The Buildin of ew Reverse Morae Paymen Plans in he Korean Housin Marke Ma, Seunryul Cho, Deokho Absrac A reverse morae sysem is reconized as an imporan financial vehicle o supplemen curren social securiy sysems for elderly homeowners. This paper develops a new paymen plan, called a raduaed monhly paymen which considers he livin expendiures for he elderly and he consumer price index and analyzes wo ypes of enure plans,: a consan monhly paymen plan and a new raduaed monhly plan based on differen scenarios on he value of house and he loneviy of borrowers in Korea. This paper evaluaes he raios of he monhly paymens o he monhly livin coss for households wih heads 65 years of ae and older hrouh he reverse morae sysem. The objecive is o deermine a beer paymen sysem for elderly households in Korea which is a rapidly ain sociey. This would help elderly homeowners selec a more appropriae paymen ype of reverse moraes based on heir life expecancy and livin coss ha can be applied o any oher rapid ain counry. Keywords: Reverse morae sysem, enure paymen plan, consan and raduaed paymen prorams. I. Inroducion Korea has experienced a rapid increase in he number of elderly households. I has radually approached he ain sociey like oher developed counries, and as a resul, he social securiy This paper was suppored by he Korea Research Foundaion Gran (KRF-25-3- B57) and will be published a Vol.42(2). Senior Research Fellow, Korea Housin Financial Corporaion Professor of Daeu Universiy(Correspondin Auhor: chodh@daeu.ac.kr)
sysem has becomes a major social issue. In order o resolve his issue, Korea has uilized a overnmen insured reverse morae sysem (Cho, e. al., 24). This sysem uilizes a loan aains a borrower s home ha does no need o be repaid as lon as hey live in heir own housin. I is he reverse ype of he paymen paern of he radiional forward morae. The sysem assiss housin rich and cash-poor elderly homeowners o access addiional income o mee livin and medical expenses hrouh he liquidaion of heir housin asses. Homeowners do no need a minimum income o qualify for a reverse morae. They can keep heir homeownerships like a forward morae bu are sill responsible for payin heir propery axes and homeowner insurance and for makin propery repairs. There are hree basic ypes of reverse morae sysems, dependin upon he paymen mehod: enure, erm, and credi line plan. A enure plan makes a monhly consan cash advance for he moraors as lon as he borrowers live in heir home. A erm plan makes a monhly consan cash advance for a fixed period and a credi line plan makes paymens up o he available principal limi whenever he borrower requess hem (HUD, 26). This sudy focuses on he enure morae because i implemens he life-ime monhly paymens for he elderly homeowners. However, his sysem pays a consan amoun monhly o elderly households wihou considerin chanes in livin expenses or he consumer price index. This paper develops a new paymen mehod, called he raduaed monhly paymen, which considers he livin coss of elderly homeowners as well as he consumer price index in order o reduce he risk of chanes of financial marke and livin condiions. These wo paymen ypes are applied o he Korean housin marke and he poenial maximum levels of he wo monhly paymen ypes are analyzed. This new paymen mehod will conribue o develop he acuarial model of reverse morae and also increase he feasibiliy of reverse morae prorams in he Korean financial marke because i reflecs he real financial marke circumsance. In order o achieve hese oals, he second secion reviews he previous sudies on he demand of he reverse morae sysem and noes is paymen plans. The hird secion builds a raduaed paymen plan of enure reverse morae, considerin livin expendiures and he consumer price index (). The fourh secion examines he sabiliy of ime series daa and evaluaes he profile, over he moraor s life-ime, of he percenae of required expendiure provided by several differen scenarios. The final secion will sues some policy implicaions of he new reverse morae paymen plans. II. Lieraure Review of he Reverse Morae Paymen Sysem As he previous descripions, several reverse morae sysems have been developed. However, here is no alernaive for securin he livin coss for he life-ime of households and
reducin he defaul risks. This paper focuses on he Home Equiy Conversion Morae (HECM) insurance demonsraion proram which is a represenaive ype of reverse morae sysems insured by he federal overnmen in he Unied Saes where he reverse morae is successfully implemened. I was creaed by he aional Housin Ac in 987 (HUD, 26) and desined o provide elderly homeowners wih a financial vehicle o ap heir housin equiy wihou sellin or movin from heir homes. I allows a borrower aed 62 and older o borrow aains he equiy in a propery ha has limied ousandin deb. In Ocober 998, Conress alered he HECM ino a permanen proram which is secured by he overnmen for he lenders and borrowers. As a resul, he numbers of loans increased o 5, and a oal of nearly 4, reverse moraes have been insured under he HECM proram since Ocober 999 (Rodda, e. al., 2). Rasmussen, e. al. (995) assered ha boh borrowers and lenders underake risk in he process. Reverse moraes pose hree main sources of collaeral risk meanin ha he loan balance may row o exceed he value of he collaeral for lenders. The hree risks are: ) he borrower may live in he propery so lon ha he coninuin paymens o he borrower exceed he value of he home; 2) ineres raes may raise hereby increasin he ineres paymens and increasin he deb; 3) he propery value may drop such ha he value is less han expeced when he loan becomes due. Moreover several scholars have noed he risks of he reverse morae sysem. Boehm and Ehrhard (992) assered ha he cash flows of a reverse morae mirrored he paern of a life insurance policy in erms of he supporin livin coss of he elderly. They (994) developed a valuaion model ha quanified he ineres rae risk inheren in fixed rae reverse moraes and showed ha he ineres rae risk of reverse moraes was reaer han ha of eiher a ypical coupon bond or a reular morae. Therefore, a reverse morae should consider chanes in fuure ineres raes. Szymanoski, Jr. (994) analyzed he risk included in reverse morae insurance and demonsraed how borrower loneviy, ineres raes and propery value chaned all affeced pricin. However, HECM only provide moraors wih a consan monhly paymen in a enure proram irrespecive of heir loneviy, livin expendiure, and consumer price index, wihou considerin he risk of reverse moraes. A monhly loan advance is fixed in nominal erms. I has he poenial o resul in a mismach beween livin expendiures and paymen amoun and also would resul in less demand for he proram if he inflaion is predic (AARP, 23). Therefore, his paper develops a new paymen ype, called a raduaed monhly paymen ha akes ino consideraion he chanes in livin expendiures and he consumers price index in order o lessen he risks of reverse morae sysem in order o reflec he real siuaion of he Korean housin financial marke and he demand of livin expendiure of elderly. 2
III. Buildin of Paymen Plan Models. The Measuremen of Fuure Housin Values The presen value of housin price o he fuure cerain ime (), which considers he monhly rowh rae of housin price ( ) and ineres rae ( r ), can be calculaed wih his equaion: PV HP HP ( + r ) + + r PV presen value of a fuure housin price HP curren housin price () HP HP ( + ) fuure value of housin price () rowh rae of housin price a ime (,2,3,,) r nominal ineres rae a ime (,2,3,,) + ) ( + r ) in equaion (). If he ime series ( The ne discoun raio is presened as ( ) of his ne discoun raio is confirmed saionary, he mean value of he ne discoun raio (DR) can be used for calculain he presen value of he fuure housin price (Hasla, e. al., 99), Ma and Cho (23)). And hen equaion () can be simplified like equaion (2). () PV + HP + r HP DR (2) PV presen value of fuure housin price HP curren housin price () averae rowh rae of housin price r averae nominal ineres rae DR (( + ) ( + r) ) mean value of ne discoun raio 2. Deerminin he Maximum Level of Loan-o-Value (LTV) This sudy deermines he poenial maximum level of LTV (Loan-o-Value) accordin o he fiures of DR in equaion (2). LTV is calculaed by muliplyin he curren housin price HP ( ) by he fiures of DR. This sudy assumes ha he required upfron coss (see noe 3) 3
of a reverse morae are 5% of he curren housin prices, based upon he sudy of Cho, Park, and Ma (24). Ma and Cho (23) showed empirically ha he fiures of DR were smaller han. and as he lenh of he mauriy became loner, he fiures of DR became smaller in he Korean financial marke. This phenomenon evenually resuls from he fac ha he mean value of he rowh rae of he housin price is less han ha of marke ineres rae in Korea. 3. Maximum Level of a Consan Monhly Paymen This sudy examines he maximum level of a consan monhly paymen based on he maximum level of oal paymen amoun ( LSUM ) over each period. I assumes he lifeexpecancies for he elderly as 2, 8, 5, and 2 years, based upon he life expecancy able and for he convenience of comparison. In a siuaion where he paymens of an annuiy are made a he beinnin of ineres conversion periods, his annuiy is called annuiy due (Muksian, 23). The maximum level of consan monhly paymens (annuiies) can be calculaed as equaion (3) in annuiy due. LSUM a (3) + i a consan monhly paymen LSUM maximum level of oal paymen amoun + i cumulaive discoun facor (CDF) remainder of borrower s expeced life i annuiy rae Afer deerminin he maximum level of lump sum ( LSUM ), he maximum level of consan monhly paymens ( a ) can be deermined usin he annuiy rae. The specified level of annuiy rae ( i ) can be decided hrouh arranemens beween lenders and borrowers. 4. Maximum Level of ew Paymen Type Graduaed Monhly Paymen This sudy develops and analyzes a new monhly paymen mehod of reverse morae sysem- he raduaed monhly paymen ha reflecs he rowh rae of livin expendiures and 4
he rowh rae of consumer prices. I is defined as follows: Provided ha he ime series of boh he rowh rae of livin expendiures and he rowh rae of consumer prices are saionary respecively, he sarin amouns of he raduaed monhly paymen ( a ) can be calculaed usin he followin relaionship. + + + I i a i a LSUM (4) LSUM maximum level of lump sum PV presen value of fuure housin price + i a presen value of consan monhly paymen + + I i a presen value of raduaed monhly paymen mean value of rowh rae of expendiure ( ), or consumer price ( ) I Based upon his relaionship, he level of sarin amouns of raduaed monhly paymens ( ) can be deermined as in equaion (5) a + + I i LSUM a (5) a base sarin amoun of raduaed monhly paymens LSUM maximum level of lump sum + + I i cumulaive discoun facor (CDF) Due o price inflaion, he risk of decreasin purchasin power acually rises wih he passae of ime. However, if a borrower selecs raduaed monhly paymens linked eiher o price inflaion or required livin expendiures, hen he risk of sufferin a shorfall in required expendiure could be, in he former case, considerably reduced or in he laer case avoided compleely. 5
VI. Comparison beween Consan Monhly Paymen Plans and Graduaed Monhly Ones. Daa This paper uses he monhly daa from he aparmen house 2 price index (APT) of Kookmin Bank from January 986 o December 23 as a proxy variable of he housin price. The monhly daa on afer-ax yields on aional Housin Bonds wih 5-year mauriy (HB5 (afer ax)) 3 of he Korea aional Saisical Office was used as a proxy variable of he marke ineres rae in he same period. The ime series of he ne discoun raio (DR ) is eneraed usin he rowh rae of APT price and he ime series of HB5 and also he rowh rae of APT by lo differencin he ime series of APT price. Fiure shows he ime series of monhly rowh raes of APT (G(APT)), HB5(afer ax), and he ne discoun raio (DR ) from January 986 o December 23..4 monhly rae.8.6.2.6.4..8.6.4.2..2..98 mean:.9975.4 -.2.96.2 86 88 9 92 94 96 98 2 -.4.94 86 88 9 92 94 96 98 2 G(APT) HB5(aer ax) DR Fiure. Monhly rowh raes of APT (G(APT)), HB5(afer ax), and he rend of DR (.986 o 2.23) In order o esimae he rowh raes of livin expendiures ( ), he ime series of monhly expendiures, (which is provided by he Korean aional Saisical Office, for salary and wae earners households for he same period), was uilized. I also conduced seasonal adjusmens o he ime series of expendiures usin he mehod of raio o movin averae. In order o obain he rowh rae of consumer prices ( ), he ime series of he quarerly consumer price index for he same period was uilized. Fiure 2 shows he index of livin expendiures () and consumer price index (). 6
4 2 2 8 6 4 2 86 88 9 92 94 96 98 2 Fiure 2. Trends of and (/4.986-4/4.23 (8yrs)) The ime series of rowh rae of expendiure ( ) was eneraed by lo differencin he seasonally adjused ime series of expendiure and he ime series of rowh rae of consumer price ( ) was eneraed by he same way. Fiure 3 shows he rowh rae of expendiure ( ) and he rowh rae of consumer price ( )..6.2.8.4. -.4 -.8 86 88 9 92 94 96 98 2 (rowh) (rowh) Fiure 3. Growh raes of expendiure ((rowh)) and consumer price ((rowh)) 2. The Mehods of he Uni Roo Tes This paper presens he es of he saionariy of ime series. A ime series is said o be saionary if he enerain funcion for he series does no iself chane hrouh ime. This 7
sudy conducs he uni roo es in order o confirm he saionariy of ime series. This sudy uses he mehods of he ADF es (Aumened Dickey-Fuller es) and PP es (Phillips-Perron es) for esin he saionariy of he ime series. ADF and PP ess use differen mehods o conrol for hiher-order serial correlaion in he series. The es reression for he ADF es is as follows. y y y m δ y + α y + ε (6) i i i m i i β + δy + α y + ε (7) i m i i β + β 2 + δy + α y + ε (8) i The ADF es makes a parameric correcion for hiher-order correlaion by assumin ha he y series follows an AR(p) process and adjusin he es mehodoloy. The ADF approach conrols hiher-order correlaion by addin laed difference erms of he dependen variable y o he rih-hand side of he reression. Phillips and Perron (988) propose ha he PP es is a uni roo es mehod ha can be used in a siuaion where he assumpion on error erm, u, does no mee he condiion of u ~ iid(, σ 2 u ). The es reression for he PP es is he AR() process. The OLS (ordinary leas squares) esimaion is primarily conduced wih he DF model and modified -saisics ofδ, coefficien from he AR() reression, o accoun for he serial correlaion in u. If he ime series of he ne discoun raio, he rowh rae of expendiure, and he rowh rae of consumer price are confirmed saionary respecively, i can be concluded ha he mean values of he ime series can be used for calculain equaion (2) o (5) in his research. Table repors he descripive saisics of he rowh raes of aparmen prices ( bonds (HB5), and he ime series of ne discoun raio (DR). APT ), housin Table. The descripive saisics of he rowh rae of APT price ( ax), and ne discoun raio APT Variable Mean Sd. Dev APT.499.3868 HB5(afer ax).798.2385 ), HB5 (afer oe: ne discoun raio.9975.432 he rowh rae of APT price APT Table 2 repors he resuls of he uni roo es of he mehods of ADF es and PP es on he 8
rowh raes of aparmen prices ( APT ) and housin bonds (HB5). Table 2. The resul of uni roo es ADF saisic PP saisic APT -4.258-6.747 HB5(afer ax) -3.257-3.8 Criical values : %: -4.3, 5%: -3.439, %: -3.39 oes.. Resuls from boh Inercep and rend are included in he es equaion. 2. ull hypohesis: es series has a uni roo. 3. Criical values for rejecion of hypohesis of a uni roo are from MacKinnon. The ADF and PP ess show ha he ime series of APT price ( ) rejec he null hypohesis ha here is a uni roo a a % level of sinificance. Bu he ime series of HB5 do no rejec he null hypohesis a a 5% level of sinificance in ADF es and a a % level of sinificance in PP es. Therefore, he ime series of he rowh rae of APT price ( saionary, bu he ime series of HB5 is nonsaionary. And his analysis should deermine wheher he nonlinear expression ( ) ( + r )) ( APT APT ) is + is iself a saionary series or no. onlinear ransformaions applied o nonsaionary ime series can yield saionary series (Hasla, e. al., 99). As Table 3 indicaes, he ime series of he ne discoun raio is saionary. This resul noes ha he mean value of he ne discoun raio ( ( + ) /( + r) ) can be used in calculain he presen value of fuure housin prices Table 3. Tes for uni roo Variable ADF saisic PP saisic Criical values ne discoun raio -3.7676-5.74 %: -3.463, 5%: -2.875, %: -2.574 oes.. Resuls from only Inercep are included in he es equaion. 3. Deerminin he Maximum Level of Lump Sum Value The maximum level of LTV (loan-o-value) can be deermined accordin o he fiures of DR in equaion (2). Based upon he mean value of he ne discoun raio ( DR.9975) in Table, he values of DR can be calculaed and i is possible o evaluae he maximum level of LTV as shown in Table 4. If i is assumed ha he curren housin value ( HP ) is 2 million Won ($ abou, Won) and he upfron coss 4 of a reverse morae loan are 5% 9
of he curren housin value ( HP 5% ), he maximum values of lump sum ( LSUM ) are shown in Table 4. Table 4. The maximum level of lump sum and loan-o value raion (uni: Korean Won( )) The remainder of borrower's expeced life ( ) 24 (2 yrs) 26 (8 yrs) 8 (5 yrs) 2 ( yrs) LTV.5.53.59.7 LSUM 94,747,59,574,97 2,749,47 34,7,69.Table assumes ha curren housin value ( HP ) is 2 million Won ($abou,). 2. I assumes ha upfron coss are 5% of housin value because borrowers finance all loan coss from a reverse morae loan wihou payin conrac coss. ) Deerminin he Maximum Level of Consan Monhly Paymens Afer deerminin he value of LSUM, he maximum level of consan monhly paymens can be deermined by usin equaion (3). Ma and Park (24) showed ha he ime series of he life insurers raio of oal asse profis (RTAP) was saionary and he mean value of life insurers RTAP was approximaely 7% per annum in Korea. This raio is applied o equaion (3) as he annuiy rae and Table 5 repors he monhly cumulaive discoun facor (CDF) usin (7/2)% as he monhly annuiy rae. The maximum level of consan monhly paymens ( a ) can be deermined usin he value of CDF as shown in Table 5. Table 5. Cumulaive discoun facor (CDF) and maximum value of consan monhly advance (uni: ) 24 (2 yrs) 26 (8 yrs) 8 (5 yrs) 2 ( yrs) CDF 29.7349 23.339.95 86.6288 a 73,32 823,54,7,55,548,8 oe:.cdf, where, i.7/2 + i 2) Deerminin he Maximum Level of Graduaed Monhly Paymens This sudy analyzes he raduaed monhly paymens ha reflec he rowh rae of expendiures and consumer prices, respecively. The maximum level of base sarin amouns
( a ) of raduaed monhly paymens is deermined usin equaion (5). Table 6 shows he resul of he uni roo es on hese ime series from he firs quarer 986 o he las quarer 23. Table 6. The resul of uni roo es Variables ADF saisics PP saisics Criical values (rowh) -6.6737-6.685 %: -3.527, 5%: -2.936, (rowh) -7.295-7.377 %: -2.5892 oe: Resuls from only Inercep are included in he es equaion. I is shown ha he saisics of boh ADF es and PP es rejec he null hypohesis ha here is a uni roo a % level of sinificance in Table 6. This analysis noes ha he wo ime series are saionary, and ha he mean value of hese variables in evaluain he maximum level of base sarin amouns ( a ) of raduaed monhly paymens is shown in equaion (5). Table 7. Descripive saisics (/4.986-4/4.23) Variables Mean Sd. Dev. Mean( per year) (rowh).263.3629.45% (rowh).494.963 4.6% Table 7 shows ha he mean value of he rowh rae of expendiures ( ha of consumer prices ( ) is.263 and ) is.494. I shows ha he mean value of rowh rae of expendiures is more han wo imes ha of consumer prices durin he las 8 years (he firs quarer 986 he las quarer 23) in Korea. Table 8 shows he monhly cumulaive discoun facors (CDF), where 7% is he annuiy rae ( i.7) and he mean values of rowh raes are.263 and.494 respecively. The maximum level of base sarin amouns ( a and a ) of raduaed monhly paymens can be deermined usin he value of CDF and CDF. Table 8. The cumulaive discoun facor (CDF) The remainder of borrower's expeced life ( ) 24 (2 yrs) 26 (8 yrs) 8 (5 yrs) 2 ( yrs) CDF 26.899 239.9777 9.679 25.35
CDF 72.2986 6.24 39.8956.2254 a 362,89 423,27 588,22,72,49 a 549,9 634,76 85,95,325,47 + oes.. CDF ; where,.263/4, i.7/2 + i 2. CDF + + i ; where,.494/4, i.7/2 3. Table assumes ha curren housin value ( HP ) is 2million won. 4. I assumes ha upfron coss are 5% of curren housin price. 5. a PV ; The base sarin amoun of usin he value of CDF 6. a PV ; The base sarin amoun of usin he value of CDF 3. Comparison of Consan and Graduaed Paymens Fiure 4 shows he maximum level of consan monhly paymens and he base sarin amouns of raduaed monhly paymens. The level of base sarin amoun usin he value of is he lowes and he level of consan monhly paymen is he hihes amon hese hree paymen mehods.,8,,6,,4,,2,,, 8, 6, 4, 2, (2 y r) (8 y r) (5 y r) ( y r) 24 26 8 2 a() a() a(co) Fiure 4. Comparison of each paymen mehod 2
Table 9 shows he raios o consan monhly paymens ( a CO.). Table 9. Raios o consan monhly paymens ( a CO.) The remainder of borrower's expeced life ( ) 24 (2 yrs) 26 (8 yrs) 8 (5 yrs) 2 ( yrs) a.5.5.58.69 a.75.77.8.86 a.... CO In he case where he remainder of he borrower s life expecancy is 24 monhs, Table 9 shows ha he level of consan monhly paymens is wo imes as lare as ha of base sarin amoun in he case of usin he value of and.33 imes as lare as ha of base sarin amoun in he case of usin he value of. However, in he raduaed monhly paymen mehods, he paymens row over ime. Fiure 5 shows he rends of monhly paymens o 26 monhs. 5 8 6 4 2 8 6 4 2 9 7 25 33 4 49 57 65 73 8 89 97 5 3 2 29 37 45 53 6 69 77 85 93 2 29 a()26 a(co)26 a()26 Fiure 5. Trends of monhly advances of each paymen mehod I shows ha he amoun of monhly paymens of he raduaed ype become hiher han ha of consan monhly paymen afer he 2h monh. Table repors monhly income and expendiure per household by he ae of household head. Accordin o he analysis of Seo and Kim (2), he appropriae level of monhly expendiure of 6 6 years of ae and over is.78 imes as lare as ha of 5-59 years of ae in Korea. 3
Table. Income and expendiure per household by he ae of household head (uni: ) Ae of household head 5-59 years : (A) 6 years and over : (B) (B)/(A) Monhly Income 2,7,,58,.69 Monhly Expendiure,663,,297,.78 oe. The number in parenhesis is he appropriae level of expendiure (ha is he mean value of required monhly expendiure) on he basis of Seo and Kim (2) Table repors he raios of raduaed paymens usin he value of o required expendiure (required expendiure.) ha are classified accordin o he level of curren housin price ( HP ). For insance, if HP is 2million won and life expecancy is 26 monhs, he level of raduaed paymens usin he value of only covers 27% of he required expendiure; if HP is 6million won, i covers 8% of required expendiure. If HP 2million won and 2, he level of raduaed paymens usin he value of chares 68% of required expendiure and if expendiure. HP 6million won, i is 24% of required Table. Raios of raduaed paymens usin he value of o required expendiure The remainder of borrower's expeced life ( ) 24 (2 yrs) 26 (8 yrs) 8 (5 yrs) 2 ( yrs) required expendiure.... RE 2million won.23.27.37.68 RE 4million won.46.54.74.36 RE 6million won.69.8.2 2.4 In he case of raduaed paymens usin he value of, he level of each raio o required expendiure in Table is consan over ime (,2,3,,) because he rowh rae of monhly paymens covers ha of livin expendiures. However he raios of consan paymens o required expendiures will decline over ime because i does no reflec he rowh rae of expendiures. The raios of raduaed paymens usin he value of o required expendiure is similar o he case of consan paymens houh i is no equal in size because he value of is smaller han ha of. 4
Table 2 shows ha he raios of consan paymens o required expendiures decline over ime. For insance, if HP 2million won and 26, he level of consan paymens a is 52% of required expendiure, ha a 26 i only covers 3% of required expendiure. These fiures are considerably hiher han he case of raduaed paymens of usin he value of (see Table ). If HP 6million won and 26, hen a i covers 56% of required expendiures, a 26 i represens 39% of required expendiures. These resuls show ha in he case of usin he value, he consan paymen is beneficial o he borrower who owns relaively he lower cos housin bu he raduaed paymen is o he hiher price homeowners even houh raios o he required expendiure decline over ime. Table 2. Raios o required expendiure (required expendiure.): consan paymens Remainder of Raios o required expendiure Housin borrower s Required wih he passae of ime Value Expeced life Expendiure (million ) T 24 2 8 26 24 24 (2 yrs) 26 (8 yrs) 8 (5 yrs) 2 ( yrs) 2...46.4.2.4.. 4..92.8.42.28.22.2 6..38.2.63.42.33.3 2..52.45.24.6.3 4..4.9.48.32.26 6..56.35.72.48.39 2..64.55.29.2 4..28..58.4 6..92.65.87.6 2..98.84.45 4..96.68.9 6. 2.94 2.52.35 Table 3 presens he raios of curren levels of raduaed paymens ha reflec consumer price ( ime. ) o he level of required expendiure and he dynamic rends of hese raios hrouh Table 3. Raios o required expendiure (required expendiure.): raduaed paymens usin he value of Remainder of borrower s Housin Value Required Expendiure Raios o required expendiure wih he passae of ime 5
expeced life (million ) T24 2 8 26 24 2..35.32.23.8.6.5 24 4..7.64.46.36.32.3 (2 yrs) 6..5.96.69.54.48.45 2..4.37.26.2.8 26 4..8.74.52.42.36 (8 yrs) 6..2..78.63.54 2..5.47.33.27 8 4..2.94.66.54 (5 yrs) 6..53.4.99.8 2..84.77.54 2 4..68.54.8 ( yrs) 6. 2.52 2.3.62 I shows ha he mehod of raduaed paymens usin he value of reflecs relaively hih levels of raios in is early saes, bu declines hrouh ime as expeced. For insance, if HP 2million won and 26, in case of 65 years old, he level of raduaed paymens of usin he value of a is 4% of required expendiure and if HP 6million won and 26, he level of raduaed paymens usin he value of a is 2% of required expendiure. These fiures are hiher han he case of raduaed paymens of usin he value of bu lower han he case of consan paymens. Meanwhile, if HP 2million won and 26, he level of raduaed paymens of usin he value of a 26 is 8% of required expendiure and if HP 6million won and 26, he level of raduaed paymens of usin he value of a 26 is 54 % of required expendiure. These fiures are lower han he case of raduaed paymens usin he value of bu hiher han he case of consan paymens. In summary, he sarin amoun of paymens for consan paymens is hiher han ha of a raduaed paymen. However, he ap becomes smaller over ime and is eliminaed afer monhs. Afer ha poin, he raduaed paymen is hiher han he consan paymen. Therefore, a raduaed paymen sysem would be beer ha a consan paymen sysem because he elderly need more money for healh care and home say coss as hey e older (Sucki, 25). I also reduces he risks of housin financial marke because i reflecs he chanes of housin price and ineres rae. Comparin he resuls of Table, 2, 3, elderly homeowners could selec more appropriae levels of reverse moraes and paymen mehods accordin o heir aes (remainder of borrower s expeced life), he curren values of heir homes, savins, oher 6
poenial social securiy benefis, and individual preferences because a raduaed paymen sysem can provide he elderly wih several differen prorams. V. Conclusions Reverse moraes have several posiive effecs for he elderly as he previous discussions. Seniors do no have o move or lose he ile over heir mos imporan asse bu he reverse moraes only allow borrowers o ap a proporion of heir housin equiy. I also suppors he spouses afer he borrowers die. Moreover he lef-over asses can be ransferred o heir heirs afer payin off he loan. This sudy conribues o wo aspecs on he reverse moraes. A firs his paper heoreically developed a new paymen plan, called a radual paymen mehod in he reverse morae sysem- ha considers he chanes in livin coss and consumer prices even hrouh a raduaed paymen mehod is available in he forward morae sysem. The paper also analyzes he paymen raios o he required expendiure of wo paymen mehods, a consan paymen which is he paymen sysem of HECM in he Unied Saes and a raduaed one ha uses he daa on four differen life expecancy roups and hree differen housin values. Second, his sudy empirically examined he effecs of wo differen reverse morae sysems in order o mee livin expendiures and o improve he qualiy of life for elderly homeowners in he Korean housin financial marke. This paper focused on he analysis of he appropriae mehods of enure paymens for reverse moraes. The raios of monhly livin coss o a consan paymen ype and a raduaed paymen ype would help elderly homeowners selec more appropriae paymen mehods of reverse moraes accordin o heir needs and heir housin values. This paper also provides more informaion abou risk, discoun raes, chanes in housin values and he consumer price index. A raduaed paymen sysem can alleviae he risk of decreasin he purchasin power on he reverse morae sysem due o lon-erm financial marke insabiliy. This proram can be applied o he housin finance marke of any oher rapid ain counry as well as he Korean housin finance marke where a reverse morae sysem will be inroduced evenually. I also is suiable for counries wih unsable financial markes because i reflecs he chanes of livin cos and he housin financial marke. These resuls sues a new paymen ype ha considers he livin coss of moraors and chanes in fuure housin prices and provides appropriae paymen alernaives based on he loneviy of moraors and housin value. Uncerainy on fuure healh and lon-erm case expenses will increase he demand of reverse morae by appin he housin asses wihou movin ou or sell heir homes. Hih level of 7
homeownership and home equiy can provide he seniors wih an imporan opporuniy o say heir own housin wihou movin ou by usin he reverse moraes. These funds can be used for he lon-erm care funds in home. Consequenly he reverse moraes can be uilized as one of he mos imporan policy alernaive for he elderly welfare. However his sudy only focused on he simulaion of several differen reverse moraes because he reverse morae sysem is no inroduced in he Korean housin financial marke. Therefore, he more specific sudies on he each differen aspec of reverse morae prorams are needed afer is inroducion in he Korean housin marke. oes Life expecancies of females are as follows; 63 years of ae: 2.3 years, 65 years of ae: 8.43 years, 69 years of ae: 5.8 years, 77 years of ae: 9.62 years (Sources: 2 Life ables, aional Saisical Office, Korea). 2 Aparmen housin is he mos popular ype which is no renal housin bu similar wih he condominium and a house price index is a naion-wide official daa which is released by he Korean overnmen. This daa is surveyed by Kookmin Bank in order o deermine he ransacion prices of ownership housin and lump sum deposi renal housin. The sarin year of his survey is 986 and is sample size is abou 9, observaions.. 3 There are several bonds such as Korea Securiies Deposiary, aional Housin Bond, and Corporaion Bond in Korea. However, aional Housin Bond is a represenaive proxy variable of he marke ineres rae in he housin marke. 4 An upfron cos is composed of he oriinaion fee (2%), upfron morae insurance premium (2%), and hird-pary closin coss and ec. This paper assumes ha oal upfron coss are 5% of housin values. 5 There is no a life expecancy daa on households. Therefore his paper uses an averae life expecancy daa of females as a proxy variable of ha of households because females live loner han males. This paper use 28 monhs (8 years) as a crieria year for comparin several differen prorams. 5 There are no daa on he livin expendiure of ae 65 years old elderly people. Therefore he daa on he ae 6 is used as a proxy variable. References American Associaion of Reired Persons (AARP), 23. Home Made Money: A Consumer's Guide o Reverse Moraes. Boehm, Thomas P., Michael C. Ehrhard., 992. Are Reverse Moraes Suiable Bank Invesmens? Real Esae Review, Fall, 4-45. Boehm, Thomas P., Michael C. Ehrhard., 994. Reverse Moraes and Ineres Rae Risk, Journal of he American Real Esae and Urban Economics Associaion 22(2), 387-48. Chinloy, Peer and Isaac F. Mebolube., 994. Reverse Moraes: Conracin and Crossover Risk, Journal of he American Real Esae and Urban Economics Associaion 22(2), 367-386. Cho, Deokho and Seunryul Ma., 24. Economic Feasibiliy of Reverse Morae Annuiy for he Elderly Housin Welfare, Housin Sudies Review 2(), 75-99. 8
Cho, Deokho., Chankyoon Park and Seunryul Ma., 24. A Sudy on Inroducion of Reverse Morae Sysem, Korea Financial Supervisory Service. Hasla, Joseph H., Michael ieswiadomy., and D. J. Sloje., 99. Are e Discoun Raios Saionary?: The Implicaions for Presen Value Calculaions, The Journal of Risk and Insurance 58 (3), 55-52. Korea aional Saisical Office, 2 Life ables, aional Saisical Office, hp://www.nso.o.kr. Korea aional Saisical Office. 26. aional Housin Bonds wih 5-Year Mauriy. hp://www.nso.o.kr Kookmin Bank. 26. Monhly Daa of aional Aparmen House Price Index, hp://kbsar.com Ma, Seunryul and Deokho Cho., 23. A Sudy on Lon Term Forecasin Mehod of Real Esae Prices for Reverse Annuiy Morae Sysem, Korean Insurance Journal he 66 h Ediion, 55-83. Ma, Seunryul. and Sanbum Park., 24. A Sudy on Life Insurer s Approaches Deerminin he Assumed Ineres Rae, Korean Journal of Insurance Sudies 5(3), 3-29. Muksian, Rober., 23. Mahemaics of Ineres Raes, Insurance, Social Securiy, and Pensions, Upper Saddle River,.J. : Pearson Educaion. Phillips, C.B. Phillips and Pierre Perron., 988. Tesin for a Uni Roo in Time Series Reression, Biomerika, Vol.75, 335-346. Rasmussen, David W., Isaac F. Mebolube and Barbara A. Moran., 995. Usin he 99 Public Use Microdaa Sample o Esimae Poenial Demand for Reverse Morae Producs, Journal of Housin Research 6(), -23. Rodda, David T., Chrisopher Herber. and Hin-Kin Lam., 2. Evaluaion Repor of FHA's Home Equiy Conversion Morae Insurance Demonsraion Final Repor, U.S. Deparmen of Housin and Urban Developmen. Scholen, Ken., 996. Your ew Reiremen es E A Consumer Guide o he ew Reverse Moraes 2nd Ediion, CHEC Press. Scholen, Ken., 998. Reverse Moraes for Beinners, CHEC Press. Seo, Jae-Eun. and Tae-Wan Kim., 2. An Analysis on he Acual Condiion of Elderly Income and A Plan o Improve he Sysem of Income Securiy, KIHASA. Sucki, Barbara R. (25), Use Your Home o Say a Home: Expandin he Use of Reverse Moraes for Lon-erm Care: A Blueprin for Acion, he aional Council on he Ain. Szymanoski, Jr., Edward J., 994. Risk and he Home Equiy Conversion Morae, Journal of he American Real Esae and Urban Economics Associaion 22(2), 347-366. US Deparmen of Housin and Urban Developmen (HUD; 26). hp://www.hud.ov 9