Mortgage Default and Prepayment Risks among Moderate and Low Income Households. Roberto G. Quercia. University of North Carolina at Chapel Hill

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2 Mortgage Default and Prepayment Rsks among Moderate and Low Income Households Roberto G. Querca Unversty of North Carolna at Chapel Hll Anthony Pennngton-Cross Marquette Unversty Chao Yue Tan Unversty of North Carolna at Chapel Hll September

3 Abstract To assess the sustanablty of affordable housng credt, a unque sample of communty renvestment loans s analyzed. Condtonal probablty (hazard) of default tends to be hgher and prepayment, lower for lower ncome groups. However, after controllng for observed mortgage and borrower characterstcs, the hazards converge and even reverse n order of magntude. Furthermore, very low-, low-, and moderate-ncome groups react wth dstnct patterns to changes n the loan-to-value rato and the local unemployment rate. Fnally, more fnancally stretched borrowers (those wth hgh debt-to ncome ratos) seem to ntate the default opton more aggressvely as home equty declnes. 2

4 I. Introducton For the last 20 years, through multple admnstratons and regardless of poltcal leanng, there has been a consstent publc polcy effort to ncrease access to homeownershp. Homeownershp rates peaked at approxmate 69 percent n 2004 through 2005 and have snce declne to approxmately 67 percent as of the second quarter of 2010 (Current Populaton Survey/Housng Vacancy Survey, Seres H-111 Reports, and Bureau of the Census) 1 The postve mpact of movng a famly from a rental unt to an owned home can come from many dfferent sources, from changes n peer groups to more cvc prde and a stronger physcal and emotonal connecton to the area and local schools (See for example, Haurn, Parcel, and Haurn 2002, Aaronson 2000, and Manturuk, Lndblad, and Querca 2010). However, as a result of the subprme bust, the near collapse of prmary and secondary mortgage markets, property markets, fnancal markets, and fnally the labor markets, the desrablty of extendng home buyng credt to low and moderate ncome famles s agan beng questoned. Cumulatve default rates on subprme loans orgnated n 2006 surpassed 35 percent and on prme loans surpassed 10 percent (Amromn and Paulson 2010). These default rates represent households that faled as homeowners. Due to the sgnfcant falure rate, some have begun to queston whether homeownershp s the best way for some households to nvest and consume shelter and housng servces (Florda 2010). 1 Avalable as of September 2010 on: 3

5 Publc polces, such as the Communty Renvestment Act (CRA), the Affordable Housng Goals for Fanne Mae and Fredde Mac, and the Federal Housng Authorty, encouraged the fnancal communty to ncrease access to credt beyond tradtonal boundares. Due to these polces and many other factors, access to credt and hence homeownershp was expanded to nclude more households wth fnancal constrants, but safety and soundness concerns stll mposed some lmtatons. Eventually, subprme lendng practces extended credt to almost any borrower, even f borrowers could not document ncome and down payment sources. As a response to the crss, t s understandable that many began to queston whether the extenson of credt was mprudent and could be at least partly to blame for the collapse of the mortgage market. Researchers fall on both sdes of the argument. Some contend that the problem was the fact that low ncome homeowners are rsker borrowers (McArdle 2009, Bhutta 2009); others contend that these borrowers are as rsky as other borrowers (and sometmes a better rsk (Van Order and Zorn 2002, Mlls and Lubuele 1994, Calem and Wacther 1999). Fnally, others contend the problem was not the borrower but the rsky subprme mortgage products themselves compared wth the less rsky communty renvestment products (Dng, Querca, L, and Ratclffe 2010). The recent lterature has focused on the performance of hgh cost subprme mortgages (Dans and Pennngton- Cross 2008 and Pennngton-Cross and Ho 2010). However, the study of the performance of communty lendng mortgages has been lmted due to data avalablty problems. 4

6 Calem and Wachter (1999) examne the loan performance of a program admnstered by one bank n Phladelpha. The data set conssts of 2,390 loans orgnated between 1988 and They fnd lower credt score and hgh debt-to-ncome rato are mportant factors predctng delnquency. They also fnd that homes that are very expensve relatve to other homes n the same census tract present hgher delnquency rsk. Querca, Stegman, Davs and Sten (2002) examne the performance of a sample of approxmately 1,000 communty renvestment loans and they fnd credt score to be mportant n predctng default and ncome, but not sgnfcantly related to default. A number of studes compare loan performances for dfferent ncome groups and neghborhoods. In an early study, Mlls and Lubuele (1994) examne neghborhood dfferences n loan performance usng loans from affordable lendng programs provded through members of the Natonal Assocaton of Affordable Housng Lenders. They study over 2,000 loans and fnd that loans orgnated n low and moderate ncome neghborhoods have better loan performance than loans orgnated n other neghborhoods. Van Order and Zorn (2000) compare the performance of loans orgnated to dfferent ncome groups and n dfferent neghborhoods usng a sample of conventonal mortgages consstng of over 400,000 loans orgnated between 1975 and However, the dataset does not contan credt score nformaton. They fnd that although defaults are hgher n low-ncome neghborhoods, dfferent neghborhoods respond to loan-to-value rato very smlarly. However, they fnd a perhaps unantcpated pattern of defaults: n 5

7 partcular, loans wth borrower ncome to neghborhood ncome ratos of 81 percent to 120 percent are less lkely to default than loans to borrowers whose rato s less than 60 percent. Borrowers wth ratos greater than 200 percent have smlar default probablty as the lowest ncome group (whose rato s less than 60 percent). Van Order and Zorn (2002) compare the performance of loans borrowed by low ncome households and mnorty households wth others. They model prepay and default usng two dfferent large data sets. They conclude that the performance of loans orgnated to low ncome and mnorty borrower s at least no worse than other loans gven that low prepayment rsks cancel out the hgh default rsks. In ths study, we buld on ths pror work and examne the default and prepayment propenstes of low and moderate ncome borrowers usng a unque sample of communty renvestment loans. The analyss dataset ncludes detaled borrower, loan and performance nformaton on a large sample of 16,000 loans. The dataset allows us to examne rsk propenstes for dfferent low ncome groups. For nstance, we are able to examne whether loans orgnated to households wth extremely low ncome levels, such as to borrowers wth ncomes less than 40 percent of area medan ncome, exhbt hgher levels of default and whether these borrowers are more or less senstve to the tradtonal economc and fnancal drvers of default and prepayment such as nterest rates, house prces, and credt scores. In general, consstent wth pror work, we fnd that lower ncome groups tend to have 6

8 hgher default and lower prepay hazards than ther hgher ncome counterparts. However, after controllng for controllng for determnants of observed rsk n a number of smulatons, we fnd that the effect s reversed and the dfference n loan performance among ncome groups becomes much smaller. Moreover, whle loan-to-value rato and local unemployment rate have a larger effect on the default decsons of low ncome groups, ref, whch measures the degree to whch the refnance opton s n the money, has a greater mpact on hgher ncome groups. Fnally, because of ts absence n much of the lterature on mortgage performance n both the subprme and prme market segments (for example, Pennngton-Cross 2003) we also examne the mportance of ablty to pay, as measured by the debt payment to ncome rato (the debt-to-ncome rato). An earler emprcal examnaton of default by Berkovec, Canner, Gabrel, and Hannan (1998), whch gnored the competng rsk of prepayment, used 1987, 1988, and 1989 Federal Housng Authorty (FHA) loans and ncluded measures of the debt-to-ncome rato. The results were nconsstent and ndcated default probabltes for loans wth debt-to-ncome ratos of 41 to 53 percent were the lowest and those over 65 percent were the hghest. The remander of the study s dvded nto 4 sectons. Next, we dscuss the emprcal strategy followed by a descrpton of the database used n the analyss. We dscuss the study fndngs n secton IV and derve mplcatons n secton V. II. Emprcal Strategy Our loan performance analyss s based on a competng rsk, proportonal hazard 7

9 framework (for example, see Deng, Qugley, and Van Order 2000 and more recently Pennngton-Cross and Ho 2010). The two termnaton events of loan default and prepay are jontly modeled whle addressng the data censorng ssue. The model starts wth the defnton of hazard rate. The hazard rate of default (prepay) at tme t s the probablty of a loan to default (prepay) at tme t gven that t has survved up to tme t. Let be the hazard rate of default ( r D ) or prepay ( r P) for loan. r Condtonal on covarates (rsk determnants) X t, the hazard rates are defned as r r Pr t T t t T t, X t t X t lm r (1) t0 t and we further assume that there s some unobserved heterogenety, whch s assumed to be ndependent of observed characterstcs, wth jont densty g the hazards are specfed as r r t X t,, exp t X t D P r r, so emprcally, 0 * (2) D P where r 0 s the baselne hazard for rsk r, and r s the mpact of observed factors on rsk r. For estmaton smplcty, we assume the same set of rsk determnants for both default and prepayment. We defne default as the frst 90-day delnquency observed on a mortgage and prepayment as the loan s pad off. Prevous studes have employed non-parametrc (for example, Deng, Qugley, and Van Order 2000) and parametrc (for example, Pennngton-Cross and Ho 2010) estmatons specfyng the baselne hazards. We employ a flexble non-parametrc baselne. We model 8

10 9 the baselne hazards wth local regresson, motvated by Cleveland (1979) and others, to smooth the product lmt estmators of prepay and default (Kaplan-Meer hazards) descrbed n Greene (2003). We choose the smoothng parameters so that they maxmze the AIC nformaton crtera (Cohen 1999). In addton, local regressons are assumed to be convex at the local level. Prepayment and default events are assumed to be ndependent and the survval functon S can be defned as: t P D P P D D P D P P D D P D P D ds t X s t X s t X t T t X t T t X t T t X t S 0,,,, exp,, *Pr,, Pr,, Pr,, (3) The log lkelhood, LL, s expressed n dscreet tme assumng rsk determnants are constant wthn each tme nterval. all P D uncensored P D r t X t S t X t LL,, log,, log (4) We allow for M groups of loans and they have dstnct prepayment and default probabltes. Unobserved heterogenetes are assumed to follow a dscrete probablty

11 dstrbuton and ponts of support or mass ponts p m sum to one. We follow Pennngton- Cross and Ho (2010) and use a logstc transformaton so that p m le n [0, 1]: qm e p m q (5) m e where, q and q 1 s normalzed to 0. m We break our sample nto four ncome groups accordng to the rato of the borrower household ncome over county area medan ncome. Usng the estmates from the ndvdual analyss, we smulate default and prepayment hazards for ndvdual ncome groups and llustrate the resultng changes n probabltes for each rsk type for each ncome group. III. Data The loan data for the analyss come from a sample of communty renvestment home purchase loans that are part of the Communty Advantage Program (CAP) 2 a program created n 1998 by Self-Help Venture Fund, n partnershp wth Fanne Mae. CAP provdes a conformng secondary market outlet for communty renvestment loans. Wth fundng from the Ford Foundaton, Self-Help purchases loans and sells them to Fanne Mae whle retanng lablty for ten years. 2 See Rley, Ru, and Querca (2009) for a bref overvew of CAP data. 10

12 To qualfy for CAP, a borrower must ft one of these crtera: 1) Income at or below 80 percent of area medan ncome (AMI), 2) Income between 80 and 115 percent of AMI, and a) The home s n a low-ncome census tract or b) The home s n a mnorty census tract (tract mnorty composton s greater than 30 percent), or c) The borrower s a mnorty. The Self-Help portfolo excludes loans whose purchase prce exceeds the apprasal prce by more than 10 percent, and whose orgnal loan-to-value rato expressed as a percentage exceeds 125 percent. The underwrtng gudelnes of ndvdual lenders are rather flexble toward the borrowers that CAP ntends to serve. For example, 2008 gudelnes show maxmum loan to value rato allowed of at least 97 percent for all lenders. The data reveals that down payments requred range from several hundred dollars to 3 percent for most lenders. Snce ts ncepton, CAP has purchased over 50,000 mortgages natonal wde (although states lke North Carolna have sgnfcantly hgher representaton). The medan borrower has ncome of $ 30,792, or 60% of ther AMI, and the medan loan amount s $ 79,000. As s typcal wth communty renvestment lendng, the majorty of CAP loans have prme loan features: thrty-year fxed-rate amortzng loans 3 wth prme-level nterest 3 There are around 9 percent adjustable rate mortgages n CAP loans. Among fxed rate mortgages, close to 99 percent of them are 30 year fxed rate loans. Table 1 provdes a more detaled breakdown by loan types. 11

13 rates (Fgure 1 compares nterest rates on CAP loans and 30-year conventonal mortgage rate by the Fredde Mac/Federal Reserve), no prepayment penaltes, no balloons, escrows for taxes and nsurance, documented ncome, and standard prme-level fees. Most CAP loans n our sample are orgnated between 1997 and Table 2 provdes a summary of loans by orgnaton year. As of June 2010, only 4.2% of CAP mortgages had experenced foreclosure snce the program started. We drop the followng loans: 1) Adjustable rate mortgages. We drop them snce Self-Help has not reported ther nterest rate hstory on a quarterly bass. 2) Manufactured housng (the the majorty of CAP loans are made to purchase sngle famly homes). 3) Loans orgnated earler than 1990s. We drop them to keep the hazard estmaton more consstent wthn the sample. 4) Loans to borrowers wth less than 5,000 dollars of annual household ncome. 5) Loans to borrowers wth a rato of household ncome to county medan ncome of less than 10 percent or more than 125 percent. We are left wth 16,283 loans whose loan and borrower nformaton s complete. In our survval analyss, we choose to analyze the performance on a quarterly bass and model loan hstory (loan age) of up to 48 quarters. Insert Fgure 1 here: Insert Table 1 here: Insert Table 2 here: 12

14 We nclude a number of loan characterstcs, debt-to-ncome rato ( dt ), borrower credt score at orgnaton (credt score), current loan-to-value rato ( cltv ), n our hazard analyss. The verson of the debt-to-ncome rato used n ths paper s commonly called the front end rato and s the rato of mortgage payments to household ncome. Households wth larger debt burdens should be more susceptble to any ncome or other debt payment shocks, thus trggerng delnquency and potentally default. The mpact of hgh debt burdens on prepayments s more ambguous. Agan, prepayments may be more lkely f they are used to refnance n the presence of a negatve shock but hgh debt burdens may also make t harder to qualfy to refnance. To examne the ssue further, an ndcator for hgh debt-to-ncome rato ( hdt ) s nteracted wth varous varables to test whether households that are stretched thn n terms of ther monthly ablty to make mortgage payments are more or less senstve to the ncentves to default and prepay a mortgage. Because credt hstory s negatvely assocated wth mortgage default and postvely assocated wth mortgage prepayment (Pennngton-Cross 2003), we nclude credt score at orgnaton (credt score). Hgh loan-to-value rato s assocated wth hgher probabltes of default (Kau, Keenan, and Km 1994) and we proxy current loan-to-value rato (cltv) usng the outstandng balance on the loan and an estmate of current house value provded by Fanne Mae. 13

15 We also construct a measure of the net present value gan from refnancng a fxed rate mortgage ( ref), commonly descrbed as the value of the refnance opton. At tme t, the gan from refnancng s the percentage reducton n dscounted value of all future mortgage payments f holdng current mortgage, PV c or refnance, PV r : PV ct PVrt ref t (6) PVct where PV jt RMT m0 1 P jt d t m (7) where j c, r, RMT s remanng mortgage term n months that vares wth t, dscount rate d t s the ten-year T-Bll rate, and RMT 1 jt RMT 1 jt 1 P jt jtq (8) where ct s the mortgage nterest rate on current mortgage and rt s the 30-year fxed conventonal mortgage rate from federal reserve (reported by Fredde Mac). We expect prepayment hazards to rse wth ref. We also nclude macroeconomc ndcators, such as local unemployment rate, mortgage rate volatlty, and house prce volatlty. The county level unemployment rate s used to proxy for labor market condtons. Hgher unemployment rates should ndcate a hgher 14

16 probablty that the borrower has lost ther job or has a lower ncome stream makng t more dffcult to make mortgage payments. Unemployment may also ncrease the use of dstressed prepayments but t also makes t harder to meet underwrtng requrements to refnance. We capture nterest rate volatlty wth the use of eght-quarter forward lookng movng varance of 30-year fxed rate conventonal mortgage rate. We expect that more volatlty of nterest rates wll reduce refnance probabltes snce borrowers may wat for nterest rates to lower even further. Smlarly, house prce volatlty ncreases the value of delayng the default (Kau and Km 1994 and Kau and Keenan 1995). If borrowers beleve that prces wll ncrease n the future and extngush the fnancal gan from defaultng they wll default sooner; or, f they beleve prces may drop even further ncreasng the sze of the gan, they may use a strategy of delayng default. We use eght-quarter forward lookng movng varance of Federal Housng Fnance Agency s House Prce Index to capture house prce volatlty. In ths paper, we address the effect of ncome dfference on loan performance. In addton to analyzng the full sample, we also look at each ncome group. We partton the sample accordng to the ncome over county medan ncome at orgnaton. After consderng the ncome dstrbuton and key qualfcatons of CAP borrowers the sample s dvded nto four groups: those wth annual ncome of 10 to 40 percent, 40 to 60 percent, 60 to 80 percent and 80 percent and above AMI. Fgure 2 gves the dstrbuton of the rato. Insert Fgure 2 here: Table 3 ncludes the defntons of varables used n the analyss. Table 4 summarzes the 15

17 varables n the full sample and Table 5 summarzes the varables for each ndvdual ncome group. Insert Table 3 here: Insert Table 4 here: Insert Table 5 here: The CAP loan and borrower characterstcs can be compared wth the Loan Performance data reported n Dans and Pennngton-Cross (2008) and Pennngton-Cross and Ho (2010). As a frst look at the performance and characterstcs of CAP loans, we plot out the Kaplan-Meer hazards and local regressons. Fgure 3 presents results based on estmatons of the default hazards for mortgages. Fgure 4 presents results based on estmatons of the prepayment hazards. Insert Fgure 3 here: Insert Fgure 4 here: An examnaton of these Fgures reveals mportant dfferences. For CAP loans, default peaks at the 7 th and 8 th quarters and prepayment peaks at the 11 th quarter. These are rather early peaks compared to the subprme fxed rate mortgages reported n Pennngton-Cross and Ho (2010) 4. For that loan sample, both default and prepayment do not peak untl loan 4 Default defned as Real Estate Owned and prepay defned as balance becomes zero and n the pror 16

18 age s well beyond 4 years. There s a sharper declne n the condtonal ncdence rates, especally for prepayment, for CAP loans. The peak loan ages for Self-Help are closer to the standard default assumpton and standard prepayment model publshed by the Publc Securtes Assocaton that are set to peak at 30 months, however, the sharp declne n prepayment rate rght after the peak s unque for CAP loans. Gven the unque shapes of baselne hazards, we choose to model the baselne under a non-parametrc framework rather than mposng a baselne shape a pror. CAP loan borrowers often have mpared credt, smlar to borrowers targeted by subprme lenders. The average credt score at orgnaton s 677 for CAP loan borrowers whle the average credt score from Loan Performance fxed rate subprme mortgages s 664 n Pennngton-Cross and Ho (2010), and 649 n Dans and Pennngton-Cross (2008) 5. On average, the loans are observed for 18 quarters (more than 4 years) whle the Loan Performance sample n Pennngton-Cross and Ho (2010) s close to 19 months. Borrowers wth hgher ncome-to-ami ratos have, on average, hgher ncome, lower debt-to-ncome ratos, larger sze loans and larger down payments. Borrowers wth the hghest ncome-to-ami rato (80 to 125 percent) have on average lower credt score at orgnaton than 40 to 60 and 60 to 80 percent ncome-to-ami groups. Ths may ndcate that lenders may be more flexble wth regard to credt hstory when ssung loans to month the loan was ether current or delnquent. 5 Mortgages analyzed by Pennngton-Cross and Ho (2010) were orgnated from 1998 to 2005 and mortgages were orgnated from 1996 to 2003 n Dans and Pennngton-Cross (2008). 17

19 hgher ncome groups. Compared wth the Loan Performance samples, CAP loans have much hgher current loan-to-value ratos especally gven the greater average loan age. Except for the hghest ncome-to-ami group, CAP loans tend to have smlar or even hgher current loan-tovalue rato as compared to the hybrd sample of Loan Performance (Pennngton-Cross and Ho 2010). IV. Estmaton Results Loan performance across ncome groups The hazard estmaton results for the full sample and for each ncome group are presented n Table 6 and 7. In the full sample, hgher debt-to-ncome rato ncreases both default and prepayment probabltes. The relatve mpact of debt-to-ncome rato on prepayment probablty s more pronounced for hgher ncome groups. Keep n mnd that the hghest ncome group n our sample s the modest ncome group. However, the mpact on default s not sgnfcant for ndvdual ncome groups. Snce the study of debt-to-ncome rato on default s lmted n the lterature, we wll explore the mpact of debt-to-ncome rato n more detal later. Insert Table 6 here Insert Table 7 here 18

20 Consstent wth pror studes, credt score and loan-to-value rato seem to be very strong ndcators for default and prepay. Credt scores (the pror ablty to pay fnancal oblgatons n a tmely fashon) are negatvely assocated wth default and postvely assocated wth prepay, whle loan-to-value rato exhbts the opposte effects. For ndvdual groups, the relatve magntudes of the mpact of credt score on default and prepay decrease wth ncome, except for the hghest ncome group. The relatve mpact of loan-to-value rato on default decreases wth ncome whle ts mpact ncreases wth ncome expect for the lowest ncome group. The varable ref s a strong and postve ndcator for both default and prepay. Ths s consstent wth Pennngton-Cross and Ho (2010). The relatve magntudes of the mpact of ref on both default and prepay ncrease for the hgher ncome groups, except for prepayment n the hghest ncome group. Local unemployment rate s postvely related to default and negatvely related to prepay. The relatve magntude of mpact on default s greatest for the lowest ncome group and shows vrtually no sgnfcant mpact for the hghest ncome group. The relatve mpact on prepay ncreases wth ncome, except for the hghest ncome group. For the most part, greater varaton n future mortgage nterest rates ncreases default and 19

21 deters prepayment. Its relatve mpact on default ncreases wth ncome, except for the hghest ncome group and t also ncreases wth ncome for prepay except for the ncome group between 60 to 80 percent of AMI. Greater varaton n local house prces has very lttle mpact on default n the full sample. In the ndvdual group estmates, t s postvely and sgnfcantly related wth default for the hghest ncome group. It s postvely related to prepay n the full sample but nsgnfcant n the ndvdual sample estmatons. Estmated Default and Prepayment Hazards To complement the above analyses, we next examne dfferences n loan performance between dfferent ncome groups n more detal through smulatons of default and prepayment hazards under dfferent scenaros. Frst, we comple the default and prepay hazards for each ncome group by loan age (up to 48 quarters) usng ther own mean characterstcs and ther own model estmates. The default and prepayment patterns are presented n Fgure 5 and 6 respectvely. Default patterns of ndvdual groups over tme decrease wth ncome except for the hghest ncome group. The default rate dfference of dfferent ncome groups vares as the loans age over tme. At the 8 th quarter (around the peak of default of dfferent ncome groups), the hghest default rate s over 30 percent hgher than the next hghest default rate and s over 70 percent hgher than the lowest default rate. 20

22 The prepayment hazards are hghest for the lowest ncome group and hghest for the hghest ncome group. The dfferences are at ther largest near the peak of the hazard n the 12 th quarter. Specfcally, n the 12 th quarter, the hghest prepayment rate s 70 percent hgher than the lowest. These results provde some of the defnng characterstcs of very low ncome lendng the loans are more lkely to default but also less lkely to prepay. Insert Fgure 5 here: Insert Fgure 6 here: Fgures 5 and 6 do not control for observed borrower or mortgage characterstcs. To help determne whether the dfferences are drven by the modeled relatonshp (coeffcent estmates) or the dfferent characterstcs of the groups, Fgures 7 and 8 smulate the baselnes for each group usng ther ndvdual model estmates but the characterstcs of the moderate ncome group (1.25>Income/AMI > 0.8). The smulated default and prepay patterns are presented n Fgures 7 and 8 respectvely. In general the baselne hazards are much more smlar, and the orderng of the results s dfferent. For example, after controllng for borrower and loan characterstcs, the lowest ncome group now has the lowest default baselne and almost the lowest prepayment baselne hazard. Ths ndcates that once observed characterstcs are controlled, lower ncome groups may even outperform hgher ncome group (default) rates wthn our sample. In addton, the smulated prepayment results usng the lower ncome group estmates produce hgher prepayment rates. 21

23 In summary, after controllng for observed borrower and loan characterstcs, the lowest ncome group (0.1<Income/AMI<0.4) defaults at the lowest probablty and prepays at almost the lowest probablty. These results ndcate that the lowest ncome borrowers have loans that are the least lkely to termnate n a neutral economc and fnancal market. Insert Fgure 7 here Insert Fgure 8 here Next, we compare the mpacts on default patterns of ndvdual rsk factors. We set the age of the loans to the12 th quarter for all models and normalze the probablty to 1 for the ntal value of each rsk factor. Fgures 9, 10, and 11 llustrate the default patterns by credt score, loan-to-value ratos, ref, and unemployment respectvely. Insert Fgure 9 here Insert Fgure 10 here Insert Fgure 12 here The comparsons show that hgher credt scores have smlar mpact on the default hazards of all ncome groups. In contrast, loan-to-value ratos have the greatest mpact on default probabltes for the lowest ncome group and the lowest mpact for the hghest 22

24 ncome group. The unemployment rate has the greatest mpact on the lowest ncome group and barely any mpact on default patterns of the hghest ncome group. Ths result lkely reflects unobservable factors such as the amount of wealth a household has to help t contnue makng mortgage payments after losng a job or earnng less money. In summary, lower ncome households are more senstve to labor market and housng market condtons. Therefore, we should expect that default rates should rse more rapdly for low and very low ncome households when house prces declne, when more very low down payment loans are orgnated, and when the labor market deterorates. A Closer Look at Debt-to-Income Rato As dscussed earler, we fnd sgnfcant mpacts of the debt-to-ncome rato on the default and prepayment propenstes n the full sample but these mpacts were statstcally nsgnfcant when the sample s dvded nto separate ncome groups. Snce the avalablty of debt-to-ncome rato nformaton n the analyss dataset offers a unque opportunty to study the mpact of ncome on loan performance, we examne more narrowly whether borrowers wth dfferent debt-to-ncome burdens respond to other rsks dfferently. Ths addtonal analyss s especally relevant for low ncome lendng f low and moderate ncome borrowers have fewer resources and thus may be more lkely to be overburdened by debt than ther hgher ncome borrowers. Not surprsngly, the data used n ths analyss (Table 5) ndcate that the debt-to-ncome rato s postvely correlated wth ncome. The hghest ncome group (1.25>Income/AMI>0.8) has an average debt-to- 23

25 ncome of 22 percent and the lowest ncome group (0.1<Income/AMI<0.4) has an average debt-to-ncome of 33 percent. 6 To smplfy the analyss, we consder debt-to-ncome ratos to be hgh f they exceed 31 percent or 38 percent or hgher (hdt) 7. Fgure 12 shows the dstrbuton of debt-toncome rato n the sample. There s no ndcaton n the dstrbuton of a mass of scores around an enforced underwrtng standard. The estmaton results are presented n Tables 8 and 9. The coeffcents can be nterpreted as addtve. Insert Fgure 12 here Insert Table 8 here Insert Table 9 here The coeffcent estmates for hdt tself and many nteracton terms are largely nsgnfcant, regardless of the defnton of debt-to-ncome rato consdered. However, some patterns are apparent. For nstance, we see a greater mpact of current loan-to-value rato on default for borrowers wth hgh debt to ncome ratos, although the estmate usng the 31 percent cutoff s barely sgnfcant at about 90 percent. Taken together, these 6 These debt-to-ncome ratos represent the ncome used by underwrters to qualfy a loan. If underwrters only nclude documented ncome untl t exceeds or meets a requred rato then the reported ncome for the hgher ncome households may be understated. If the actual ncome was avalable nstead of the documented ncome t may be that the debt-to-ncome rato would be even lower for hgher ncome households. 7 Tradtonally, Fanne Mae gudelnes set a debt-to-ncome lmt of 38% for communty mortgages (see for example Fanne Mae seller servce gude for 2006, Part X, Chapter 3, Secton 304: Underwrtng Communty Lendng Mortgages (08/31/02): The borrower's total debt-to-ncome rato should not exceed 38 percent - unless a hgher rato s adequately offset by another Contrbutory Rsk factor that decreases the lkelhood of mortgage default. The current government sponsored loan modfcaton program, the Home Affordable Modfcaton Program (HAMP), requres partcpatng lenders to brng debt-to-ncome ratos to 31 (see U.S. Department of Treasury 2009). 24

26 results show that households saddled wth greater housng burdens may respond more aggressvely to equty poston and other default trggers. In addton, a hgh debt-toncome rato s assocated wth a lower propensty to prepay the loan. Conclusons Even pror to the Great Recesson, there was an ongong debate about the desrablty of extendng credt to low and moderate ncome famles because of the belef that such extensons of credt would be too costly. Part of ths debate was based on the contenton that the hgher default rsks exhbted by these borrowers could be compensated by lower prepayment rsks. Ths study contrbutes to the understandng of default and prepayment rsks among low and moderate ncome households by carryng out a comprehensve analyss based on a competng rsk proportonal hazard model usng a unque sample of over 16,000 communty renvestment loans that ncludes detaled loan and borrower characterstcs ncludng debt-to-ncome rato. Overall, consstent wth pror studes, we fnd that low and very low ncome groups exhbt hgher default but lower prepayment probabltes. The estmated default and prepay hazards (condtonal quarterly probablty) tend to peak much earler than those reported for subprme loans elsewhere n the lterature. However, after controllng for observed loan and borrower characterstcs, the dstance 25

27 between probabltes become smaller and the order of magntude s reversed. The predcted probablty of default s lowest for the lowest ncome group (0.1<Income/Area Medan Income < 0.4) and almost the lowest for the probablty of prepayment. Whle the default patterns of dfferent ncome groups by credt score are very smlar, the default patterns vary greatly for changes n the equty poston and the unemployment rate. Lower ncome groups tend to be more senstve to equty poston and local unemployment rate changes. Overall, these fndngs suggest that whle the expected propensty of a low ncome loan to termnate s relatvely low n adverse economc condtons n the labor market or the housng market loans made to low ncome households should be expected to deterorate more quckly. Our results also offer evdence that debt-to-ncome rato s mportant n determnng default patterns for ths sample of low ncome borrowers. Borrowers wth hgher debt-toncome rato are found to be more senstve to equty poston. A hgher loan-to-value rato s assocated wth a hgher default rsk for households burdened by large mortgage payments. These fndngs provde some emprcal support for current efforts to modfy loans to reduce housng payments to 31 percent of household ncome. They are consstent wth pror work by Dng and Querca (2009) who encourage decson makers to talor loan modfcatons to the unque characterstcs of the borrower, loan, and market, ncludng the use of meanngful prncpal reducton. 26

28 Acknowledgements We would lke to thank Anthony Yezer, Davd Rbar, and Janneke Ratclffe for helpful comments, and Sarah Rley for help wth data. 27

29 References Amromn, G., and A. L. Paulson Default Rates on Prme and Subprme Mortgages: Dfferences and Smlartes. Proftwse News and Vews September: Aaronson, D A Note on the Beneft of Homeownershp. Journal of Urban Economcs 47 (3): Berkovec, J., G. Canner, S. Gabrel, T. Hannan Dscrmnaton, Competton, and Loan Performance n FHA Mortgage Lendng. Revew of Economcs and Statstcs 80(2) Bhutta, N GSE Actvty and Mortgage Supply n Lower-Income and Mnorty Neghborhoods: The Effect of the Affordable Housng Goals. The Journal of Real Estate Fnance and Economcs 2010 May: Calem P. S. and S. M. Wachter Communty Renvestment and Credt Rsk: Evdence from an Affordable-Home-Loan Program. Real Estate Economcs 27 (1): Cohen, R. A An Introducton to PROC LOESS for Local Regresson. Proceedngs of the 24th SAS Users Group Internatonal Conference, Paper 273. Dans, M. A., and A. Pennngton-Cross The delnquency of subprme mortgages. Journal of Economcs and Busness 60(1-2): Deng, Y., J. M. Qugley, and R. Van Order Mortgage Termnatons, Heterogenety and the Exercse of Mortgage Optons. Econometrca 68(2): Dng, L. and R. G. Querca Talorng Loan Modfcatons: When s Prncpal Reducton Desrable. Workng Paper. Center for Communty Captal, Unversty of North Carolna, Chapel Hll. Dng, L., R. G. Querca, W. L, and J. Ratclffe Rsky Borrowers or Rsky Mortgages: Dsaggregatng Effects Usng Propensty Score Models. Journal of Real Estate Research. Forthcomng Florda, R Homeownershp Is Overrated: Today's economy requres a more moble workforce. Wall Street Journal Onlne, June 7th Greene, W Econometrc Analyss 5 th edton. Upper Saddle Rver: NJ Haurn, D., T. Parcel, and R. Haurn Does Homeownershp Affect Chld Outcomes? Real Estate Economc 30(4): Kau, J., D. Keenan, and T. Km Default Probabltes for Mortgages. Journal of Urban Economcs 35 (3): Kau, J., and Km, T Watng to Default: The Value of Delay. Journal of Amercan Real Estate and Urban Economcs Assocaton 22 (3): Kau, J., and D. Keenan An Overvew of the Opton-Theoretc Prcng of Mortgages. Journal of Housng Research 6 (2):

30 Manturuk, K., M. Lndblad, and R. G. Querca Homeownershp and Cvc Engagement n Low-Income Urban Neghborhoods: A Longtudnal Analyss. Workng Paper. Center for Communty Captal, Unversty of North Carolna, Chapel Hll. McArdle, M Rethnkng the CRA. The Atlantc, Jun 26 th, downloaded from Mlls, E. M. and L. S. Lubuele Performance of Resdental Mortgages n Lowand Moderate-Income Neghborhoods. The Journal of Real Estate Fnance and Economcs 9: Pennngton-Cross, A Credt Hstory and the Performance of Prme and Nonprme Mortgages. The Journal of Real Estate Fnance and Economcs 27(3): Pennngton-Cross, A. and G. Ho The Termnaton of Subprme Hybrd and Fxed Rate Mortgages. Real Estate Economcs 38(3): Querca R. G., M. A. Stegman, W. R. Davs, and E. Sten Performance of Communty Renvestment Loans: Implcatons for Secondary Market Purchases. N. P. Retsnas and E. S. Belsky edtors. Low-Income Homeownershp. Jont Center for Housng Studes: Cambrdge, Massachusetts and Brookngs Insttuton Press: Washngton, D.C. Querca, R. G., S. F. Rley, and H. Ru Communty Advantage Program Database: Overvew and Generalzaton. Ctyscape, 11(3). U.S. Department of Treasury Homeowner Affordablty and Stablty Plan: Executve Summary. Press Releases. U.S. Department of the Treasury. Downloaded from on Van Order, R. and P. Zorn Performance of Low-Income and Mnorty Mortgaes. N. P. Retsnas and E. S. Belsky edtors. Low-Income Homeownershp. Jont Center for Housng Studes: Cambrdge, Massachusetts and Brookngs Insttuton Press: Washngton, D.C. 29

31 Table 1: Number of Loans by Loan Type Loan Type Number of Loans AdjusTable-rate mortgage, 10 year term. 106 AdjusTable-rate mortgage, 15 year term. 263 AdjusTable-rate mortgage, 20 year term. 193 AdjusTable-rate mortgage, 25 year term. 120 AdjusTable-rate mortgage, 30 year term. 3,470 Fxed-rate mortgage, 10 year term 26 Fxed-rate mortgage, 15 year term 364 Fxed-rate mortgage, 20 year term 122 Fxed-rate mortgage, 25 year term 93 Fxed-rate mortgage, 30 year term 41,697 Fxed-rate mortgage, 40 year term 12 Total 46,466 Table 2: Number of Loans by Year Orgnated Year Number of Loans , , , , , , , , , , , , , Total 46,476 30

32 Vares wthn Each Loan Constant wthn Each Loan Table 3: Varable Defntons Varable dt credt score cltv ref unemp_rate varmrate varhp hdt hdt*fco hdt*cltv hdt*ref hdt*unemp hdt* varmrate hdt* varhp Defnton Debt-to-ncome rato. The fracton of combned ncome that goes toward mortgage payments Borrower's credt score at orgnaton Current loan-to-value rato Percentage reducton n present value of future payments f refnance nto the market rate County level unemployment rate Varance of future natonal mortgage rate Varance of MSA level house prce ndex reported by Federal Housng Fnance Agency Indcator for loans wth hgh debt-to-ncome rato Interacton between credt score and hdt Interacton between cltv and hdt Interacton between ref and hdt Interacton between unemp_rate and hdt Interacton between varmrate and hdt Interacton between varhp and hdt Table 4: Descrptve Statstcs of Self-Help Mortgage Data -- Full Sample Full sample Mean Std Dev orgnal balance $83,473 $33,436 annual ncome $30,930 $10,102 credt score dt or front-end rato ncome / am Loans 16,283 ref loan age cltv unemp_rate varmrate varhp Observatons 212,149 31

33 Vares wthn Each Loan Constant wthn Each Loan Table 5: Descrptve Statstcs of Self-Help Mortgage Data -- by Income Group Income/AMI (10% -40%) Income/AMI (40%-60%) Income/AMI (60%-80%) Income/AMI (80%-125%) Mean Std Dev Mean Std Dev Mean Std Dev Mean Std Dev orgnal balance $58,793 $21,973 $78,357 $28,867 $94,564 $33,958 $104,111 $39,740 annual ncome $18,416 $4,148 $27,289 $5,938 $36,683 $7,326 $47,614 $11,092 credt score dt ncome / am Loans 2,109 7,120 5,981 1,073 ref loan age cltv unemp_rate varmrate varhp Observatons 30,053 93,724 75,163 13,209 32

34 Table 6: Completng Rsk Results for Full Sample and Each Income Group -- Default Full sample Income/AMI (10% -40%) Income/AMI (40%-60%) Income/AMI (60%-80%) Income/AMI (80%-125%) Coef Std Err Coef Std Err Coef Std Err Coef Std Err Coef Std Err dt 0.098* credt score * * * * * cltv 0.208* * * * * ref 0.285* * * * * unemp_rate 0.174* * * * varmrate 0.196* * * * * varhp * loc * * * loc * * q q * * * * * Loans 16,283 2,109 7,120 5,981 1,073 Obs 212,149 30,053 93,724 75,163 13,209 Loglke -39,509-5,030-17,091-14,554-2,554 Notes: * ndcates sgnfcance at 95 percent. loc1 and loc2 are shft parameters of the two heterogenety groups. q1 and q2 are logstc transformaton parameters for the heterogenety mass ponts. q1 s normalzed to zero. 33

35 Table 7: Completng Rsk Results for Full Sample and Each Income Group -- Prepay Full sample Income/AMI (10% -40%) Income/AMI (40%-60%) Income/AMI (60%-80%) Income/AMI (80%-125%) Coef Std Err Coef Std Err Coef Std Err Coef Std Err Coef Std Err dt 0.074* * * * * credt score 0.224* * * * * cltv * * * * * ref 0.437* * * * * unemp_rate * * * * * varmrate * * * * * varhp 0.040* loc * * * * loc * * * * * q q * * * * * Loans 16,283 2,109 7,120 5,981 1,073 Obs 212, ,209 Loglke -39,509-5,030-17,091-14,554-2,554 Notes: * ndcates sgnfcance at 95 percent. loc1 and loc2 are shft parameters of the two heterogenety groups. q1 and q2 are logstc transformaton parameters for the heterogenety mass ponts. q1 s normalzed to zero. 34

36 Table 8: Completng Rsk Results by Debt-to-Income Rato -- Default Debt-to-Income Rato Cutoff at 38% Debt-to-Income Rato Cutoff at 31% Coef Std Err Coef Std Err dt 0.099* credt score * * cltv 0.206* * ref 0.275* * unemp_rate 0.174* * varmrate 0.195* * varhp hdt hdt*credt score 0.223* hdt*cltv 0.169* hdt*ref hdt*unemp_rate hdt*varmrate hdt*varhp loc * * loc q1.. q * * Loans 16,283 16,283 Obs 212, ,149 Loglke -39,498-39,494 Notes: * ndcates sgnfcance at 95 percent. loc1 and loc2 are shft parameters of the two heterogenety groups. q1 and q2 are logstc transformaton parameters for the heterogenety mass ponts. q1 s normalzed to zero. 35

37 Table 9: Completng Rsk Results by Debt-to-Income Rato -- Prepay Debt-to-Income Rato Cutoff at 38% Debt-to-Income Rato Cutoff at 31% Coef Std Err Coef Std Err dt 0.092* * credt score 0.226* * cltv * * ref 0.432* * unemp_rate * * varmrate * * varhp 0.034* hdt * * hdt*credt score hdt*cltv hdt*ref * hdt*unemp_rate hdt*varmrate hdt*varhp loc * * loc * * q1.. q * * Loans 16,283 16,283 Obs 212, ,149 Loglke -39,498-39,494 Notes: * ndcates sgnfcance at 95 percent. loc1 and loc2 are shft parameters of the two heterogenety groups. q1 and q2 are logstc transformaton parameters for the heterogenety mass ponts. q1 s normalzed to zero. 36

38 Fgure 1: Fredde Mac 30-Year Fxed Mortgage Rate vs. CAP Sample Mortgage Rates at Orgnaton Fgure 2: Dstrbuton of Household Income over County Medan Household Income at Orgnaton 37

39 Fgure 3 Non-Parametrc Default Hazards Fgure 4 Non-Parametrc Prepayment Hazards 38

40 Fgure 5: Default Pattern for Each Income Group (Own Characterstcs, Own Model) Fgure 6: Prepay Pattern for Each Income Group (Own Characterstcs, Own Model) 39

41 Fgure 7: Default Pattern Predcted by Dfferent Income Group Estmates for Income Group 4 (Income/AMI >0.8) Characterstcs Fgure 8: Prepay Pattern Predcted by Dfferent Income Group Estmates for Income Group 4 (Income/AMI >0.8) Characterstcs 40

42 Fgure 9: Default Probablty Changes (Normalzed to 1) and Credt Score for Dfferent Income Groups at Quarter 12 (Own Characterstcs, Own Model) Fgure 10: Default Porbablty Changes (Normalzed 1) and Loan-to-Value Rato for Dfferent Income Group at Quarter 12 (Own Characterstcs, Own Model) 41

43 Fgure 11: Default Probablty Changes (Normalzed to 1) and Unemployment for Dfferent Income Group at Quarter 12 (Own Characterstcs, Own Model) Fgure 12: Dstrbuton of Debt-to-ncome rato at Loan Orgnaton 42

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