High LTV Loans and Credit Risk

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1 Hgh LTV Loans and Credt Rsk Brent Ambrose Professor of Fnance and Kentucky Real Estate Professor Unversty of Kentucky Lexngton, KY (859) and Anthony B. Sanders John W. Galbreath Char and Professor of Fnance The Oho State Unversty 2100 Nel Avenue Columbus, OH (614) October 3, 2002 We thank Paul Malatesta, Kerry Vandell, and Abdullah Yavas for ther helpful comments and suggestons. An earler verson of ths paper was presented at the Georgetown Unversty Credt Research Center Subprme Lendng Symposum.

2 Hgh LTV Loans and Credt Rsk Abstract Ths study examnes the prcng of hgh-ltv debt to determne whether state-specfc default laws have an mpact on the avalablty and cost of that debt. We develop a smple theoretcal model that provdes predctons concernng borrower and lender choce of mortgage terms under dfferng assumptons regardng state default regulatons. We examne whether lenders ratonally prce loans to hgher rsk borrowers and whether borrowers n states that lmt lender ablty to seek default remedes pay hgher credt costs. Our results ndcate that lenders ratonally prce loans to hgher rsk borrowers for the most part; however, when we focus on smaller and smaller FICO scores buckets, the results ndcate that the mean actual loan rates are hgher than those predcted by our model. The results also ndcate that state-specfc default laws do have an mpact on the prce of credt. The results also show that there s a greater degree of error n the prcng of hgh LTV loans to low FICO borrowers than to hgh FICO borrowers.

3 Hgh LTV Loans and Credt Rsk I. Introducton Debt usage contans mportant sgnals regardng borrower qualty and thus reveals nformaton. Whle the use of debt s wdely recognzed n the nformaton asymmetry lterature, unfortunately, few studes have ted the sgnalng aspect of debt usage to broader market condtons where legal restrctons and regulatons also nteract to determne optmal debt usage. Gven the debate currently surroundng the ssue of predatory lendng practces, t s mportant for publc polcy analysts to understand the equlbrum tradeoff between debt amount and cost and the mpact that the regulatory envronment has on ths tradeoff. Several observatons exst on the use of hgh debt levels. For example, n the resdental mortgage market t s well understood that hgh loan-to-value (LTV) loans carry sgnfcant default rsk. Tradtonal opton prcng models, where default s endogenous and determned only by nteracton of house value and nterest rates, fnd that the default opton value s sgnfcant when the LTV s greater than 100%. 1 As a result, hgh-ltv loans are usually junor debt wth lower prorty of clam on the asset, wth the majorty of hgh-ltv loans orgnated for the purpose of debt consoldaton. Furthermore, hgh debt levels are also correlated wth the probablty of bankruptcy. Thus, hgh-ltv loans are often lke unsecured debt or credt cards, and as a result, the equlbrum tradeoff between borrower credt sgnals, debt amount and cost, and regulatory envronment should be most apparent n ths market. 1 See Kau and Keenan (1995) and Querca and Stegman (1992) for an overvew of the opton-prcng model as appled to mortgages and mortgage default.

4 The goal of ths study s to examne the prcng of hgh-ltv debt and determne whether state-specfc default laws have an mpact on the avalablty and cost of that debt. Thus, we begn wth a revew of the theoretcal models of borrower choce of credt and credt avalablty. From ths revew, we develop a smple theoretcal model that provdes predctons concernng borrower and lender choce of mortgage terms under dfferng assumptons regardng state default regulatons. Usng the predctons as a gude for the emprcal analyss, the study has three man objectves. Ths frst s to determne whether lenders ratonally prce loans to hgher rsk borrowers. The second s to determne the mpact of borrower protecton laws on the prce of credt and the thrd s whether borrowers n states that lmt lender ablty to seek default remedes pay hgher credt costs. The emprcal fndngs wll provde nsghts nto the role of state specfc default and foreclosure laws on the equlbrum supply of credt and ts costs. These nsghts should enable polcy makers to better assess the adequacy of current borrower protecton laws wth respect to the evolvng hgh-ltv debt market. Furthermore, by recognzng the general equlbrum nature of the credt market, the analyss wll provde polcy makers wth a sold framework for assessng the valdty of the accusatons of predatory lendng wthn ths market. II. Hgh LTV Mortgages A varety of mortgages are orgnated n the U.S. that have dfferent characterstcs n terms of prorty (frst and home equty loans), loan-to-value rato (LTV) and credt qualty of the borrower (A-rated and B/C-rated borrowers). We would 2

5 expect that the dfferent mortgages would have dfferent default rates as well as dfferent prepayment rates. For llustratve purposes, we compare the prepayment rates and 90-day delnquency rates for three mortgage products. The frst mortgage product s a senor mortgage wth low LTVs (80% and less). The second mortgage product s a home equty loan (whch s junor n prorty to the frst mortgage). The thrd mortgage product s a hgh LTV second mortgage whch s junor to the frst mortgage and can have aggregate LTVs up to 125% of house value. Chart 1 presents the prepayment rates on the three dfferent mortgage products (based on pool-level prepayments on mortgage-backed securtes). The prepayment on the frst mortgage s represented by a Resdental Fundng Corporaton mortgage-backed securty (RFMSI 1997-S5) whch had a weghted-average coupon (WAC) of 8.16% and a weghted-average LTV (WALTV) of 74.30% as of May The prepayment on the home equty loan s represented by a Money Store mortgage-backed securty (TMSHE 1996-D) whch had a WAC of 11.15% and a WALTV of 72.60% as of May The prepayment on the hgh LTV loan s represented by a Frstplus Fnancal mortgagebacked securty (Frstplus ) whch had a WAC of 14.11% and a WALTV of % as of May All three mortgages had approxmately the same weghtedaverage maturty (WAM) as of May The RFMSI 1997-S5 frst mortgage deal had the hghest prepayment rates of the three mortgages. The Frstplus LTV loan deal had the lowest prepayment rates of the three mortgages. The TMSHE 1996-D home equty loan deal was n the mddle of the other two loans n terms of prepayment speeds. Clearly, the Frstplus

6 1 125 LTV had the desrable feature of havng the hghest nterest rate (WAC = 14.11%) and the lowest prepayment speed (whch would gve nvestors a greater number of coupon payments at the hghest rate of the three mortgages). The only negatve to the Frstplus LTB loan deal would be delnquences and default. Chart 2 depcts the 90-day delnquency rates on the three mortgages over the same perod of tme. In terms of delnquences, the RFMSI 1997-S5 frst mortgage deal experenced the lowest 90-day delnquency of the three mortgage types durng the December 1997 through August 2000 perod. Ths s not surprsng gven that Resdental Fundng has very hgh credt standards for the mortgages n ther pool. The TMSHE 1996-D home equty loan deal, on the other hand, had the hghest 90-day delnquency rate among the mortgage types whle Frstplus LTV loan deal had delnquences somewhere n between. Whle t seems perplexng that the 125 LTV deal (wth a WLTV of %) actually had lower 90-day delnquences than the home equty loan deal (wth a WLTV of 72.60%), t s not really surprsng. In order to convnce nvestors to purchase mortgage-backed securty deal wth a WALTV of %, the 125 LTV loans usually requre better credt scores for the borrowers n order to quell nvestor concerns regardng potental defaults. Gven that the Frstplus Fnancal 125 LTV mortgage has a hgher nterest rate than the Money Store home equty loan (and substantally hgher aggregate LTV) yet a lower ncdence of ex-post delnquences, t s of nterest to examne the role that the borrower s credt scores and LTV play n the determnaton of the 125 LTV nterest rate. In the next secton, we develop a model that provdes predctons concernng second loans amounts and costs gven dfferences n state specfc laws and regulatons. 4

7 III. The Model We begn by assumng a two-perod model where the borrower has an ntal ~ ncome endowment of W 0 wth an expectaton that ncome n perod one wll be W 1. For smplcty, we assume that the borrower utlzes perod zero ncome and debt to fnance consumpton and enters nto debt contracts to maxmze perod one total wealth (ncome plus assets). Lenders can verfy the ntal ncome endowment but are only able to observe an mperfect credt qualty sgnal (θ) of the expectaton of perod one ncome. 2 We assume that θ s dstrbuted over the nterval [0,1] where larger values of θ sgnal hgher expectatons of perod one ncome. 3 The borrower purchases a housng unt for V 0 at tme 0 utlzng secured debt M to partally fund the purchase where M<V 0 and W 0 V 0 - M. That s, we assume the ntal ncome endowment s suffcent to cover the downpayment on the house. For smplcty, we also assume that the debt plus nterest s due n perod 1 and s denoted as M =M(1+r m ). In order to lmt potental losses, the lender underwrtes the mortgage loan by controllng the loan-to-value rato (M/V 0 ) and settng mnmum credt qualty levels (θˆ ). The lender determnes the LTV rato based on perod one expectatons of property value ~ ~ ( V 1 =E[V 1 ]) and ncome ( W 1 =E[W 1 ]). 4 Thus, the lender determnes the ntal loan ~ ~ amount such that V 1 + W 1 >M. 5 2 Verfcaton of borrower wealth at loan orgnaton through examnaton of tax returns and bank accounts s common practce. 3 Typcal credt qualty sgnals (such as those compled by Far, Isaac & Co.) combne nformaton regardng borrower ncome, assets, debts, and payment hstory nto a numerc score that s predctve of borrower potental to default on future debt payments. 4 For hgh LTV levels (M/V 0 > 0.80), lenders requre that borrowers purchase mortgage nsurance effectvely rasng the cost of borrowng. ~ ~ 5 The condton that V 1 + W 1 >M assumes that lenders beleve that strategc default can be lmted through enforcement of borrower defcency judgments. We explctly allow for ths n the analyss below. 5

8 The borrower also fnances non-housng consumpton (C 0 ) by borrowng unsecured debt (P) that s also due n perod 1 wth the amount due denoted as P =P(1+r p ). Snce P s unsecured, the lender looks to expected perod one ncome for repayment, and thus, the amount of unsecured debt avalable at perod 0 s based on the ~ expectaton of ncome ( W 1 ) and the borrower s credt score. Snce the credt score provdes a sgnal of expected perod 1 ncome, the hgher the borrower s credt sgnal (θ), the greater the amount of unsecured debt made avalable. Gven that mortgage debt has a senor clam to the perod 1 assets and ncome, the nterest rate on secured debt s lower than unsecured debt (r m <r p ). Note that f the lender s able to utlze rsk-based prcng, then the nterest rate and loan amount wll be ndexed to θ such that r m ( θ ) r p ( θ) M ( θ ) P( θ) < 0, < 0, > 0, and > 0. 6 If realzed perod 1 ncome and θ θ θ θ house values (W 1 and V 1 ) are greater than P and M, respectvely, then all debts are pad n full and the borrower s perod 1 net wealth poston s W 1 -P +V 1 -M >0. Turnng to the condtons under whch the borrower would default, we recognze that uncertanty s captured n the model va perod 1 ncome and house values. Furthermore, state-level regulatons regardng borrower rghts and responsbltes can have consderable mpact on expected default losses (or recovery rates) and as result would mpact borrower credt costs n equlbrum. For example, Ambrose, Buttmer, and Capone (1997) document that a sgnfcant delay can exst between borrower default (mssed payment) and lender foreclosure. Ambrose and Buttmer (2000) then show that ths delay ntroduces a number of potental optons to the borrower wth respect to curng 6 Ambrose, LaCour-Lttle, and Sanders (2002) emprcally verfy ths predcton by demonstratng that borrower credt rsk s negatvely related to the credt spread on frst mortgages. 6

9 default pror to the lender foreclosng on the property. Usng these concepts, Ambrose and Pennngton-Cross (2000) dscuss how state laws that defne the foreclosure process and establsh credtor rghts can mpact the supply of mortgage credt. 7 For example, state default laws can mpact the credt supply by defnng how foreclosure s accomplshed and whether credtors may pursue other borrower assets n the event that the collateral sale does not dscharge the debt. Furthermore, state bankruptcy laws and regulatons allow borrowers to protect a porton of ther housng equty and non-housng property va homestead and personal property exemptons. 8 In order to ntroduce state level default costs to the analyss, we defne γ as the probablty that the lender wll be able to recover default losses through foreclosure sale or defcency judgments. Thus, γ les on the nterval (0,1] where γ=1 denotes states wth strong lender protecton laws and γ 0 denotes states wth strong borrower protecton laws. If γ=0, then the borrower has no ncentve to repay the debt and wll default n every case wth the unnterestng equlbrum result that no lender would enter nto a loan contract. We now consder the varous borrower and lender perod 1 payoff condtons assumng extreme values for γ. Fgure 1 shows the payoff condtons for the secured and unsecured lenders as well as the borrower. In Panel A, we assume that γ=1 mplyng that the lenders are able to foreclose on the borrower s assets to satsfy an outstandng clam. Case 1 shows the payoff postons when the total value of all assets s greater than the debt outstandng. In ths stuaton, the borrower obvously pays off all loans and has a 7 Pence (2002) confrms ths fndng usng HMDA loan level data. 8 As dscussed by Berkowtz and Hynes (1999) and Ln and Whte (2001), Federal bankruptcy law provdes a homestead exempton of $7,500 but each state s allowed to set ts own exempton level. As a result, ndvdual state homestead exempton levels vary wdely wth some beng unlmted and others beng very restrcted. Ln and Whte (2001) note that personal property exemptons have smaller varaton across states. 7

10 postve wealth poston. In Case 2, we show the payoff when the value of the house s greater than the secured mortgage debt, but perod one wealth s less than the unsecured debt (W 1 <P ). As a result, the borrower defaults on the unsecured debt and the unsecured credtor s recourse s to seze the personal assets to satsfy the unsecured debt P. Snce the unsecured credtor s unable to attach the borrower s housng equty, the borrower s net perod one wealth poston s (V 1 -M ) and the unsecured credtor suffers a net loss (P -W 1 ). Fnally, Case 3 consders the payoffs f the house value s less than the secured mortgage amount. Ths s the classc mortgage default condton trggered by negatve equty. In ths stuaton, the secured lender forecloses on the property and suffers a loss equal to M -V 1 -W 1. Nothng remans for the unsecured lender who thus suffers a loss of P and the borrower s net perod one wealth poston s zero. In Panel B, we show the perod one payoffs assumng the borrower resdes n a very low default cost state. We assume that the probablty of foreclosng and recevng a payoff n the event of default s postve, but small. Agan, Case 1 shows that the payoffs are the same as n Panel A snce the borrower has no fnancal ncentve to default. However, n Case 2, the payoff to the unsecured lender s smaller snce (W 1 )γ< W 1 and the payoff to the borrower s now (W 1 (1-γ)+(V 1 -M )). Thus, as the cost of default declnes (costs to the lender assocated wth foreclosure ncrease), the borrower s expectaton of keepng a porton of her perod one wealth n the event of default ncreases. Fnally, Case 3 shows that the unsecured lender s payoff s zero when default occurs on the secured debt snce all assets that can be collected are used to payoff the secured lender s poston. 8

11 Panel C shows the perod one outcomes assumng that P s now fnanced wth a secured second mortgage. The payoff condtons n Case 2 are altered to reflect the ablty of the junor secured lender to seze part of the borrower s housng equty. Snce V 1 -M >0, the payoff to the secured second lender s greater than the payoff to the unsecured lender ([V 1 +W 1 -M ]γ> [W 1 ]γ). The secured second lender s gan s drectly offset by the borrower s loss; and, as a result, n states where borrower default costs are low, the unsecured lender has an ncentve to entce the borrower to swtch from unsecured debt to secured debt by offerng more generous loan terms for junor secured debt than for unsecured debt. The mplcatons of our model wth respect to borrower qualty and loan amount contrast wth the model predctons of Brueckner (1994, 2000), who develops a smple two-perod model of borrower default that examnes the mpact of borrower rsk on choce of loan amount. Brueckner s model s based on default beng trggered by declnes n the underlyng collateral asset value and hs analyss mples that low rsk borrowers self-select smaller loans whle hgh-rsk borrowers select larger loans. Ths result s based on the observaton that default costs appear to be mportant n understandng the emprcal ncdence of default. Brueckner s model follows from the nformaton asymmetry arguments frst appled to the nsurance market by Rothschld and Stgltz (1976). Rothschld and Stgltz s (1976) analyss of the nsurance market demonstrated that when nsurers cannot dscern rsky applcants from non-rsky applcants, the safe applcants sgnal ther rsk profle by applyng for less nsurance than the rsky applcants. Smlarly, Brueckner s model ndcates that, n the presence 9

12 of non-trval default costs, only hgh-rsk borrowers are wllng to pay the premum for a hgh LTV rato. 9 However, our predctons are consstent wth those presented by Harrson, et al (2002), who modfy Brueckner s model to examne the mpact of borrower ncome on default. Borrower ncome s not explctly consdered n the orgnal Brueckner model where default s motvated by changes n house value. Rather than allow default to be motvated by uncertan future asset values, Harrson, et al (2002) motvate default based on uncertanty regardng the borrower s future ncome (holdng the asset value fxed). Thus, default occurs f the borrower s future ncome s nsuffcent to repay the debt n the presence of a declne n asset value. Wth default condtonal on ncome, ther model shows that when default costs are hgh, rsky borrowers choose low LTV ratos to mnmze default costs. However, ther model provdes addtonal nsghts by ndcatng that when default costs are low, rsky borrowers may actually choose hgher LTV ratos. To summarze, our analyss mples that borrowers n states wth low default costs wll have hgher secured second loan amounts relatve to borrowers n states wth hgh default costs. Furthermore, our model also mples that secured junor loan amounts should be drectly correlated wth borrower credt qualty snce the lender looks to both the underlyng collateral as well as future ncome for loan repayment. That s, our model predcts that hgher qualty borrowers wll have hgher loan amounts relatve to lower qualty borrowers. Ths s consstent wth the predctons of Harrson et al (2002) and drectly counters to the predctons of Brueckner (1994, 2000). In addton, to the extent 9 Brueckner s model s consstent wth models corporate borrowerng. For example, Bolton and Scharfsten (1996) develop a model of debt ssuance that predcts that low-rsk frms should borrower from a greater number of credtors whle hgh-rsk frms wll only borrower from a few credtors. Ther model also mples that low rsk borrowers wll have larger second loans relatve to hgh-rsk borrowers. 10

13 that lenders are able to dfferentate borrower qualty based on credt scores, we expect that loan costs should be negatvely related to borrower credt scores. IV. Data In order to test the predctons from our model, we employ a dataset of 132,184 second mortgage loans orgnated for securtzaton between 1995 and Ths dataset s unlke most other mortgage datasets n that these mortgages represent second loans that are secured by the underlyng property. However, n many cases, when the orgnal mortgage loan balance s combned wth the second loan amount, the total mortgage debt exceeds the value of the collateral asset. As a result, these loans are often referred to as 125% LTV loans. The 125 desgnaton denotes the fact that the maxmum LTV rato s normally 125 percent of the property collateral value. In order to make the dataset as clean as possble, we nclude only subordnate loans wth sngle-famly resdental collateral. The dataset contans nformaton regardng the borrower s reason for desrng the mortgage, allowng a test of whether loans orgnated for the purpose of debt consoldaton dffer from loans orgnated for other purposes (home mprovement, refnancng, etc.). Table 1 shows the dstrbuton of the loans by orgnaton year. We note that the majorty of the mortgages (50%) were orgnated n The mortgages were orgnated across the US, but have sgnfcant concentraton n Calforna (21.5%) wth the next hghest concentraton n Florda (7.8%). 10 Consstent wth Texas bankng laws 10 A table detalng the geographc dstrbuton of mortgages orgnatons s avalable from the author upon request. 11

14 regardng second mortgages, there were only 206 loans orgnated n Texas. Furthermore, consstent wth the fndngs of Ambrose, LaCour-Lttle, and Sanders (2002), we fnd that the orgnaton spread for hgh credt qualty borrowers s sgnfcantly lower than the orgnaton nterest rate spread for low credt qualty borrowers (Table 2). 11 In order to estmate the mpact of state-specfc default laws, we follow the analyss of Ambrose and Pennngton-Cross (2000) who categorze the states based on whether credtors must use judcal or non-judcal foreclosure and whether the states have ant-defcency judgment statutes. 12 From the lender s perspectve, ths classfcaton system defnes a hgh default cost state as one that requres judcal foreclosure proceedngs but does not allow defcency judgments. Smlarly, a low default cost state s one that does not requre judcal foreclosure and allows lenders to obtan defcency judgments aganst borrower assets. Gven that defcency judgments ncrease the rsk to the borrower, the theory proposed by Harrson et al (2002) suggests that borrowers n states that allow defcency judgments should self select lower debt amounts than borrowers n states that lmt defcency judgments, all else beng equal. As a prelmnary test of ths hypothess, we report n Table 3 the mean total debt loan-to-value rato and senor debt loan-to-value ratos based on whether or not the borrower lves n a state that allows defcency judgments. We fnd that borrowers n states that have do not allow defcency judgments 11 The orgnaton nterest rate spread s defned as the mortgage contract rate at orgnaton less the 10-year Treasury rate at date of orgnaton. 12 Judcal foreclosure proceedng are more costly and tme-consumng than non-judcal proceedngs snce credtors are requred to obtan a court order to foreclosure on the property to satsfy the debt. Antdefcency judgment statutes prohbt credtors from attachng other assets or garnshng future wages to satsfy losses that occur due to default. 12

15 carry sgnfcantly hgher senor debt amounts but lower total debt amounts than borrowers n states that allow defcency judgments. Snce judcal foreclosure has the percepton of provdng greater borrower protecton than non-judcal foreclosure proceedngs, total debt amounts and junor loan amounts n states that requre judcal foreclosure should be hgher than n states that allow non-judcal foreclosure. Thus, Table 3 also reports the mean total loan-to-value ratos and senor loan-to-value rato classfed by state law regardng foreclosure. Contrary to expectatons, we fnd that mean senor loan-to-value ratos are sgnfcantly lower n states that requre judcal foreclosure. 13 However, total debt loan-to-value ratos are hgher n states that requre judcal foreclosure. Snce default costs are n general a zero sum game (borrower protectons lmt lender default recovery and pro lender regulatons ncrease potental borrower losses), one possble explanaton for ths result s that lenders may raton credt n states where legal regulatons lmt lender abltes to quckly recover assets n case of default. Snce most borrowers n default do not have other assets to attach, lenders may vew defcency judgments as less mportant than the ablty to utlze non-judcal foreclosure proceedngs. When factorng borrower credt and nformaton sgnalng, Harrson et al (2002) suggest that holdng default costs constant, hgh qualty borrowers n hgh default cost states self-select hgher loan amounts whle low qualty borrowers self select lower loan amounts to mnmze the potental cost of default. Therefore, we test whether hgher rsk borrowers select larger loans and whether hgher rsk borrowers n hgh default cost states select lower loan amounts, holdng all else constant. Table 4 shows the dfferences n mean loan-to-value ratos based on whether the borrower s FICO score s greater than or 13 Ths s consstent wth the fndngs of Pence (2002). 13

16 less than the average FICO score n the sample. Consstent wth our theory, hgher qualty borrowers do have sgnfcantly hgher senor loan amounts. However, lower qualty borrowers have hgher loan-to-values based on total debt. Ths fndng s nconsstent wth the debt-sgnalng hypothess proposed by Bolton and Scharfsten (1996). Holdng all else constant, Bolton and Scharfsten s (1996) theory s that lower rsk borrowers wll have larger second loans as they are n a poston to take on more debt. In the regresson analyss dscussed below, we test whether lenders prce loans based on borrower rsk and default costs. Merton (1974) predcts that borrower yeld spreads are a postve functon of total debt. In contrast, the model predcts that lenders wll offer borrowers lower spreads to entce them to swtch from unsecured personal debt to secured mortgage debt. Ths last test should provde nsght nto the queston of whether lenders engage n predatory lendng practces by chargng nterest rates unrelated to borrower credt rsk. V. Emprcal Modelng One of the prmary problems wth analyzng the mpact of state level default costs on the avalablty of credt s the endogenous relatonshp between the mortgage loan terms, the loan amount, the collateral qualty, and the borrower s credt qualty. Ths endogenous relatonshp s wdely recognzed n the lterature that examnes borrower choce concernng loan amount and housng consumpton. For example, Ambrose, LaCour-Lttle, and Sanders (2002) employ a smultaneous equatons system to recognze 14

17 the well-known endogenous relatonshp between LTV and house value. 14 However, our analyss s more complcated n that we examne the borrower s choce of junor loan debt and the mpact of default costs on the avalablty and cost of that debt. In ths context, the amount of housng consumpton s already determned. Thus, the endogenous terms are related to the amount of the second loan, ts costs (nterest rate spread), and loan term, assumng that the borrower s house (collateral) value, credt qualty and ncome are exogenous to the decson. Therefore, to control for ths endogenous relatonshp we estmate the followng system va non-lnear three-stage least squares regresson (3SLS): Spread = α 0 + α1 log( loanamt ) + α J + α j= 13 σ rtreas α YrDUM j + α yeldcurve + α credtspread + α Term + α FICO + α k= 17 α QtrDUM k ( r r ) mkt treas + α D + α debtconsol + α cashout + α mprove ε 4 9 (1.) log ( loanamt ) = β + β Spread + β Term + β frstmtgbal 0 + β cashout + β mprove + + β house + β FICO + β J + β D + β debtconsol j= 11 β YrDUM j k = 15 β QtrDUM k + ε (2.) Term = γ Spread 0 + γ 1 + γ 2 log( ) + γ D j= 6 γ YrDUM j loanamt + 12 k = 10 + γ FICO + γ J γ QtrDUM k 3 + ε 4 (3.) 14 See Lng and McGll (1998) for an example of a smultaneous equaton model where mortgage demand s a functon of borrower ncome, nonhousng wealth, desred housng consumpton, and demographc characterstcs, and housng consumpton s a functon of the level of mortgage debt as well as economc and demographc factors. 15

18 where Spread s the second mortgage orgnaton spread, loanamt s the second (junorsecured) loan amount, Term s the term of the second loan, r mkt s the current mortgage rate as proxed by the Fredde Mac 30-year fxed-rate mortgage rate, r treas s the 10-year constant maturty treasury rate, yeldcurve s the market yeld curve (10-year constant maturty treasury rate less the 1-year constant maturty treasury rate), credtspread s the bond market credt rsk spread as proxed by the dfference n the BAA and AAA corporate bond rates, FICO s borrower s credt score at orgnaton, house s the value of the house at second loan orgnaton, frstmtgamt s the frst (senor) mortgage amount, debtconsol s the percent of the second loan used for debt consoldaton purposes, cashout s the percent of the second loan that s taken as cash at closng, mprove s the percent of the second loan used for home mprovement purposes, D s a dummy varable denotng states that allow lenders to pursue defcency judgments aganst borrowers n default, J s a dummy varable denotng states that requre judcal foreclosure proceedngs, YrDUM s a seres of dummy varables denotng the year of orgnaton ( wth 1995 beng the reference year), and QtrDUM s a seres of three dummy varables denotng the orgnaton quarter (the frst quarter s the reference). The orgnaton Spread s calculated as the effectve yeld assumng a 10-year holdng perod less the 10-year constant maturty treasury rate. In calculatng the effectve yeld, we nclude the mpact of closng costs and ponts. Approxmately 10% of the sample had mssng or ncorrectly coded closng cost amounts. Thus, we mputed the closng costs on loans wth mssng data usng the mean closng cost amount for the top 75 percent of the sample. The dataset does not contan actual nformaton about the ponts charged to borrowers; however, dscussons wth lender representatves ndcate 16

19 that the lender unformly charged 8 ponts on all loans orgnated. Thus, n estmatng the effectve yeld we also assume that 8 ponts were charged at orgnaton. Gven the large number of observatons avalable, we segmented the sample nto an estmaton subsample and a holdout subsample. The estmaton subsample was created by randomly drawng 75 percent of the full sample wth the remanng 25 percent held as the holdout sample. The mortgage spread system was estmated usng the estmaton subsample wth the holdout subsample used for testng model ft and accuracy. Table 6 presents the non-lnear 3SLS parameter estmates for the mortgage spread system. As expected, the estmated coeffcents for loan spread, term, and loan amount ndcate a negatve relatonshp between loan amount and cost (loan amounts declne as the cost ncreases) and a postve relatonshp between cost and term and loan amount and term. Consstent wth the model developed above, the parameter estmates show that borrower credt qualty (FICO score) s negatvely related to credt cost and loan amount. That s, hgher qualty borrowers (hgher FICO scores) have lower second loan orgnaton spreads all else beng equal. In addton, borrower credt qualty s postvely related to the mortgage term wth hgher qualty borrowers selectng longer-term loans. Ths s counter to the debt-sgnalng hypothess dscussed by Flannery (1986) that hgher qualty borrowers are less susceptble to fnancal shocks and can thus borrower over shorter terms. However, our result s consstent wth the Damond s (1991) theory that low qualty borrowers are unable to ssue longer-term debt snce lenders are unwllng to lend longer term. Furthermore, after controllng for other factors, the model parameter estmates ndcate that hgher qualty borrowers actually have lower second loan amounts. 17

20 Ths s counter to the smple comparson of means reported earler. However, ths result s consstent wth Brueckner s (2000) theory that, n equlbrum, hgher qualty borrowers do not request larger loan amounts. The model coeffcents provde strong support for a postve relatonshp between borrowers n states that requre judcal foreclosure proceedngs and the second loan terms. The parameter estmates ndcate that borrowers n states that requre judcal foreclosure have hgher second loan amounts, pay more for the loan (orgnaton spread s larger), and borrower over a shorter term. However, we fnd the opposte effect for states that lmt borrower defcency judgments. The negatve coeffcents for defcency judgments n the spread and loan amount equatons ndcate that borrowers n states that prevent lenders from seekng defcency judgments have lower spreads and loan amounts. Ths s consstent wth the theory that lenders tradeoff loan costs wth loan amounts. The results are also consstent wth the theory that lenders restrct credt n states wth regulatons that lmt ther ablty to recover losses (ant-defcency judgment statutes) whereas lenders do not restrct credt n states that smply ncrease the costs assocated wth default (requre judcal foreclosure) but do not lmt the lender s ablty to recover losses. The coeffcents regardng the use of funds do not reveal a sgnfcant relatonshp between loan amount or cost and the percentage of funds used to consoldate other debts. However, we do fnd that that the cost of second loan debt s sgnfcantly lower as the percentage of the loan amount used for home mprovements or cash out ncreases. At the same tme, borrowers seekng loans for home mprovements or to cash out also have lower amounts. 18

21 Examnng the other macro economc and borrower specfc factors, we see that borrowers wth hgher house values have hgher second loan amounts whle borrowers wth larger frst mortgages have lower second mortgages. We also fnd that the cost of second loans s postvely related to the mortgage market nterest rate spread and the overall market credt rsk premum (corporate bond credt rsk spread). Ths s consstent wth a number of prevous studes who fnd that the mortgage market s ntegrated wth the larger captal markets. 15 VI. Model Predctons In Table 7 we report the mean and medan spread, second loan amount, and loan term predcton errors for the estmaton sample usng the parameter estmates reported n Table 6. Snce the mean predcton errors can be skewed by extreme outlers, we chose to focus on the medan values. The frst row reports the mean and medan predcton errors (resduals) for the full sample. The medan values ndcate that the model tends to underft the spread and overft the loan amount and term. We next dvde the sample based on borrower FICO score and note that the spread predcton error appears to be smaller for the low FICO sample (FICO scores less than 684). For the hgh FICO subsample, the predcted spread s 25 bass ponts lower than the actual whle the medan error for the low FICO subsample s only 0.76 bass ponts lower. We also estmate the mpact of the borrower s reason for the orgnatng the second loan. Analyss of the resduals ndcates that the predcton error s hghest for borrowers usng at least 90% of the loan amount for debt consoldaton (123 bass ponts for hgh FICO borrowers and 94 bass ponts for low FICO borrowers). 15 For example, see Gonzalez-Rvera (2001) and Kolar, Fraser, and Anar (1998) for example. 19

22 We also examne the predcton errors for hgh qualty and low qualty borrowers based on ther state default regulatons. We classfy hgh default cost states (from the lender s perspectve) as states that requre judcal foreclosure proceedngs (J=1) but do not allow defcency judgments (D=1). Low default cost states are classfed as those that do not requre judcal foreclosure (J=0) but allow defcency judgments (D=0). Interestngly, we fnd that the spread predcton error s unformly negatve (model over predcts the spread) across all state default regulaton categores for the hgh qualty borrower subsample. However, the model appears to unformly under predct loan costs for the low FICO subsample (errors are postve). In the fnal secton of Table 7, we hghlght the predcton errors for hgh and low default cost states based on borrower qualty assumng funds used for debt consoldaton. The model errors are slghtly greater for states wth hgh default costs. In Table 8 we assess the estmated systems predcted accuracy usng the hold-out sample as an out-of-sample test. Predcted spread, loan amount, and term were estmated va Newton s method for each observaton n the holdout sample usng the parameter coeffcents reported n Table 6. Snce ths s an out-of-sample test, the mean predcton errors for the full sample are no longer zero. The results ndcate that the system has a relatvely hgh predctve accuracy. The mean spread error s 0.1 bass ponts and the medan spread error s 12 bass ponts. As n Table 7, we fnd that the model tends to over estmate the spread for hgh qualty borrowers and under predct the spread for low qualty borrowers. However, the degree of error s larger for hgh qualty borrowers than for low qualty borrowers. 20

23 By controllng for borrower rsk characterstcs, nterrelated loan terms, market condtons, and state-level default laws, we are able assess the degree of under- or overprcng of junor secured mortgages. We create a seres of hypothetcal borrowers dfferentated by rsk and locaton. For example, we segment the holdout sample nto very hgh and very low qualty borrowers where very hgh qualty s defned as any borrower wth a FICO score above the 75 th percentle of the whole sample (FICO>706) and very low qualty s defned as any borrower wth a FICO score below the 25 th percentle of the whole sample (FICO < 658). Next we calculate the ndependent varable means for these hgh and low qualty subsamples further segmented by whether ther state requres judcal foreclosure (J=1) or does not allow defcency judgments (D=1). Usng the relevant mean values of these hypothetcal borrowers, we then estmate predcted loan spreads, term, and amounts. Comparng these predcted values to the actual means for each borrower segment wll allow us to quantfy the degree of lender under or over prcng. Table 9 shows the comparson for borrowers lvng n hgh default cost and low default cost states. Consstent wth the predcton errors reported above, we see that predcted as well as actual spreads are lower n low default cost states. However, t s nterestng to note that low qualty borrowers are consstently over-charged relatve to the model predctons. For example, the nterest rate charged on a loan to a low qualty borrower lvng n a hgh cost state was, on average, 64 bass ponts hgher than the predcted value. On the other hand, hgh qualty borrowers lvng n states wth hgh default costs were consstently under charged by 18 bass ponts, on average. 21

24 VII. Summary and Conclusons The hgh LTV mortgage examned n ths paper s an nterestng twst on the home equty loan contract n that t has a hgher nterest rate and aggregate LTV than tradtonal home equty loans. As the market contnues to grow for the varous permutatons of home equty loans, the mpact of credt on mortgage rates becomes qute mportant (partcularly when compared to conformng frst mortgages purchased by the government sponsored agences where credt rsk s of lttle concern). In ths paper, we examne the prcng of hgh-ltv debt and determne whether state-specfc default laws have an mpact on the avalablty and cost of that debt. Frst, we fnd that lenders ratonally prce loans to hgher rsk borrowers for the most part; however, when we focus on smaller and smaller FICO scores buckets, the results ndcate that the mean actual loan rates are hgher than those predcted by our model. Second, we examne the mpact of borrower protecton laws on the prce of credt and f borrowers n states that lmt the lender s ablty to seek default remedes pay hgher credt costs; we fnd that states that do not requre judcal foreclosure and allow defcency judgments on hgh LTV loans have lower lendng rates (by about 33 bass ponts) than loans n states that requre judcal foreclosure and do not allow defcency judgments. Thrd, we fnd that there s a greater degree of error n the prcng of hgh LTV loans to low FICO borrowers than to hgh FICO borrowers. Stated n a dfferent way, t s more dffcult to explan the rate charged to lower credt rsk borrowers n that the rates charged are hgher than those predcted by our ratonal model of loan prcng. 22

25 REFERENCES Ambrose, B.W., and R.J. Buttmer, Jr. Embedded Optons n the Mortgage Contract. The Journal of Real Estate Fnance and Economcs 21:2 (2000), Ambrose, B.W., R.J. Buttmer, Jr., and C.A. Capone, Jr. Prcng Mortgage Default and Foreclosure Delay. Journal of Money, Credt, and Bankng 29:3 (1997), Ambrose, B.W., and A. Pennngton-Cross. Local Economc Rsk Factors and the Prmary and Secondary Mortgage Markets. Regonal Scence and Urban Economcs 30:6 (2000), Ambrose, B.W., M. Lacour-Lttle, and A. Sanders. Credt Spreads and Captal Structure: Evdence from the Mortgage Market, Oho State Unversty Workng Paper (2002). Berkowtz, J. and R. Hynes. Bankruptcy Exemptons and the Market for Mortgage Loans. Journal of Law and Economcs 42 (1999), Bolton, P. and D. Scharfsten. Optmal debt structure and the number of credtors. Journal of Poltcal Economy 104:1 (1996), Brueckner, J.K. Mortgage Default wth Asymmetrc Informaton. Journal of Real Estate Fnance and Economcs 20 (2000), Brueckner, J.K. Unobservable Default Propenstes, Optmal Leverage, and Emprcal Default Models: Comments on Bas n Estmates of Dscrmnaton and Default n Mortgage Lendng: The Effects of Smultanety and Self-Selecton. Journal of Real Estate Fnance and Economcs 9:3 (1994), Damond, D. Debt Maturty Structure and Lqudty Rsk. Quarterly Journal of Economcs (1991), Flannery, M. Asymmetrc Informaton and Rsky Debt Maturty Choce. Journal of Fnance 41 (1986), Gonzalez-Rvera, G. Lnkages Between Secondary and Prmary Markets for Mortgages. Journal of Fxed Income (2001), Harrson, D.M., T.G. Noordewer, and A. Yavas. Do Rsker Borrowers Borrow More?. Pennsylvana State Unversty Workng Paper (2002). Kau, J.B. and D.C. Keenan. An Overvew of the Opton-Theoretc Prcng of Mortgages. Journal of Housng Research 6:2 (1995),

26 Kolar, J.W., D.R. Fraser, and A. Anar. The Effects of Securtzaton on Mortgage market Yelds: A Contegraton Analyss. Real Estate Economcs 26:4 (1998), Ln, E.Y., and M.J. Whte. Bankruptcy and the Market for Mortgage and Home Improvement Loans. Journal of Urban Economcs 50 (2001), Lng, D.C., and G.A. McGll. Evdence on the Demand for Mortgage Debt by Owner- Occupants. Journal of Urban Economcs 44 (1998), Merton, R.C. Theory of Ratonal Opton Prcng. Bell Journal of Economcs 4 (1974), Pence, K.M. Foreclosng on Opportunty: State Laws and Mortgage Credt. Board of Governors of the Federal Reserve System workng paper (2002). Querca, R., and M.A. Stegman. Resdental Mortgage Default: A Revew of the Lterature. Journal of Housng 3 (1992), Rothschld, M. and J. Stgltz. Equlbrum n Compettve Insurance Markets: An Essay on the Economcs of Imperfect Informaton. Quarterly Journal of Economcs 90 (1976),

27 Chart 1. Hstorcal Prepayments for Three Mortgage Products % Hstorcal Prepayment 60.00% 50.00% CPR 40.00% 30.00% 20.00% 10.00% 0.00% Dec-97 Feb-98 Apr-98 Jun-98 Aug-98 Oct-98 Dec-98 Feb-99 Apr-99 Jun-99 Aug-99 Oct-99 Dec-99 Feb-00 Apr-00 Jun-00 Aug-00 Age of Collateral (months) FIRSTPLUS 125 LTV97-1 Money Store Home Equty 1996-D RFMSI Whole Loan 25

28 Chart 2. Hstorcal 90-day Delnquency for Three Mortgage Products. Hstorcal 90 Day Delnquency 18.00% 16.00% 90 Day Delnquency 14.00% 12.00% 10.00% 8.00% 6.00% 4.00% 2.00% 0.00% Dec-97 Feb-98 Apr-98 Jun-98 Aug-98 Oct-98 Dec-98 Feb-99 Apr-99 Jun-99 Aug-99 Oct-99 Dec-99 Feb-00 Apr-00 Jun-00 Age of Collateral (months) FIRSTPLUS 125 LTV97-1 Money Store Home Equty 1996-D RFMSI Whole Loan Source: Bloomberg. 26

29 Fgure 1: End of Perod 1 Net Payoff Postons for the Borrower and Lenders. Panel A: Hgh Default Cost State (γ=1) Perod 1 Outcome Condton Borrower Secured Unsecured Borrower Acton Lender Lender Case 1: V 1 > M Payoff All M P V 1 +W 1 -M -P W 1 > P Debt Case 2: V 1 > M W 1 < P Default on Unsecured M W 1 V 1 -M V 1 -M < P Case 3: V 1 < M W 1 < P Debt Default on All Debt V 1 +C Panel B: Low Default Cost State (0<γ<1) Perod 1 Outcome Condton Borrower Secured Unsecured Borrower Acton Lender Lender Case 1: V 1 > M Payoff All M P V 1 +W 1 -M -P W 1 > P Debt Case 2: V 1 > M W 1 < P Default on Unsecured M [W 1 ]γ (1-γ)[W 1 ]+ [V 1 -M ] V 1 -M < P Case 3: V 1 < M W 1 < P Debt Default on All Debt [V 1 +W 1 ]γ 0 (1-γ)[V 1 +W 1 ] Panel C: Low Default Cost State (0<γ<1) and Secured 2 nd Lender Perod 1 Outcome Condton Borrower Secured Secured 2 nd Borrower Acton Lender Lender Case 1: V 1 > M Payoff All M P V 1 +W 1 -M -P W 1 > P Debt Case 2: V 1 > M W 1 < P Default on 2 nd Loan M [V 1 +W 1 -M ]γ (1-γ) [V 1 +W 1 -M ] V 1 -M < P Case 3: V 1 < M W 1 < P Default on All Debt [V 1 +W 1 ]γ 0 (1-γ)[V 1 +W 1 ] 27

30 Table 1: Dstrbuton by Orgnaton Year Year Frequency Percent , , , Total 132, Table 2: Mean Loan Orgnaton Spread by Borrower FICO Score (Standard Devatons n parentheses) Borrower Fco Range mean std dev [0, 658) [658, 682) [682, 706) [706+) Table 3: Mean Loan Amounts Classfed by State Foreclosure Laws. (Standard Devatons n parentheses) Defcency Judgments Judcal Foreclosure Not Not Allowed Allowed t-stat. Requred requred t-stat. Senor Debt LTV *** *** (14.54) (13.60) (15.03) (13.88) Total Debt LTV *** *** (12.45) (13.01) (12.65) (12.70) N 79,831 52,353 93,167 39,017 Note: t-statstc test for equalty of means under assumpton of unequal varance. *** sgnfcant at the 1% level. 28

31 Table 4: Mean Loan Amounts Classfed by Borrower FICO Score. (Standard Devatons n parentheses) FICO Scores Hgh FICO Low FICO t-stat. Senor Debt LTV *** (14.53) (13.99) Total Debt LTV *** (13.10) (12.31) N 61,473 70,711 Note: t-statstc test for equalty of means under assumpton of unequal varance. Hgh FICO borrowers have FICO scores greater than the mean FICO score for the sample (684) and Low FICO borrowers have FICO scores less than or equal to the mean FICO score for the sample. *** sgnfcant at the 1% level. 29

32 Table 5: Descrptve Statstcs Varable Label N Mean Std Dev Orgnal_Interest_Rate Junor Mortgage Interest Rate Loanamt Junor Mortgage Loan Amount $31, $12, Yeld Junor Mortgage Effectve Interest Rate Spread Junor Mortgage Orgnaton Spread Frstmtgbal Frst Mortgage Loan Amount $94, $45, Value House Value (Apprased) $114, $49, Loan_To_Value Loan_To_Value (total debt) FICO Borrower FICO Score r mkt 30 - Fxed Conventonal Market Rate Yeldcurve 10 year Treasury - 1 year Treasury σ r treas Standard Devaton of 10-year Treasury Credtspread Baa - AAA Bond Spread J 1=requre judcal D 1=allows defcency

33 Table 6: Non-lnear Three-Stage Least Squares Estmaton of Mortgage Orgnaton Terms (t-statstcs reported n parentheses) Spread log(loanamt) Term Intercept *** *** *** (81.25) (26.28) -(23.81) Spread *** *** -(14.39) (13.64) log(loanamt) *** *** -(38.83) (121.03) Term *** *** (31.41) (111.41) FICO *** -4.30E-04 * * -(20.58) -(1.84) (1.60) debtconsol 4.40E (0.02) (0.44) homemprove *** *** -(15.23) -(2.96) cashout *** *** -(15.65) -(3.31) J *** *** *** (7.29) (4.29) -(4.16) D *** *** *** -(26.27) -(22.53) (22.34) (r mkt -r treas ) *** (7.37) σ treas *** -(3.95) yeldcurve *** (5.53) credtspread *** (13.73) frstmtgbal -5.61E-08 * -(1.62) Value 1.07E-07 *** (4.36) Yr *** *** *** -(9.96) -(5.09) (4.99) Yr *** *** *** -(16.29) -(11.37) (11.20) Yr *** *** *** -(23.35) -(20.94) (21.10) Yr *** *** *** -(14.00) -(9.56) (9.56) Qtr ** *** (0.35) (2.23) -(2.26) Qtr * (1.93) (0.14) -(0.18) Qtr *** *** *** -(5.49) -(3.01) (2.94) 31

34 *** sgnfcant at the 1% level. ** sgnfcant at the 5% level. * sgnfcant at the 10% level. 32

35 Table 7: Mean (Medan) Predcton Errors (Estmaton Sample) (Actual Predcted) Number of Observatons Spread Log(Amount) Term Full Sample 99, (0.1266) (0.0264) ( ) Hgh Fco Borrower 47, (0.2500) (0.0303) ( ) Low FICO Borrower 51, (0.0076) (0.0233) ( ) Hgh FICO Borrower Debt Consoldaton 4, (1.2313) -(0.0929) -(4.0076) Home Improvement (0.4612) (0.1725) ( ) Cash Out 1, (0.3230) (0.2867) ( ) Low FICO Borrower Debt Consoldaton 6, (0.9373) -(0.0534) (8.2084) Home Improvement 1, (0.5444) (0.2878) ( ) Cash Out (0.7495) (0.1385) (4.5451) Hgh FICO Borrower Judcal=0, Defcency = 0 14, (0.2951) (0.0334) ( ) Judcal=0, Defcency = 1 18, (0.2221) (0.0301) ( ) Judcal=1, Defcency = 0 12, (0.2550) (0.0165) ( ) Judcal=1, Defcency = 1 1, (0.0334) (0.1395) ( ) Low FICO Borrower Judcal=0, Defcency = 0 17, (0.0291) (0.0205) ( ) Judcal=0, Defcency = 1 18, (0.0874) (0.0460) ( ) Judcal=1, Defcency = 0 14, (0.0180) -(0.0043) ( ) Judcal=1, Defcency = 1 1, (0.3769) (0.0950) ( ) Hgh FICO Borrower, Debt Consoldaton Low Cost (J=0, D=0) 1, (1.1466) -(0.0851) -(3.0290) Hgh Cost (J=1, D=1) (1.1720) -(0.0260) -( ) Low FICO Borrower, Debt Consoldaton 33

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