THE RISK AND RETURN OF HOME OWNERSHIP. Bert Kramer

Transcription

1 THE RISK AND RETURN OF HOME OWNERSHIP Ber Kramer Applied Paper No Sepember 2010

2 OFRC WORKING PAPER SERIES THE RISK AND RETURN OF HOME OWNERSHIP Ber Kramer 1 Applied Paper No Sepember 2010 Orec Finance Research Cener P.O. Box 4074, 3006 AB Roerdam Max Euwelaan 78, The Neherlands, ABSTRACT In several counries he economic crisis has again confroned homeowners wih he risks of heir ownership. Price-increases are no self-eviden. The uncerainy of he coss of home ownership has increased. We will presen a sochasic model by which he coss and risks of home ownership will be deermined simulaneously. The coss of home ownership consis of wo componens: he difference beween he buying price plus ransacion coss a he sar of he occupaion period and he selling price a he end of he occupaion period; and he home ownership relaed cash flows during he occupaion. An imporan risk facor is he difference beween he expeced price-increase of he house and he uncerain acual price developmen during he occupaion period. Oher risks are for insance he uncerainy of he inflaion influencing mainenance and he uncerainy of he fuure coss of refinancing he deb. We will deermine hose risks wih a sochasic analysis, also aking ino accoun he correlaion beween house price increases, inflaion and he ineres rae. The levels of he coss are amongs ohers dependen on he amoun of own funds invesed in he house and he lengh of he occupaion period in he house. We show ha jus looking a he volailiy of house prices underesimaes he rue risk of owner occupaion, especially for longer occupaion periods and wih high iniial loan-o-value raios. Keywords: home ownership, user coss, risk analysis JEL Classificaion: C15, C32, D14, D31, R29 1 The auhor is senior researcher a he Orec Finance Research Cener. Please commens and quesions o Ber.Kramer@orec-finance.com. The auhor would like o hank Johan Conijn, Frans Schilder, Marc Francke and paricipans of he 2010 AREUEA Inernaional Meeing in Roerdam for valuable commens and suggesions.

3 1 Inroducion In several counries he economic crisis has again confroned home owners wih he risks of heir ownership. The curren crisis reminds us ha house prices are volaile and can drop dramaically. The credi crisis ended a period of coninuously increasing house prices across Europe and Norh America. In he Neherlands, house prices have increased coninuously from 1985 up o The las ime before he credi crisis ha he UK and he US had experienced dropping house prices was in he early 1990s. In he pas decades, many governmens have promoed home ownership. Parly due o hese governmen policies, home ownership raes have increased in a lo of counries. In he Neherlands, he home ownership rae increased from around 51% in 1998 o 59% in 2009 (source: Cenral Bureau of Saisics). Likewise, he home ownership rae in he US increased from 62% in 1960 o 68% in And some oher counries, like Spain and Greece, have even higher home ownership raes a around 85%. For hose new home owners, who did no really experience previous house marke crises, home ownership migh have appeared o be an almos risk free invesmen. This is, however, evidenly no he case as is highlighed by, for insance, he increased foreclosure raes in he US and he increasing numbers of forced sales in he Neherlands 2. In he Neherlands, as in a lo of oher counries, home owners remain liable for he morgage deb ha remains afer he house is sold. Therefore, poenial home owners should know he risk reurn profile of home ownership o make he righ decision. Tha is, can hey really afford o buy a house. The coss or reurn of home ownership consiss of a leas wo or hree componens: 1. The difference beween he buying price plus ransacion coss a he sar of he occupaion period and he selling price a he end of he occupaion period; 2. The user coss during he occupaion; 3. If applicable: invesmens in he house (exensions, dormers, ). Mos debae around home ownership and risk has focused on house price risk and / or on morgage deb and he probabiliy of morgage defaul (credi risk). So he focus of his lieraure is on he volailiy of house prices and how o hedge his risk. See for insance Case e al (1993); Eichholz (1997); Englund e al (2002); Iacoviello & Oralo- Magné (2002); Banks e al (2004); Cae e al (2004); and Quigley (2006). Smih e al (2008) discuss a second ype of housing risk overinvesmen ino a single asse, overdependence on housing wealh, and vulnerabiliy o he under-performance of housing asses. All his lieraure has focused on only one of he componens of home ownership risk. Oher risk facors like he uncerain developmen of he user coss, noise in he ransacion price and ime on he marke (liquidiy risk) are no included in hese analyses. In earlier sudies on user coss, he focus was on he size of hese coss and no on he uncerainy herein; see for insance Hendersho & Slemrod (1983), Poerba (1984, 1992), Conijn (1995), Haffner (2000) and Himmelberg e al (2005). So uncerainy in he developmen of he user coss over he enire occupaion period was no aken ino accoun. 2 The number of forced sales in he Neherlands has increased seadily from 695 in 2002 (0.019% of all owner occupied houses) o 2,256 in 2009 (0.055%); source: Kadaser. This is sill very low compared o recen foreclosure raes in he US, which have been around 0.25% per monh in 2009 and early 2010 (source: realyrac.com). 2

4 The main conribuion of his paper is, ha we presen an inegral analysis of house price risk and user cos risk o esimae he risk of home ownership over he enire occupaion period. Such an inegral analysis is necessary as house price risk and user cos risk are (parly bu no perfecly) correlaed. Furhermore, home ownership risk is a funcion of he occupaion period of owner occupiers. The inclusion of liquidiy risk and noise in he ransacion price is lef for furher research. In he nex secion we discuss how we calculae he expeced reurn on home ownership. In secion 3 we describe how he risk of home ownership can be esimaed. In secion 4 we apply our approach o he Duch insiuional seing; and show esimaes for he risk reurn profile of home ownership for differen occupaion periods and iniial loan-o-value raios. Secion 5 concludes. 3

5 2 The reurn on home ownership The reurn on home ownership is a funcion of he iniial buying price including ransacion coss, he annual coss and offseing benefis of ownership during he occupaion period and he selling price a he end of he occupaion period. Annual coss and benefis during he occupaion period are: Morgage ineres paymens; Mainenance coss; Propery insurance coss; Propery axes; Tax on impued ren; and Fiscal benefis of morgage ineres deducibiliy 3. A commonly used concep o measure he annual cos of ownership is he user cos approach. Some references are Hendersho & Slemrod (1983), Poerba (1984, 1992), Conijn (1995, Haffner (2000) and Himmelberg e al (2005). A common specificaion of he annual user coss for he Duch insiuional se-up is: UC = I + i ( V M ) + rp V + O + PT + PI + Tc + ( d a) V F (2.1) where: I i rp V M O PT PI Tc a d F morgage ineres paid required rae of reurn on invesed equiy risk premium value of he propery morgage mainenance propery axes (levied by municipaliies) propery insurance aribued ransacion coss (expeced) house price appreciaion rae depreciaion, coss of major repairs Fiscal benefi morgage ineres deducibiliy minus ax on impued ren. Noe ha he specificaion in Eq. (2.1) also includes componens ha are no cash flows: required rae of reurn on invesed equiy (also known as opporuniy coss), risk premium, aribued ransacion coss and value increase of he house. We are ineresed in he money weighed reurn (or inernal rae of reurn) on home ownership over he enire occupaion period. This is he consan rae of reurn a which he iniial invesmen and he inermediae cash flows ogeher equal he ne receips a he end of he occupaion period. Therefore, we are only ineresed in he cash flow componens of he user coss. The opporuniy coss and risk premium are no aken ino accoun. The ransacion coss are included in he iniial invesmen and no spread ou over he enire occupaion period. And he value increase maerializes in he difference beween he buying and he selling price of he house. 3 In he Neherlands, ineres paymens are deducible from income ax, where he marginal ax rae progressively depends on he heigh of he income. 4

6 Propery axes, propery insurance and ax on impued ren are all based on he value of he propery in he previous year. In he Duch case, he ne fiscal benefi is based on he difference beween he morgage ineres paid and he ax on impued ren. The fiscal benefi canno be negaive. So wih no or jus a very small morgage, in which case he ax on impued ren would be larger han he ineres paymen on he morgage, he fiscal benefi is se o zero. Thus, in our approach we use he following nominal cash flow based user coss CF : CF = m lv V O PI p V τ m lv V ir V ) = ( 1+ a d) V ( 0 1 +, (2.2) V (2.3) O (2.4) = ( 1+ o ) O 1 PI (2.5) = ( 1+ c ) PI 1 wih m he morgage ineres rae paid in year, lv he iniial loan-o-value raio (i.e., he morgage divided by he buying price of he house V 0 ), p and ir he propery ax rae and ax on impued ren rae as a percenage of he value and τ he marginal ax rae, o and c he appreciaion raes of mainenance coss and consrucion coss of new houses respecively. In our esimaion of he risk of home ownership, we assume ha he variables m, a, o and c are sochasic. We are ineresed in he reurn on home ownership over he enire occupaion period. We will disinguish wo reurn measures: he reurn on invesmen (ROI) and reurn on equiy (ROE). These measures are calculaed as he consan rae of reurn a which he iniial (oal or equiy) invesmen and he inermediae cash flows ogeher equal he ne receips a he end of he occupaion period. Thus, we are ineresed in he (inernal rae of) reurn r ha solves he following equaion: I T CF = (1 + r) VT + (1 + r) T = 1 wih T he expeced occupaion period. We assume ha all cash flows during he occupaion period are paid halfway each year (on average). Unforunaely, no closed form formula exiss for he exac derivaion of r from Eq. (2.6). I should be solved ieraively. As will be explained in Secion 3, we have o solve Eq. (2.6) for a large number of scenarios. To reduce calculaion ime we will use he Modified Diez mehod o obain an esimae of he reurn on home ownership. Modified Diez is a very common calculaion mehod used in invesmen performance analysis o deermine he performance of an invesmen porfolio based on money-weighed cash flows. I assumes a consan rae of reurn during he period. Each cash flow is weighed by he amoun of ime i is held in he porfolio. This mehod was inroduced in Diez & Kirschmann (1983). I is an improved version of he original (Midpoin) Diez mehod inroduced in Diez (1966). The Modified Diez approximaion works fine as long as he inermediae cash flows are relaively small compared o he iniial invesmen (buying price of he house plus ransacion coss). As he user coss during he occupaion period usually are jus a fracion of he value of he house, his condiion is normally me., (2.6) We calculae Modified Diez approximaions for boh he reurn on invesmen (ROI) and reurn on equiy (ROE) of home ownership. The approximaion formulas are: 5

7 r CF r I sum V = T T = CF, T T = 1 (1 + c) V (1 + c) V 0 0 T = 1 + CF sum CF, (2.7) (2.8) 1/ T ROI = (1 + ) 1, (2.9) E r I VT (1 + c) V0 CF = 1 =, (1 + c lv) V + CF 0 T sum (2.10) 1/ T ROE = (1 + ) 1. (2.11) r E wih CF he inermediae (midyear) cash flows and he buying price plus ransacion coss as he iniial invesmen. See Appendix A for he derivaion of hese formulas. Noe ha we assume an ineres-only morgage. We will exend our analysis o oher morgage ypes in secion 4.2 below. 6

8 3 The risk of home ownership As he credi crisis has shown us once more, home ownership is no risk-free. The coss of and reurn on home ownership are uncerain. The developmen of house prices can be very volaile, influencing amongs ohers he selling price and axes. When he ineres rae on he morgage is no fixed, changes in he morgage ineres rae influence he morgage ineres paymens and ax gains. Floaing rae morgages generally depend on he shor (3-monh) ineres rae. Fixed rae morgages depend on he long ineres rae (10-, 20- or even 30-year). The propery insurance premium will depend on he developmen of he coss of rebuilding he house, and mainenance coss will depend on inflaion and prices se by painers, conracors, eceeras. Thus, he user coss and selling price are uncerain and influenced by differen economic risk facors. We will firs discuss he characerisics of he relevan Duch hisorical ime series in Secion 3.1. In Secion 3.2 we presen he scenario simulaion model we will use o esimae he risk of home ownership. 3.1 Daa The relevan hisorical ime series for he Neherlands are shown in Figure 3.1. All ime series are in nominal erms. Figure 3.1: Duch hisorical ime series for home ownership relaed economic facors Sources: Ineres raes Bloomberg; Consrucion coss CBS; Mainenance coss Elsevier; House prices CBS/Kadaser & NVM. As can be seen in Figure 3.1, house prices are much more volaile han he oher ime series. The consrucion cos appreciaion rae represens he developmen of he coss o build a new house 7

9 (relevan for he propery insurance premium). Mainenance cos appreciaion raes are relevan for exising houses. For mainenance coss, we only have daa available from As our daa sample runs from 1970 o 2009, we assume ha he appreciaion rae of mainenance coss equals ha of consrucion coss in he period The saisical characerisics are summarized in Tables 3.1 and 3.2. Table 3.1: hisorical characerisics of economic risk facors Average Sd. dev. Minimum Maximum Price inflaion 3.70% 2.71% -0.50% 10.20% Ineres rae (10yr) 6.75% 2.10% 3.35% 11.28% Ineres rae (3m) 5.89% 2.72% 0.27% 11.63% Consrucion coss 4.87% 4.02% -2.43% 13.85% Mainenance coss 4.65% 3.69% 0.83% 13.85% House prices 6.70% 8.66% % 34.56% Table 3.2: correlaion marix Ineres 10y Ineres 3m Consrucion Mainenance House prices Price inflaion Ineres 10y 1.00 Ineres 3m Consrucion Mainenance House prices Price inflaion The developmen of consrucion coss and mainenance coss are posiively correlaed wih comparable hisorical averages. Consrucion cos appreciaion raes are, however, more volaile han mainenance cos appreciaion raes. Consrucion cos appreciaion raes are also posiively correlaed wih house price changes. Changes in house prices are negaively correlaed wih changes in he ineres rae. These correlaions and volailiies have o be aken ino accoun when looking a he uncerainy in he reurn on (or he risk of) home ownership. Wheher he long or he shor ineres rae is relevan depends upon he ype of morgage. 8

10 3.2 Simulaion model We use scenario analysis o esimae he risk of home ownership. We apply economeric ime series modeling o obain he disribuion funcion for he reurn on home ownership. The reurn on home ownership is a funcion of he (nominal) sochasic variables m, a, o and c from Eq. (2.2) (2.5). The model is esimaed on a daa se wih hisorical ime series for he variables used. More specifically, we use a so-called Vecor Auoregressive (VAR) model of order 1. This is a relaively simple model in which curren values of economic variables are linearly relaed o pas values of he same se of variables. In mahemaical noaion he VAR model of order 1 is given by Y = A( Y 1 µ ) + ε, ε ~ N(0, Σ) µ (3.1) where Y is a vecor wih he values of he economic variables a ime, ε is a vecor of residuals or one-sep forecas errors, which are assumed o be mulivariae Normally disribued wih a zero mean vecor and covariance marix Σ. The coefficien marix A describes he linear relaion beween curren and pas values of he economic variables. The VAR model can also be inerpreed as a se of individual equaions for he relevan economic variable, where each variable is regressed on is own lagged value and on he lagged values of oher economic variables. Noe ha we consider each series in deviaion from is average value: we firs de-mean he daa, and only afer ha esimae he VAR model. Despie he simple srucure of he model i is well able o describe o mos imporan dynamic characerisics of annually observed economic variables on an annual horizon. These characerisics no only include averages and sandard deviaions bu also correlaions and auo- and crosscorrelaions, measuring he conemporal and ineremporal dependencies beween he economic variables. This combinaion of simpliciy and flexibiliy has conribued o he populariy of VAR models following Chrisopher Sims s aricle Macroeconomics and Realiy in Economerica (1980). In paricular Cenral Banks have on a wide scale used VAR models for forecasing purposes, and also in ALM analyses VAR models are playing an imporan role. Examples are given by Boender e al. (2007), Campbell & Viceira (2002), Hoevenaars e al (2003) and Kramer & Van Welie (2001)). The key characerisics of he 500 scenarios from he VAR model are summarized in Tables 3.3 and 3.4. These characerisics can be compared wih Tables 3.1 and 3.2 o check he adequacy of he generaed scenarios. Noe ha he (arihmeic) scenario averages per variable are no based on hisorical averages bu are explici inpu o he model. How hese levels are esablished is discussed in he nex secion. 9

11 Table 3.3: scenario characerisics of economic risk facors Average Sd. dev. Minimum Maximum Price inflaion 2.00% 2.62% -1.00% 15.00% Ineres rae (10yr) 4.50% 2.10% 0.00% 12.94% Ineres rae (3m) 3.50% 2.67% 0.00% 15.00% Consrucion coss 3.30% 4.06% -5.00% 20.00% Mainenance coss 3.30% 3.32% -4.75% 20.00% House prices 4.13% 8.88% % 43.75% Table 3.4: correlaion marix scenarios Ineres 10y Ineres 3m Consrucion Mainenance House prices Price inflaion Ineres 10y 1.00 Ineres 3m Consrucion Mainenance House prices Price inflaion We calculae he ROI and he ROE of home ownership over he enire occupaion period for he 500 scenarios from he VAR model. From hese 500 differen ROI and ROE realizaions we calculae he median reurn and he sandard deviaion. We will vary he assumpions wih respec o he occupaion period, he fixed ineres rae period for he morgage and he relaive size of morgage (iniial loan-ovalue raio) o es for he sensiiviy of he resuls. 10

12 4 A Duch example Based on he approach described in secions 2 and 3, we have calculaed he risk (sandard deviaion) and expeced (median) reurn of home ownership for he Duch insiuional se-up. The following parameer values are used for Eq. (2.2): Mainenance: O 0 = 0.009V 0 (Koning e al, 2006) Propery insurance premium: PI 0 = 0.001V 0 (Koning e al, 2006) Tax on impued ren: ir = 0.55% 4 Propery ax: p = 0.11% 5 Marginal ax rae: τ = 42% 6 Transacion coss: c = 10% 7 Depreciaion: d = 0.83% (Conijn, 1995) In conras o he scenario volailiies and correlaions, which are based on he characerisics of hisorical daa ( in his case), he (long erm) scenario averages per variable are no based on hisorical averages bu are explici inpu o he model. Tha is, for he ineres raes and for he house price, mainenance and consrucion cos appreciaion raes we do no use he hisorical averages bu our own prognoses, parly based on academic lieraure. Furhermore, in our analysis we will only focus on long erm expeced developmens. We will absrac from he curren (pos?) credi crisis saring poin. We expec a long erm average price inflaion of 2%, in line wih he (maximum) inflaion arge se by he European Cenral Bank (ECB). We assume a shor (3 monh) real ineres rae (including inflaion risk premium) of 1.5% and a long (10 year) real ineres rae of 2.5%. So he expeced long run shor erm ineres raes correspond o an average mauriy spread of 1% beween he 10-year and 3-monh ineres rae. The average spread has been 1.06% for he Neherlands in he period (source: DNB) and 0.86% in he period The spread consiss of he mauriy spread in real raes (0.75%) and he assumed mauriy spread in he inflaion risk premium (0.25%). Hisorically, he credi spread for morgages compared o governmen bonds was around 100 basis poins. Therefore, we assume he following nominal expeced morgage ineres raes (m ): 5.5% for a fixed rae morgage (i.e., fixed over he enire occupaion period), 4.5% for a floaing rae morgage. To deermine he expeced long erm house price appreciaion rae, we use he house price predicion model of Francke (2010b). Based on he inflaion and ineres rae expecaions presened above, ogeher wih an expeced wage inflaion of 3% and an expeced GDP growh of 2.2%; his model 4 This percenage is valid for houses wih a fiscal value above 75,000. For cheaper houses, lower percenages apply. The supply of houses wih a value below 75,000 is, however, limied. The naional average value was 241,000 in 2009; and on a municipaliy level he lowes average is sill 138,000 for Heerlen (source: Cenral Bureau of Saisics). For houses wih a fiscal value above 1,000,000 a higher percenage applies: in % for he par above one million. This percenage will increase o 2.35% in In our analysis, we will neglec his non-lineariy in he ax rae as here are relaively few houses wih a value above one million. 5 Propery ax is levied by municipaliies. The ax raes differ significanly beween municipaliies; wih a minimum of 0.033% and a maximum of 0.181% in 2010 (source: Allers e al, 2010). 6 In 2010, his rae is valid for Duch ciizens, age < 65, wih an income beween 18,218 and 54,367. The 2010 modal income is around 32, The main componen is he ransfer ax (6%); oher componens are broker coss and coss relaed o obaining a morgage. 11

13 predics a nominal long erm average yearly house price increase (a) of 4.13%. Correced for depreciaion (d), his gives an nominal expeced yearly value increase of an exising house of 3.3% 8. In real erms, he long erm expeced yearly house price increase is 2.13%. This is somewha below he hisorical average of 3%. Hisorically, he appreciaion rae of consrucion coss is 0.3%-poins above wage inflaion. As we assume a long-erm expeced wage inflaion of 3.0%, his leads o a nominal expeced long-erm appreciaion rae of consrucion coss of 3.3%. Finally, we assume he nominal expeced appreciaion rae of mainenance coss o be equal o ha of consrucion coss. Noe ha he expeced long-erm levels for he parameers will only influence he expeced reurn on home ownership. The impac on he volailiy of he reurn will be very small. As in our model he resuls are insensiive o he iniial buying price V 0, we can focus on he sensiiviy of he resuls o he expeced occupaion period, he iniial loan-o-value raio and he choice beween a fixed and a floaing morgage rae. The resuls wih a fixed morgage rae are presened in Figures 4.1 o 4.4 in his secion. The resuls wih a floaing morgage rae are presened in Appendix B. The ables wih he resuls are presened in Appendix C. We can draw a number of conclusions from he resuls in he ables and figures. Firs of all, he ransacion coss push he reurns downwards wih shor occupaion periods (< 10 years, see Figures 4.1 and 4.3). Second, even wihou a morgage, he volailiy of he reurn on home ownership exceeds he volailiy of he house price for occupaion periods > 5 years (see Tables C1 and C2). Thus, solely focusing on house price risk underesimaes he oal risk of home ownership. The observed fac ha house price risk and home ownership risk diverge for longer occupaion period can be explained by he increasing relaive size of he cumulaive user coss wih longer horizons; which increases he sensiiviy o exreme scenarios wih, for insance, long periods of high inflaion. This leads o an increasing probabiliy of very negaive reurns. Third, for he average occupaion period of 15 years and wih 100% iniial LTV, he sandard deviaion of he ROI is 14.6% (see Table C1). This is smaller han he sandard deviaion of he annual reurn on invesmens in a well-diversified equiy or high yield credis porfolio in maure markes (which is around 20%). Noe, however, ha we are acually esimaing he annualized geomeric reurn over he enire occupaion period. And he sandard deviaion of he 15-year annualized geomeric reurn on a maure marke equiy porfolio is much smaller han ha of he 1-year reurn; and also much smaller han he sandard deviaion of he ROI found here. For common occupaion periods and LTV raios, he volailiy of he ROE lies in he 30% - 50% range (see Table C2). This volailiy is han ha of invesmens in emerging marke equiy or venure capial. The median ROI roughly lies in he [-1.5%; +1%] range (see Table C1), and he median ROE in he [-10%; +1%] range (see Table C2) for common values of he occupaion period and he iniial LTV raio. Fourh, for occupaion periods up o 15 years floaing morgage raes lead o more volaile reurns han fixed morgage raes (compare Tables C3 and C4 wih Tables C1 and C2). For longer occupaion periods floaing morgage raes lead o less volaile reurns wih higher median reurns. So raional home owners should ake he expeced occupaion period ino accoun when considering he choice beween a fixed and a floaing morgage rae. 8 Koning e al (2006) assume a yearly depreciaion-correced expeced house price increase of 2.6%, OpMaa (2009) assumes an average of 4.26%. 12

14 Finally, wih low iniial loan-o-value raios (up o around 50%, depending on he occupaion period) and an occupaion period of more han 10 years, he expeced reurn (excl. opporuniy coss) is posiive (see Figures 4.1 and 4.3). Figure 4.1: Median ROI, fixed morgage rae Figure 4.2: Sandard deviaion ROI, fixed morgage rae 13

15 Figure 4.3: Median ROE, fixed morgage rae Figure 4.4: Sandard deviaion ROE, fixed morgage rae Noe ha he resuls presened in his secion are in nominal erms. We have also performed hese analyses in real erms. In his case, he median reurns are around 2%-poins lower (as could be expeced given he expeced price inflaion of 2%); and he ROI sandard deviaions are a lile bi lower, bu he difference is always less han 1%-poin. The ROE sandard deviaions are also comparable. So he conclusions remain he same wih real reurns. The resuls in real erms can be obained from he auhor. 14

16 4.1 Correcion for foregone ren paymens In he resuls presened in he previous secion, no correcion was made for he fac ha a home owner does no have o pay ren. So if you move from a renal house o an owner occupied house, you have a gain of ren ha does no have o be paid anymore. As here is no ougoing or ingoing renal cash flow, his gain is no aken ino accoun in he pure cash flow approach used so far. However, people have o live somewhere and one could argue ha herefore hese foregone renal coss should be aken ino accoun as if hese foregone renal coss were incoming cash flows. We herefore es he sensiiviy of our previous conclusions wih respec o his poin. As a proxy for he foregone ren paymens, we assume ha he alernaive (renal) house would be comparable o he house ha has been bough. Tha is, we assume ha he value of he alernaive renal house is equal o he house ha has been bough. Francke (2010c) repors yearly rens as a percenage of he value of he house in he 2.5% - 4% range for Duch social housing and esimaes marke rens in he 4% - 5% range. In he Neherlands, he social renal secor consiues around 75% of he oal renal secor. Thus, i is no eviden ha we should assume ha he alernaive would be o pay marke ren. Therefore, in our example we assume ha he yearly gain of foregone ren paymens is equal o 4% of he value of he house. The resuls wih a fixed morgage rae are presened in Appendix D. We focus on he ROI, as he ROE resuls are no reliable due o he small amoun of own funds invesed wih higher LTV raios in his case (and he corresponding problems wih division by zero). The gain of foregone ren paymens leads o a median ROI ha is beween 3% and 4% higher han in he calculaion wihou ren paymens. For shor occupaion periods up o 10 years, he sandard deviaions are approximaely equal wih and wihou ren correcion. For longer occupaion periods, he volailiy is generally lower afer correcing for rens; excep when no morgage is used o finance he house. See Table D1. Wihou a morgage, he sandard deviaions and reurns are now reasonably in line wih he geomeric reurns on maure marke equiy. The median reurns are, however, sill on he low side given he sandard deviaion when he iniial LTV raio is relaively high. So even if we correc for he fac ha home owners do no have o pay ren, we conclude ha poenial home owners should no buy a house jus for invesmen purposes; especially no if hey need morgage financing. From a pure invesmen poin of view, buying a house seems o have a raher negaive risk reurn profile. If we swich from reurns in nominal erms o reurns in real erms, hen wih occupaion periods up o 15 years he resuls are quie similar. See Table D2 in comparison wih D1. The sandard deviaions of he real reurns are a lile bi lower, bu he differences are no very large. For longer occupaion periods, however, he differences become larger. Tha is, he volailiy of real reurns is much lower han ha of nominal reurns. Wih long horizons, he nominal reurns are more sensiive o exreme scenarios wih, for insance, long periods of high inflaion. In real erms, he impac of hese scenarios on he saisics is smaller. 15

17 4.2 Influence of morgage ype In he analysis so far, we have assumed an ineres only morgage. To analyze he sensiiviy of he resuls o his assumpion, we have also analyzed he risk and reurn for endowmen morgages and annuiies. An endowmen morgage is a morgage loan arranged on an ineres-only basis where he capial is inended o be repaid by an endowmen policy. Tha is, he cusomer pays ineres on he capial borrowed, and also makes paymens o an endowmen policy. The objecive is ha he invesmen made hrough he endowmen policy will be sufficien o repay he morgage a he end of he erm. The ineres rae received on he endowmen policy is equal o he ineres rae on he morgage loan. On a gross basis (i.e., wihou axes), an endowmen morgage is comparable o an annuiy loan. The monhly morgage paymen is roughly equal o ha of an annuiy loan wih he same ineres rae. However, insead of using he difference beween he gross annuiy paymen and he ineres o repay par of he loan, his amoun is pu ino he endowmen policy. The advanage of his consrucion in he Duch siuaion is, ha he use of ax deducibiliy of morgage ineres paymens is maximized, while he ax advanage decreases wih every repaymen on an annuiy morgage. The main resuls for he real ROI including a correcion for foregone rens are summarized in Table E.1 in Appendix E 9. From his able, we can conclude ha he general conclusions so far for ineres only morgages also hold for endowmen and annuiy morgages. As wih ineres only morgages, boh he reurn and risk on home ownership increase wih he occupaion period. For shor occupaion periods, he resuls for endowmen and annuiy morgages are very similar. Especially for longer occupaion periods, he median ROI is higher for endowmen morgages ha for annuiy morgages; he maximum difference is 0.3%-poins. This is compleely due o he ax effec. However, he median ROI on ineres only morgages is up o 1.2%-poins higher han he median ROI on endowmen morgages. The volailiy of he ROI is lowes wih ineres only morgages and highes wih annuiy morgages. Thus, overall he ROI risk reurn profiles for endowmen and annuiy morgages are worse han hose for ineres only morgages. Bu he conclusion ha home buyers should ry o minimize he iniial loan-o-value raio sill holds. For he ROE, he conclusions are somewha differen. Endowmen morgages lead o he highes median ROE s and he lowes volailiies; and ineres only morgages give he lowes median ROE s wih he highes volailiies. However, for higher iniial LTV raios and for longer occupaion periods, he ROE calculaions suffer from he fac ha in many scenarios invesed equiy becomes very small or even negaive. This problem is more severe for ineres only morgages han for endowmen and annuiy morgages. Therefore, he ROE conclusions are more difficul o inerpre. 9 We assume ha he ineres rae paid is independen of he ype of morgage. 16

18 5 Conclusions The main conclusion from his paper is, ha jus looking a he volailiy of house prices underesimaes he rue risk of owner occupaion, especially for longer occupaion periods and wih high iniial loan-o-value raios. The sandard deviaion of he ROI of home ownership increases wih he occupaion period and wih higher LTV raios. If we correc he reurns for he fac ha you would have o pay ren when you do no own a house, hen he resuls are no as negaive. Wihou a morgage, he sandard deviaions and nominal reurns are reasonably in line wih he geomeric reurns on maure marke equiy. The median reurns are, however, sill on he low side given he sandard deviaion when he iniial LTV raio is relaively high. For occupaion periods up o 15 year, he differences in volailiy beween nominal and real reurns are relaively small. For longer occupaion periods combined wih reurns ha are correced for foregone ren, however, he differences become larger. Tha is, he volailiy of real reurns is much lower han ha of nominal reurns. Wih long horizons, he nominal reurns are more sensiive o exreme scenarios wih, for insance, long periods of high inflaion. In real erms, he impac of hese scenarios on he saisics is smaller. The volailiy of he real reurn on home ownership is, however, sill larger han he volailiy of real house price changes. So poenial home owners should no buy a house jus for invesmen purposes when hey need morgage financing. From a pure invesmen poin of view, buying a house wih a morgage has a raher negaive risk reurn profile. This conclusion is boh relevan for boh (poenial) home owners and for morgage providers. The added value of owning a house should come from oher, nonmoneary, benefis like more choice and higher qualiy a he owner occupied marke han in he renal marke, and more flexibiliy o adjus he house o your desires and needs. In our approach, we probably sill underesimae he rue risk. Poenial risk increasing facor we did no ake ino accoun are noise in he ransacion price and he ime on he marke (liquidiy risk). Francke (2010a) esimaed he noise in he ransacion price on he Duch housing marke o be normally disribued wih an average of zero and a sandard deviaion of 7%. For longer occupaion periods, he impac of ransacion noise will be insignifican due o ime diversificaion and he increasing impac of he cumulaive user coss. For shor occupaion periods, ransacion noise can have a significan impac on home ownership risk. As he curren credi crisis has shown, houses can remain on he marke for a long ime when house prices are dropping. Especially when he home owner is no willing o (significanly) lower he asking price. Tha is, in price booms, he marke is ypically more liquid wih frequen ransacions and houses selling quickly, whereas in buss here are fewer sales and many houses remain on he marke for a long ime (see for insance De Wi e al (2010)). 17

19 References Allers, M. A., C. Hoeben, J. Bol, and L. A. Toolsema Alas van de lokale lasen 2010 [Alas of local charges 2010]. COELO, Groningen. Banks, J., R. Blundell, Z. Oldfield, and J. P. Smih House price volailiy and housing ownership over he life cycle. UCL Discussion Papers in Economics Boender, C.G.E., C. Der, F. Heemskerk and H. Hoek, (2007), A Scenario Approach of ALM, in Mulvey and Ziemba (eds). Handbook on Worldwide Asse Liabiliy Managemen, par II Campbell, J.,Y. and L.M. Viceira, (2002), Sraegic Asse Allocaion, Oxford Universiy Press. Case, K. E., R. J. Shiller, and A. N. Weiss Index-based fuures and opions in real esae. Journal of Porfolio Managemen (winer): Cae, P., N. Girouard, R. Price. and C. Andre Housing markes, wealh and he business cycle. OECD Economics Deparmen Working Paper, 394. Conijn, J. B. S Enkele financieel-economische grondslagen van de volkshuisvesing [Some Financial-Economic Principles of Housing]. Delfse Universiaire Pers, Delf. Crisopherson, J. A., D. R. Cariño, and W. E. Ferson Porfolio Performance Measuremen and Benchmarking. McGraw-Hill, USA. De Wi E., P. Englund and M.K. Francke Price and Transacion Volume in he Duch Housing Marke. Tinbergen Insiue Discussion Paper /2. Diez, P. O "Pension Fund Invesmen Performance - Wha Mehod o Use When." Financial Analyss Journal, January/February. Diez, P. O., and J. R. Kirschmann "Evaluaing Porfolio Performance." in J. L. Maginn and D. L. Tule (eds.) Managing Invesmen Porfolios: A Dynamic Process. Warren, Gorham & Lamon, Boson. Second ediion published in Eichholz, P. M. A He risico van een eigen huis [The risk of owning a house]. ESB 82: 776. Englund, P., M. Hwang, and J. M. Quigley Hedging housing risk. Journal of Real Esae Finance and Economics 24: Francke, M. 2010a. Casamerics. English summary of inaugural lecure. Universiy of Amserdam. Francke, M. K. 2010b. How bloaed is he Duch housing marke? Real Esae Research Quarerly, April: Francke, M. K. 2010c. Comparing Marke Rens from a User Cos and a Reacion Model. Paper presened a he 2010 AREUEA Inernaional Meeing, June 2010, Roerdam. Haffner, M. E. A Coss and Fiscal Subsidies in Owner Occupaion: Mehods and Oucomes. Journal of Housing and he Buil Environmen 15: Hendersho, P. H., and J. Slemrod Taxes and he User Cos of Capial for Owner-Occupied Housing. AREUEA Journal 10: Himmelberg, C., C. Mayer, and T. Sinai Assessing High House Prices: Bubbles, Fundamenals and Mispercepions. Journal of Economic Perspecives 19 (4): Hoevenaars, R.P.M.M., R.D.J. Molenaar, and T.B.M. Seenkamp Simulaion for he Long Run. Chaper 10 in B. Scherer (Ed.), Asse and Liabiliy Managemen Tools. Risk Books, London. Iacoviello, M. and F. Oralo-Magné Hedging housing risk in London. Journal of Real Esae Finance and Economics 27: Koning, M., R. S. Nisal, and J. Ebreg Woningmarkeffecen van aanpassing fiscale behandeling eigen woning [Housing-marke effecs of reforming he deducibiliy of home morgage ineres]. CPB Documen 128. Cenraal Planbureau, The Hague. Kramer, B. and T. van Welie An Asse Liabiliy Managemen Model for Housing Associaions. Journal of Propery Invesmen & Finance 19:

20 OpMaa Advies Verbeering sabiliei en updae Fair Value-model [Advice Improvemen sabiliy and updae Fair Value model ]. 10 December Poerba, J. M Tax Subsidies o Owner-Occupied Housing: An Asse-Marke Approach. The Quarerly Journal of Economics 94: Poerba, J. M Taxaion and Housing: Old Quesions, New Answers. The American Economic Review 82: Quigley, J Real esae porfolio allocaion: he European consumers perspecive. Journal of Housing Economics 15: Sims, C Macroeconomics and Realiy. Economerica, 48: Smih, S. J., B. A. Searle, and N. Cook Rehinking he Risks of Home Ownership. Journal of Social Policy 38:

21 Appendix A: Modified Diez approximaions In he Modified Diez formula, he denominaor consiss of he iniial invesmen (he buying price plus ransacion coss in his case) plus he sum of he cash flows weighed by he lenghs of ime over which hey were in he porfolio. The weighed cash flows comprise a beginning adjusmen, from which an adjused beginning value 10 n 1 j=1 ABV = I + w CF, (A.1) o j can be calculaed. Similarly, by calculaing a corresponding adjused ending value j n 1 AEV = V (1 w ) CF, (A.2) n j=1 he Modified Diez formula can be wrien as j j Vn I o CF j AEV AEV ABV j= 1 r = 1 = =, (A.3) n 1 ABV ABV I + w CF The modified Diez mehod gives he reurn over he enire (occupaion) period. This reurn is annualized o obain he reurn on home ownership. The ROI calculaion does no ake he iniial receip and he final repaymen of he morgage ino accoun, bu only he inermediae morgage ineres paymens. Wih he ROE, he iniial receip of he full morgage amoun and he repaymen of he morgage a he end of he occupaion period are included. Wih an ineres-only morgage, he iniial invesmen I 0 and he final value / receip V n boh conain he same morgage amoun (lv V 0 ). Consequenly, for he ROE he morgage amoun only appears in he denominaor of Eq. (A.3). o j= 1 n 1 j j 10 This derivaion was aken from Crisopherson e al (2009). 20

22 Appendix B: Figures for floaing morgage raes Wih a floaing morgage ineres rae, he morgage rae paid changes each year based on he relevan shor ineres rae scenario. The resuls are summarized in Figures B.1 o B.4. Figure B1: Median ROI, floaing morgage rae Figure B2: Sandard deviaion ROI, floaing morgage rae 21

23 Figure B3: Median ROE, floaing morgage rae Figure B4: Sandard deviaion ROE, floaing morgage rae 22

24 Appendix C: Tables wih resuls Table C1: Saisics ROI wih fixed morgage rae Median ROI Occupaion period (Sd. dev.) % LTV -0.15% (5.63%) 1.09% (5.24%) 1.52% (5.13%) 1.37% (5.05%) 1.61% (11.13%) 20% LTV -0.93% (5.68%) 0.36% (5.39%) 0.81% (5.42%) 0.69% (9.55%) 0.99% (18.37%) 40% LTV -1.49% (5.73%) -0.16% (5.53%) 0.33% (5.84%) 0.25% (15.62%) 0.57% (19.90%) 60% LTV -2.05% (5.78%) -0.68% (5.70%) -0.15% (9.70%) -0.20% (18.40%) 0.17% (26.70%) 80% LTV -2.60% (5.84%) -1.20% (5.89%) -0.62% (10.85%) -0.65% (21.58%) -0.23% (30.13%) 100% LTV -3.16% (5.89%) -1.71% (6.12%) -1.09% (14.59%) -1.10% (25.24%) -0.64% (33.47%) house price 2.83% (5.66%) 3.14% (5.09%) 3.27% (4.82%) 2.98% (4.55%) 3.06% (4.24%) Table C2: Saisics ROE wih fixed morgage rae Median ROE Occupaion period (Sd. dev.) % LTV -0.15% (5.63%) 1.09% (5.24%) 1.52% (5.13%) 1.37% (5.05%) 1.61% (11.13%) 20% LTV -1.13% (6.96%) 0.43% (8.42%) 0.95% (15.48%) 0.81% (22.71%) 1.14% (29.41%) 40% LTV -2.30% (9.42%) -0.24% (17.48%) 0.47% (32.70%) 0.34% (36.40%) 0.76% (39.54%) 60% LTV -4.35% (19.71%) -1.33% (35.02%) -0.26% (41.16%) -0.35% (45.09%) 0.27% (44.26%) 80% LTV -8.87% (39.52%) -3.44% (45.88%) -1.53% (48.44%) -1.49% (49.15%) -0.47% (48.70%) 100% LTV % (53.08%) -9.60% (52.56%) -4.34% (51.34%) -3.77% (51.31%) -1.76% (50.65%) house price 2.83% (5.66%) 3.14% (5.09%) 3.27% (4.82%) 2.98% (4.55%) 3.06% (4.24%) 23

25 Table C3: Saisics ROI wih floaing morgage rae Median ROI Occupaion period (Sd. dev.) % LTV -0.15% (5.63%) 1.09% (5.24%) 1.52% (5.13%) 1.37% (5.05%) 1.61% (11.13%) 20% LTV -0.75% (5.69%) 0.36% (5.40%) 0.95% (5.41%) 0.74% (11.29%) 1.12% (17.85%) 40% LTV -1.21% (5.75%) -0.15% (5.56%) 0.55% (5.74%) 0.36% (14.36%) 0.73% (20.31%) 60% LTV -1.70% (5.81%) -0.60% (5.75%) 0.18% (8.68%) 0.00% (16.81%) 0.33% (23.98%) 80% LTV -2.17% (5.88%) -1.01% (6.08%) -0.19% (12.41%) -0.32% (18.48%) 0.04% (27.01%) 100% LTV -2.61% (5.95%) -1.43% (7.45%) -0.55% (14.67%) -0.67% (23.21%) -0.28% (32.67%) house price 2.83% (5.66%) 3.14% (5.09%) 3.27% (4.82%) 2.98% (4.55%) 3.06% (4.24%) Table C4: Saisics ROE wih floaing morgage rae Median ROE Occupaion period (Sd. dev.) % LTV -0.15% (5.63%) 1.09% (5.24%) 1.52% (5.13%) 1.37% (5.05%) 1.61% (11.13%) 20% LTV -0.92% (6.98%) 0.43% (9.21%) 1.12% (15.52%) 0.87% (21.51%) 1.28% (28.86%) 40% LTV -1.87% (9.43%) -0.22% (17.94%) 0.78% (30.77%) 0.50% (34.57%) 0.97% (38.75%) 60% LTV -3.62% (19.33%) -1.17% (33.95%) 0.32% (41.22%) 0.00% (43.86%) 0.54% (44.20%) 80% LTV -7.35% (39.12%) -2.99% (45.48%) -0.48% (47.29%) -0.77% (49.04%) 0.08% (48.06%) 100% LTV % (54.05%) -8.39% (52.78%) -2.18% (52.02%) -2.21% (51.24%) -0.80% (50.62%) house price 2.83% (5.66%) 3.14% (5.09%) 3.27% (4.82%) 2.98% (4.55%) 3.06% (4.24%) 24

26 Appendix D: Resuls correced for foregone ren Table D1: Saisics ROI; fixed morgage rae; correced for foregone ren; in nominal erms Median ROI Occupaion period (Sd. dev.) % LTV 3.70% (5.69%) 4.92% (5.36%) 5.55% (5.41%) 5.66% (7.51%) 5.44% (23.16%) 20% LTV 2.88% (5.72%) 4.10% (5.44%) 4.78% (5.48%) 4.89% (6.04%) 4.64% (18.43%) 40% LTV 2.30% (5.76%) 3.54% (5.52%) 4.25% (5.60%) 4.34% (5.96%) 4.13% (17.69%) 60% LTV 1.72% (5.81%) 2.98% (5.62%) 3.72% (5.77%) 3.81% (7.63%) 3.85% (19.89%) 80% LTV 1.15% (5.85%) 2.44% (5.74%) 3.20% (6.00%) 3.31% (11.12%) 3.42% (21.20%) 100% LTV 0.58% (5.90%) 1.89% (5.86%) 2.70% (7.82%) 2.80% (16.24%) 2.95% (22.03%) house price 2.83% (5.66%) 3.14% (5.09%) 3.27% (4.82%) 2.98% (4.55% 3.06% (4.24%) Table D2: Saisics ROI; fixed morgage rae; correced for foregone ren; in real erms Median ROI Occupaion period (Sd. dev.) % LTV 1.88% (5.37%) 2.77% (4.74%) 3.49% (4.48%) 3.59% (4.42%) 3.88% (4.82%) 20% LTV 1.08% (5.41%) 1.98% (4.82%) 2.71% (4.59%) 2.78% (4.52%) 3.10% (4.66%) 40% LTV 0.51% (5.45%) 1.45% (4.92%) 2.19% (4.73%) 2.24% (4.72%) 2.64% (4.95%) 60% LTV -0.06% (5.49%) 0.91% (5.02%) 1.68% (4.91%) 1.74% (6.68%) 2.10% (14.41%) 80% LTV -0.63% (5.54%) 0.37% (5.14%) 1.19% (5.16%) 1.28% (10.44%) 1.61% (17.40%) 100% LTV -1.19% (5.59%) -0.15% (5.27%) 0.71% (7.04%) 0.83% (15.59%) 1.14% (19.93%) house price 1.02% (5.35%) 1.00% (4.51%) 1.26% (4.05%) 0.99% (3.69%) 1.09% (3.31%) 25

27 Appendix E: Resuls for differen morgage ypes Table E1: Saisics ROI for differen morgage ypes; fixed morgage rae; correced for foregone ren; in real erms Occupaion Period (yrs) % LTV Median ROI Sd. Dev. Median ROI Sd. Dev. Median ROI Sd. Dev. Median ROI Sd. Dev. Median ROI Sd. Dev. ineres only 1.08% 5.41% 1.98% 4.82% 2.71% 4.59% 2.78% 4.52% 3.10% 4.66% endowmen 0.84% 5.42% 1.74% 4.86% 2.48% 4.65% 2.55% 4.60% 2.90% 4.74% annuiy 0.82% 5.43% 1.72% 4.88% 2.44% 4.68% 2.49% 4.66% 2.86% 4.86% 40% LTV Median ROI Sd. Dev. Median ROI Sd. Dev. Median ROI Sd. Dev. Median ROI Sd. Dev. Median ROI Sd. Dev. ineres only 0.51% 5.45% 1.45% 4.92% 2.19% 4.73% 2.24% 4.72% 2.64% 4.95% endowmen 0.02% 5.49% 0.98% 5.01% 1.75% 4.89% 1.81% 6.65% 2.17% 12.15% annuiy -0.01% 5.49% 0.93% 5.03% 1.67% 4.94% 1.69% 6.76% 2.03% 16.30% 60% LTV Median ROI Sd. Dev. Median ROI Sd. Dev. Median ROI Sd. Dev. Median ROI Sd. Dev. Median ROI Sd. Dev. ineres only -0.06% 5.49% 0.91% 5.02% 1.68% 4.91% 1.74% 6.68% 2.10% 14.41% endowmen -0.79% 5.55% 0.22% 5.18% 1.05% 5.26% 1.14% 11.31% 1.44% 17.95% annuiy -0.83% 5.56% 0.14% 5.21% 0.93% 5.44% 0.98% 14.44% 1.24% 20.44% 80% LTV Median ROI Sd. Dev. Median ROI Sd. Dev. Median ROI Sd. Dev. Median ROI Sd. Dev. Median ROI Sd. Dev. ineres only -0.63% 5.54% 0.37% 5.14% 1.19% 5.16% 1.28% 10.44% 1.61% 17.40% endowmen -1.60% 5.63% -0.53% 5.37% 0.36% 9.41% 0.52% 16.24% 0.80% 22.91% annuiy -1.65% 5.63% -0.63% 5.42% 0.19% 9.69% 0.30% 19.37% 0.54% 26.14% 100% LTV Median ROI Sd. Dev. Median ROI Sd. Dev. Median ROI Sd. Dev. Median ROI Sd. Dev. Median ROI Sd. Dev. ineres only -1.19% 5.59% -0.15% 5,27% 0.71% 7.04% 0.83% 15.59% 1.14% 19.93% endowmen -2.40% 5.70% -1.27% 5.61% -0.32% 10.59% -0.13% 20.69% 0.22% 27.03% annuiy -2.46% 5.71% -1.40% 5.69% -0.53% 12.38% -0.41% 23.12% -0.09% 30.96% 26

28 27