An Empirical Investigation of Collateral and Sorting in the HELOC Market

Transcription

1 An Emprcal Inestgaton of Collateral and Sortng n the HELOC Market By Shubhass Dey & Luca Dunn * Abstract Ths research explores the role that collateral plays n sortng borrowers accordng to rsk classes n the secured credt market. Two dstnct paradgms exst n the commercal loan market lterature on rsk-sortng based on collateral: (a) the sortng-by-obsered-rsk paradgm, whch predcts a poste assocaton between collateral and borrower rsk; and (b) the sortng-by-prate-nformaton paradgm, whch postulates a negate relatonshp. We emprcally test whch of these paradgms explans the rsk/nterest rate dsperson n the market for collateralzed Home Equty Lnes of Credt (HELOCs). Whereas for tradtonal loans the focus s on Loan-to-Value ratos, here we ntroduce the concept of Borrowng-to-Value rato, whch s the releant crteron for lnes of credt snce credt extended s not necessarly borrowed. Usng a maxmum lkelhood procedure, we smultaneously estmate the HELOC borrowng leel and the HELOC rate of nterest. Our results support the sortng-by-prate-nformaton paradgm. * Dey, Senor Economc Analyst, Bank of Canada, Ottawa, Canada; Dunn, Professor of Economcs, Oho State Unersty, Columbus, Oho.

2 . Introducton Collateral has always played an mportant role n commercal and real estate lendng. Wth the emergng mportance of home equty lendng, secured credt s also ganng ground n the consumer market for lnes of credt. The dsperson of nterest rates n the secured credt market depends prmarly on the role that collateral plays n sortng borrowers accordng to ther rskness. In ths regard, theoretcal studes hae predcted dfferent roles for collateral n sortng equlbra of the secured credt market. The two major explanatons of the collateral-rsk/nterest rate connecton are: (a) the sortng-byobsered-rsk paradgm whereby obserably rsker borrowers are requred to pledge more collateral than less rsky borrowers; and (b) the sortng-by-prate-nformaton paradgm whereby low-rsk borrowers sgnal ther credt worthness by pledgng more collateral than ther hgh-rsk counterparts. These opposng hypotheses hae not been tested n the market for HELOCs. Here we emprcally nestgate ther aldty n the market for collateralzed HELOCs and fnd that the sortng-by-prate-nformaton paradgm domnates. The hgher the amount of collateral pledged, the lower s the rate of nterest charged by banks for HELOCs. Furthermore, we pont out that the Loan-to- Value (LTV) crteron often used by banks to prce HELOC loans fals to take account of the man feature of a lne of credt, namely that there s a dfference between the loan extended and the actual amount borrowed. Here we ntroduce the concept of the Borrowng-to-Value rato (BTV), whch s the approprate measure of rsk, and hence the releant determnant of nterest rates, n the market for secured lnes of credt such as HELOCs.

3 Background and Preous Lterature Although ssues concernng the use of collateral hae been explored n a arety of settngs n the preous lterature on the credt market, most of ths work has focused on commercal loans. Ths earler work ncludes Barro (976), Jensen and Mecklng (976), Scott (977), Smth and Warner (979), and Stulz and Johnson (985). An explanaton for the secured lendng arrangement whch was not specfcally addressed n ths earler lterature s the sortng role of collateral n asymmetrcally nformed enronments. In the bankng communty, howeer, the use of collateral has been assocated wth obserably rsker borrowers (Morsman, 986). Ths s referred to as the sortng-by-obsered-rsk paradgm. Consstent wth ths ew, Swary and Udell (988) proded a motaton for the use of collateral by suggestng that secured debt may be useful n enforcng optmal frm closure (or bankruptcy). Boot, Thakor, and Udell (99) consdered a model where the borrower s rsk type s obserable to the lender whle the borrower s acton s prately known, and they dered suffcent condtons under whch obserably rsker borrowers pledge more collateral n equlbrum. Boot and Thakor (994), usng a model of mult-perod loan contracts, hae also found edence n faor of ths paradgm. Another strand of the theoretcal lterature n the commercal loan market has focused on nformaton about rsk known only to borrowers, leadng to the sortng-byprate-nformaton paradgm. Besanko and Thakor (987a) found that lenders are at an nformatonal dsadantage wth respect to borrower default probabltes, and n equlbrum, low-rsk borrowers pledge more collateral than ther hgh-rsk counterparts. Besanko and Thakor (987b) found a smlar negate relatonshp between collateral and 3

4 borrower rsk under loan contractng wth a mult-dmensonal prcng menu. Chan and Kanatas (985) and Bester (985) found that low-rsk borrowers pledge more collateral than hgh-rsk borrowers because collateral-assocated costs produce dfferent margnal rates of substtuton between collateral and nterest rates. Bester ncorporated collateral as screenng mechansm n the Stgltz and Wess (98) credt ratonng model and showed that ratonng then becomes unnecessary. Chan and Thakor (987) examned the form of the optmal secured loan contract assumng the exstence of both aderse selecton and moral hazard. Igawa and Kanatas (990), assumng moral hazard exsts due to the use of collateral, showed that the optmal secured loan contract for hgher qualty borrowers noles oer-collateralzaton; whereas self-fnancng and unsecured credt are chosen by the ntermedate and lowest qualty borrowers respectely. Emprcal studes of collateral and rsk based on bank fles and surey data n the market for commercal loans nclude that of Orgler (970), Hester (979), and Berger and Udell (990), who concluded that rsker borrowers pledge more collateral. Berger and Udell (995) found that collateral use decreases sgnfcantly wth the length of the relatonshp wth the bank, a fact that was theoretcally explaned n the earler paper by Boot and Thakor (994). More recent theoretcal work on the use of collateral n commercal loans has been put forward n a context of symmetrc nformaton wth the exstence of entrepreneurs oeroptmstc ealuaton of ther project (de Meza and Southey, 996) or costly state erfcaton (Bester, 994). Preous studes nolng collateralzaton n the consumer loan market hae largely focused on mortgage and auto loans. Although recently the research on secured 4

5 consumer credt has expanded to nclude Home Equty Loans (HELs) and HELOCs, none of ths work, to our knowledge, has addressed the ssue of sortng by collateral (Chen and Jensen, 985; Canner, Fergus and Luckett, 988; DeMong and Lndgren, 990; Eugen, 993; Canner and Luckett, 994; Esenhauer, 994; Delaney, 994; Salandro and Harrson, 997; Canner, Durkn, and Luckett, 998; and Azcorbe, Kennckell, and Moore, 003). Loan-to-Value s. Borrowng-to-Value Loan-to-Value rato (LTV) has tradtonally been a major explanatory arable n the assessment of the rsk assumed by the banks and hence n the determnaton of the rate of nterest. For tradtonal loans, the amount of credt extended by a bank s actually borrowed; and therefore banks assume the rsk of the entre loan amount proded to the borrower. LTV (as opposed to the alue of the collateral alone) should logcally explan a sgnfcant porton of the rsk/nterest rate spread of n both the consumer and corporate secured credt market. Howeer, t s not approprate to use LTV to explan the nterest dsperson of collateralzed lnes of credt such as HELOCs. A lne of credt allows a consumer to borrow up to a predetermned credt lmt. Banks do not assume any rsk unless the borrower, rrespecte of hs/her rsk-type, borrows on the lne. Therefore the broader category of Borrowng-to-Value rato (BTV), and not LTV, s the releant measure of the rsk assumed by banks n the case of lnes of credt a pont whch has been neglected n preous research. Actual borrowng s typcally not obsered a pror by banks durng the determnaton of ther rsk exposure, and hence the nterest rate, for lnes of credt. Howeer, banks can use ther substantal nformaton on consumer 5

6 borrowng patterns to make estmates of borrowng. Such borrowng estmates, as well as the alue of collateral pledged, should deally be consdered when settng the terms of the loan and loan-prce dsperson for collateralzed lnes of credt such as HELOCs. In ths paper, we emprcally nestgate of the relatonshp between the alue of collateral and credt rsk wthn the market for HELOCs. The econometrc model that we use estmates the borrowng of a household wth the HELOC rate of nterest as an endogenous arable. The HELOC rate of nterest s determned by the amount of the collateral pledged by borrowers, borrowers credt hstores, and such characterstcs of agreed secured loan contracts as the requred frequency and rate of repayment. We examne the nature of the nformaton asymmetry that exsts between borrowers and lenders n the HELOC market and explan how the alue of collateral, along wth estmated borrowng, helps to mtgate ths nformaton asymmetry. Our emprcal work supports a negate assocaton between the alue of the collateral pledged by borrowers and the HELOC rate of nterest charged by banks, as opposed to the poste assocaton typcally found n the emprcal lterature on commercal loans.. Data The data set used n ths study conssts of a pooled sample from the 995 and 998 rounds of the U.S. Sureys of Consumer Fnances (SCF). We use data for the 5,995 households who hae poste equty n ther homes. There are two types of sample members: All arables were conerted to 998 dollars. 6

7 Type I: D H = r H = 0, where D H and r H are the obsered HELOC debt and nterest rate respectely. Type II: D H > 0 and r H > 0. The descrpte statstcs for HELOC debtors and HELOC non-debtors n ths data set are presented n Appendx A. 3. An Econometrc Model We wll consder the followng arables n our model: Defntons of Varables W Wealth of the consumer t Income tax rate; 0 < t < C Cost of collateralzaton δ Dscount factor; 0 < δ < τ Fxed cost 3 of HELOC; τ > 0 α Requred rate of repayment; 0 < α < Followng Dey and Dunn (004), the consumer s dscounted expected lfetme utlty from optmally carryng D H* amount of HELOC debt s V H* = V H (W, r H, δ, α, t, τ, c, D H* ). Hence for household we hae, D H* = h (W, τ, c, t, r H, α, δ ). Counterparts from the Data We wll use the followng emprcal quanttes to represent the arables of the model: Wealth Factors W : equty n the home, lqud assets, other non-fnancal assets, and household sze. These are perceed costs related to the rsk of home-loss;, where C = c (D H ), > c > 0. 3 Ths noles upfront costs such as apprasal fees, closng costs, and annual fees. 7

8 Rsk Factors R : a dummy arable based on the ncdence of delnquency, dummes capturng household s atttude towards rsk, and the repayment rate α. Tax Factors T : a ector ncludng a dummy arable whch determnes whether household temzes tax-deductons or not and household ncome. Mortgage Factors M : a ector ncludng ncdence of mortgage debt, debt repayment frequency, and mortgage rate of nterest. Dscount Factors S : a ector ncludng age, ncome, household sze, ethncty, and educaton leel. Snce the fxed costs of obtanng HELOCs (τ ) hae no araton across households, τ = τ. Therefore, the fxed costs go nto the constant term of the HELOC debt equaton. The margnal cost of collateralzaton c s consdered to be a functon of the nddual s rsk-type represented by R as gen aboe. The dscount factor δ s captured by the ector S. The ector T as defned aboe captures the ncome tax rates t. Hence we hae c = α 0 + α R + ε, t = α + α 3 T + ε δ = ϕ S + η Substtutng for c, t, δ and τ nto D H* ; usng W and α, we hae a quas-reduced form equaton for D H*, D H* = γr H + β X + () where X s a ector of exogenous arables nfluencng D H*. Usng the amount of collateral pledged by household,.e. the home equty, R, and M, we hae a reduced form equaton for r H, r H = β X + () where X s a ector of exogenous arables nfluencng r H. 8

9 We consder the followng econometrc model: D r H H = D H * ' = β X = γr + H ' + β X + f D H* >0 r H D H = 0 = 0 otherwse where and follow barate normal wth zero means, arances and respectely, and wth coarance. If X contans at least one arable that s not ncluded n X, then all the parameters of the model are dentfed. The ector M contans nformaton about the ncdence of mortgage debt among households, mortgage rates of nterest they face, and ther debt repayment frequency. Snce all banks use the same credt bureau nformaton to assess the rsks of all loan applcants, the HELOC rate of nterest should be correlated wth the mortgage rate of nterest. Howeer, after controllng for the HELOC rate of nterest, the amount borrowed on the HELOC can reasonably be assumed not to depend on the mortgage rate of nterest. Hence we can logcally nclude at least one arable n ector X, namely the mortgage nterest rate, whch s not ncluded n ector X. In order to correct for the endogenety present n the HELOC debt equaton, our two-stage estmaton procedure uses an estmate of the HELOC rate of nterest rˆ H as an nstrument. We use a maxmum lkelhood procedure to estmate the econometrc model. A consumer s obsered to carry debt on HELOC f D H* > 0. Substtutng the HELOC nterest rate equaton nto the HELOC debt functon, the HELOC debt-holdng decson can be wrtten as 9

10 0 β X + γβ X > - ( + γ ) or, I > where, N (0, + γ + γ ) N (0, ). The lkelhood of obserng a HELOC non-debtor s ) ( ) ( ) ( Pr / I I I d e I ob ϖ π ϖ = Φ Φ = = < where Φ s the standard normal cumulate densty functon. Hence the lkelhood of the data consstng of N obseratons, wth N HELOC non-debtors s + = = Φ = N N N b I L ), ( ) ( = ) ( ) ( ) ( N N N n n I + = = Φ where b (.) s the barate normal densty functon, n (.) s the normal densty functon and = D H - β X - γr H = r H - β X. We know that ~ N (0, ) ( ), ρ ρ N, where. ρ = Let, ) ( ρ = c and. c F ρ = The correspondng log-lkelhood functon can be wrtten as

11 log L = N I log[ Φ( )] + φ + = = N+ N N = N+ φ( F ) where φ(.) s the standard normal densty functon. A mult-step procedure was used to estmate the parameters of the model, frst usng the two-stage probt method as descrbed n Lee et al. (980). Ths two-step procedure yelds consstent estmates of all parameters, and these estmates were used as ntal alues for the fnal maxmzaton of the log-lkelhood functon. c 4. Emprcal Results The arables used n the emprcal analyss are found n Table below. Ths s followed by Table where the results for the maxmum lkelhood estmaton for the HELOC rate of nterest are presented. The alue of collateral (HOMEQUITY) has a sgnfcant negate nfluence on the HELOC rate of nterest charged by banks. Therefore our maxmum lkelhood estmaton prodes emprcal support for the sortng-byprate-nformaton paradgm. Borrowers who pledged hgher amounts of collateral sgnal ther superor rsk-types and therefore are rewarded wth lower nterest rates by the banks. Among HELOC debtors, those who carry mortgage debt (MORTGAGE = ) get lower HELOC nterest rates from banks. The mortgage rate of nterest (MORTGAGERATE) has a poste effect on HELOC nterest rates, as expected from the dscusson aboe. Fnally, we fnd emprcal edence of a poste assocaton between the arable capturng repayment frequency (REPAYMENTFREQ) and the HELOC rate of nterest.

12 Table : Defntons of Varables Varables HELOCDEBT HELOCRATE HOMEQUITY LIQUIDASSETS OTHERASSETS TAX DELINQUENCY INCOME REPAYMENTRATE MORTGAGE HIGH-RISKTAKER c AVERAGE-RISKTAKER NOT-RISKTAKER MORTGAGERATE AGE EDUCATION ETHNICITY HOUSEHOLDSIZE REPAYMENTFREQ e Explanaton HELOC debt HELOC rate of nterest a Equty n home Lqud assets Other non-fnancal assets Itemze ncome tax deductons 0 Otherwse Behnd n payments by two months or more 0 Otherwse Income The requred rate of repayment b Household has some knd of mortgage debt 0 Otherwse Aboe aerage rsk-taker 0 Otherwse Aerage rsk-taker 0 Otherwse Not a rsk-taker 0 Otherwse Mortgage rate of nterest d Age of the household head Years of schoolng of the household head Non-whte 0 Otherwse Sze of household 0 No or flexble repayment requred Less frequent than monthly repayment requred Monthly repayment requred 3 More frequent than monthly repayment requred a Maxmum nterest rate charged among the dfferent HELOCs taken out by the household. b Fracton of HELOC and mortgage debt repad. c Household s rsk-tolerance on a to 4 scale. d Maxmum nterest rate charged among the dfferent mortgage loans taken out by the household. e Maxmum of the repayment frequency on HELOC and mortgage debt.

13 Table : Full Informaton Maxmum Lkelhood Estmates of the HELOC Rates of Interest Maxmum Lkelhood Varables Coeffcent S.E. CONSTANT *** 0.78 HOMEQUITY ** NOT-RISKERTAKER HIGH-RISKTAKER DELINQUENCY REPAYMENTRATE MORTGAGE -3.7 *** MORTGAGERATE 0.46 *** REPAYMENTFREQ.67 *** 0.39 *** Sgnfcant at % leel; ** Sgnfcant at 5% leel; * Sgnfcant at 0% leel Table 3 presents the results of the maxmum lkelhood estmaton for HELOC debt. The arables INCOME, OTHERASSETS, HOUSEHOLDSIZE, and HOMEQUITY are all sgnfcant wth sgns as expected. Households wth hgh tolerance for rsk are found to hold greater amounts of HELOC debt, as are those who temze ther taxes, snce ths debt s tax-deductble. The endogenous arable, the HELOC rate of nterest, s found to depress HELOC debt-holdng. The only sgnfcant socoeconomc arable s AGE, wth adancng age decreasng the amount of HELOC debt held. The maxmum lkelhood estmates of the error arances ( and ) are both sgnfcant. Fnally, the estmate for ρ s found to be poste and sgnfcant. 3

14 Table 3: Full Informaton Maxmum Lkelhood Estmates of HELOC Debt Maxmum Lkelhood Varables Coeffcent S.E. CONSTANT HOMEQUITY LIQUIDASSETS OTHERASSETS HOUSEHOLDSIZE HIGH-RISKTAKER NOT-RISKTAKER DELINQUENCY INCOME TAX REPAYMENTRATE AGE EDUCATION ETHNICITY HELOCRATE *** *** 4.7 * *** *** 6.03 * *** * ρ.404 *** *** *** Log-L = *** Sgnfcant at % leel; ** Sgnfcant at 5% leel; * Sgnfcant at 0% leel 5. Summary and Conclusons Ths paper has addressed the use of collateral n HELOCs. We hae explored the role that collateral plays n sortng borrowers by ther rsk-types, thereby explanng the obsered spread of HELOC rates of nterest. The framework used here dstngushes between a lne of credt and a loan. Whle the full amount of a tradtonal loan s actually borrowed, wth a lne of credt, the amount of actual borrowng may be dfferent from the amount of credt extended. Therefore we proceed under the assumpton that the actual or estmated borrowng amount s the releant measure of the lender s exposure to rsk for a 4

15 lne of credt. We thus make a dstncton between the Loan-to-Value rato (LTV), whch has tradtonally been used as a measure of rsk, and the Borrowng-to-Value rato (BTV), whch should be estmated when consderng secured lnes of credt such as HELOCs. Our econometrc analyss has utlzed an estmate of the HELOC borrowng, along wth the alue of the collateral pledged and the HELOC nterest rate, n a smultaneous equatons model whch assumes a prcng scheme reflectng the concept of BTV. Usng the Surey of Consumer Fnances, 995, 998 data wth a maxmum lkelhood procedure, we hae estmated the leel of HELOC debt as a functon of releant arables. Ths ncludes the endogenous arable, the HELOC rate of nterest, whch s found to hae a sgnfcant negate nfluence on HELCO debt. We hae also estmated the HELOC rate of nterest as a functon of home equty pledged as collateral and other exogenous arables. Preous research has found the sortng-by-obsered-rsk paradgm to be emprcally domnant n the secured commercal loan market. Howeer, n the market for HELOC loans, we fnd that relately low-rsk borrowers sgnal ther rsk type by pledgng larger amounts of collateral and thereby recee lower nterest rates, thus supportng the sortng-by-prate-nformaton paradgm. References Azcorbe, Ana M.; Kennckell, Arthur B.; Moore, Ken B. Recent Changes n U.S. Famly Fnances: Edence from 998 and 00 Surey of Consumer Fnances. Federal Resere Bulletn, January 003, 89(), pp. -3. Barro, Robert J. The Loan Market, Collateral and Rates of Interest. The Journal of Money, Credt and Bankng, Noember 976, 8(4), pp Berger, Allen N. and Udell, Gregory F. Collateral, Loan Qualty, and Bank Rsk. Journal of Monetary Economcs, January 990, 5(), pp

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19 APPENDIX A Means of Varables for HELOC Debtors and HELOC Non-Debtors * HELOC Varables Debtors Mean HOMEQUITY 64.9 (74.7) LIQUIDASSETS 48.0 (95.) OTHERASSETS 489. (76.9) INCOME 00.8 (49.7) TAX 0.8 (0.4) REPAYMENTRATE 0.03 (0.07) HOUSEHOLDSIZE 3. (.3) MORTGAGE 0.8 (0.4) MORTGAGERATE 6.3 (3.5) DELINQUENCY 0.0 (0.) AGE 50.8 (.4) EDUCATION 4.9 (.) REPAYMENTFREQ.0 (0.3) HIGH-RISKTAKER 0.4 (0.5) NOT-RISKTAKER 0. (0.4) ETHNICITY 0. (0.3) HELOC Non-Debtors Mean 33.9 (899.) 6.8 (6) (389.9) (3905) 0.7 (0.5) 0.0 (0.).7 (.4) 0.6 (0.5) 4.8 (4.3) 0.03 (0.) 53.8 (5.) 4. (.8). () 0.3 (0.5) 0.3 (0.4) 0. (0.3) * All monetary arables are n thousands of dollars. 9