Risk and return for single family housing in Sweden Is the average investor compensated for the risk taken when buying a single family house?

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1 Sockholm School of Economics Thesis in Finance Tuor: Professor Peer Englund Presenaion: 08:15, 12 h June, 2007 Venue: Sockholm School of Economics, room 750 Discussans: Jonas Ahlgren, Niklas Edman and Philip Erlandsson Risk and reurn for single family housing in Sweden Is he average invesor compensaed for he risk aken when buying a single family house? Peder Wessel & Erik Jennefel ABSTRACT This hesis invesigaes he relaionship beween risk and reurn in he single family housing marke in Sweden for he ime period I compares he risk adjused reurn of he single family housing marke o he Swedish sock marke. The risk adjused reurn is compared on a five and 10 year ime horizon of invesmen. Addiionally, i is invesigaed wheher meropolian and non-meropolian areas differ in respec o risk, reurn and risk adjused reurn. We find ha here is a posiive relaionship beween risk and reurn in he Swedish single family housing marke for he ime period. However, he risk adjused reurn is lower for he single family housing marke han ha of he Swedish sock marke. I is also found ha he risk adjused reurn in he single family housing marke is higher for a longer ime horizon of an invesmen. Finally, i is esablished ha meropolian areas have a higher risk, reurn and risk adjused reurn han non-meropolian areas in he single family housing marke. ) 19226@suden.hhs.se; ) 80322@suden.hhs.se Acknowledgmens: Foremos, we would like o hank Professor Peer Englund, our uor, for his invaluable inpu hroughou he wriing of his hesis. We would also like o hank Marcelo Carvalho for his helpful insighs regarding saisical analysis. Finally, we would like o hank Annika Wessel for her inpus wihin he field of sudy as well as our fellow sudens who provided helpful commens on our hesis.

2 TABLE OF CONTENTS 1 INTRODUCTION Purpose and research problem Conribuion Ouline 2 2 THEORETICAL FRAMEWORK Risk Cross secional Regressions on Volailiy CAPM Sharpe Raio Facors affecing he reurn of an invesmen in real esae Propery price index Average prices of properies Transacion Price/Assessed Value (K/T) 7 3 PREVIOUS FINDINGS 8 4 HYPOTHESES Risk and reurn relaionship in he single family housing marke Risk adjused reurn on he single family housing marke compared o he sock marke The effec of he ime horizon Risk and reurn in meropolian areas Risk Reurn Risk adjused reurn 10 5 DATA OMXSPI and OMXBGI Risk free rae K/T Assessed Values Propery price index Average useful floor space Mainenance cos for co-operaives Average ren fee Reliabiliy of Daa 13 6 METHODOLOGY Assumpions Time of invesmen Ren Financing of asse Tax Transacion coss Mainenance and operaing coss Depreciaion Ne Ren Dividend payou Meropolian areas Summary of assumpions Mehod of sampling Linking he K/T Esimaion of assessed values Calculaing he reurn on he real esae invesmen 21

3 6.6 Calculaing he reurn on he sock marke invesmen Risk adjused reurn Time horizon of invesmen Comparing risk adjused reurn wihin he real esae marke Comparing risk adjused reurn beween he real esae marke and he sock marke 25 7 ANALYSIS Risk and reurn relaionship in he single family housing marke Risk adjused reurn on he single family housing marke compared o he sock marke The effec of ime horizon Risk and reurn in meropolian areas Risk Reurn Risk adjused reurn 31 8 ROBUSTNESS TEST Non-saionariy Examinaion of residuals 33 9 LIMITATIONS CONCLUSION FURTHER STUDIES REFERENCES Aricles Books Inerne sources APPENDIX Median ren/propery value calculaion Mainenace and repair cos New buil houses (porion of oal sock) 40

4 P. Wessel & E. Jennefel Sockholm School of Economics 1 INTRODUCTION Housing is a subjec ha affecs mos people. I is a cenral par of mos individuals economic environmen and ofen consiues a large par of he individual s economic budge. Housing can be divided ino differen caegories. Firsly, owning or rening, secondly, living as a single family or as muliple families in one propery. A single family house is a residenial srucure designed o include only one dwelling. Basically, he sereoypical family house. A he end of 2005, over 3.7 million people aged beween lived in single family housing 1 in Sweden. Hence, a majoriy of he populaion aged beween lived in a single family house. As such, he caegory single family housing should have he larges amoun of invesors. The real esae marke is a opic ha has gahered much ineres from he media and he general public. Given he naure of real esae, housing has a dual role of boh consumpion and invesmen. From he beginning of year 2000 unil he end of 2006 he nominal general price increase of single-family houses in Sweden has been 86% 2. I is ofen menioned in media ha he price level is rapidly increasing. There is however also a risk in his financial invesmen. This risk is also menioned frequenly in media, bu in erms of a possible upcoming bus in he marke, such as he real esae marke crisis in he end of he 80 s and early 90 s. Despie he srong ineres from boh he general public and he media, here seems o be lile academic research on he acual risk and he analysis on he reurn in comparison o he risk. The reurn, or perhaps more imporanly, he level of risk and he cos of obaining he reurn is a crucial quesion for he invesor. 1 Saisics Sweden (Bosads- och byggnadssaisik årsbok 2007) 2 Saisics Sweden (Propery Price Index) 1

5 P. Wessel & E. Jennefel Sockholm School of Economics 1.1 PURPOSE AND RESEARCH PROBLEM Inspired by he sudy conduced by Cannon, Miller and Pandher 3, which invesigaes and concludes a posiive correlaion beween reurn and volailiy in he U.S. meropolian housing marke, we are ineresed if his holds rue also in he Swedish real esae marke. Furhermore, we would like o look a wheher risk is refleced in he reurns, bu also if i is sufficienly compensaed by looking a he risk adjused reurn. By looking a he risk adjused reurn for single family housing and comparing i wih he risk adjused reurn of he sock marke, he invesor should be able o more accuraely deermine he profiabiliy of he invesmen. 1.2 CONTRIBUTION To our knowledge, our sudy is he only aemp o invesigae he risk and reurn on he Swedish single-family housing marke using he volailiy as explanaory variable. We hope o shed ligh on some facors affecing he profiabiliy of invesing in his marke. 1.3 OUTLINE Firs we presen he heoreical framework summarizing he basic heory on facors affecing invesmens in real esae and financial insrumens. Secondly, we presen previous findings wihin he field from boh he Swedish as well as he U.S. marke. Thereafer, we coninue wih presening our hypoheses followed by a presenaion of he daa and he mehodology. Finally, we provide he analysis ogeher wih a robusness es and conclusions, followed by a discussion abou furher sudies ha can be conduced. 3 Cannon, Miller and Pandher (2006) 2

6 P. Wessel & E. Jennefel Sockholm School of Economics 2 THEORETICAL FRAMEWORK Presened below, are he measuremens of he amoun of risk wihin boh real esae and he sock marke. Then he facors affecing reurn in real esae, which is followed by he mehods of measuring he price developmen wihin real esae. 2.1 RISK Risk can be defined as he deviaion from he expeced reurn of an asse. 4 The volailiy is a measure of his deviaion. Furhermore, he risk can be divided ino wo componens, sysemaic risk and idiosyncraic risk. The firs componen, he sysemaic risk, is a non-diversifiable risk which sems from he marke risk. The marke risk, or he sysemaic risk, is he variance of he marke reurn. The second componen, he idiosyncraic risk, is a diversifiable risk which is due o an individual asse s unique circumsances. Hence by buying a single real esae propery, he buyer akes on boh marke risk plus he individual asse s unique risk. 2.2 CROSS SECTIONAL REGRESSIONS ON VOLATILITY CAPM The Capial Asse Pricing Model (CAPM) is a se of predicions concerning equilibrium expeced reurns on risky asses. 5 The sysemaic risk facor, or bea, is calculaed by aking he covariance beween he asse s reurn and he marke s reurn and dividing i by he marke s variance. Hence: Cov ( r, r ) i M β i = (1) 2 σ M Furhermore, CAPM prices only he sysemaic risk, which should funcion when a porfolio consiss of several asses. However, a normal individual buying a single-family house does no have he opporuniy o diversify his invesmen in he same way as he could when choosing his porfolio on he sock marke. Buying a single-family house normally represens a large porion 4 Bodie, Kane and Marcus (2002) 5 Ibid 3

7 P. Wessel & E. Jennefel Sockholm School of Economics of he individual s wealh and invesing capaciy. Furhermore, an average individual does no hold houses ha he or she does no use for living. Hence, he level of diversificaion is very limied. We herefore hink ha a CAPM model is no he mos appropriae approach o measure he risk and reurn relaionship when i comes o single-family houses. Insead, we will use he normal volailiy 6 measure and compare if reurn is higher when a higher degree of volailiy is presen. We hus use he following model in order o see wha he relaionship beween reurn and volailiy has been during he ime period on single-family houses in Sweden: ri α α Vol i + ε = i (2) Assume r i represens he average annual reurn for he single family houses in region i = 1,..., n( n = ). In order o invesigae he role of volailiy (Vol) on reurns on he propery invesmen, reurns are decomposed using he cross secional regression. Where Vol is he reurn volailiy for he mean priced house in each region i over he years andε is he sandard Gaussian error Sharpe Raio In order o compare wo differen invesmen opporuniies in a saisfacory manner, he Sharpe raio is ofen used. 7 The Sharpe raio is a reward o variabiliy raio which measures he reward, defined as reurn, in consideraion o he risk, defined as volailiy. [ R R f ] [ R R ] [ R R ] E E f S = = (3) Var σ S = Sharpe raio E = Expeced reurn R = Reurn on asse f 6 The sandard deviaion of he change in value of a financial insrumen wih a specific ime horizon 7 Bodie, Kane and Marcus (2002) 4

8 P. Wessel & E. Jennefel Sockholm School of Economics R f =Reurn on risk free asse σ = Sandard deviaion of he asse Hence, he Sharpe raio indicaes how well an invesor is compensaed for he risk aken. We are aware ha he Sharpe raio has is limiaions when i comes o measuring he compensaion of risk when he marke is declining. For insance if wo asses boh los 5% in value bu a differen risk levels, which was bes o inves in beforehand? Facors affecing he reurn of an invesmen in real esae Looking a an invesmen in a single family house i consiss of differen consiuens: Capial reurn - being he increase or decrease in he propery s value over he invesmen horizon. The benefi of no having o pay he opporuniy cos of rening an equivalen house Operaing, mainenance cos and depreciaion of he propery asse Propery ax Transacion coss The capial reurn on a single-family house can be expressed as: P C (4) ( ) = ( T ) T re 1, T P When he ime period is one year, (T-) = 1 and hence equaion (1) becomes: 1 1 P P P P, T ( ) = ( T ) T 1 ( 1) T T T re = 1 = 1 = 1 C (5) P P P P The benefi of no having o pay he opporuniy cos of rening an equivalen house can be expressed as: Opporuni ycos = OC = P oc (6) The mainenance and depreciaion coss are expressed as: Mainenanc e Cos = MC = P mc (7) 5

9 P. Wessel & E. Jennefel Sockholm School of Economics Depreciaion = P δ (8) ( oc mc ) = P nr Ne Ren = OC MC Depreciaion = P δ (9) Propery ax = Assessed Value ax rae (10) For he equaions above, he coss expressed in small leers, for insance coss in percenage of price. The oal yearly reurn on he invesmen can be calculaed by using equaions 4-10: re PT P PT = P = C ( re ) + OC MC Depreciaion Propery ax = ( oc mc ) 1+ P nr Assessed Value ax rae oc, represens he 1+ P δ Assessed Value ax rae = (11) Propery price index During he ime period invesigaed here have been several readjusmens o he assessed value 8 of he propery sock in Sweden. These have been se in 1981, 1990, 1996 and Using he assessed values, Saisics Sweden (SCB) divides he properies ino differen caegories which hen are used wih a weighing sysem consruced by SCB. Using hese wo componens, SCB calculaes he propery price index o show he price developmen in Sweden. An Achilles heel wih he propery price index is ha i requires a cerain amoun of ransacions in each caegory group for he resuls o be reliable. This implies ha he propery price index, hough good as a measure of he price developmen in Sweden, canno be conduced wih reliable resuls on municipaliy level due o he lack of sufficien ransacions wihin each caegory group Average prices of properies Using he average prices of properies sold during a ime period in order o see he price increase over he ime period is no a good measure. The reason for his is ha he real esae marke is a heerogeneous marke and he properies ransaced over ime periods can differ subsanially in 8 Assessed value = The value se for he propery by he ax auhoriies (generally 75% of marke value) 9 SCB (Hur mäer man prisuvecklingen på småhus?) 6

10 P. Wessel & E. Jennefel Sockholm School of Economics for insance sandard and size. Therefore he comparabiliy of properies ransaced during differen ime periods may be quie limied. In order o increase he comparabiliy anoher parameer mus be added. Such a parameer could be he assessed value of he propery Transacion Price/Assessed Value (K/T) The K/T measure is simply he ransacion price divided by he assessed value. Due o he fac ha he assessed value is aking ino accoun facors such as sandard and size, he K/T measure is adjused for he possible differences beween differen properies. Hence, wih he K/T measure i is possible o evaluae he price developmen of properies even if he ransaced properies over ime have differen characerisics. In order o illusrae we use an example: K/T value wihin municipaliy Assessed value of propery Assumed value of propery 2 1,000, ,000,000 = 2,000,000 If he K/T value in a municipaliy is 2, he average ransacion in he municipaliy has a ransacion price wice ha of he assessed value of ha specific propery. Using his informaion, a house owner can assume ha his propery has a value wice ha of he assessed value for his propery. 7

11 P. Wessel & E. Jennefel Sockholm School of Economics 3 PREVIOUS FINDINGS Real esae can be seen as boh an invesmen in an asse class as well as consumpion good. Following he line of reasoning in economics, an asse wih higher risk should also yield a higher reurn. This has been proven o hold also wihin real esae, a leas in he U.S. marke. Cannon, Miller and Pandher conduced a sudy on he meropolian areas in he U.S. marke in 1995 hrough They used a panel daa se comprising of 7,234 ZIP codes falling in 155 urban meropolian saisical areas. Their sudy shows ha higher volailiy is rewarded by higher reurn, which is in conformance wih he general risk-reurn hypohesis. Furhermore, hey find ha housing reurns increase by 2.48% annually for a 10% rise in volailiy. Anoher approach is o esimae he bea coefficien for an asse and use he CAPM in is plain form, or a modified version, and describe he reurn due o he amoun of risk underaken, represened by he bea. According o CAPM, an asse class wih higher sysemaic risk is expeced o generae a higher reurn. However, for he Swedish real esae marke, here have no been any significan resuls proving ha a risk premia is presen. Ahlberg and Lindensjö conduced a sudy in 2005 covering he Swedish house price indices from 1981 hrough 1999 using a CAPM approach. 11 Their sudy could no find significan resuls of a risk premia in he Swedish housing marke. Hence, i seems ha he Swedish real esae marke s reurn is no well explained using CAPM. Insead, we would like o invesigae wheher he reurn in he single family housing marke can be explained by volailiy in Sweden, as i has successfully been done by Cannon e. al. in he U.S. 10 Cannon, Miller and Pandher (2006) 11 Ahlberg and Lindensjö (2005) 8

12 P. Wessel & E. Jennefel Sockholm School of Economics 4 HYPOTHESES We have divided our hypoheses ino four differen caegories: is here a relaionship beween risk and reurn, if so, is he risk appropriaely rewarded, does he risk-reward relaionship depend on ime horizon of invesmen, and finally, is he risk-reurn relaionship differen for meropolian/non-meropolian areas. Las in his secion, a able is presened summarizing he hypoheses. 4.1 RISK AND RETURN RELATIONSHIP IN THE SINGLE FAMILY HOUSING MARKET When invesing, he raional invesor requires a higher reurn for a higher risk. This should hold rue also for house owners, who have invesed in heir home. Do single-family houses show greaer reurn for higher risk? We sae he following firs hypohesis: H1: There is a posiive relaionship beween risk and reurn in he Swedish single family housing marke 4.2 RISK ADJUSTED RETURN ON THE SINGLE FAMILY HOUSING MARKET COMPARED TO THE STOCK MARKET According o normal economic heory, he risk adjused reurn for any invesmen should be he same. Thus he risk adjused reurn of single family housing should be equivalen o ha of he sock marke. Hence our second hypohesis will be: H2: The risk adjused reurn for he single family housing marke is equal o ha of he Swedish sock marke 4.3 THE EFFECT OF THE TIME HORIZON Invesors have differen ime horizons for heir invesmens depending on facors such as age, mobiliy and family condiions. Therefore, we are ineresed in wheher he ime horizon of invesmen affecs he risk and reurn relaionship. If here were no ransacion coss, we would expec here o be no difference in he risk and reurn relaionship depending on he ime horizon of he invesmen. However, we assume ha hese ransacion coss occur. If he ransacion cos can be spread ou over a longer ime period, he effec on he yearly reurn diminishes, making he single family housing invesmen beer off. Furhermore, having a longer ime horizon for he invesmen should lead o a lower risk, making he invesmen more 9

13 P. Wessel & E. Jennefel Sockholm School of Economics profiable. Hence, we expec o find a posiive relaion beween he reurn and a longer ime horizon, while we expec a negaive relaion beween he risk and a longer ime horizon of invesmen for single family housing. Thus i leads us o he following hypohesis: H3: The lengh of he ime horizon of he invesmen affecs he risk and reurn relaionship posiively for he single family housing in Sweden 4.4 RISK AND RETURN IN METROPOLITAN AREAS Risk As menioned earlier, single family housing propery value consiues of wo componens, land and a building. Assuming a building can be moved, i should be valued a approximaely he same price regardless locaion. Land however, canno be moved or creaed, and he supply is herefore in-elasic. Making he land value more dependen on demand and changes in demand will lead o large flucuaions in price. Furhermore, since land canno be moved, is value is dependen on locaion. Assuming ha land is more scarce in meropolian areas, he land value should also be higher in meropolian areas. Ceeris paribus, his should lead o land value making ou a larger porion of he propery s value in meropolian areas compared o non-meropolian areas. From his and given he expeced volaile naure of land, he properies value in meropolian areas should relaively be more volaile compared o non-meropolian areas Reurn Following he reasoning above, he higher expeced risk of an invesmen in single family housing in meropolian areas, should yield higher reurns compared o non-meropolian areas Risk adjused reurn Finally, we expec ha he risk adjused reurns should be equal in meropolian and nonmeropolian areas. From he above reasoning, we sae he following hree hypoheses: 10

14 P. Wessel & E. Jennefel Sockholm School of Economics H4: The risk of an invesmen in single family housing is higher in meropolian areas H5: The reurn of an invesmen in single family housing is higher in meropolian areas H6: The risk adjused reurn of an invesmen in single family housing is equal in meropolian and nonmeropolian areas To conclude, we presen our six hypoheses in he following able: Table 1. Hypoheses H1 There is a posiive relaionship beween risk and reurn in he Swedish single family housing marke H2 H3 H4 H5 H6 The risk adjused reurn for he single family housing marke is equal o ha of he Swedish sock marke The lengh of he ime horizon of he invesmen affecs he risk and reurn relaionship posiively for he single family housing in Sweden The risk for an invesmen is lower in meropolian areas The price increases are higher in he meropolian areas The risk adjused reurn is higher in meropolian areas 11

15 P. Wessel & E. Jennefel Sockholm School of Economics 5 DATA The daa ses colleced are presened below ogeher wih he source of he daa. 5.1 OMXSPI AND OMXBGI We have gahered daily daa for he Swedish Sock Exchange which includes he dividend payous. This daa is only available from unil using he OMXBGI. Therefore, we also gahered daily daa for he res of he ime period from 1981 using he OMXSPI, which does no include dividend payous, in order o ge a full coverage of our sample period. 5.2 RISK FREE RATE The risk free rae in Sweden has been colleced from he Cenral Bank of Sweden for he ime period Due o he fac ha he ineres used by he Cenral Bank has changed over he ime period, we have been forced o gaher hree differen ypes of ineres raes. Firs we gahered he discoun rae for he ime period o , secondly we gahered he marginal rae from unil and finally we gahered he repo rae from unil K/T For he enire ime period daa for K/T values on municipaliy level has been available from Saisics Sweden. 5.4 ASSESSED VALUES Unforunaely, he assessed values on municipaliy level for he ime period previous o 2003 has no been accessible from Saisics Sweden or any oher daa source. Insead, he assessed values had o be colleced on couny level, available from Saisics Sweden for he enire ime period. 5.5 PROPERTY PRICE INDEX The propery price index for Sweden has been gahered from Saisics Sweden for he ime period

16 P. Wessel & E. Jennefel Sockholm School of Economics 5.6 AVERAGE USEFUL FLOOR SPACE The average useful floor space per single family housing uni has been gahered from Saisics Sweden. 5.7 MAINTENANCE COST FOR CO-OPERATIVES Due o lack of daa on he mainenance cos of single-family housing, daa has been gahered for he average mainenance cos for co-operaives as a subsiue for he ime period This daa was available from Saisics Sweden. 5.8 AVERAGE RENT FEE The average ren fee in Sweden was colleced from Saisics Sweden covering he years RELIABILITY OF DATA We believe ha he daa from Saisics Sweden and he Cenral Bank of Sweden is reliable as hese are insiuions wih no privae ineress. Furhermore, we also believe ha he primary daa colleced from OMX mees any requiremens of reliabiliy, since his is a company which specifically deals wih he rus of is daa presened. 13

17 P. Wessel & E. Jennefel Sockholm School of Economics 6 METHODOLOGY Firsly we presen he assumpions ha are made. Secondly, he mehod of sampling and how he K/T values are linked are presened. Thereafer, he mehods applied in he analysis are presened. 6.1 ASSUMPTIONS Time of invesmen I is assumed ha all invesmens will be made in he beginning of a year and all disinvesmens will occur a he end of a year Ren As saed in secion 2.2.3, owning a house and living in i reduces he cos for he invesor of living in erms ha he does no have o pay a ren o a landlord. During he 10 year ime period he average ren over he average propery value for single family houses had a median value of 5.5% which we assume o be he ren porion of he properies hroughou our ime period. 12 Owning a house and using he benefi of living in i consiues a value for he invesor in form of he opporuniy cos of rening an equivalen home. A enan has o pay ren o his landlord, while an owner of a home does no. Hence we price he benefi by quanifying he value of rening an equivalen home. This value should hus be included when calculaing he reurn on he invesmen Financing of asse We assume ha he invesor will no borrow capial in order o make his invesmen. 12 See Appendix

18 P. Wessel & E. Jennefel Sockholm School of Economics Tax Propery ax There was a ax reform in Sweden in 1990 which led o ha he legislaion of real esae ax changed subsanially from he one before. 13 Afer 1990, he ax on housing became a fixed percenage a 1.0% of he assessed value 14. Previously, he ax on housing was consruced such ha boh he ax rae and he amoun of he assessed value o be axed were posiively correlaed wih he owner s income. According o Peer Englund, professor of Banking and Insurance, he median propery owner was axed on 2% of he assessed value, and had a marginal ax rae of 50% during he ime period of Hence, our esimae for he effecive real esae ax during he ime period on he assessed value is 1.0%. Hence, according o our assumpions, he median household s ax pressure has no changed during our sample period. Addiionally, Swedish legislaion has made new buil houses exemp from propery ax he firs five years and he following five he propery is o fify percen exemp from propery ax. Looking a he years beween he median percenage of he single-family house sock made up of houses younger han six years was 1.57% and houses older han five bu younger han 11 years was 1.34% 15. Since more han 97% of he single family house sock is no ax exemp, we decided o assume ha all single family housing is reaed in he same way regarding propery ax, i.e. is liable for propery ax Tax shield If an invesor borrows money in order o make he invesmen, a ax shield occurs. This ax shield is he same regardless if he invesmen is made in a propery or in socks. We have no aken he ax shield in consideraion when comparing he reurn on he sock marke and he real esae marke. 13 Swedish law, SFS (1990:650) 14 Swedish law, SFS (1984:1052) 15 See Appendix

19 P. Wessel & E. Jennefel Sockholm School of Economics Capial gains ax The ax on real esae capial gains compared o sock capial gains has differed hisorically. As an example, afer 1989 he par of a capial gain on propery ha is axed amouns o 70%, whereas he capial gain ax on equiy is based on 100% of he capial gain. A big difference is ha i has been possible for a house owner o avoid capial gains ax by invesing again in anoher real esae propery, of equal or greaer value. Thus, he invesor can effecively for a long period of ime avoid being axed on he capial gain, as long as he capial gain is re-invesed ino anoher propery. 16 This opporuniy has however no been possible wihin he sock marke. Given hese discrepancies, he differences on pre and afer ax reurns can be subsanial. Depending under wha circumsance he invesor has invesed, he afer ax scenario can differ. By his we mean, facors such as age, mobiliy and family condiions. For example, a young person invesing in a house is likely o buy a larger house and hus probably also more valuable house, when saring a family. However, when an old person is moving he migh inves in a smaller and hus probably also less expensive house. Under hese circumsances, he young invesor is able o enroll he capial gain ino he new invesmen, whereas he old person canno do so. Ceeris paribus, he afer ax reurn for he young and old invesor differs subsanially, while hey have exacly he same pre ax reurn. Due o his discrepancy we choose o look a he pre ax reurn on housing. In order o be able o compare he invesmen in he real esae single-family house marke wih he sock marke, we have o be consequen and use he pre ax measure for he sock marke reurn. We leave i up o he invesor o calculae he afer ax scenario (capial gain) according o heir own individual ax circumsances Transacion coss When making an invesmen, cerain ransacion coss occur. For insance, when buying a propery a real esae agen ofen akes ou a fee from he seller and he buyer has o pay a fee in order o be he righful owner of he propery, i.e. regisraion of ile. Hence, he seller pays a 16 Poerba (1984) 16

20 P. Wessel & E. Jennefel Sockholm School of Economics ransacion fee o he real esae agen, while he buyer pays a fee in form of a samp duy. The Swedish legislaion 17 imposes a samp duy of 1.5%, which we assume has been he consan samp duy hrough he ime period Similarly here are ransacion coss for invesing in he sock marke. Usually a brokerage fee is paid when buying or selling a financial insrumen. We assume ha when making he invesmen in real esae, he invesor pays 1.5% of he acquisiion price in samp duy. When exiing he invesmen, he invesor pays 3% of he selling price o he real esae agen. Furhermore, we assume ha when invesing in he sock marke, he invesor pays 0.5% of he ransacion price boh when invesing and exiing Mainenance and operaing coss We believe here are wo main scenarios when invesing in single-family housing. Eiher he invesor will use i for his own living or suble he house o a enan. We assume ha he mainenance coss will be carried by he owner of he propery. Mainenance coss can be such hings as paining, insuring ec. Regardless of wheher he invesor decides o buy a house o live in, o ren a house or o ren an aparmen, we assume he has o pay he operaing coss himself. Hence, we see he operaing coss as a cos ha should no be linked wih he ype of invesmen he invesor decides o make and herefore we exclude operaing cos from our analysis. The median operaing cos of a single-family house during he ime period was 1.12%. 19 Based on his, we assume ha he mainenance cos during he ime period was 1% Depreciaion A single family house propery consiss of wo componens, land and a building. We assume ha he average propery has a value disribuion of fify percen o each of he componens. Land does no depreciae, as do houses. We assume ha a normal house, if mainained, should las 100 years. We herefore assume ha he depreciaion rae of he house is 1% yearly. Hence, he acual depreciaion of he propery should be 0.5% yearly. 17 Swedish law, SFS (1984:404) 18 Nordea (Carina Enedoer) 19 See Appendix

21 P. Wessel & E. Jennefel Sockholm School of Economics Ne Ren Since we assume ha he opporuniy cos of rening, mainenance cos and depreciaion are consan porions of he single family house price ( P ) we also assume ha he ne ren ( ) nr is consan. Using an opporuniy cos of rening a 5.5%, a mainenance cos of 1.0% and a depreciaion rae of 0.5% yearly we end up wih a ne ren of 4.0%: ac = ac = 5.5% mc = mc = 0.5% δ = δ = 1.0% nr = nr = 5.5% 0.5% 1.0% = 4.0% The ne ren of 4.0% for he Swedish real esae marke can be assumed reasonable, since i has been used previously wihin his field of sudy Dividend payou For he 10 year ime period unil , he average yearly dividend payou has been colleced comparing he OMXBGI and he OMXSPI. The average yearly dividend amouned o 2.07%. For he ime period we assume here was a consan yearly dividend payou policy equivalen o 2.0% Meropolian areas We assume ha he following counies are o be considered meropolian areas, Sockholms län, Uppsala län, Skåne län and Väsra Göaland län. This assumpion is made from he fac ha he four larges ciies in Sweden are locaed in hese counies. 21 Furhermore, we assume ha all municipaliies wihin hese counies are meropolian areas. 20 Englund, Hwang and Quigley (2002) 21 SCB (Folkmängden per äor 2005) 18

22 P. Wessel & E. Jennefel Sockholm School of Economics Summary of assumpions Table 2. Assumpions Time of invesmen Ren Ineres rae Liquidiy Invesmens a year beginning and divesmens a year end 5.5% hroughou ime-period Cos of borrowing is he same for he wo ypes of invesmens The same amoun of capial can be borrowed for he wo ypes of invesmens Tax - Propery ax 1% on he assessed value - Tax shield No aken ino consideraion - Capial gains ax Pre-ax measure is used (i.e. cap gains ax excluded) Single family housing: 1.5% samp duy paid a invesmen and 3% Transacion coss agency fee paid a divesmen. Sock marke: 0.5% fee a boh invesmen and divesmen Mainenance and operaing coss 1% of rue value for single family housing Depreciaion 0.5% yearly depreciaion Ne ren 4% Dividend payou 2% Meropolian areas Sockholms län, Uppsala län, Skåne län and Väsra Göaland län 6.2 METHOD OF SAMPLING In he oal daa colleced, all municipaliies exising in Sweden in 2005 are included. However, for reliabiliy reasons, municipaliies wih a leas one year of less han 30 ransacions have been dropped. Thus by keeping daa from municipaliies wih a leas 30 sales per year, he sample for each municipaliy can be assumed o be diversified. From his we assume ha he idiosyncraic risk componen becomes negligible. Furhermore, he municipaliies ha did no exis hroughou he enire ime period of were dropped. 238 municipaliies ou of 290 remain in he sample. 19

23 P. Wessel & E. Jennefel Sockholm School of Economics 6.3 LINKING THE K/T Figure 1 Figure Acual value developmen compared o Assessed Value Adjused vs none adjused K/ T Acual Value of Propery Assessed Value Adjused Unadjused In figure 1 above, he acual price developmen of a propery and is assessed value is shown. To describe he propery value developmen, he K/T value canno be used wihou adjusmens. The K/T values indicae he increase in propery value for he ime period wih he same assessed value. However, when he assessed value is revised, he K/T values will have a endency o show a zig-zag movemen since he denominaor has changed, as illusraed in figure 2. In order o compare over periods of differen assessed values for he same propery, he K/T values mus be adjused using he same assessed value in he denominaor. The assessed value used as base is he assessed value for he propery in The linking is conduced using he following equaion: Z *, j = Z, j AV AV, j 1981, j (12) Where Z * = Adjused K / T value Z = K / T value AV = Assessed Value = Year j = region 6.4 ESTIMATION OF ASSESSED VALUES As saed previously, he average assessed values on municipaliy level were no available. Therefore, an esimaion using he couny level has been made. Each municipaliy has been given he same average assessed value as he couny i belongs o. This leads o cerain limiaions since 20

24 P. Wessel & E. Jennefel Sockholm School of Economics i is likely ha he municipaliies wihin he couny differ and hus he assessed value on he couny level for each municipaliy migh lead o poenially differen resuls han he acual developmen. Figure 3. Biased Z values wihin couny Z value Year True Z value for municipaliy 1 True Z value for municipaliy 2 Z value for municipaliy 1 (couny) Z value for municipaliy 2 (couny) Assume wo differen municipaliies wihin he same couny ha have a differen price developmen of single family housing, illusraed by he solid lines in figure 3 above. The assessed values for he municipaliies are readjused in 1990, based on he price developmen for each municipaliy. The municipaliy wih a beer price developmen over he las assessed value period will have a relaively higher increase in assessed value compared o he municipaliy wih a poorer price developmen. However, as menioned before, he municipaliy assessed values are lacking and insead he couny level of assessed value has been used. The couny level assessed value is a form of average of he municipaliies wihin he couny. This leads o ha he price developmen for each municipaliy wihin he couny is converged oward each oher, as illusraed by he doed lines in he figure. However, his should only affec he daa every ime here is a readjusmen of he assessed values. This occurs four imes over he sample period. 6.5 CALCULATING THE RETURN ON THE REAL ESTATE INVESTMENT In order o ge an esimaion of he prices for each municipaliy hroughou he ime period, we * use he adjused K/T value ( Z ). Using equaion (11) we can replace P wih Z *, obaining: 21

25 P. Wessel & E. Jennefel Sockholm School of Economics re Z Z Z = Z * T * = C * T * 1+ Z ( re ) * * + OC MC Depreciaion Propery ax = ( oc mc ) nr Assessed Value ax rae 1+ Z δ Assessed Value ax rae = (13) To calculae he reurn of he invesmen we use he yearly reurns calculaed according o equaion (10) in order o build an index. Index Index ( 1981) ( T ) = 100 [( 1+ re ) + ( 1+ re ) ( + re )] j j = 100, j + 1, j 1 T, j (14) Where =1982 j = region From his he reurn on he invesmen in he real esae marke, can be calculaed. However, from he indices presened above, adjusmens mus be made for ransacion coss. Index Index ( T = x) ( T = k) ( ma) ( 1 s) Yearly reurn on invesmen = ( x k ) 1 1 (15) Where x = Time of exi k = Time of invesmen ma = Real esae agen fee s = Duy samp For calculaing he risk of he invesmen, he unbiased esimaor of he populaion sandard deviaion has been used. i= 1 ( ) 2 y i y 1 n σ = (16) n 1 However, his measure for risk is no flawless, for insance in periods of consanly high reurns, he sandard deviaion can become large, even hough he invesmen has generaed very high reurns. I can be discussed wheher flucuaions in really high reurns represen risk. j j 22

26 P. Wessel & E. Jennefel Sockholm School of Economics 6.6 CALCULATING THE RETURN ON THE STOCK MARKET INVESTMENT For calculaing he index of he sock marke a similar mehod has been used, as wih he real esae invesmen. Index Index ( 1981) j = 100 ( T ) = 100 [( 1+ re ) + ( 1+ re ) ( + re )] T (17) Where = 1982 From his he reurn on he invesmen in he sock marke, can be calculaed. However, from he indices presened above, adjusmens mus be made for ransacion coss. Index Index ( T = x) ( T = k) ( c k ) ( 1 c ) Yearly reurnoninvesmen = ( x k ) 1 1 (18) Where x = Timeof exi k = Timeof invesmen c c x k = Courageonexiing = Courageoninvesing Assuming ha c = c c he equaion can be rewrien as: x k = ( T = x) ( T = k) ( 1 c) Index 2 Yearly reurnoninvesmen = ( x k ) 1 (19) Index Similarly, as for he risk measure of he real esae invesmen, he unbiased esimaor of he populaion sandard deviaion has been used for he sock marke invesmen. i= 1 ( ) 2 y i y 1 n σ = (20) n 1 As saed previously, his measure for risk is no flawless. I conains he same drawbacks as he risk measure used for he real esae invesmen. x 23

27 P. Wessel & E. Jennefel Sockholm School of Economics 6.7 RISK ADJUSTED RETURN In order o esimae he risk adjused reurn, he Sharpe raio has been used. The Sharpe raio has been menioned in he heory segmen and will be used as described accordingly. 6.8 TIME HORIZON OF INVESTMENT The sample daa covers 25 years, hence he yearly reurn can be calculaed for 24 years. To invesigae differences beween ime horizons, wo differen ime horizons have been used. These are: 10 year ime horizon 5 year ime horizon For he wo ime horizons, he number of invesmen opporuniies varies. For he 10 year ime horizon, here are 15 invesmen opporuniies (1982,1983,,1995,1996) and for he 5 year ime horizon, here are 20 invesmen opporuniies. The yearly reurn for each ime horizon and invesmen opporuniy has been calculaed for each municipaliy. Thereafer, he average of he yearly reurns for each ime horizon has been calculaed, and is assumed o be he expeced reurn for he municipaliy if an invesor holds a propery over he ime horizon. Furhermore, he sandard deviaion of he yearly reurns for each ime horizon has been calculaed for each municipaliy. 6.9 COMPARING RISK ADJUSTED RETURN WITHIN THE REAL ESTATE MARKET The counies are ranked afer heir Sharpe raios for each ime horizon. This was no conduced for he municipaliy level, due o he overwhelming amoun of daa and hus he difficuly of presening i in a meaningful manner. To add o his, we invesigae he differences beween meropolian and non-meropolian areas wihin Sweden, on municipaliy level. This was conduced by esing wheher here were any significan differences in he Sharpe raios beween meropolian and non-meropolian municipaliies. 24

28 P. Wessel & E. Jennefel Sockholm School of Economics 6.10 COMPARING RISK ADJUSTED RETURN BETWEEN THE REAL ESTATE MARKET AND THE STOCK MARKET Using he calculaed Sharpe raios, i has been analyzed wheher he municipaliies have ouperformed he risk adjused reurn for he sock marke during he same ime horizon of invesmen. 25

29 P. Wessel & E. Jennefel Sockholm School of Economics 7 ANALYSIS The empirical analysis is presened below. Each hypohesis is analyzed and discussed separely and in he same order as hey were lised in able RISK AND RETURN RELATIONSHIP IN THE SINGLE FAMILY HOUSING MARKET The risk and reurn relaionship for a 10 year invesmen in he Swedish single family housing marke is ploed in figure 4. The observaions in he figure are he 238 municipaliies kep in he sample. The correlaion beween risk and reurn seems o be slighly posiive, bu o be cerain more saisical calculaions mus be compued. Figure 4. Reurn (%) Risk vs Reurn 10 year invesmen Risk - sd (%) The daa sample consiss of municipaliies wih differing amouns of ransacions per year. The ransacions per year for each municipaliy range beween 30 and 1610 in he kep sample. Thus, i can be assumed ha heeroscedasiciy 22 is presen in our daa. Therefore, he OLS regression was conduced using he robus sandard errors, presened in able 2 below: Table 2. Invesmen Horizon (years) 10 5 Adjused R^ Sandard error Observaions Inercep coefficien Sandard error inercep coefficien P-value of inercep Sd coefficien Sandard error sd coefficien P value of sd Lower end of 95% confidence inerval for sd coefficien Rejec H 0 NO NO 22 Condiional variances of dependen variable are no consan 26

30 P. Wessel & E. Jennefel Sockholm School of Economics This able shows ha for he 10 year ime horizon he correlaion beween risk and reurn is posiive and has a coefficien of Hence for a 10% increase in risk, he reurn increases by 3.30%. This is saisically significan a he 95% level since he p-value is less han The relaionship is posiive also for he five year ime horizon and is saisically significan a he 95% level. Having a 10% increase in risk leads o an increase in he yearly reurn of 7.42%. The large discrepancy beween he risk and reurn relaionship coefficiens may possibly in par be explained by he varying inerceps. The inercep for he 10 year horizon lies close o he risk free ineres rae which had an average of 8.15% for he equivalen ime horizon. However, for he 5 year invesmen, he inercep coefficien was esimaed o be 4.50% while he risk free rae for he 5 year ime horizon averaged a 7.75%. In heory, he esimaes for he inercep coefficien should equal ha of he risk free rae. Since he esimaes of he inerceps for boh ime horizons are lower han he risk free rae, i could be inerpreed ha he invesor has no been sufficienly compensaed. For boh ime horizons he lower end of he 95% confidence inerval for he risk and reurn relaionship is posiive. Hence i is likely ha he risk reurn relaionship for he single family housing in Sweden is indeed posiive. However, i is worh menioning ha he inercep coefficiens, which are boh significan a he 95% level, differ from he risk free rae compued from he Cenral Bank of Sweden for each respecive ime period. This, ogeher wih he fac of he low adjused 2 R for he 10 year ime horizon, one should be cauious inerpreing he daa. However from he above resuls, we can conclude: We accep H1 saing here is a posiive relaionship beween risk and reurn in he Swedish single family housing marke. 27

31 P. Wessel & E. Jennefel Sockholm School of Economics 7.2 RISK ADJUSTED RETURN ON THE SINGLE FAMILY HOUSING MARKET COMPARED TO THE STOCK MARKET The Sharpe raio for he municipaliies has been compared o he Sharpe raio of he OMX for he respecive ime horizons. The hypohesis ha he difference beween he municipaliy single family housing Sharpe raio and he OMX is equal o zero has been esed agains he alernaive hypohesis ha hey are differen. Hence; H H 0 1 = Sharpe raio = Sharpe raio RE RE = Sharpe raio Sharpe raio OMX OMX As he number of observaions are 238, hus larger han 30, he cenral limi heorem is applicable and he difference beween he wo Sharpe raios should be normally disribued. The resuls are presened below in able 3: Table 3. Time Horizon 10 years 5 years d sd n obs cri Rejec H 0 YES YES The negaive obs indicae ha he single family housing Sharpe raio is worse han he OMX for boh ime periods and he resuls are significan a he 95% level since >. 23 Thus we obs cri can rejec he null hypohesis and favor he alernaive hypohesis ha hey are differen. 24 This leads us o conclude: H2: We rejec he hypohesis ha he risk adjused reurn for single family housing marke is equal o ha of he Swedish sock marke. Insead he alernaive hypohesis ha he risk adjused reurn for he single family housing in Sweden is worse han ha of he sock marke. 23 Newbold (1995) 24 The daa has also been esed excluding he negaive Sharpe raios, as he appropriaeness of negaive Sharpe raios can be quesioned. This gave similar resuls, where he adjused reurn for he single family housing in Sweden underperformed ha of he OMX. 28

32 P. Wessel & E. Jennefel Sockholm School of Economics 7.3 THE EFFECT OF TIME HORIZON The risk adjused reurn in single family housing may be dependen of he ime horizon of he invesmen. In he analysis, he 10 and 5 year ime horizons have been compared on municipaliy level. The null hypohesis being ha Sharpe raio of he 10 year invesmen is greaer han ha of he 5 year. Hence: H 0 H = Sharpe raio 1 = Sharpe raio > Sharpe raio Sharpe raio 5 5 Since he appropriaeness of negaive Sharpe raio values can be quesioned, he municipaliies wih negaive Sharpe raios during boh ime horizons have been dropped. From his, 153 municipaliies remain for he comparison. Table 4 below presens he difference beween he Sharpe raio of he wo ime horizons. The resuls show ha here seems o be a posiive effec of invesing in he 10 year ime horizon compared o he 5 year ime horizon. Thus we canno rejec he null hypohesis of he 10 year invesmen horizon being superior o ha of he 5 year horizon. Table 4. Increasing from 5 o 10 year ime horizon mean (10) mean (5) sd(10) sd(5) n 153 Z obs Z cri Rejec H 0 NO This leads us o conclude: H3: The lengh of he ime horizon affecs he risk and reurn relaionship posiively when increasing he ime horizon from 5 o 10 years. Acceping he H3 hypohesis, migh seem conradicory o he reurn risk relaionship coefficiens obained in secion 7.1. However, he large differences in he esimaed coefficiens in he regression in secion 7.1, are o a large exen a resul of he wo esimaed inerceps obained 29

33 P. Wessel & E. Jennefel Sockholm School of Economics for he 5 and he 10 year horizons. However, using he Sharpe raio he inercep is he risk free rae per definiion. Therefore, he analysis using he Sharpe raio should give a beer comparison regarding he wo invesmen horizons. 7.4 RISK AND RETURN IN METROPOLITAN AREAS Regarding he meropolian areas he amoun of municipaliies are 101 and he number of nonmeropolian municipaliies are hus 137 in he sample. Since he number of observaions exceeds 30, he cenral limi heorem is applicable for he following analyses Risk The null hypohesis being ha he difference is zero and he alernaive being ha he meropolian areas have a differen risk compared o non-meropolian areas. Hence: H H 0 1 = Risk = σ mero Mero σ = Risk non mero Non mero = σ mero = σ non mero The resuls from his are presened in ables 5 and 6 below: Table 5. Table 6. Risk in mero vs non-mero, 10 yrs Risk in mero vs non-mero, 5 yrs mean(mero) mean(mero) mean(non-mero) mean(non-mero) sd(mero) sd(mero) sd(non-mero) sd(non-mero) n(mero) 101 n(mero) 101 n(non-mero) 137 n(non-mero) 137 Z obs Z obs Z cri ±1.96 Z cri ±1.96 Rejec H 0 YES Rejec H 0 YES I can be seen from boh ime horizons ha he Z obs is posiive and greaer han Z cri, hence we rejec he null hypohesis of he risk being equal in he wo differen regions. The risk in he meropolian areas is significanly higher compared o he non-meropolian areas a he 95% significance level for boh ime horizons. We hus conclude: We accep he H4 hypohesis of he risk being differen (higher) in meropolian areas compared o nonmeropolian areas. 30

34 P. Wessel & E. Jennefel Sockholm School of Economics Reurn The null hypohesis being ha he difference is zero and he alernaive being ha he meropolian areas had a higher reurn. Hence: H H 0 1 = Reurn = Reurn Mero Mero = Reurn Reurn Non mero Non mero The resuls from his are presened in ables 7 and 8 below: Table 7. Table 8. Reurn in mero vs non-mero, 10 yrs Reurn in mero vs non-mero, 5 yrs mean(mero) mean(mero) mean(non-mero) mean(non-mero) sd(mero) sd(mero) sd(non-mero) sd(non-mero) n(mero) 101 n(mero) 101 n(non-mero) 137 n(non-mero) 137 Z obs Z obs Z cri ±1.645 Z cri ±1.645 Rejec H 0 YES Rejec H 0 YES I can be seen from boh ime horizons ha he Z obs is posiive and greaer han Z cri, hence we rejec he null hypohesis of he reurn being equal in he wo differen regions. The reurn in he meropolian areas is significanly higher compared o he non-meropolian areas a he 95% significance level for boh ime horizons. We hus conclude: We accep he H5 hypohesis of higher reurn in meropolian areas for boh ime horizons Risk adjused reurn The null hypohesis being ha he wo areas have he same risk adjused reurns and he alernaive being ha hey have differen risk adjused reurns. Hence: H 0 = Sharpe raio H = Sharpe raio 1 mero mero = Sharpe raio Sharpe raio non mero non mero The resuls from his are presened in ables 9 and 10 below: 31