle (1998) to an emprcal analyss of Western Australan housng data. Whereas most prevous studes have focused upon hedonc methods to predct future house prces, ths study also ncorporates repeat-sales data so that predcted and actual sellng prces of ndvdual propertes are avalable for analyss. The results support the vew that dosyncratc nformaton dffuson processes exst wthn housng markets. These processes are nfluenced by levels of aggregaton wthn the data across spatal regons. Keywords: Housng, tradng rules, nformaton effcency, repeat sales INTRODUCTION Is t possble to consstently dentfy and trade under-prced propertes proftably n Australan housng markets? Ths paper tests ths proposton emprcally by adaptng a tradng (buyng) rule prevously appled by Lnneman (1986) and Londervlle (1998) to North Amercan housng markets. The tradng rule s ntutvely appealng n the current era of electronc nformaton for housng n that predcted results can be evaluated aganst actual results by examnaton of the hstorcal record of housng transactons that nclude repeat-sales of the same housng unt. Informaton and commentary concernng house prces have appeared frequently n the popular press durng the recent era of rapd house prce growth n Australan housng markets. Major natonal and state newspapers regularly provde reports of housng market actvty. It s apparent n many press reports that some commentators beleve that specfc market segments and/or suburbs mght be under-prced relatve to others; therefore bargan buyng opportuntes exst. Ths vew promotes a percepton of neffcent housng markets, n that sutably nformed partcpants can trade proftably on the rght nformaton. Ths study extends the work of Lnneman (1986) who developed a tradng strategy to test housng market effcency usng hedonc regressons of recent transactons as a model to predct future house prces. In ths way, t s possble to dentfy homes that are undervalued at the tme of sale. If under-valued propertes can be dentfed and traded 136 Pacfc Rm Property Research Journal, Vol 11, No 2
proftably, then an opportunty to earn abnormal profts exsts and the housng market s neffcent. Lnneman s orgnal (1986) study was lmted by data problems, n that owners estmates of house values were used n assocaton wth actual sale prces. Londervlle (1998) used repeat-sales data to overcome ths problem. Ths study extends a smlar tradng rule to examne whether results vary accordng to levels of spatal dsaggregaton of the data. THEORY AND RELATED LITERATURE The central theme of ths paper relates to Fama s (1970) effcent markets hypothess (EMH) paradgm for testng how nformaton nfluences asset prces. Fama argued that t was not enough to suggest that markets were neffcent purely because nformaton nfluenced prces. To demonstrate that a market s neffcent, there must be some way of explotng the value of nformaton so that nvestors can earn abnormal returns. Numerous tradng rule strateges have been developed to test levels of market effcency n many dfferent asset markets, although there have been very few studes applyng rgorous tradng rules to housng markets. Effcency n the housng market s desrable for the same reasons that effcency s desrable n other product or securtes markets. If prces provde accurate sgnals for purchase or dsposton of housng assets, then they facltate the correct allocaton of scarce fnancal resources. Several authors have suggested that f real estate markets are nformatonally effcent, then the dstrbuton of market prces should accurately reflect the full range of characterstcs and rsks assocated wth ndvdual real estate assets (Gau (1987), Gatzlaff and Trtroglu (1995)). Ths defnton of real estate market effcency nfers that n an nformatonally effcent real estate market, errors n the prcng of real estate assets are random. Ths proposton s tested specfcally n the emprcal tests that follow. Meese and Wallace (1994) proposed an alternatve vew. They examned the present value relaton (PVR) for housng. They argued that the effcent market condton n housng markets requres the real expected return for home ownershp to equate to the real homeowner cost of captal. Ths argument suggests that another mplcaton of the effcent markets hypothess s that n an effcent housng market, observed prces are also correctly captalsed rents for those housng assets. Ths proposton s relevant to the emprcal study that follows, n that the methodology provdes an mputed rental beneft that mght be usefully appled n future tests of the PVR n housng markets. Gatzlaff and Trtroglu (1995) provded a comprehensve revew of studes examnng real estate market effcency. They argued that real estate market effcency should not be vewed as an absolute concept, rather more one of degree. Gven housng market mperfectons, t s lkely that housng markets are not as effcent as securtes markets and that some regonal housng markets are more or less effcent than others. It s also lkely that housng markets captalse dfferent types of nformaton at dfferent rates and Pacfc Rm Property Research Journal, Vol 11, No 2 137
n dfferng degrees. Some nformaton may be fully captalsed, whereas prces may fal to reflect some other sets of nformaton. The emprcal study to follow utlses spatal dsaggregaton as a tool for analyss. Housng markets can be dsaggregated accordng to varous crtera, where smlarty s most commonly defned by spatal regon. The mplct assumpton beng that the spatal market segment represents a relatvely homogenous asset market and the varance decomposton of housng prces has a prncpal fxed effect accordng to the spatal (neghbourhood) crtera defnng segmentaton. Where a housng market s dsaggregated accordng to spatal crtera, then the dstance between neghbourhoods becomes a determnant of prce dsperson and spatal dstrbuton of prces becomes relevant. There have been some mportant emprcal studes testng nformaton dffuson processes n and between specfc geographc market segments (Clapp, Dolde and Trtroglu (1995), Dolde and Trtroglu (1997)). These studes provde evdence of ratonal learnng behavour n housng markets. Ther results ndcate that housng market partcpants learn most from past prces n ther own spatal regons. Trtroglu and Clapp (1994) showed emprcally that spatal barrers can alter nformaton dffuson processes n housng markets. More recently, spatal dstrbuton models have been used to examne varyng autocorrelaton propertes of house prces (Gllen, Thbodeau and Wachter, 2001). Tradng rules have been utlsed n several studes examnng effcency n housng markets (Gau (1985 and 1987), Case and Shller (1989), Lnneman (1986)). Gau s ntal studes utlsed small specfc sets of data, whereas Case and Shller used large sets of data for major US ctes. They used several models to test whether observed seral dependence n house prce seres could be exploted. Frst they used a model of housng returns wth an ndex supplemented wth rental nformaton and reported that the seral dependence n the tme seres could be used n some ctes to generate profts hgher than those that could be acheved wth a nave buy and hold strategy. They reported consderable varaton n the results for tests between dfferent ctes ndcatng that these tests are probably more approprate for use wth dsaggregated data. Case and Shller (1989) also used a tradng rule procedure wth prce changes estmated from a repeat-sales ndex. The procedure nvolved regressng changes n ndvdual house prces between tme t and a subsequent perod on nformaton avalable at tme t 1. Under the effcent market hypothess, anythng n the nformaton set at tme t should have no explanatory power for ndvdual house prce changes subsequent to that date. Case and Shller argued that t s qute natural to set up a test for the effcent market hypothess n ths way, as an nvestor wantng to explot seral dependence n a tme seres needs to be able to forecast future house prces accurately. Lnneman (1986) provded an mportant contrbuton by ntroducng a cross-sectonal approach that addressed some of the specfc ssues assocated wth real estate market structure and ndvdual house prce formaton processes. The buyng rule used hedonc 138 Pacfc Rm Property Research Journal, Vol 11, No 2
regressons of recent transactons as a model to predct future house prces. The key thrust of ths tradng strategy s that there are two types of error assocated wth the use of hedonc analyss of a housng market. The frst s defned as analyst or measurement error, assocated wth errors-n-varables or ncorrect specfcaton of the hedonc model. The second s transactor error, where market partcpants ether sell too cheaply, or pay too much. The expected transactor error component would be zero n a perfectly nformed market. Lnneman argued that t s emprcally mpossble to dstngush between analyst and transactor errors. Hs tradng rule procedure s based upon the mportant assumpton that as the explanatory power of hedonc prcng equatons ncreases, then analyst error wll decrease. Ths work was further developed by Londervlle (1998) who ntroduced methodology to analyse rsk-adjusted buyng rules. DATA AND METHODOLOGY The Lnneman (1986) tradng rule used hedonc regressons of recent transactons as a model to predct future house prces. Followng the hedonc prcng lterature, the value of an ndvdual property V can be represented: where V f Z ; a U (1) Z s a vector of relevant structural and neghborhood trats, a s a parameter vector representng shadow prces of these trats and U s a random error term. Lnneman s tradng strategy dentfed two types of error from equaton (1), analyst or measurement error (nose) and transactor error, where market partcpants ether sell too cheaply or pay too much. The key element of the tradng rule s n dentfcaton of transactor errors, whch provde arbtrage opportuntes for nformed nvestors. Indvdual property nformaton can be used n perodc cross-sectonal analyss to dentfy sellers who undervalue ther housng unts, U 0. If these propertes can be purchased at or below the askng prce and subsequently resold at or above market value U 0, then arbtrage profts are possble. By usng a large repeat-sales sample, t s possble to analyse the hstorcal record of house sales by applyng ths tradng rule. Lnneman s full tradng strategy model also accounted for the mpact of captal gans tax and transacton costs. He concluded that propertes wth negatve estmaton errors dd on average earn hgher apprecaton returns. However, when the level of transacton costs assocated wth US housng were at market levels, on average excess returns could not be acheved. There are several dffcultes assocated wth applyng Lnneman s full tradng strategy n Australan housng markets. Frst, captal gans tax assumptons cannot be appled as a constant to all house sales as owner-occuped housng s exempt. Second, over a longer Pacfc Rm Property Research Journal, Vol 11, No 2 139
sample perod, there are varatons n levels of transacton costs that make the selecton of these varables arbtrary. Londervlle (1998) also recognsed these problems when testng a longer tme-seres of repeat-sales and smplfed the tradng strategy. Consder the logarthmc functonal form shown as equaton (1). The sze of the error, U requred for postve profts, wll also depend on the level of transacton costs and taxes on the sale of the property relatve to the prce of the property. As an example, n logarthmc form, a level of U 0. 10 as a level of estmaton error for undervalued propertes mples a prce of 90% of the estmated value gven the hedonc equaton. In ths case, the purchaser s buyng a property at a 10% dscount on the estmate of market value. To test the tradng rule, a comprehensve data set of selected repeat-sales for the Perth metropoltan area was provded by the W.A. Valuer General s Offce (VGO). Accurate hedonc data seres requre sutable data for ndvdual house characterstcs. The data set was selected on the bass of avalablty of nformaton for specfc structural characterstcs of ndvdual housng unts. Intally, cross-sectonal hedonc regressons were estmated usng twelve months of data for perodc estmatons. The model was appled to the aggregate Perth housng market wth the estmatng equaton beng of the followng form: LnP t 0 1Ln( AREAt ) 2Ln( AGEt ) 3Ln( CARSt ) t (2) In ths model, LnP t represents the natural logarthm of sellng prce for property at tme t and the varables Ln AREA ), Ln( AGE ), Ln( CARS ) are the natural logarthms ( t t t for the buldng area, buldng age and number of car bays for property at tme t and t represents the regresson dsturbance term. The functonal form shown n equaton (2) s a functonal form that can be appled effectvely to the aggregate Perth data for all sample perods. The results for the cross-secton regressons used to predct sellng prces are summarsed n Table 1. 140 Pacfc Rm Property Research Journal, Vol 11, No 2
Pacfc Rm Property Research Journal, Vol 11, No 2 141 Table 1: Summary of hedonc regressons Year N S.E.E. Adj R 2 Constant (t) LN_area (t) LN_age (t) LN_cars (t) 1988 1,667 0.23 0.68 7.03 (78.7) 0.95 (49.5) 0.00 (-0.6) 0.22 (5.6) 1988-89 3,397 0.23 0.67 7.20 (111.8) 0.93 (66.9) -0.001 (-0.3) 0.31 (10.9) 1989 3,065 0.19 0.74 7.42 (126.2) 0.90 (71.1) -0.01 (-2.8) 0.34 (14.0) 1989-90 3,115 0.21 0.69 7.69 (125.4) 0.85 (63.8) -0.025 (-6.9) 0.22 (9.0) 1990 3,640 0.22 0.67 7.72 (130.8) 0.84 (65.5) -0.03 (-9.3) 0.15 (6.8) 1990-91 4,061 0.23 0.65 7.48 (121.8) 0.88 (66.6) -0.027 (-7.8) 0.19 (8.6) 1991 3,895 0.24 0.63 7.48 (114.2) 0.88 (62.8) -0.03) (-6.4) 0.23 (9.4) 1991-92 4,022 0.24 0.64 7.42 (115.1) 0.90 (64.9) -0.029 (-7.3) 0.19 (8.0) 1992 4,623 0.25 0.64 7.32 (120.3) 0.93 (70.8) -0.03 (-7.9) 0.16) (7.7) 1992-93 5,049 0.26 0.65 7.33 (127.3) 0.93 (75.1) -0.023 (-6.7) 0.19 (9.7) 1993 5,712 0.26 0.68 7.20 (129.9) 0.96 (81.4) -0.02 (-6.4) 0.22) (12.5) 1993-94 6,385 0.27 0.67 7.15 (127.3) 0.99 (82.7) -0.022 (-6.5) 0.21 (11.9) 1994 5,687 0.28 0.65 7.24 (116.2) 0.98 (74.0) -0.02 (-6.5) 0.18) (9.0) 1994-95 4,183 0.29 0.65 7.10 (93.7) 1.01 (63.0) -0.017 (-3.8) 0.17 (7.6) 1995 3,638 0.30 0.66 7.04 (83.4) 1.02 (57.9) -0.02 (-4.4) 0.17 (6.7) 1995-96 3,284 0.31 0.64 7.20 (77.6) 1.00 (51.5) -0.039 (-7.0) 0.17 (6.2) 1996 2,789 0.34 0.61 7.37 (68.8) 0.97 (43.3) -0.06 (-8.4) 0.20 (6.3) 1996-97 2,359 0.35 0.59 7.42 (61.4) 0.96 (38.1) -0.058 (-7.6) 0.16 (4.6) 1997 2,299 0.34 0.61 7.28 (61.2) 0.99 (39.8) -0.05 (-6.4) 0.18 (5.3)
2,199 7.02 1.05-0.039 0.21 1997-98 0.65 0.33 (58.8) (42.0) (-5.3) (6.8) Regresson results: A new regresson was run every 6 months usng a twelve-month sample perod. Snce the data used s repeat-sales, there s a lack of subsequent (second) sales n the later perods of the sample. To overcome ths problem, the sample was truncated as at the end of 1998. Ths cross-secton specfcaton enables a sutable sample perod to be used wth a suffcent volume of transactons to assure statstcal valdty. In order to further test the tradng strategy, the hedonc data was also segmented accordng to suburb. Four suburbs, Scarborough, Maylands, Como and South Perth, were selected as the four hghest rankng suburbs for volume of transactons n the sample perod tested. By selectng spatal data sets, the nfluence of regonal dfferentals that were present n the aggregate data for equaton (2) s removed, thereby removng a major source of analyst error n the resdual terms. To mprove the explanatory power of the cross-sectonal regressons and reduce the level of analyst error for each suburb, addtonal varables were added to equaton (2) so that varyng complex hedonc models are estmated for each perod. Here the emphass s on maxmsng the explanatory power of the regressons. The method used was to estmate stepwse regressons n order to select the best combnaton of statstcally sgnfcant explanatory varables. In summary, the average adjusted R squared result for these complex hedonc models was n the vcnty of 80% - 90%, whereas for the smple hedonc models n Table (1) t was n the vcnty of 60% - 70%. The standard error of estmate (SEE) for the complex models was sgnfcantly lower than for the smple model results shown n Table (1). Each regresson equaton was used to predct values of propertes that sold durng the subsequent sx months based upon ther ndvdual hedonc characterstcs. The dfference between the actual sellng prce of each property and the predcted prce usng the prevous perod hedonc equaton s e the estmaton error: where yt e y P (3) t t 1 s the predcted prce of property usng tme t, the sx month cross-secton of hedonc data and P t 1 s the actual sellng prce of property n the subsequent sx month sample perod. It s mportant to note that ths term s not a regresson resdual but the estmaton error from predctng future sale prces from hstorcal data from the prevous perod. 142 Pacfc Rm Property Research Journal, Vol 11, No 2
For further analyss, the ndvdual sales are grouped nto four portfolos accordng to the sze of e. ( e.10, 0.10 e 0, 0 e 0.10 and e 0. 10 ) 0 The tradng strategy assumes that a property wth a negatve estmaton error of -0.10 has a value of approxmately 90% of true market value accordng to sale prces of smlar propertes n the recent past. If ths dfference s due to prcng error by the seller, then an arbtrage proft opportunty (excess return) exsts f the property can be sold at or above 100% of ts true market value at the subsequent sale. Excess returns, ER, were calculated: ER R Rf (4) where R s a nomnal annualsed nternal rate of return (IRR) for each par of sales of an ndvdual property and Rf s a proxy measure for the rsk-free rate of return durng the relevant holdng perod. Consstent wth methodology of the fnance lterature, Rf s the pre-tax yeld at the ntal purchase date for a government bond wth maturty of comparable length to the holdng perod was subtracted from R to obtan the excess return. To complete the emprcal analyss, the results are tested for statstcal sgnfcance. Consstent wth Londervlle (1998), the results are analysed wth the Sharpe rato (rewardto-varablty rato) to adjust the returns for rsk and test whether there are statstcally sgnfcant dfferences between the returns for any of the portfolos. The statstcal test for dfference between two Sharpe ratos for two portfolos and j s the hypothess test where H : Sh Sh 0 and the test statstc assumes a Z dstrbuton. The hgher the 0S1 j value of the rato, the better the portfolo has performed, snce the return per unt of rsk s hgher. 1 R 1 sale _ t1 sale _ t 12 1 h 1 12 12 1 where sale_t represents the ntal sellng prce, sale_t1 represents the subsequent sellng prce and h represents the holdng perod expressed n dscrete calendar months. Pacfc Rm Property Research Journal, Vol 11, No 2 143
EMPIRICAL RESULTS The results n ths secton are presented sequentally so that frst the tradng rule as appled to the aggregate Perth housng market are dscussed, followed by the spatally segmented market samples. From equatons (3) and (4), Table 2 summarses the excess returns and the mean estmaton error e at the tme of purchase for each of the four portfolos for the aggregate Perth data. Note that there are more postve estmaton errors than negatve errors n these tables. Ths s because e s an estmaton error and not a regresson resdual. An mportant feature of the excess returns s the postve skewness n the dstrbuton. For ths reason, both the mean and medan are reported as measures of central tendency. In Part A, the full sample s analysed. One fact that s mmedately evdent s the very hgh standard devaton of excess returns. Whereas the mean of -2.2% ndcates that on average excess returns are close to zero, the standard devaton of 88.9% confrms very sgnfcant varaton n ndvdual property returns. It can be seen that the greatest varaton s wthn the e < - 0.10 undervalued portfolo where the mean excess return s -0.1% and the standard devaton s 142.7%. All other portfolos confrm lower level negatve excess returns and lower relatve standard devatons. Ths suggests the possblty of sgnfcantly dfferent levels of rsk between portfolos. The man cause of ths varaton n excess returns becomes evdent when Parts B and C of Table 2 are analysed. Here the sample s further dvded nto short holdng perods of one year or less and longer holdng perods of more than one year. For short holdng perods, the mean excess return s 34.5% and when the e < - 0.10 undervalued portfolo s used, t s 54.8%. These returns are accompaned by standard devatons of 349.3% and 529.8% respectvely. The other portfolos are also accompaned by postve excess returns and hgh standard devatons. The medan excess return fgures are much lower for all groups, but stll sgnfcantly postve. Ths confrms hgher excess returns and postve skewness n the excess returns for short holdng perods. 144 Pacfc Rm Property Research Journal, Vol 11, No 2
Table 2: Return and estmaton-error statstcs for varyng portfolos Part A: Full Sample Range of Est. Error Total sample e < - 0.10-0.10 < e <0 0 < e < + 0.10 e > + 0.10 Excess Return (%) Estmaton Error Mean Medan Std. Dev. Mean Medan Std. Dev. N -2.2% -5.1% 88.9% 0.03 0.02 0.28 37,086-0.1% -5.1% 142.7% -0.26-0.23 0.14 11,830-3.0% -5.6% 79.8% -0.05-0.05 0.03 5,650-4.1% -5.4% 20.7% 0.05 0.05 0.03 5,736-3.0% -4.8% 31.6% 0.31 0.26 0.18 13,870 Part B: Short Holdng Perods One Year or Less Range of Est. Error Total sample e < - 0.10-0.10 < e <0 0 < e < + 0.10 e > + 0.10 Excess Return (%) Estmaton Error Mean Medan Std. Dev. Mean Medan Std. Dev. N 34.5% 5.1% 349.3% 0.03 0.01 0.33 2,364 54.8% 5.7% 529.8% -0.30-0.27 0.17 847 38.6% 4.2% 337.1% -0.05-0.05 0.03 311 16.4% 3.5% 86.0% 0.05 0.05 0.03 288 20.1% 5.3% 118.3% 0.36 0.30 0.21 918 Pacfc Rm Property Research Journal, Vol 11, No 2 145
Range of Est. Error Total sample e < - 0.10-0.10 < e <0 0 < e < + 0.10 Part C: Long Holdng Perods More Than One Year Excess Return (%) Estmaton Error Mean Medan Std. Dev. Mean Medan Std. Dev. N -4.7% -5.3% 6.5% 0.03 0.02 0.27 34,722-4.3% -5.4% 7.2% -0.26-0.22 0.13 10,983-5.4% -5.8% 5.7% -0.05-0.05 0.03 5,339-5.2% -5.6% 6.1% 0.05 0.05 0.03 5,448 e > + 0.10-4.6% -5.0% 6.3% 0.31 0.26 0.18 12,952 Propertes are dvded nto portfolos based on the sze of the estmaton error (actual transacton prce less prce predcted by most recent regresson pror to sale). Excess return for each property s measured as annualsed property apprecaton less the yeld at the tme of the ntal purchase on a government bond of smlar duraton to the holdng perod between property transactons. 146 Pacfc Rm Property Research Journal, Vol 11, No 2
In Part C, t s evdent that when only long holdng perods are consdered the mean excess returns are negatve for all portfolos, there s less postve skewness and the standard devatons are very much lower. The calculaton of excess returns s derved from house prce changes excludng any mplct housng dvdend accrung to the homeowner or nvestor. If t s assumed that ths dvdend s n the regon of 4% - 5% per annum, then the excess returns for all groups n the sample are very close to zero. Ths would be the expectaton for an effcent housng market. The benefts of debt fnancng and tax relef are also not consdered n ths tradng strategy and t s lkely that these factors would also ncrease returns to some nvestors. These results ndcate qute clearly that there are ncentves to nvestors n short-term tradng for some housng unts. In Table 2 Part B, the e < - 0.10 undervalued portfolo shows clearly the hghest level of returns ndcatng that knowledge of an ndvdual housng unt s estmaton error s useful nformaton that can be used by an nvestor. However, the accompanyng very hgh standard devaton confrms a correspondng hgher level of rsk. All other portfolos for short holdng perods n Part B confrm postve excess returns ndcatng that the regresson model used contans analyst error, n that postve estmaton errors (over-prced propertes) are stll beng traded short term for postve excess returns. An mportant consderaton here s that there s lkely to be consderable captal expendture nvolved wth these short-term transactons. The data have been screened so that only buldngs wth the same man buldng area are used n the sample, confrmng that there have been no addtons to the structure. It s not possble to check for nternal renovatons. The lkely scenaro s that many of these short-term transactons are housng unts that are purchased, substantally renovated and quckly re-sold. The level of captal expendture nvolved together wth transacton costs would further reduce the levels of excess returns recorded here. Londervlle (1998) also used the Sharpe rato (reward-to-varablty rato) to adjust the returns for rsk and test whether there are statstcally sgnfcant dfferences between the returns for any of the portfolos. The hgher the value of the rato, the better the portfolo has performed, snce the return per unt of rsk s hgher. The results for these tests are reported n Table 3. Pacfc Rm Property Research Journal, Vol 11, No 2 147
Table 3: Sharpe rato analyss for dfferent portfolos Range of Estmaton Error at Tme of Purchase Part A: Sharpe Rato Values All Holdng Perods 1989-1998 Sharpe Rato Short Holdng Perods 1993-1998 Long Holdng Perods 1989-1998 Total sample e < - 0.10-0.10 < e <0 0 < e < + 0.10-0.09 0.45-0.84 0.06 0.30-0.77-0.08 0.17-0.95-0.49 0.30-0.81 e > + 0.10-0.40 0.52-0.86 Notes: The Sharpe rato s calculated as the mean excess return earned by propertes n the portfolo dvded by the standard devaton of the excess returns for propertes n the portfolo. 1. The short holdng perod sample was restrcted for several groups n the early sample perods, wth a lack of observatons for 1989-1993. The short holdng perod sample uses the 1993-98 sample perod to overcome ths problem. Part B: Statstcal Sgnfcance of Dfferences n Sharpe Ratos Range of ZSh Compared wth Portfolo of All Propertes for Same Tme Perod Estmaton Error at Tme of Purchase All Holdng Perods Short Holdng Perods Long Holdng Perods e < - 0.10-0.10 < e <0 0 < e < + 0.10 0.14 0.15 0.07 0.01 0.28 0.11 0.40 0.16 0.03 e > + 0.10 0.31 0.07 0.02 Notes: Z Sh s a test statstc to measure whether the Sharpe rato for each portfolo s sgnfcantly dfferent from the Sharpe rato for the portfolo of all propertes. None of the test statstcs s statstcally sgnfcant, leadng to the concluson that the rsk-adjusted performance s the same for all portfolos, ncludng those of undervalued propertes. 148 Pacfc Rm Property Research Journal, Vol 11, No 2
Unlke the results for excess returns n Table 2, there are not clear patterns emergng wth the Sharpe ratos. Hgher value ratos ndcate a lower volatlty n excess returns. It s evdent n Part A that the Sharpe ratos for all holdng perods are very low for the total sample and the undervalued e < - 0.10 and -0.10 < e <0 portfolos. The ratos are hgher for the other groups. The ratos are also hgher when only short holdng perod and long holdng perod transactons are measured. The results for short holdng perods should be treated wth some cauton, as the sample was restrcted for several groups n the early sample perods, wth a lack of observatons for 1989-1993. The short holdng perod sample uses the 1993-98 perod to overcome ths problem. The ratos for long holdng perods use the same tme seres as for all holdng perods and are sgnfcantly hgher confrmng that the volatlty n excess returns decreases when short holdng perods are excluded from the sample. In Part B of Table 3, the statstcal sgnfcance of the dfference between rato values s analysed to assess whether the performance of any portfolo s sgnfcantly dfferent than the performance for the total sample. The Z Sh statstc tests the null hypothess that the dfference n the Sharpe rato for two portfolos s zero. The statstc s compared wth the standard normal dstrbuton. None of the ndvdual Sharpe ratos s sgnfcantly dfferent from the Sharpe ndex for the total property portfolo at even a 10% level. In ths case, the null hypothess that the rsk-adjusted return performance of all portfolos was the same could not be rejected. A number of prevously mentoned studes confrm that nformaton dffuson processes wthn housng markets are sgnfcantly nfluenced by spatal proxmty. Ths suggests that market partcpants are more lkely to base prcng decsons on the bass of local nformaton sets determned by spatal crtera than by factors nfluencng the aggregate housng market n general. Can these local nformaton sets be used to develop tradng strateges to explot nformatonal neffcences? Mght these results for a tradng rule be more effectve f regonal data sets were used? In order to further test ths applcaton of the tradng strategy, the hedonc data were segmented accordng to suburb. Four suburbs, Scarborough, Maylands, Como and South Perth, were selected on the bass that these suburbs were the four hghest rankng suburbs for volume of transactons n the sample perod tested. By selectng spatal data sets, the nfluence of regonal dfferentals that were present n the aggregate data s removed, thereby removng a major source of analyst error n the resdual terms. Table 4 summarses the excess returns for each of the four suburbs and the four portfolos. The full sample of all holdng perods s analysed n Part A consstent wth the analyss of the aggregate data n Table 2. Z Sh Pacfc Rm Property Research Journal, Vol 11, No 2 149
150 Pacfc Rm Property Research Journal, Vol 11, No 2 Error Range Table 4: Spatal regons - return statstcs for varyng portfolos Part A: All Holdng Perods All Suburbs Scarborough Maylands Como South Perth Mean Med S N Mean Med S N Mean Med S N Mean Med S N Mean Med S N Total sample -1.4-4.6 35.8 6,882-1.7-3.9 24.7 2,150-2.3-5.3 47.5 2,029-2.4-5.0 24.7 1,455 1.7-3.9 40.5 1,248 e < - 0.10 3.8-3.4 65.5 1,595 2.9-2.9 50.0 448 3.8-4.1 89.5 535 2.8-3.7 39.4 269 5.9-2.5 54.7 343-0.10 < e <0-2.2-4.6 25.6 1,375-2.2-3.8 11.5 488-3.4-5.2 18.2 388-3.1-5.1 10.9 293 1.7-4.3 57.3 206 0 < e < + 0.10-3.1-4.6 18.1 1,560-2.8-3.7 8.3 578-5.2-6.3 8.8 394-2.2-4.9 31.5 379-1.2-3.7 17.2 209 e > + 0.10-3.4-5.2 14.8 2,352-3.4-4.9 10.8 636-4.6-5.7 12.4 712-4.9-5.7 9.6 514 0.1-4.4 23.7 490 Error Range Part B: Short Holdng Perods Only All Suburbs Scarborough Maylands Como South Perth Mean Med S N Mean Med S N Mean Med S N Mean Med S N Mean Med S N Total sample 31.0 6.9 121.4 537 22.9 6.9 89.4 140 26.8 4.7 152.9 185 25.1 7.2 84.0 107 55.3 19.9 126.4 105 e < - 0.10 63.0 11.8 205.3 147 59.6 12.6 183.7 30 64.0 7.5 267.6 57 57.3 18.2 124.4 22 67.4 25.5 150.7 38-0.10 < e <0 24.0 6.1 88.9 100 17.3 6.4 35.2 28 13.3 1.7 54.5 35 15.1 8.7 29.1 25 89.3 12.4 227.6 12 0 < e < + 0.10 18.1 5.9 65.5 97 11.8 8.3 18.9 34 5.6 5.7 20.3 30 38.8 8.3 124.8 22 29.7 4.0 66.3 11 e > + 0.10 16.8 4.4 42.0 193 11.1 3.8 27.0 48 10.7 2.7 32.2 63 5.1 1.8 29.0 38 41.9 24.1 63.4 44 150 Pacfc Rm Property Research Journal, Vol 11, No 2
Pacfc Rm Property Research Jpurnal, Vol 11, No 2 151 Error Range Part C: Long Holdng Perods Only All Suburbs Scarborough Maylands Como South Perth Mean Med S N Mean Med S N Mean Med S N Mean Med S N Mean Med S N Total sample -4.1-4.8 7.0 6,345-3.4-4.3 7.3 2,010-5.2-5.7 7.3 1,844-4.6-5.3 6.0 1,348-3.2-5. 6.7 1,143 e < - 0.10-2.2-3.8 8.8 1,448-1.2-3.2 9.2 418-3.4-4.6 8.7 478-2.1-4.0 9.2 247-1.8-2.9 8.1 305-0.10 < e <0-5. -4.9 6.1 1,275-3.4-5. 6.5 460-5.1-5.4 6.7 353-4.8-5.3 4.4 268-3.7-4.7 5.6 194 0 < e < + 0.10-4.5-4.7 5.9 1,463-3.8-3.9 6.0 544-6.1-6.4 6.4 364-4.7-5.1 5.0 357-2.9-4.0 5.7 198 e > + 0.10-5.2-5.5 6.4 2,159-4.6-5.3 6.9 588-6.0-6.1 6.7 649-5.7-5.9 5.1 476-4.0-4.8 6.2 446 Ths table provdes results for excess returns estmated wth a cross-sectonal tradng rule for repeat-sales. Four sample suburbs were selected. Results are gven for each ndvdual suburb sample and for a pooled sample of all suburbs. Propertes are dvded nto portfolos based on the sze of the estmaton error (actual transacton prce less prce predcted by most recent regresson pror to sale). Excess return for each property s measured as annualsed property apprecaton less the yeld at the tme of the ntal purchase on a government bond of smlar duraton to the holdng perod between property transactons. Short holdng perods are one year or less. # Tests of statstcal sgnfcance usng Sharpe ratos are completed for long holdng perods (all suburbs) n Table 5. Pacfc Rm Property Research Journal, Vol 11, No 2 151
One fact that s mmedately evdent s the lower standard devaton of excess returns than that reported for the aggregate data. For all suburbs, the mean of -1.4% ndcates that on average excess returns are close to zero. The standard devaton of 35.8% confrms sgnfcant varaton n ndvdual property returns, although ths s much lower than the 88.9% standard devaton reported for the aggregate data. The greatest varaton n excess returns s wthn the e < - 0.10 undervalued portfolo where the all suburbs mean excess return s 3.8% and the standard devaton s 65.5%, agan much lower than for the aggregate sample. All other portfolos confrm lower level negatve excess returns and lower relatve standard devatons. In general, ths trend s consstent for all of the ndvdual suburb samples except South Perth where three of the portfolo groups have postve excess returns. Ths confrms the results from the analyss of the aggregate data where there are sgnfcant dfferent levels of rsk between portfolos. As wth the aggregate data, the man cause of the varaton n excess returns becomes evdent when Parts B and C of Table 4 are analysed. Here the sample s further dvded nto short holdng perods of one year or less, and longer holdng perods of more than one year. For all suburbs, the short holdng perod mean excess return s 31% and when the e < - 0.10 undervalued portfolo s used t s 63%. These returns are accompaned by standard devatons of 121% and 205% respectvely. These returns are smlar to those for the aggregate data shown n Table 2; however the standard devatons are much lower. When examnng short holdng perods only, the other portfolos are also accompaned by postve excess returns and hgh standard devatons. Ths result s consstent for all ndvdual suburb samples. The medan excess return fgures are much lower for all groups but stll sgnfcantly postve. Ths confrms hgher excess returns and postve skewness n the excess returns for short holdng perods. In Part C of Table 4, t s evdent that when only long holdng perods are consdered, the mean excess returns are negatve for all portfolos, there s less postve skewness and standard devatons are very much lower. If the mplct rental dvdend were ncluded, then on average the long-term nvestment returns shown n Part C would be slghtly postve or very close to zero. Ths s a consstent trend for all of the suburb samples. Consstent wth results for the aggregate sample, there are qute clearly ncentves to nvestors n short-term tradng for some housng unts. In Part B, the e < - 0.10 undervalued portfolo shows clearly the hghest level of returns, whch suggests that knowledge of an ndvdual housng unt s estmaton error s useful nformaton. The accompanyng hgh standard devatons confrm a correspondng hgher level of rsk. As noted prevously, there s lkely to be consderable captal expendture nvolved wth these short-term transactons. The lkely scenaro s that many of these short-term transactons are housng unts that are purchased, substantally renovated and quckly re-sold. 152 Pacfc Rm Property Research Journal, Vol 11, No 2
The results for Part C are nterestng n that they dsplay a clear herarchy n longer run returns based on levels of estmaton error. The hghest levels of excess returns (lowest negatve numbers) all apply to the e < - 0.10 undervalued portfolos, and the excess returns decrease as expected wth the changes n estmaton error, a clear pattern for the majorty of suburb samples. It s notable that the same pattern s not so evdent for smlar tests wth the aggregate data summarsed n Table 2. It s qute clear that there are patterns of varyng levels of return but there are also varyng levels of rsk, as confrmed by the varatons n the standard devatons. Are these dfferences n returns sgnfcant on a rsk-adjusted bass? Consstent wth analyss of the aggregate data the Sharpe rato (reward-to-varablty rato) tests are presented n Table 5. The data used for these tests conssts of the all suburbs data for long holdng perods only (see Table 4) as results for the aggregate data confrm that there s too much volatlty n returns caused by the nfluence of short holdng perods for there to be any statstcally sgnfcant dfferences between portfolos. As wth the analyss of the aggregate data n Table 3, none of the ndvdual portfolo Sharpe ratos s sgnfcantly dfferent from the Sharpe rato for the total property portfolo at even a 10% level. The null hypothess that the rsk-adjusted return performance of all portfolos was the same could not be rejected. Whle t s clear that ndvdual propertes dentfed as undervalued accordng to ther estmaton error earn on average hgher excess returns, the hgher rsk assocated wth these portfolos ndcate that t s dffcult to acheve abnormal rsk-adjusted profts. Pacfc Rm Property Research Journal, Vol 11, No 2 153
Table 5: Spatal regons - Sharpe rato analyss for dfferent portfolos Range of Estmaton Error at Tme of Purchase Total sample e < - 0.10-0.10 < e <0 0 < e < + 0.10 Sharpe Rato All Suburbs Long Holdng Perods 1989-1998 -0.61 ZSh Compared wth Portfolo of Total Sample for Same Tme Perod _ P-value -0.16 0.45 (0.65) -0.72 0.12 (0.90) -0.72 0.11 (0.91) e > + 0.10-0.86 0.25 (0.80) Notes: The Sharpe rato s calculated as the mean excess return earned by propertes n the portfolo dvded by the standard devaton of the excess returns for propertes n the portfolo. Z Sh s a test statstc to measure whether the Sharpe rato for each portfolo s sgnfcantly dfferent from the Sharpe rato for the portfolo of all propertes. None of the test statstcs s statstcally sgnfcant, leadng to the concluson that the rsk-adjusted performance s the same for all portfolos, ncludng those of undervalued propertes. _ CONCLUDING SUMMARY AND OPPORTUNITIES FOR FURTHER RESEARCH In general, these results are consstent wth Lnneman (1986) and Londervlle (1998) n that they confrm that the estmaton error for a property can be used to dentfy propertes that may be undervalued and wll on average earn hgher excess returns than other propertes. The ablty to effectvely dentfy under-valued propertes s mproved wth smaller spatal regon data sets. Whle the Sharpe rato tests ndcate that ths nformaton cannot be used consstently to earn abnormal returns, these results provde some mportant nformaton and drectons for further research. These results make t clearly evdent that there are ncentves to short-term tradng and the results of ths tradng are mproved by dentfyng undervalued propertes based on estmaton error. There s a lot of nose present wth the data n the form of undentfed captal expendture, and debt fnancng, but t s clear that ths short-term tradng s an mportant segment of actvty wthn the market. As much of ths s lkely to be renovaton actvty, t s clear that these short-term transactons carry hgher levels of rsk. Does ths ndcate that the market for these propertes s neffcent? The housng market s unlke the stock market as only a very small number of partcpants can be consdered as 154 Pacfc Rm Property Research Journal, Vol 11, No 2
actve traders. The majorty of partcpants mght be classfed as consumers of housng servces and not traders. In terms of Fama s (1970) dscusson of market effcency, ths tradng actvty s probably closest to the strong-form of market effcency. It s lkely that nsde operators, full-tme housng market partcpants who possess an ntmate knowledge of local markets undertake much of ths short-run tradng actvty. In many cases, they mght be nvestng ther full tme labour as well as captal, confrmng hgher levels of rsk. Past prce and publcly avalable nformaton on property characterstcs can be used effectvely to dentfy under-valued propertes and these propertes can be effectvely traded to yeld excess returns. It s also lkely that captal expendture mpacts on longer-term transactons. The ndvdual propertes that are dentfed as under-valued are lkely to have hgher levels of physcal obsolescence assocated wth the buldngs. Ths wll requre hgher levels of captal expendture to mantan the buldngs n the longer term. The varyng levels of captal expendture for longer holdng perods s lkely to nfluence the standard devatons and therefore t s lkely that the under-valued segments of the market wll exhbt hgher levels of rsk. As ths has been a desktop analyss wthout any feld nspectons, t remans unclear whether these returns are hgher on a rsk-adjusted bass. It s lkely that the explanatory power of prcng models could be further mproved by traders wth the ad of physcal nspecton of propertes and detaled local knowledge of specfc regons. Ths knowledge could be used n specfyng addtonal ndependent varables such as specfc sub-regons wth access to vews or nfluental factors operatng wthn the regon. It s possble that some parts of ths methodology can be further adapted to examne the present value relatonshp (PVR) wthn housng markets and also to construct some new varables that can be used n further tme seres analyss of housng markets. The present value relaton for housng (PVR) examnes the nfluence of the user cost of housng over tme. An mplcaton of the effcent markets hypothess s that n an effcent housng market, prces are correctly captalsed rents. The calculaton of excess returns n equaton (4) s derved from house prce changes excludng any mplct housng dvdend accrung to the homeowner or nvestor. The results ndcate that n general for holdng perods of longer than one year, excess returns for ndvdual propertes calculated on ths bass are negatve. In an effcent housng market, f the dvdend to housng D were to be added to the left hand sde of equaton (4), then excess returns would be zero. ER D R Rf D 0 (5) Under the PVR, ths would be the expectaton for an effcent housng market as prces would reflect correctly captalsed rents and opportuntes to explot excess returns would Pacfc Rm Property Research Journal, Vol 11, No 2 155
not exst. If t s assumed that housng markets are effcent and that excess returns do not exst, ER = 0, then we can abbrevate equaton (5) to: D R Rf (6) Wth equaton (6), we are able to back out an assumed mplct annual rental dvdend, D, for ndvdual propertes from a par of repeat-sales. Ths varable D s related to a specfc holdng perod for an ndvdual property wthn a specfc tme perod and provdes a number of opportuntes for further research. Intally ths varable can be used wth aggregate cty-wde data n tme seres analyss to examne how the mplct rental dvdend mght vary over tme n perods of varyng demand for housng. The results n ths study suggest that varyng levels of nformatonal effcency exst wthn housng markets and some of these varatons are explaned by spatal nfluences. If ths varable s used to analyse specfc market segments, the results n ths study suggest that there wll be systematc varatons that wll provde useful further nsghts as to the nature of nformatonal effcency n housng markets. REFERENCES Case, K. E., and Shller, R.J. (1989). The Effcency of the Market for Sngle-Famly Homes, The Amercan Economc Revew, 79, 125-137. Clapp, J.M., Dolde, W., Trtroglu, D. (1995). Imperfect Informaton and Investor Inferences from Housng Prce Dynamcs, Real Estate Economcs, 23, 239-269. Clapp, J.M., Trtroglu, D. (1994). Postve Feedback Tradng and Dffuson of Asset Prce Changes: Evdence from Housng Transactons, Journal of Economc Behavour and Organzaton, 24, 337-355. Dolde, W., and Trtroglu, D. (1997). Temporal and Spatal Informaton Dffuson n Real Estate Prce Changes and Varances, Real Estate Economcs, 25, 539-565. Fama, E. F. (1970). Effcent Captal Markets: A Revew of Theory and Emprcal Work, Journal of Fnance, 25, 383-420. Gatzlaff, D.H., and Trtroglu, D. (1995). Real Estate Market Effcency: Issues and Evdence, Journal of Real Estate Lterature, 3, 157-189. Gau, G. W. (1985). Publc Informaton and Abnormal Returns n Real Estate Investment, Journal of Amercan Real Estate and Urban Economcs Assocaton, 13, 15-31. 156 Pacfc Rm Property Research Journal, Vol 11, No 2
Gau, G.W. (1987). Effcent Real Estate Markets: Paradox or Paradgm?, Journal of the Amercan Real Estate and Urban Economcs Assocaton, 15, 1-15. Gllen, K., Thbodeau, T., and Wachter, S. (2001)). Ansotropc Autocorrelaton n House Prces, Journal of Real Estate Fnance and Economcs, 23, 5-30. Lnneman, R. (1986). An Emprcal Test of the Effcency of the Housng Market, Journal of Urban Economcs, 20, 140-154. Londervlle, J. (1998). A Test of a Buyng Rule for Underprced Apartment Buldngs, Real Estate Economcs, 26, 537-553. Meese, R., Wallace, N. (1994). Testng the Present Value Relaton for Housng Prces: Should I Leave My House n San Francsco?, Journal of Urban Economcs, 35, 254-266. Pacfc Rm Property Research Journal, Vol 11, No 2 157