Singapore Centre for Applied and Policy Economics

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1 Singapore Cenre for Applied and Policy Economics Reverse Morgages as Reiremen Financing Insrumen: An Opion for Asse-rich and Cash-poor Singaporeans by Ngee-Choon Chia and Alber K C Tsui Deparmen of Economics SCAPE Working Paper Series Paper No. 2005/03 - Apr 2005 hp://n2.fas.nus.edu.sg/ecs/pub/wp-scape/0503.pdf

2 Reverse Morgages as Reiremen Financing Insrumen: An Opion for Asse-rich and Cash-poor Singaporeans Ngee-Choon Chia and Alber K C Tsui Deparmen of Economics Naional Universiy of Singapore 10 Ken Ridge Crescen Singapore ABSTRACT The unique way of financing housing hrough he mandaory savings sysem in Singapore has creaed a class of asse-rich and cash-poor Singaporeans. This paper provides a framework o assess he viabiliy of a reverse morgage (RM) marke so ha such insrumens may be harnessed as a source of financing reiremen income for home owners. Based on differen cos of capial, we esimae he probabiliy of loss for boh he privae supplier and public provider of RMs. The probabiliy of loss is compued by hree major componens: choice of replacemen raio and propery growh rae; forecas of cohor survival probabiliy by join-life; and generaion of yield curves o discoun he fuure cash flows. The sochasic forecas of survival probabiliy is esimaed using he Lee-Carer demographic model based on he abridged life ables. The discoun facor for fuure cash flows are generaed from sochasic ineres raes. Our simulaion resuls indicae ha based on he benchmark scenario, RM insrumens by privae providers are likely o achieve abou 50% replacemen raio for he 4-room public housing owners. However, he marke may be missing if a replacemen raio of 70% is required. Keywords: incomplee reverse morgage marke, replacemen raio, probabiliy of loss, risk free ineres, breakeven annuiy Corresponding Auhor: Chia NC, Deparmen of Economics, Naional Universiy of Singapore, Singapore ; Tel: (65) ; ecscnc@nus.edu.sg 1

3 1. Inroducion Housing equiy forms a large fracion of he non-pension wealh for elderly households in many developed counries. For insance, abou 33% of he oal financial asse in he US is occupied by housing asses in 2000 (Poerba, 2001). I is even higher for Japan a 63.9% (Noguchi, 1997). If here is a mechanism o unlock housing equiies, i will poenially help o alleviae povery among elderly homeowners and o finance reiremen expendiures. Reverse morgage (RM) insrumen essenially is designed o allow propery owners o obain loans in he form of reiremen annuiies, using heir residenial asses as collaerals; and repaying he loans by selling he house upon heir deah. I hus affords an alernaive means for elderly homeowners o borrow agains he financial equiy embodied in heir homes, while sparing hem from he emoional disrupion of moving ou of or selling heir abodes. There are many forms of RM, bu he basic idea is ha he propery will be revered o he RM supplier a he end of a period or upon he deah of he reverse morgagor. In convenional morgages, he loan quanum is dependen on he borrower s abiliy o pay. However for RM, he loan quanum depends on he appraised value of he propery, he projeced rae of house price appreciaion, he age and sex of he homeowners, he levels of ineres raes and he required loan. 1 There are also coss involved in aking ou hese RM loans. RMs differ in erms of he ypes of loan advance and he ime frame. Loan advance can be aken as a lump sum or as a regular income 1 For example, in US he minimum qualifying age is se a 62 years, and he average age is around 72 years. In Singapore, he average qualifying age is 62. Gender plays a role as male and female has differen life expecancy. 2

4 sream. The erms of he RM can eiher be fixed-erm or enure. In a fixed erm RM, he period of loan advance is fixed, usually 10, 15 or 20 years. Empirical sudy by Kuy (1998) indicaes ha he use of home equiy conversion morgage producs could possibly raise abou 29% of he poor elderly homeowners in he US above he povery line. In addiion, he equiy released could poenially help o finance long erm care among he elderly, where relaively large sum of money are required (Gibbs, 1992). 2 The usefulness of such a RM scheme is conceivably greaer in counries where land prices are exremely high (for example, Japan) or where here is a skewed invesmen porfolio owards home ownership (for example, Ausralia) or where here is a deliberae public policy owards home ownership (for example, Singapore). 3 While some empirical sudies suppor he poenial effec of RM, ohers do no. For example, Hancock (1998) examines he impac of equiy release scheme on he ne income of older homeowners in Briain and finds ha he increased income is no significan for some of he oldes homeowners. Theoreically, here is poenial in unlocking housing wealh o help alleviae povery and mee healh care needs of he elderly. However, in realiy, RM markes have remained weak. Mayer and Simmons (1994) and Caplin (2002) aribue his o he subsanial loads in he RM marke because of moral hazard and adverse selecion problems. Oher major barriers include produc designs, availabiliy of informaion, beques moives and he desire o keep house equiy 2 Sheiner and Weil (1993) found ha besides shocks o family saus, healh shocks also conribued o he decline in home equiy a older ages. 3 The share of land asses in real asses is 83.4% in Japan and 36% in US. (see Noguchi, 1997). Ausralian home ownership is in excess of 70% (Beal, 2001), whereas home ownership in Singapore is in excess of 90%. 3

5 as precauionary savings. These auhors conclude ha o unleash he poenial of RM insrumen, here is a need for policy makers o provide insiuional and legal suppor for he RM marke. For he case of feasibiliy of RM in Japan, Michell and Piggo (2003) highligh he need o faciliae informaion on housing values and ransacions and credi worhiness of borrowers. Simulaions by McCarhy e al. (2002) indicae ha a ypical Singapore worker would have around 75% of his reiremen wealh in housing asse from age 50. Such a concenraion surpasses ha of an American elderly household who would have 20% of heir reiremen wealh in housing asse. In fac, some aemps have been made o unleash he housing asse as alernaive o financing reiremen needs in Singapore. In January 1997, he NTUC Income, a local insurance firm, launches he firs RM scheme. Bu he marke has remained hin, wih only 180 cusomer base. The average monhly draw down is $1800; and he average propery value is $1.6 million. 4 RM remains unpopular as i is only available o privae propery owners and no o public housing owners. In addiion, he high profi margin se by he privae provider virually reduces he monhly annuiy payous generaed for he RM buyers. In his paper, we shall explore wheher RM can be harnessed as an insrumen o finance reiremen expendiures for he asse-rich and cash-poor elderly Singaporeans. Mos RM sudies have focused on he demand side of he marke and examine he effec of equiy release on ne incomes. For examples, Merrill e al. (1994), Hancock 4 See Iner-Miniserial Commiee on Ageing Populaion, 1999, p

6 (1998), Veni and Wise (1991, 2001) and Michell and Piggo (2003) calculae he enure or life RM ha would provide he homeowners wih monhly paymens over he borrower s remaining life afer reiremen. In hese sudies, he maximum amoun of RM loan is calculaed and hen he lump-sum loan is convered o lifeime annuiies wih monhly paymens. The analyses hen focus mainly on he demand for RM o augmen he incomes of he elderly homeowners. Our approach in his paper is differen because we consider boh he demand and supply facors of he RM marke. They include he replacemen raio, he iniial appraised value of he propery, he growh rae of house price appreciaion, he age and sex of he homeowners, various coss of capial and he probabiliy of loss. The organisaion of he res of he paper is as follows. In Secion 2, we provide an overview of he housing marke in Singapore, focusing on he unique way of financing housing hrough he compulsory savings mechanism. Secion 3 describes he mehodology and calibraion procedure used in he Mone Carlo experimens. The calibraion of he reiremen annuiy consiss of hree major componens. The firs par assesses he adequacy of he monhly annuiy paymens o finance reiremen a he firs breakeven monh for differen iniial propery values and appreciaion raes. Second, he Lee-Carer (1992) model is adoped o forecas cohor survival probabiliy a each posreiremen age for he household using he abridged life ables for Singapore. Third, he discoun/accumulaion facor for fuure cash flows are generaed from hree ineres rae models, including wo deerminisic and one sochasic ineres rae environmens. Secion 4 presens simulaion resuls and analysis on he firs breakeven monh and he 5

7 probabiliy of loss for boh he privae supplier and he public provider of RM. The final secion concludes he sudy and draws some policy implicaions on he role of public provider o complee he RM marke. 2. Housing Marke and Housing Finance in Singapore Afer independence from he Briish in 1959, he new Singapore governmen was se o solve he housing shorage which saw many living in slums. The Housing Developmen Board (HDB) was se up in 1960 o build emergency public housing on sae-owned land. These 1-room o 3-room public housings were leased o ciizens a sandardised and affordable raes, which averaged $20 and $30 per room in suburban and urban zones respecively. However in February 1964, in line wih he sraegy of making privae home ownership an invesmen in he sake of he counry, HDB inroduced a scheme o encourage exising enans o own heir flas. Under he Home Ownership Scheme for he People, HDB offered subsided morgage loans wih an aracive repaymen scheme. The loan quanum was se a 80% of he price of a new fla wih repaymen periods of eiher 5, 10 or 15 years. However, he home-ownership rae remained low a only 5% by December This was due o he low purchasing power of households a ha ime. To furher ease financing difficuly on he demand side, he governmen inroduced a unique sysem which is closely inegraed o he compulsory savings scheme or he Cenral Providen Fund (CPF) sysem. The CPF, which was insiued in 1955, was originally a reiremen savings scheme. I is a fully funded and a defined 6

8 conribuion sysem. Under he CPF, every employee and employer is required o conribue a proporion of he wage o he CPF which is credied ino he individual s personal accouns. 5 In Sepember 1968, he CPF inroduced he Approved Housing scheme which allowed HDB purchasers o wihdraw heir savings o finance he purchase of public housing. Funds can be wihdrawn for down-paymen, samp duies, morgage paymens and ineres incurred for he purchase. The CPF Approved Housing Scheme marked he beginning of a series of schemes in which mandaory savings were used in relaion o housing finance. 6 I also ses off a gradual liberalisaion of CPF from merely a reiremen vehicle o insrumens o help finance meri goods consumpion such as educaion and healh care. 7 In order o achieve a naion of homeowners, HDB also implemened supply side regulaions and subsidies. Firs, he opion o ren was made unaracive or effecively unavailable for he majoriy due o sric eligibiliy crieria. Second, he public housing was priced affordably hrough governmen supply and price discouns, enabling buyers o purchase HDB flas a below marke prices. However, unlike mos meri good programs, hese subsidies are no financed primarily from axes or oher governmen revenues, bu 5 In 1955, he rae of conribuions was only 10%. Since 1968, he rae has increased, rising o a peak of 50% in The rae is currenly graduaed according o age, wih an average rae of 36%. More deails on he CPF and he CPF-HDB link are discussed in he nex secion. Also, see Chia and Tsui (2003a) for he insiuional deails regarding he CPF. 6 In 1981, he use of CPF savings was exended o he purchase of privae residenial privae propery. See Phang and Tan (1991) for a chronological accoun of he liberalizaion of he use of reiremen savings in he CPF for housing finance in Singapore. 7 See Chia and Tsui (2003b) for he link beween compulsory savings and he financing of healh care in Singapore using he medical savings accouns. 7

9 raher from land rens ha are capured hrough sae ownership and acquisiion. 8 Indeed, nearly 80% of he land in Singapore is owned by he sae. Under he Land Acquisiion Ac, he governmen is empowered o acquire land a is discreion from privae land owners and a prices below marke prices. 9 Hence, compared o privae secor developers who have o purchase or cos land a marke raes, producer coss for public secor housing is lower and HDB is able o sell is flas a below marke prices. The success and susainabiliy of HDB o build public housing and pricing flas a affordable prices is due o he srong insiuional suppor from he governmen. HDB s annual defici is fully covered by governmen gran. The cumulaive governmen gran received since he esablishmen of HDB in 1960 amouned o $10,533 million. In he fiscal year 2000/01, HDB received $920 million o cover he defici. (HDB, Annual Repor 2001). HDB also receives wo main governmen loans o finance is operaions. Firs, he Housing Developmen Loans is used o finance he developmen programmes and operaions. Ineres rae is pegged a wo percen poins above he floaing CPF ineres rae wih a repaymen erm of 20 years. The second is he Morgage Financing Loans o finance he morgage loans graned o he purchasers of HDB flas. The abiliy of HDB o obain loans from he governmen a below marke raes implies ha HDB is able o subsidise he morgage financing rae for is buyers. The morgage financing rae 8 As such, he supply side price discouns have lile impac on governmen expendiure and is no a significan expendiure iem. According o Asher and Phang (1997), receips from land ren have enabled he governmen o keep expendiure on housing a no more han 2% of oal governmen expendiure in any fiscal year. 9 For example, beween 1973 and 1987, he governmen acquired land under he Land Acquisiion Ac a l973 raes raher han a marke raes of compensaion. For deails, see Phang (1996). 8

10 is pegged a 0.1% above he ineres raes paid by he CPF for he compulsory savings and is abou 2% below he housing morgage ineres raes of commercial banks. 10 The HDB Home Ownership Scheme and is link o he CPF housing financing scheme, ogeher wih many supply side insrumens, have skewed he housing enure choice owards owner occupaion, paricularly owards he owner-occupied public housing. This is evidenced from he fall of HDB renal occupancy of 100% in he early 1960s o 76 % a he end of 1970 and o 38% in 1981 and finally o 7% in Afer almos four decades since he incepion of Home Ownership Scheme in 1964, 85% of Singapore s populaion resides in public housing; wih 93% of he public housing residens owning he unis hey occupied. (See Figure 1). Furhermore, HDB flas consiue 80% of he residenial housing sock in Singapore. 11 == inser Figure 1 == One consequence of he owner-occupied housing policy is ha housing becomes he mos imporan non-financial asses for Singaporeans. This can be gleaned from Table 1. Compared o France (47%), Japan (40%), US (28%) and UK (34%), Singapore has he highes raio of household residenial propery asses relaive o oal asses (a 51%). This is also rue for housing asse relaive o personal disposable income and GDP. 10 The CPF ineres rae on he ordinary accoun is pegged o he average of 12-monh fixed deposi and monh-end savings raes of he local banks rae. 11 See Saisical Highlighs (2003). 9

11 In he Naional Survey of Senior Ciizens (1995), 63.1% of elderly aged 60 and above repored housing among heir asses and 48.4% cied heir own house as heir mos imporan asse. While he provision of early wihdrawal from CPF savings has helped in housing finance, i has also dilued is original inen as a reiremen savings scheme, hereby reducing he accumulaed amoun available for reiremen needs. Indeed, he CPF-HDB link has creaed a class of asse-rich and cash-poor households, whose savings are plasered on he wall. The issue is how o unlock he housing equiy and o liquidae hese asses for old age consumpion purposes. == inser Table 1 == 3 Modelling reverse morgages Our model builds on he approach by Tse (1995b). I consiss of hree main pars, namely he reamen of he monhly annuiies as replacemen raios, he use of survival raios and various ineres rae models, respecively. However, we make four exensions o Tse s approach. Firs, we provide an economic inerpreaion of he pre-supposed level of life annuiy which is se according o differen arge replacemen raios o ensure adequae pos-reiremen living. Second, like Tse (1995b), Lachance and Michell (2002) and Chia and Tsui (2003a), he Cox-Ingersoll-Ross (CIR) model is used o generae yield curves for discouning and accumulaing cash flows. Bu monhly ineres raes are generaed insead of 6-monh raes. This faciliaes he compuaion of he monhly accumulaed loan value and expeced profi. Our approach also allows deah o happen monhly insead of in he middle of he year as assumed by Tse. Third, unlike Tse s 10

12 analysis which is based on a single period life able, we esimae and forecas moraliy raes using he Lee-Carer (1992) demographic model. Based on he forecass, we furher consruc he cohor moraliy raes using he approach by Bourbeau e al. (1997). More discussion is given in Secion 3.3. Fourh, Tse s assessmen of he RM marke is mainly based on some assigned profi margin issued by privae RM suppliers. However we also assess he viabiliy of RMs based on risk-free ineres raes. This implies ha some nonprofi organisaions, for example, he governmen who has access o low-cos capial, may be able o launch such a financial insrumen in he case of an incomplee RM marke. Hence our analysis bears significan policy implicaions for a missing marke. The naure of he RM marke enails lenders graning various guaranees o borrowers. Firs, RM insrumen has a residency guaranee in which he morgagors are allowed o remain in heir propery unil deah, regardless of he loan amoun. Second, under income guaranee, he monhly annuiy paymen will coninue as long as he homeowner lives in he home. Third, under repaymen guaranee, repaymen will only occur afer he demise of he las couple, hereupon he propery is sold. Fourh, being a non-recourse loan, he accumulaed loan value canno exceed he accumulaed propery value and he morgagor s oher asses canno be used o repay he loan. All hese guaranees ineviably spell differen risks for he lender, which are refleced by hree differen ineres raes. The risks for he lender include he longeviy of he borrowers. The longer he life expecancy of he lender, he higher is he probabiliy of loss for he lender as he accumulaed loan value may exceed he accumulaed propery 11

13 value. 12 As repaymen is over a longer ime frame, here are risks associaed wih volailiies of ineres raes and propery prices. I is crucial o disinguish hree ypes of ineres raes used in our model. 13 Firs, he cos of capial, denoed by r, is a risk-free rae of ineres, which represens he opporuniy cos of using funds. Second, an ineres rae i is used o discoun he fuure value of loan and repaymen cash flows. This ineres rae can be inerpreed as he lending rae which includes risk premium o reflec he uncerainy o he lender in he even ha a he ime of repaymen, he accumulaed loan value exceeds he accumulaed propery value. This is parly due o moraliy uncerainy which affecs he lengh of residence and he uncerainy on propery appreciaion raes. We assume i = r Third, an ineres rae y is used o discoun he loan balance ha incorporaes he necessary profi margin. I can be regarded as he cos of borrowing for he lender o finance he RM loan. We assume y = r for he privae supplier. The spread beween y and i also reflecs he inermediary role of he lender who has access o lower cos fund a y bu charges he borrower i for he use of fund. We assume ha he elderly do no have any ousanding morgage and ha a enure join life RM is aken up by a married elderly, boh of he same age. The eligible couple will hen receive a fixed monhly annuiy a he beginning of each monh ill he end of life. Furhermore, we assume ha he couple will no move ou of heir home. 12 See Phillips and Gwin (1993) and Michell and Piggo (2003) for an excellen exposiion of he risks facing he RM suppliers. Besides longeviy risk, ineres rae risk and propery appreciaion risk, hey also discuss specific house appreciaion risk and expense risk. 13 For example, Boehm and Ehrhard (1994) show ha compared o oher ypes of ineres-bearing asses, ineres rae changes are riskier for RMs. Boh Tse (1995b) and Michell and Piggo (2003) also incorporae he differen risks when modelling ineres raes. 12

14 Alhough deah is a random process, for convenience we assume ha deah occurs a he end of he monh. The RM will coninue upon he deah of one spouse. Only upon he deah of he las survivor would he loan be repaid hrough he sale of he propery. However, he propery sale will iniiae one monh afer deah and ha he sale will be compleed afer hree monhs. 3.1 Presen value of esimaed profi The privae supplier gives a RM loan o he homeowner in he form of monhly life annuiy payou. The monhly payou is accumulaed wih ineres unil he repaymen period. Le A denoes he fixed monhly payou from he RM. For exposiion purposes, we assume ha he elderly receive he firs monhly annuiy payou a age 62 and coninue o receive he payou a he beginning of each monh ill deah of he las survivor. We assume a maximum life span of 105 years, so ha can ake any value from 1 o 528 monhs. Upon he deah of he las surviving spouse in monh, he oal accumulaed loan balance (L ) is: L = AU j=1 j B = 1,, 528 (1) where U j is he accumulaion facor used o sum up he level monhly annuiy A from age 62 o he ime of deah a ime. Denoing i j as he nominal ineres rae which reflecs he supplier s cos of capial a monh j, U j can be expressed as follows: = i + n U j 1 (2) n= j 12 As i akes four monhs o complee he sale, B in equaion (1) is he addiional accumulaion facor given by: 13

15 4 i = + n+ B 1 (3) n= 1 12 In he simulaions, deerminisic and sochasic ineres raes are generaed o accumulae and discoun he fuure cash flows. Besides ineres rae charges, he supplier also levies oher adminisraive coss, including an originaion fee for iniiaing he RM insrumen. We assume ha he originaion fees, denoed by λ, are fully borne by he RM buyer and i is borrowed from he supplier who incorporaes he amoun ino he loan. As in Tse (1995b), we also se he originaion fee a 1% of he appraised value of he propery. Besides he originaion fee, closing coss are incurred a he ime of sale of he propery. Such coss cover fees for ile search and ile insurance, legal and appraisal services, surveys and inspecions, morgage axes, credi checks and oher relaed ransacion coss. 14 The closing cos, denoed by τ, is se a 3.5% of he iniial appraised value of he propery, which is he usual rae charged in Singapore. The accumulaed value of he propery ne of all ransacion coss is given by P as follows: P = P ( + 1) /12 * ( 1 λ)(1 + α τ U ) 0 ( ) (4) + 4 j= 1 ( 1+ i 12) * U = (5) j 14 In he Unied Saes, he Home Equiy Conversion Morgage (HCEM) imposes 2 % (of home value) for originaion and closing fee and 2% insurance premium. Besides hese cos, oher loading facors include insurance cos a 0.5 % over and above he ineres rae charges. 14

16 where P 0 is he iniial appraised propery value; α represens he rae of propery appreciaion or he annual growh rae of he appraised value of he propery. * U is he accumulaion facor o compue he cash flow of he propery, including he four-monh lags o complee he sale of he house. i j is he ineres rae charged by he supplier a monh j. In wha follows, we consider he profi maximizing behaviour of he RM suppliers under uncerainy. There are wo major sources of uncerainies. Besides he sochasic ineres rae movemens, he oher source comes from he ime of deah of he las survivor which in urn deermines he ime of repaymen. A he ime of repaymen, he supplier will compare he accumulaed ne value of he propery (P ) wih he value of he accumulaed loan (L ) o assess he profiabiliy of supplying he RM insrumen. During he iniial monhs of he launched RM, he accumulaed loan is definiely smaller han he accumulaed value of propery. However, as he RM progresses and as he ime of residence lenghens, he accumulaed loan becomes bigger and subsequenly i may exceed he accumulaed value he house. As such, i is necessary o compue he firs breakeven monh m* such ha a = m*, he accumulaed loan (L m* ) is greaer han he accumulaed ne value of he propery (P m* ). Hence, for all > m*, we have L > P. In oher words, if he borrower survives m* monhs or longer, he accumulaed ne propery value will fall shor of he accumulaed annuiy payous, hereby he supplier incurs a loss. As he probabiliy of loss is dependen on he moraliy of he RM holder, we define he probabiliy of loss o he supplier (γ) as: 15

17 528 γ = q (6) = m* where 62 denoes he probabiliy ha deah occurs wihin monh given ha he q 11 borrower has survived (-1) monhs from age 62. We nex examine he flow of funds for he supplier in erms of receips and coss. As a non-recourse loan, he oal value of he loan canno exceed he sale value of he propery. Thus a any repaymen monh, he receip (Q ) or he maximum claim amoun by he supplier is he minimum of he accumulaed loan L and he accumulaed appraised ne value of he propery P, ha is, Q = min {L, P } (7) The presen value of he cos o he RM supplier for providing he monhly level payou A up o he period is C, such ha: C = AW j j= 1 (8) where y 0 = 0 and j 1 1 = y 1 + n W j (9) n= 1 12 We assume ha he privae supplier has access o a lower cos of capial. The spread beween y and i hen represens he inermediary role of he RM supplier who charges he borrower a a higher rae for he use of fund, aking ino accoun he risk premium and profi margin. 16

18 Hence, he presen value of profi (π ) generaed a monh which is discouned o age 62 is given by: π = Q V C (10) where V is he appropriae discoun facor for Q given by: = + 4 y + n V 1 (11) n= 1 12 The mean presen value of profi (MPVP) is obained by weighing π (10) by he moraliy of he las survivor o obain: in equaion 528 MPVP = π q (12) = Noe ha he probabiliy of he las survivor who dies wihin he h monh given survival in he (-1) h monh from age 62 can be compued as follows: 15 1q 1 x= 1p62 p 62 (13) where p62 denoes he probabiliy of survival of he las spouse up o monhs from age 62. The Lee-Carer (1992) demographic model and he Bourbeau and Legare approach are adoped o forecas cohor survival probabiliy a each pos-reiremen age for he household using he abridged life ables for Singapore. Deailed are given in Chia 15 For compuaional simpliciy, we assume ha he married couples are of he same age and he evens of deahs are independen in probabiliy. See Chaper 10 of Jordan (1975) for deails. 17

19 and Tsui (2003a). In wha follows we highligh he major procedures required o calibrae he discoun facors and he join life survival raios respecively. 3.2 Ineres raes The presen value of he calibraed cash flows of reiremen expenses are o be discouned by he appropriae yield curves. As here are no consensus for modeling ineres raes 16, we follow Tse (1995a), Lachance and Michell (2002), and Chia and Tsui (2003a) o generae sochasic shor-erm ineres raes using he discreized version of he Cox, Ingersoll and Ross (1985) shor-erm model: 17 r = r + ( ra r ) + β r ε + 1 θ (14) where r is he shor-rae a ime. The second erm on he righ-hand side of (3) capures he deerminisic rend which consiss of he long-erm average ineres rae, r a, and he speed of mean-reversion, θ, respecively. For θ > 0, r is expeced o decrease and rever o r a if he curren rae is above he long-run mean, and vice versa. The hird erm capures he sochasic par, consising of independenly and idenically disribued sandard normal random variable ε +1 ; and β is he volailiy parameer. For comparison, we also employ wo deerminisic ineres rae models o discoun he fuure cash flows: he consan yield curve (CYC) model and he fixed yield curve (FYC) model. The CYC has a fla annual rae for all duraions. Choices include 16 See Term-Srucure Models in Campbell, Lo and MacKinlay (1997, Chaper 11). 17 Tse (1995a) is he only available empirical sudy on he sochasic behaviours of 3-monh Treasury-bill raes in Singapore and finds ha he CIR model provides reasonable replicaes of he yield curves.. 18

20 2%, 3% and 4%, respecively. The FYC is based on he average of he available hisorical raes for he governmen bonds since They comprise 2.3% for 3-monh bills, 2.5% for 1-year bills, 3.0% for 2-year bonds, 3.9% for 5-year bonds, 3.8% for 7- year bonds, 4.3% for 10-year bonds and 3.9% for he 15-year bonds, respecively. We use he 15-year rae as proxy for spo raes wih longer duraions. Spo raes for oher duraions below 15 years are obained by he mehod of inerpolaion. 3.3 Survival probabiliies Appropriae moraliy raes of he las survivor are required o compue he presen value of profi for he RM suppliers as given in equaions (10) o (12). We follow he approach by Chia and Tsui (2003a) o consruc he required survival probabiliies for he join life saring from age 62, up o and including 105. Basically he consrucion akes hree main seps. Firs, we predic he fuure moraliy raes of he elderly based on he abridged life ables using he Lee-Carer model (1992, 2000) for he male and female elderly of age 60 o 85 and above: ln m x = a x + b x k + ε x (15) k = µ + φ k -1 + η (16) where m x is he cenral deah rae in age class x in year ; a x is he addiive age-specific consan, reflecing he general shape of he age schedule; b x is he responsiveness of moraliy a age class x o variaions in he general level; k is a ime-specific index of he general level of moraliy; µ and φ are parameers; ε x is he error o he acual age schedule, assuming o follow a normal disribuion wih zero mean and a consan 19

21 variance; and η is he whie noise. The Lee-Carer model has been successfully applied o he G7 counries o forecas life expecancy a birh. See Tuljapurkar e al. (2000). For hose elderly aged above 85, he inerpolaion mehod proposed by Wilmoh (1995) is used. Second, we calibrae he abridged cohor life ables based on he prediced moraliy raes obained from Sep 1 using echniques developed by Bourbeau e al. (1997). Third, we conver he calibraed abridged cohor moraliy raes ino annual moraliy raes by Pollard (1989) s mehodology, and hen o monhly moraliy raes. Fourh, ransform he moraliy raes o survival raes up o fracional ages is ransformed o monhly inerval. Finally, we obain he join life moraliy raes by assuming he evens of deah are independen in probabiliy, and ha he married elderly are of he same age. 1 q XY = 1 p XY p XY where he probabiliy of las survivor is given by: p = 1 q * q (1 p ) (1 p ) XY X Y = 1 X Y = p X + py p X py 20

22 4. Calibraion and simulaion resuls Mone Carlo experimens are conduced o explore he feasibiliy of launching RM insrumens for public housing owners in Singapore. We obain values of L and P by simulaions using equaions (1) and (4) under differen model parameerisaion, including he iniial home value (P 0 ), he differen raes of propery appreciaion (α), he differen ineres rae pahs o reflec differen risk premium, and under differen join cohor survival probabiliies. All compuaions and esimaions are coded in Gauss. Despie he infinie ineres-rae pahs generaed by he CIR model as described in equaion (13), we have confined our simulaions o 5,000 runs. In our simulaion, we choose 4-room public housing owners as he benchmark household. This is suppored by he empirical evidence ha he greaes proporions of HDB owners (abou 39%) in year 2002 are in 4-room flas. In fac, 68% of he residens are living in HDB 4-room or larger flas or privae housing, up from 52% in While a decade ago, he greaes proporions of he HDB owners (abou 35%) were in 3-room flas. Because of greaer affluence, 42% of hese 3-room HDB owners have moved o 4- room or larger flas or privae properies in Table 2 shows he price range of he new 4-room flas offered by HDB for differen residenial zone and own in In pricing new flas for sale, HDB akes ino consideraion he affordabiliy facor. The prices of new 4-room fla are pegged o he average household income levels o ensure 18 See Singapore Deparmen of Saisics, (2001), Table

23 ha a leas 70% of all household can afford o purchase a new 4-room fla. I also shows he average valuaion of resale fla a marke prices, which varies according o locaion. 19 == inser Table 2 === Table 3 describes he average floor area of he differen public housing ypes and he profile of he households in erms of he average annual household income for differen housing ypes. The viabiliy of he RM insrumen o finance reiremen is assessed by comparing monhly annuiy paymens o he replacemen raios. These raios are expressed agains pre-reiremen household incomes. We se he benchmark mean household income a $3719 and he median household income a $ == Inser Table 3 === Table 4 summarises he value of parameers used in he benchmark scenario. We firs esimae he accumulaed loan amoun (L ) in equaion (1) by seing various monhly annuiy payous, saring from $900 and increasing i in seps of $100. For each level of payou, we compue he associaed ne accumulaed propery value P which is given in 19 Since March 1971, a resale marke in HDB flas emerged when owners of HDB flas were allowed o sell heir flas a marke prices, subjec o eligibiliy requiremens. The governmen inervenes in he HDB resale marke by seing he minimum occupancy period requiremen before resale is possible. In 1971, he period was se a hree years and was exended o five years in I has remained so unil 1979 when i was relaxed o wo and half year. The acive resale HDB marke has led o he senimen ha public housing is a cash cow for he milking of housing subsidies. (The Srais Times, April 19, 1997). As of January 2003, he minimum occupancy period was furher reduced o one year. 20 For he general populaion, he Census of Populaion 2000 indicaes ha he average household income in 2000 is $4,943 and he median household income is $3,607. Bu for HDB dwellers, he average household income is lower a $3,719 and he median household income is $3000. (HDB, 2000). 22

24 equaion (4). As long as P exceeds L, he supplier will make a profi. However a a paricular breakeven monh m*, such ha > m*, L will exceed P. As can be observed from Table 5, our simulaion resuls are consisen wih he inuiion ha he firs breakeven monh for he supplier is sooner for higher han lower annuiy payous. Table 5 also abulaes he probabiliy of loss for differen levels of monhly annuiy payous, using equaion (6). == Inser Table 4 === The presen value of profi (PVP) in equaion (10) depends on sochasic ineres rae flucuaions. Using he CIR model as described in Secion 3.3, we generae a yield curve o obain he corresponding PVP, and run 5000 replicaions o obain he mean value of PVP (MPVP). Table 5 also abulaes he values of MPVP, he sandard deviaion of PVP and is values a he 5 h and 95 h perceniles as well as he probabiliy of loss and he firs breakeven monhs a various monhly level annuiies. == inser Table 5 == Table 5 shows ha a he an iniial propery value of $240,000, and a monhly annuiy level of $1500, he probabiliy of loss for he supplier is only , wih a laer firs breakeven monh, which occurs a m* = 478. However, when he monhly annuiy payou is increased o $1600, he probabiliy of loss will be much higher a , wih he firs breakeven monh occurring sooner a m* = 350. If he privae RM supplier is 23

25 risk averse and prefers a smaller probabiliy of loss, hen he will pick a lower level of monhly annuiy, say a $900. Bu here may be no demand for he RM as he replacemen raio will be much lower han he expeced 70%. 21 Hence, he compleeness of he RM marke depends on seing an annuiy payou ha is adequae o finance reiremen expendiure, while minimising he probabiliy of loss o he supplier. Table 5 also indicaes ha when he monhly payou is increased o $1700 o achieve a replacemen raio of 46% of he pre-reiremen average income, he probabiliy of loss o he supplier is almos cerain a This is in sark conras o he negligible probabiliy of loss when he monhly annuiy payou is $1400. Hence we may inerpre he difference of $300 as he loading facor levied by he RM supplier. In his case he loading facor can be as high as 21% ($300/$1400). Our findings are consisen wih Caplin and many oher auhors who accord he incompleeness of he reverse morgage marke o he high loading facor. We nex evaluae he RM marke when he supplier is a non-profi moivaed supplier, for example he governmen. As profi is no a major consideraion for he public provider, in our compuaion of he accumulaed loan value (L ) in equaion (1), risk-free ineres rae r is used insead of he risk-embedded rae y which incorporaes he risk premium and profi margin. For easy comparison, we define he breakeven annuiy as he annuiy which yields zero MPVP for he privae supplier. We repea he simulaion 21 There is no single accepable replacemen raio. McGill e al., (1996) recommend using a replacemen rae of 73%. In Canada, financial planners ypically give a raio of 70% of pos-reiremen income as being required o mainain a comparable sandard of living experienced before reiremen. 24

26 process o obain he new breakeven monh for he public provider using he breakeven annuiy. Table 6 abulaes simulaion resuls which compare he adequacy of he RM insrumens provided by profi or non-profi moivaed suppliers of RM. These include he mean monhly payou a he breakeven annuiy, is sandard deviaion, he 5 h and 95 h perceniles, he probabiliy of loss, he firs breakeven monh, and replacemen raio based on he mean and median monhly income of he household. We repea he simulaions using differen iniial propery values assumpion, ranging from $220,000 o $300,000. == inser Table 6 == As can be observed from Table 6, for a given propery value of $220,000, he mean breakeven monhly payou is $1475. This level of breakeven annuiy represens a replacemen raio of 49% of he average household income. However, here may be no privae supplier as he probabiliy of loss is close o 0.581, implying ha i is highly probable ha he accumulaed loan balance is higher han he ne value of he propery a he ime of repaymen. Hence he RM marke fails. Can he governmen inervene in his marke? Table 6 indicaes ha a he same average breakeven annuiy, bu he probabiliy of loss for he public provider is now almos negligible as he public provider has lower cos of fund and is able o charge he loan balance a he risk free ineres rae. 25

27 In addiion, a a higher iniial propery value of $300,000, he homeowner can expec o unlock he housing equiy o yield an income which is almos 67% of he prereiremen average income. Bu again he marke may be missing as he probabiliy of loss for he privae supplier is sill high a However, he probabiliy of loss is only for a public provider. Furhermore, compared o he privae supplier, he firs breakeven monh for he public provider occurs 176 monhs laer. We concur ha profiabiliy is vial for he privae RM suppliers bu no so for he public supplier. Figure 2 displays he probabiliy of loss for boh he public and privae supplier using differen levels of monhly annuiy payous. I also compares he probabiliy of loss for various propery appreciaion raes. As can be gleaned from Figure 2, he probabiliy of loss is smaller a higher appreciaion raes. For example, when he annuiy level is a $1600, he probabiliy of loss for he privae provider is when α is 5%. Bu a a higher appreciaion rae a 6%, he probabiliy of loss is lower a In addiion, he probabiliy of loss for a privae supplier always lies o he lef of ha for a public provider, implying ha he public provider is able o suppor a reasonably higher level of life annuiy compared o he privae supplier. Hence he marke is more efficien under a public han a privae supplier. == inser Figure 2 == Boh Figure 2 and Table 7 show ha he compleeness of he RM marke depends on he appreciaion raes of he propery (α). Table 7 shows ha a α = 6%, he mean 26

28 monhly breakeven payou is $2154, hence implying a high replacemen raio of 72%. This no doub will arac a demand for RM. However, here may be no privae supply as he probabiliy of loss is This is due o he non-discourse naure of RM. However a a lower appreciaion rae of 3%, he mean monhly breakeven payou is $879, represening a low replacemen raio of 30%. The probabiliy of loss for he privae supplier is 0.5 and for a public provider. This is undesirable as even he public provider will suffer a loss. == inser Table 7 == Figure 3 plos he simulaed firs breakeven monh m* a differen monhly annuiy levels for boh he public provider and he privae supplier. As can be gleaned, he higher is he appreciaion rae, he higher is he breakeven monh. For example, using he benchmark parameers, when α =5%, he average firs breakeven monh for he public provider is a he 338 h monh compared o 511 h monh for he privae supplier. Wih α = 6%, he firs breakeven monh for he public provider and he privae supplier is a he 490 h and 364 h monh, respecively. == inser Figure 3 == Table 8 presens simulaion resuls using differen risk-free ineres raes, 3%, 4% and 5%. As he RM supplier charges a higher ineres rae, he lower is he mean breakeven payou annuiy and RM becomes less adequae o finance reiremen. A he 27

29 benchmark risk-free ineres rae of 3%, he monhly annuiy payou is $1609 which implies a replacemen raio of 54%. However a a higher ineres rae of 5%, he monhly payou is $1067, hereby implying a mere replacemen raio of 36%. == inser Table 8 == Moreover, values of he breakeven annuiy are affeced by various yield curves used in he simulaion exercises. Table 9 abulaes he simulaed mean breakeven monhly annuiy payou wih he yield curves generaed by he Cox, Ingersoll and Ross (CIR) sochasic model, fixed yield rae (FYC) and he consan yield curve (CYC) models, respecively. In general boh he CIR and FYC models give consisen values of probabiliy of loss and he firs breakeven monh. However, hose values generaed from he CYC model deviae subsanially from hose generaed from he CIR and FYC models. This may due o using fla raes o discoun cash flows. However, he simulaed values are relaively robus o ineres raes generaed by he CIR and FYC models. == inser Table 9 == 5. Conclusion We have examined he monhly annuiy payous in erms of replacemen raios and drawn implicaions on he adequacy of RM in financing reiremen needs. Using Mone Carlo simulaions, we compue he mean presen value of profi for differen levels of annuiy, he probabiliy of loss and he firs breakeven monh. We compare he 28

30 viabiliy of he RM under a privae supplier and a public provider based on differen coss of capial. Such a comparison yields policy implicaions on he role of HDB. Our simulaion resuls sugges a ransformed role for HDB from a public housing provider o a RM provider. This is because HDB has access o lower-cos funds, hereby enabling i more able o funcion as a supplier of RM in cases when he privae supplier fails. Our simulaion findings indicae ha alhough mos public housing homeowners have heir wealh ied up in heir flas, propery values are inadequae o suppor reiremen expendiure a he 70% replacemen raio. If hese home owners are willing o lower heir expecaion o aain a abou 54% of he reiremen income, hen i is possible o conver heir house ino a sream of fuure income by borrowing from he public supplier. However, a replacemen raio a 54% may be moderaely low compared o he recommended raio of 70% in mos of he developed counries. Bu here are alernaive sources of reiremen income in Singapore. For example, an imporan source is family suppor, paricularly from he children. 22 The living arrangemen among he elderly esifies o srong family suppor. As can be observed from Appendix 1, less han 13% of he elderly are no living wih spouse of children. Only 6.6% of he elderly live alone. In 2000, abou 60% of he elderly live wih heir working children. This is especially so for he elderly aged 75 and over. Abou 50% of hese old-old live wih he children only. Our sudy is no wihou caveas. For insance, we have no facored in he enure of HDB flas. As mos HDB flas are on lease for 99 years, finance companies may no 22 In Singapore, here is a Parens Mainenance Bill, whereby children are legally obliged o care for heir elderly parens. 29

31 be willing o ake on a fla wih less han 60 years lef on he enure. A more viable financing opion is for home owners o down-grade o smaller flas and hen o conver he financial gains from heir exising flas ino some forms of annuiy insrumens. In fac, in March 1998, HDB inroduced he Sudio Aparmen Scheme, whereby he elderly fla owners could sell off heir flas in he resale marke and use par of he proceeds o buy a smaller sudio aparmen from HDB. 23 The remaining fund may be used o op up heir medical savings accoun o ensure ha he elderly have adequae funds o mee heir medical needs or i may be invesed in annuiies which yield regular monhly income. Furhermore, since Ocober 2003, many HDB-imposed resricions on public housing were lifed, hereby allowing fla owners o moneise heir asses o suble he enire flas. Anoher cavea is ha we have excluded oher social dimensions in his paper which could possibly affec he success of RM. These facors include beques moives and he psychological relucance among he elderly o morgage heir homes o financial insiuions. Such social norms are likely o prevail so ha even wih a public provider, he RM marke may remain hin. These issues are lef for fuure invesigaion. 23 The sudio aparmens are smaller, which come in wo sizes - 35 o 45 sq m. They are specially equipped wih elderly-friendly feaures and are sold on a 30-year lease. 30

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