Evaluation of Reverse Mortgage Programs in Korea

Transcription

1 IRES IRES Workin Paper Series Evaluaion of Reverse Morae Prorams in Korea Seunryul Ma Yonhen Den April, 201

2 Evaluaion of Reverse Morae Prorams in Korea Seunryul Ma Governmen Employees Pension Research Insiue, Korea Yonhen Den Naional Universiy of Sinapore Absrac We analyze an acuarial model of reverse morae prorams in Korea. Our analyses provide a comparison beween he reverse morae loans srucured wih consan monhly paymens and hose ha make raduae monhly paymens which are indexed o he rowh rae of consumer prices. Usin he oal annual loan cos measure, we find ha he raduae monhly paymens approach is more efficien han he consan monhly paymens approach. Our analyses also confirms ha youner ae cohors are more sensiive o chanes in heir loan erms. We propose herefore ha he erms of reverse morae prorams should be srucured more conservaively for he relaively youner borrower roups. The resuls provide useful informaion o reverse morae borrowers considerin he various paymen opions, and perinen uidelines for he fuure operaion of reverse morae sysems in Korea and elsewhere. JEL classificaion: G21; G22; G28 Keywords: Insurance premium srucure; Reverse morae; Consan monhly paymens; Graduae monhly paymens; Toal annual loan coss raes

3 Evaluaion of Reverse Morae Prorams in Korea 1. Inroducion Korea is rapidly becomin an ain sociey. However, social securiy sysems are larely insufficien o secure he livin coss of is elderly. A overnmen-insured reverse morae proram was launched for he firs ime by he Korean overnmen in July , and reverse moraes have recenly come o be reconized in Korea as an imporan financial vehicle by which elderly homeowners can supplemen he exisin social securiy sysems. This paper evaluaes he appropriaeness of curren Korean reverse morae model. I compares alernaive paymen schemes currenly adoped in he Korean reverse morae proram, and provides uidelines for he fuure operaion of he reverse morae sysem. A reverse morae conrac allows a senior homeowner o ake ou a loan aains he equiy of his or her home. The lender makes annuiy paymens o he borrower as a percenae of he value of he house. In such a loan, he paymen sream of he morae conrac is reversed. The borrower does no have o make paymens on he loan as lon as he or she coninues o live in i, bu when he borrower becomes deceased and no loner occupies he house, he lender akes over he propery. Reverse moraes herefore allow equiy rich bu cash poor senior homeowners o conver par of heir home equiy ino ax-free cash wihou havin o sell heir homes. I ives he seniors financial sabiliy and independence, and also allows hem he opporuniy o reain conrol of he homes hey live in. The developmen of reverse morae prorams in he Unied Saes can be raced back o he 1960 s. The mos popular reverse morae proram in he U.S. currenly is he Home Equiy Conversion Morae (HECM) proram, which is he only reverse morae insured by he U.S. federal overnmen. The HECM was developed by he Deparmen of Housin and Urban Developmen (HUD) in 1987 o accomplish hree broad objecs: (1) o permi he conversion of home equiy ino liquid asses o mee he special needs of elderly homeowners; (2) o encourae and o increase he paricipaion of he primary and secondary morae markes in converin home equiy ino liquid asses; and (3) o deermine he exen of demand for home equiy conversion and he ypes of home equiy conversion moraes ha bes serve he needs of elderly households (Szymanoski, 1994). Alhouh numerous reverse morae producs have been developed since hen, here are hree major producs currenly on he marke, 1 Followin he inroducion of reverse morae proram for he elderly homeowners, since January 1, 2011, Korean overnmen also launched a new reverse morae proram for he elderly farmers who are income-poor bu farmland-rich for he firs ime in he world. However, in his analysis, we only focus on he problems relaed o he reverse morae proram for he elderly homeowners. 1

4 i.e., HUD s HECM, Fannie Mae s proprieary Home Keeper Morae, and Financial Freedom s proprieary Cash Accoun. Of hese hree major reverse morae producs, he HECM proram is currenly considered he safes because i is insured by he U.S. federal overnmen. Over 95 percen of all reverse morae borrowers choose he HECM produc. If hey choose an alernaive o he HECM, a privae eniy provides he uaranee insead. For example, Fannie Mae, he lares non-bankin financial services company in he world, uaranees he Home Keeper Moraes, and Financial Freedom, currenly he lares privae reverse morae lender and servicer in he U.S., uaranees he Cash Accoun (Ballman, 2004). Mayer and Simons (1994 a, b), Case and Schnare (1994), Merrill, Finkel, and Kuy (1994), and Fraanoni (1999) provide evidence of he sron demand for reverse moraes amon houserich, cash-poor elderly homeowners in he U.S.. Turnin o Korea, Cho, Park, and Ma (2004) esimaed ha he poenial demand for reverse morae producs in he counry could well exceed half a million homeowners aed 60 and over. Lim and Cho (1999), Cho and Ma (2004), and Cho, Park and Ma (2004) similarly demonsraed he poenial demand for reverse morae loans amons elderly homeowners in he Korean housin marke. The auhors suesed ha he overnmen-insured reverse morae sysem play an imporan role in supplemenin social securiy sysems currenly in place for he elderly in Korea. Followin from he HECM proram ha is prevalen in he U.S., reverse morae paymens can be dispensed in several ways. The borrower may choose o receive a lump sum cash paymen in advance, or in a enure plan, paymen can be made in pre-deermined monhly or annual amouns o be paid as lon as he owner resides in he house. Alernaively, in a erm plan, an annuiy can be paid for a fixed number of years (as deermined by he owner) ha is hen divided ino monhly cash paymens. Boh he enured and erm plans can be aumened by a line of credi secured aains he home s value, and muliple combinaions of he above opions are possible. Afer examinin he choices, he Korean overnmen firs decided o adop a enure plan wih consan monhly paymens for is reverse morae prorams 2. Afer a year, i launched alernaive enure plans wih eiher raduae monhly paymens peed o inflaion, or decreasin monhly paymens. Amon hese hree plans, consan and raduae monhly paymens plans are he subjec of he analyses in he curren paper. Because he consan monhly paymen plan provides a fixed monhly amoun for as lon as he borrower has he house as his (her) primary residence, he real value of he cash paid o hem 2 Policy makers in Korea posi ha paymens should be uaraneed over he borrower s lifeime, a leas in nominal erms. Monhly paymens are required by Korea reverse morae law in order o preven borrowers from usin up heir lump sum paymens wihou careful consideraion of heir fuure needs. I is for his reason ha we focus on he mehod of monhly paymens in his analysis. 2

5 monhly is likely o decline over ime because of inflaion. Considerin ha almos all public pension prorams in Korea are desined o provide full proecion aains inflaion, he monhly paymen plan in which monhly paymens are indexed o he rowh rae of consumer prices 3 provides an added sense securiy. For all is obvious benefis, he reverse morae proram presens a number of risks o boh he borrowers and he lenders. Under he HECM proram, hese risks are proeced hrouh he FHA morae insurance proram. 4 Reverse morae insurance premiums consis of an upfron sum and addiional monhly morae premiums (MIP) colleced from he borrowers. For he susainable operaion of he reverse morae sysem, i is imporan o consruc an appropriae insurance premium srucure which reflecs he expeced claims properly. Losses due o insurance claims are expeced o occur in he even ha he borrower s oal ousandin loan balance exceeds he appreciaed value of his (her) propery a he ime he loan is due and payable. However, i is well documened ha he exac imin of a loan becomin due and payable is boh unknown and difficul o esimae (Rodda, Herber and Lam, 2000, and Rodda, e al., 2003). When inroducin he overnmen-insured reverse morae proram in Korea, i was desirable o adop a sysem similar o he HECM proram in he U.S. as his had been esed and successfully improved many imes since is incepion in Consequenly, he Korean reverse morae model adoped he same insurance premium srucure as ha in he U.S. HECM proram. The exisin lieraure, includin Boehm and Ehrhard (1992, 1994), Szymanoski (1994), Chinloy and Mebolube (1994), Rodda, Herber and Lam (2000), Rodda, e al. (2003), Rodda, Lam and Youn (2004) and Pu, Fan and Den (2013), provides a horouh analysis of he risks associaed wih reverse morae loans, and presens pricin models for reverse moraes in he U.S.. More recenly, several empirical sudies have been published ha analyze reverse morae sysem in Korea. Yoo (2002) sudied he economic effecs of he reverse morae sysem, while Ma and Cho (2004) and Cho, Park and Ma (2004) analyzed he paymen plans of reverse moraes, and analyzed reverse morae relaed risks. Sun (2005) analyzed life insurer s sraeies for operain he reverse morae loans. Cha and Jun (2008) analyzed he pricin models prevalen in reverse morae insurance, and Ma (2006; 2008) suesed mehods for alleviain risks embedded in he consan monhly paymen proram. Lew and Ma 3 In HECM proram, o provide readily available cash for unexpeced expenses and ive borrowers a hede aains risin prices, i also allows o add a line of credi o a consan monhly advance (The American Associaion of Reired Person, 2005). 4 If he lender fails o provide paymens o he borrower, he insurer (uaranor) will ake over ha responsibiliy. Afer he borrower dies or move ou of he home, he insurer ensures ha he sale value of he home will cover he oal loan amoun. If he sale price is less han he accumulaed paymens plus ineres, he insurer pays he difference o he lender (Rodda e al., 2003). 3

6 (2012) compared reverse moraes on homes for elderly homeowners o ha of farmlands reverse moraed by elderly farmers, focusin on heir comparaive cos efficiency. The curren paper builds on his lieraure by lookin more closely a he appropriaeness of curren Korean reverse morae model. I compares he consan monhly paymen proram o he raduae monhly paymen proram, and provides uidelines for he fuure operaion of he reverse morae sysem. The Toal Annual Loan Coss (TALC) raes were firs evaluaed in order o calculae he acual efficiency of borrowers coss. A sensiiviy analysis was hen conduced of he reverse morae pricin models in order o beer undersand he insurer s level of risk. These calculaions were made based on a se of scenarios ha differed in erms of ineres raes and he level of appreciaion in housin prices. The remainder of he paper is oranized as follows: secion 2 presens he backround of Korean reverse morae proram, secion 3 presens an acuarial model of Korean reverse moraes focusin on enure plans, secion 4 repors he resuls of he analysis, and he las secion presens our conclusions. 2. The Korean reverse morae proram The Korean overnmen-insured reverse morae proram was firs launched in July To be eliible for a reverse morae loan, borrowers iniially had o own heir home, and be a leas 65 years. However, in Ocober 2008, he minimum eliible ae was lowered o 60 years in order o beer mee ciizen needs. As oulined above, reverse morae prorams are associaed wih many differen ypes of cash advances. Table 1 compares he paymen forms possible under he U.S. HECM and he Korean reverse morae proram. Table1. Comparison of paymen ypes: U.S. HECM proram vs Korean reverse morae (KRM) Tenure advances Paymen ype HECM KRM consan monhly paymen raduae monhly paymen - decreasin monhly paymen - Term advances consan monhly paymen - Tenure advances combined wih line of credi Term advances combined wih line of credi - Tenure advances: borrowers coninue ein monhly advances unil hey die, sell heir home, or permanenly move away. 4

7 Term advances: borrowers coninue ein monhly advances for a specific period of ime Line of credi: a personal accoun ha he borrower conrols. The borrower decides when o make a cash wihdrawal from his accoun, and how much cash o wihdraw Under he HECM proram, borrowers can chane heir paymen opions any ime durin he life of heir loan, subjec o a small fee. However, his is no possible afer closin a loan in he Korean model. Cash advances in he Korean model ake he form of enure paymens, or enure paymens alon wih a line of credi. In he laer, lump sum wihdrawals are capped a 50% of loan principal ( PL 0 ). In boh cases, borrowers can selec from consan, raduae, or decreasin paymens. The Korean Housin Finance Corporaion, which is he uaranor of he Korean reverse morae proram, has repored ha he number of reverse morae borrowers has risen rapidly wih ime. Fiure1 shows he annual number of reverse morae borrowers from he ime of he morae s incepion o Au Fiure1. Number of Borrowers in Korean Reverse Morae The mean value of he monhly paymens was 1,030 housand won % of borrowers of Korean reverse moraes received amouns of beween 500 housand and a million won as monhly paymens. Table 2 shows he disribuion of borrowers in he Korean reverse morae proram up o July 31, Table2. Disribuion of borrowers in he Korean reverse morae proram 5 On Oc. 7, 2012, US 1.0 dollar was equivalen o Korean 1, won. 5

8 Ae cohors and above (The averae borrowers ae is 73) House Value Below 100 million won million won million won million won million won 500 million won and over (The averae House Value is 278 million won) Paymen Types Tenure advances Tenure advances combined wih a line of credi Paymen Opions Consan Graduae Decreasin 11.2% 21.2% 28.6% 22.6% 16.4% 9.5% 30.6% 24.5% 15.1% 8.6% 11.7% 61.3% 38.7% 76.5% 0.9% 22.6% 3. Acuarial Model of Korean Reverse Morae 3.1. Korean Governmen sponsored Reverse Morae Model We compue he breakeven level of monhly paymens in he Korean reverse morae model usin he rial and error mehod under he condiion ha he presen value of he morae insurance premium (PVMIP) is equal o he expeced loss (PVEL) followin he radiional principle of insurance pricin (Ma, 2008). PVMIP Up 0 T ( x) 1 i 1 mip p x 1 T xmax OLB H 1 1 i mip OLB 1 pm m,,0 d * x OLB OLB pm1m 1i 1 H H 1 0, PVEL (1) 6

9 where, Up 0 is he upfron morae insurance premium, paymen period unil loan erminaion, OLB value, is he ousandin loan balance, will survive a x and pm mip is he rowh rae of housin price, x 1 x,, i * d x Tx is he remainder of he is he monhly morae insurance premium, is he monhly paymens, p x H is he probabiliy ha a borrower is he expeced house a ae x is he probabiliy ha a loan will be erminaed beween he ae is he expeced ineres rae, and m is he rae of insurance premium. In equaion (1), he expeced ineres rae i sands for expeced value of he acual ineres rae of he loan durin is period. To simplify hins for he seniors borrowin money under he reverse morae proram, he Korean overnmen adoped a fixed ineres rae. This fixed rae is used o calculae he ousandin loan balance ( OLB ) in each period, and is used also in he calculaion of he PVMIP and PVEL. Borrowers receive he paymens in he form of an annuiy unil he loan is erminaed. This expeced ineres rae is differen from he acual ineres rae ( r ) ha is chared a he iniiaion of he reverse morae loan. Lenders chare adjusable ineres raes on reverse morae loans and he rae is deermined by addin he predeermined marin of 1.1% o he CD (cerificae of deposi) rae a ime. In his case, he CD rae becomes he reference ineres rae ( r CD 1.1% ). Because he CD raes flucuae, he insurer of he reverse morae proram could face eiher a ne loss or ain. Maximum consan monhly paymen Under he consan monhly paymen scheme, he annuiy paymen he condiion ha PVMIP is equal o PVEL. pmc is compued under NPL0 pm c (2) 1 T ( x) i1 m where pm = he annuiy paymen (consan monhly paymen) c NPL 0 = he ne value of loan principal ( NPL0 PL Up 0 0 ) 7

10 PL 0 H 0 LTV ( LTV = Loan o Value raio 6 ) Maximum raduae monhly paymens The raduae monhly paymens scheme alleviaes he risk of a decrease in purchasin power over ime as paymens are indexed o he mean value of he rowh rae of consumer prices. We can calculae he minimum amoun ( he condiion ha PVMIP is equal o PVEL. pm0 ) of he raduae monhly paymens under pm o T ( x) 1 0 NPL 0 1 c 1 i1 m (3) where pm 0 c = he base amoun of raduae monhly paymen = he mean value of he rowh rae of consumer prices 3.2. Toal Annual Loan Coss (TALC) raes The TALC rae is he annual averae rae ha includes all he coss involved in a reverse morae, wihou considerin he survival probabiliies of he loan. The advanae of he TALC mehod is ha i presens he oal cos of he loan usin a sinle rae a he specific period ( n ) when he borrowers reach he ae of 100 (Scholen, 1996). Consan Monhly paymen Under he consan monhly paymens scheme, we can calculae he TALC raes (TALCR ) a he period n in equaion (4) usin a rial and error mehod. Min OLB, H pm 1 TALCR n n n c 0 n (4) Graduae Monhly Paymen 6 LTV is he raio of presen value of he morae benefis o he borrower s iniial house value. In oher words, i is he raio of a sinle lump sum premium in immediae annuiy o he house value. 8

11 In he case of raduae monhly paymens, we can also calculae TALC raes a period in equaion (5) usin he rial and error mehod.. Min n OLB, H pm 1 c TALCR n n n n (5) 3.3. The value of key facors Loan survival s and erminaion probabiliies Because hisorical daa on reverse morae erminaion raes (he probabiliy ha he loan will become due and payable) were simply no available, he U.S. HUD used a number of unesed assumpions in deerminin probable erminaion raes, includin ha he prepaymen rae would be 0.3 imes he moraliy rae of he younes borrower in he family 7. In he Korean reverse morae model, he loan erminaion probabiliy was eneraed under he assumpion ha he prepaymen rae would be 0.2 imes he 2005 moraliy rae for females. This adjusmen was made afer considerin Koreans demoraphic daa. This daa was updaed in 2012, and he 2010 moraliy rae was insead adoped in he acuarial model (Lew and Ma, 2012). The relaionship beween he monhly loan survival probabiliies ( probabiliies ( * d x ) is demonsraed below. p x ) and he erminaion * dx px dx px 1 p x (6) where d x = modified moraliy rae afer considerin he prepaymen rae a ae x d x q x 1.2, qx = 2010 moraliy rae for females a ae x Fiure2 shows he loan survival probabiliies ( ha were applied in he acuarial model of Korean reverse moraes. p x ) and Loan erminaion probabiliies ( d ) * x 7 HECM loans erminae when he borrower leaves her home permanenly, simply chooses o pay off he loan, or when she dies. Because acual erminaion relaed daa was no ye available when he premiums were oriinally se, an assumpion was made ha erminaions would occur a 1.3 imes he rae of moraliy (Rodda, Lam and Youn, 2004). 9

12 Fiure2. Loan survival and erminaion probabiliies (a ae 65 and ae 85) The rowh rae of housin prices, and expeced ineres raes In he Korean reverse morae model, he rowh rae of housin prices was assumed o be 3.5% per annum, based on he mean housin price rowh rae in he years beween 1986 and Because he mean value of he 10-year overnmen bond raes was 5.12% beween June 2002 and May 2007, he expeced ineres rae was assumed o be 7.12% per annum in his period afer addin a lender s marin of 2%. Because of subsequen chanes in he economic environmen, he housin price rowh rae was adjused in Feb 2012 o 3.3%, and he expeced ineres rae was also adjused o 6.33% in he acuarial model (Lew and Ma, 2012). Upfron cos In he Korean reverse morae model, he up-fron insurance premium is 2% of a house s value. The monhly morae insurance premium (MIP) is calculaed based on an annual rae of 0.5% of he loan s ousandin balance. In his analysis, we assume ha he up-fron cos involves only an up-fron premium of 2% of he home s value 8. When deerminin he level of 8 In he HECM, afer loan closin, every borrowers is required o pay 2 percen of he maximum claim amoun (adjused propery value) as an up-fron (iniial) insurance premium, as well as a monhly MIP accordin o he annual rae of 0.5% of he loan s ousandin balance (Rodda, Herber and Lam, 2000, and Rodda e al., 2003). The iemized coss of a HECM loan includes an oriinaion fee, hird-pary closin coss, an up-fron morae insurance premium, a monhly MIP, a servicin fee, and ineres (AARP, 2005). In 1999, he ypical HECM borrowers paid $1,800 in oriinaion fees, $1,500 in closin coss, $2,100 in up-fron insurance premiums or a oal of $5,400 for iniiain a HECM (Rodda, Lam and Youn, 2004). In his analysis, we assume ha he up-fron cos is composed only of he up-fron insurance premium (2% of housin values) because he oher coss are relaively small in he Korean reverse morae model. The up-fron cos creaes a lare hurdle ha has essenially blocked he refinancin of reverse moraes. Therefore, prepaymen raes in reverse morae loans can be conrolled by he upfron coss (Szymanoski, 1994, and Rodda, Lam and Youn, 2004). 10

13 he monhly paymen, we firs evaluae he presen values of he expeced claim losses and he expeced insurance premiums under he predeermined insurance premium srucure. Nex, if here is a discord in presen values of he PVEL and PVMIP, we modify he level of he monhly paymens usin a rial and error mehod. 4. The Resuls 4.1. The LTV raios and monhly paymens As indicaed earlier, we focus in his paper on wo paymen mehods possible under he enure plan. One is he consan monhly paymens mehod, and he oher is he raduae monhly paymen mehod which is indexed o he rowh rae of consumer prices. The LTV raios and monhly paymen levels which saisfy he condiions of he acuarial equivalence principle (PVMIP=PVEL) are as follows. We assume in our analysis ha he up-fron cos is 2% of housin value. Table3 shows he maximum values of he LTV raios and he monhly paymens when he price of all he borrowers homes is assumed o be 300 million won. Table3. Maximum value of LTV raios and monhly paymens (uni: Korean 1,000 won) Cons Grad PL 0 125, , , , , ,146 PVMIP 16,111 14,806 13,327 11,768 10,302 9,072 LTV 41.82% 48.33% 55.95% 64.75% 74.41% 83.72% pm c ,042 1,284 1,616 2,091 PL 0 132, , , , , ,886 PVMIP 14,879 13,782 12,528 11,192 9,922 8,844 LTV 44.19% 51.23% 59.36% 68.56% 78.36% 87.29% pm 0 Noe: 1. PL 0 = 300 million won * LTV raio ,008 1,319 1, The mean value of he rowh rae of he consumer price index was assumed o be 3% per annum 3. Cons: consanly monhly paymen proram, Grad: raduae monhly paymen proram As Table3 demonsraes, because here is a proporional relaionship beween he level of LTV and a borrower s ae, a relaively older roup of borrowers could receive larer monhly paymens han a relaively youner roup of borrowers. Fiure3 illusraes he LTV raios of borrowers on boh he consan and raduae monhly paymen prorams accordin o he borrower s ae. We can confirm ha he LTV raios of he consan monhly paymen proram are relaively smaller han ha of he raduae monhly paymen proram for individuals in he 11

14 same ae roup. The resuls indicae on averae ha he borrowers who selec he raduae opion ain reaer profis from he reverse morae proram. Fiure3. Comparison of LTV raios Fiure4 shows he rend of monhly paymens in Korean reverse morae prorams. In he raduae monhly paymen proram, he level of monhly paymen increases by 3% each year as we can see from Grad 65 (he case of a borrower aed 65) and Grad 85 (he case of a borrower whose ae is 85) in Fiure4. Fiure4. Trend of monhly paymens in Korean Reverse Moraes 12

15 4.2. Evaluain oal annual loan coss (TALC) raes In he raduae monhly paymen proram, he level of LTV is bier han in he consan monhly paymen proram, bu he value of he PVMIP is smaller. Thus, we expec he value of he TALC o also be smaller in he raduae monhly paymen proram compared o he consan monhly paymen proram. We evaluae he values of he TALC raes on boh he paymen prorams. Table4 repors he raes evaluaed a various imes ( = n) accordin o he borrowers ae. Table4. Toal annual loan coss Ae 65 Ae 75 Ae 85 n Cons Grad Cons Grad Cons Grad % 38.47% 24.32% 28.00% 18.03% 19.50% % 10.65% 9.16% 9.16% 8.29% 8.04% % 7.85% 7.76% 7.28% 7.41% 6.85% % 6.65% 7.14% 6.41% 1.69% 0.80% % 4.96% 3.37% 2.09% % 2.78% Under he HECM proram, here is a overall cap ha comes ino effec if he borrower s risin loan balance rows equal o he value of he home. This limi is called he non-recourse limi (AARP, 2005) and is se a 93% of he home s value, leavin 7% for he coss of sellin he home (Scholen, 1996). In he Korean reverse morae proram, he non-recourse limi was assumed o be 91% of he home s value afer akin ino accoun pariculariies of he Korean housin marke. Fiure5 shows he TALC raes by comparin wo monhly paymen plans in he case of borrowers aed 65 and 85, respecively. 13

16 Fiure5. TALC raes (Ae 65 and 85) TALC raes decline over ime because he raio of up-fron coss o oal deb shrinks over ime, and also because he borrowers oal ousandin loan balances a ime =n is limied by he value of heir homes. In Fiure5, approximaely afer n=72 and a ae 65 and 85, he TALC raes in he mehod of consan monhly paymens (Cons) become bier han ha of he raduae monhly paymens (Grad). From he borrowers perspecive, Fiure5 suess ha he mehod of raduae monhly paymens (Grad) is on averae more cos efficien han he consan monhly paymens (Cons) mehod because of chanes in he borrowers life expecancy. A borrower is expeced o live an addiional 252 monhs a ae 65, and an addiional 84 monhs a ae 85. Thus, borrowers who believe ha heir lifeime is likely o exceed ha of he eneral populaion may benefi realy by selecin he mehod of raduae monhly paymens. In he real world, however, as we repored in Table 2, only 0.9% of Korean reverse morae borrowers selec he raduae monhly paymens opion. Accordin o a recen sudy by Kim and Ma (2011), he demand for reverse moraes in Korea is fuelled mainly by elderly individuals whose public pension is insufficien o mee heir livin expenses. Such borrowers perhaps selec he consan monhly or decreasin monhly paymen plan because such plans ive hem a relaively lare amoun of money upfron. However, his indicaes also ha reverse morae borrowers in Korea do no reconize he economic benefi of he raduae monhly paymen scheme. 9 We hope his analysis provides perinen informaion for fuure borrowers faced wih he ask of selecin heir paymen opions. 9 We examined he TALC raes in he mehod of decreasin monhly paymens (Dec) and found he raes in Dec o be bier han Cons afer n=72 a ae 65 and

17 4.3. Sensiiviy analysis In his secion, we examine he chanes in insurer s risk ha resul from he flucuaion in boh house price appreciaion raes and in ineres raes. The acuarial model for Korean reverse moraes currenly assumes a 3.3% per annum appreciaion rae in house prices, and an expeced ineres rae of 6.33% per annum. The simulaed resuls from acuarial model are enerally quie sensiive o he assumpions on house price appreciaion and ineres raes (Rodda, Herber and Lam, 2000). For sensiiviy esin, we assume hree possible annual house price appreciaion raes ( = 2.3%, 3.3%, 4.3%), and hree possible ineres raes ( i =5.5%, 6.33%, 7.0%). We es he raes usin daa for borrowers aed 65 and 85. Tables 5 and 6 repor he resuls of he sensiiviy analyses of he acuarial model by lookin a he house price appreciaion raes and expeced ineres raes for borrowers aed 65 (i.e. relaively youner borrowers roup) and 85 (i.e. relaively older borrowers roup). In Tables 5 and 6, and in Fiure 6, we see ha he variabiliy in he raios of PVEL o PVMIP is disincly hiher for he relaively youner ae roup (e.. ae 65) han for he relaively older ae roup (e.. ae 85) due o chanes in he loan erms. These resuls sues ha he maniudes of sensiiviy for he older borrowers is hiher han ha of youner ones (e.. ae 65) who are more sensiive o he shock of chanes in house price and ineres raes han he relaively older ae roup (e.. ae 85). Table5. Resuls of he Sensiiviy Tes (Consan monhly paymens) (uni: Korean 1,000 won) Ae Assumpion Combinaion PL 0 =4.3%, Opimisic =4.3%, 65 sable pessimisic Ae Assumpion Combinaion 85 Opimisic sable pessimisic pm c PVEL PVMIP PVEL/PVMIP , i =5.5% i =6.33% 3,177 14, =4.3%, i =7.0% 7,230 14, =3.3%, =3.3%, 145, =3.3%, =2.3%, =2.3%, i =6.33% 29,412 14, =2.3%, pm c PVEL PVMIP PVEL/PVMIP i =5.5% 8,315 15, i =6.33% 14,806 14, i =7.0% 19,984 14, i =5.5% 23,218 15, i =7.0% 33,704 14, i =5.5% PL 0 =4.3%, 3,504 9, =4.3%, i =6.33% 5,040 9, =4.3%, i =7.0% 6,325 9, =3.3%, i =5.5% 7,377 9, i =6.33% 9,072 9, =3.3%, 251,146 2,091 =3.3%, i =7.0% 10,415 9, =2.3%, i =5.5% 11,885 9, =2.3%, i =6.33% 13,554 9,

18 =2.3%, i =7.0% 14,839 9, Table6. Resuls of he Sensiiviy Tes (Graduae monhly paymens) (uni: Korean 1,000 won) Ae Assumpion Combinaion PVEL PVMIP PVEL/PVMIP =4.3%, , Opimisic =4.3%, i =6.33% 3,423 13, =4.3%, 65 =3.3%, sable =3.3%, i =6.33% 153, ,782 13, =3.3%, =2.3%, pessimisic =2.3%, i =6.33% 26,888 13, =2.3%, Ae Assumpion Combinaion PVEL PVMIP PVEL/PVMIP Opimisic 85 sable pessimisic i =5.5% PL 0 pm 0 i =7.0% 6,566 13, i =5.5% 8,828 14, i =7.0% 17,696 13, i =5.5% 22,352 14, i =7.0% 30,031 13, PL 0 pm 0 =4.3%, 3,806 8, =4.3%, =4.3%, i =7.0% 6,199 8, =3.3%, i =5.5% 7,440 8, =3.3%, 261,886 1,778 =3.3%, =2.3%, =2.3%, =2.3%, i =5.5% i =6.33% 5,115 8, i =6.33% 8,844 8, i =7.0% 9,954 8, i =5.5% 11,617 8, i =6.33% 12,969 8, i =7.0% 14,016 8, Fiure6. Sensiiviy Comparisons (Raios of PVEL o PVMIP) The resuls in Table 5 and Table 6 indicae ha he PVEL values will be alered boh by flucuaions in he housin price rowh raes, and in he expeced ineres raes. However, he 16

19 PVMIP value will only be chaned by flucuaions in he expeced ineres rae. Considerin he resuls of he sensiiviy es (Tables 5 and 6), i becomes clear ha he acuarial model adoped for Korea s sinle insurance premium srucure should be se up more conservaively for he relaively youner borrower roup han for he older borrower roup. This is because he variabiliy in he PVEL o PVMIP raio is more sensiive o poenial shocks in he rowh rae of housin price and o expeced ineres raes in he relaively youner roup. Under he sinle insurance premium srucure adoped here, we can consider sein he expeced ineres rae (i ) in accordance wih he borrowers ae. In order o consruc a simple model which can be easily undersood by elderly home owners, we choose o fix he expeced ineres rae in he model. Also for he sake of simpliciy, he presen values of expeced insurance premiums and expeced claim losses are assumed o say consan reardless of he loan duraion. However, considerin he cash flow risks from each conrac, i is pruden o expec ha ineres raes will in fac differ markedly accordin o loan duraion. Followin from his, he expeced ineres rae for he relaively youner ae roup should be hiher han ha of older borrowers. Consequenly, monhly paymens calculaed usin he more realisic ineres raes would be lower han ha calculaed usin he curren Korean reverse morae model for he relaively youner ae roup. The curren paper analyzed Korean reverse morae prorams usin a deerminisic model of housin prices and ineres raes. However, he ineres rae associaed wih a borrower s ousandin loan balance will ineviably flucuae afer he loan is closed, as will he reference ineres rae (ha is he yield on a CD wih a 91 day mauriy). As such, housin values can also be expeced o move sochasically. Followin from his, if he reverse morae lender coninuously pays a consan amoun o borrowers every monh accordin o he equaions and assumpions in his analysis, he reverse morae insurer could suffer serious marke risks in he lon erm. Therefore, i is imporan o follow his sudy wih an evaluaion of a reverse morae insurer s risk afer considerin he sochasic processes of housin prices and ineres raes, as well as afer considerin he loneviy risk. 5. Conclusion Insurance claim losses are expeced o occur in he even ha a borrower s oal ousandin loan balance exceeds he marke value of he propery a he ime he loan is due and payable. A reasonable insurance premium srucure can preven reverse morae lenders o be overly exposed o he marke risks. We analyzed he Korean reverse morae sysem focusin primarily on he consan monhly paymens mehod and he raduae monhly paymens 17

20 mehod where monhly paymens are indexed o he rowh rae of consumer prices. We evaluaed he values of he TALC raes associaed wih hese moraes, and found ha from a borrower s perspecive, he raduae monhly paymens approach is more efficien han he consan monhly paymens approach. Finally, we conduced a sensiiviy analysis and found ha he youner ae roup (e.. ae 65) is more sensiive o he shocks in fuure house price appreciaion raes and ineres raes compared o he relaively older ae roup (e.. ae 85). Therefore, he acuarial model in he Korean reverse morae sysem should be se more conservaively for youner han older borrowers. The resuls of his sudy offer valuable insih ino he acuarial model of he reverse morae sysem and informaion provided can beer inform he selecion of paymen opions by reverse morae borrowers. Mos imporanly perhaps, he findins of he presen sudy provide useful uidelines for he fuure operaion of reverse morae sysems in Korea. References AARP (The American Associaion of Reired Person), Home Made Money: A Consumer s Guide o Reverse Moraes. Ballman, T. E., The Reverse Morae Hand Book: A Consumer s Guide for Senior Homeowners. Jawbone Publishin Co. Boehm, T. P., Ehrhard, M. C., Are reverse moraes suiable bank invesmens? Real Esae Review Fall, Boehm, T. P., Ehrhard, M. C., Reverse moraes and ineres rae risk. Journal of he American Real Esae and Urban Economics Associaion 22(2), Case, B., Schnare, A. B., Preliminary evaluaion of he HECM reverse morae proram. Journal of he American Real Esae and Urban Economics Associaion 22(2), Cha, I. K. and Jun, H. J. A Sudy on he Pricin Model in Reverse Morae Insurance Usin Opion Theory, The Journal of Risk Manaemen 19(1), Chinloy, P., Mebolube, I. F., Reverse moraes: conracin and crossover risk. Journal of he American Real Esae and Urban Economics Associaion 22(2), Cho, D. H., Ma, S. R., Economic feasibiliy of reverse morae annuiy for he elderly housin welfare. Korea Housin Sudies Review 12(1), Cho, D. H., Park, C. K., Ma, S. R., A Sudy on Inroducion of Reverse Morae Sysem. Korea Financial Supervisory Service. Fraanoni, M. C., Reverse morae choices: A heoreical and empirical analysis of he borrowin decisions of elderly homeowners. Journal of Housin Research 10(2), Kim, J. J., Ma, S.R., A Sudy on he Deerminans of he Demand for Reverse Morae in Korea. Mimeo. Lew, K. O., Ma, S. R., A Sudy on Evaluain Toal Loan Cos Rae of he Reverse Morae Producs. Housin Sudies Review 20(3),