Post on 04-Jun-2018
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High LTV Loans and Credit Risk
Brent AmbroseProfessor of Finance and Kentucky Real Estate Professor
University of KentuckyLexington, KY 40506-0034
(859) 257-7726ambrose@uky.edu
and
Anthony B. SandersJohn W. Galbreath Chair and Professor of Finance
The Ohio State University2100 Neil Avenue
Columbus, OH 43210(614) 688-8609
sanders.12@osu.edu
October 3, 2002
We thank Paul Malatesta, Kerry Vandell, and Abdullah Yavas for their helpful comments andsuggestions. An earlier version of this paper was presented at the Georgetown University Credit ResearchCenter Subprime Lending Symposium.
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High LTV Loans and Credit Risk
Abstract
This study examines the pricing of high-LTV debt to determine whether state-specificdefault laws have an impact on the availability and cost of that debt. We develop asimple theoretical model that provides predictions concerning borrower and lender choiceof mortgage terms under differing assumptions regarding state default regulations. Weexamine whether lenders rationally price loans to higher risk borrowers and whetherborrowers in states that limit lender ability to seek default remedies pay higher creditcosts. Our results indicate that lenders rationally price loans to higher risk borrowers forthe most part; however, when we focus on smaller and smaller FICO scores buckets, theresults indicate that the mean actual loan rates are higher than those predicted by ourmodel. The results also indicate that state-specific default laws do have an impact on theprice of credit. The results also show that there is a greater degree of error in the pricing
of high LTV loans to low FICO borrowers than to high FICO borrowers.
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High LTV Loans and Credit Risk
I. Introduction
Debt usage contains important signals regarding borrower quality and thus reveals
information. While the use of debt is widely recognized in the information asymmetry
literature, unfortunately, few studies have tied the signaling aspect of debt usage to
broader market conditions where legal restrictions and regulations also interact to
determine optimal debt usage. Given the debate currently surrounding the issue of
predatory lending practices, it is important for public policy analysts to understand the
equilibrium tradeoff between debt amount and cost and the impact that the regulatory
environment has on this tradeoff.
Several observations exist on the use of high debt levels. For example, in the
residential mortgage market it is well understood that high loan-to-value (LTV) loans
carry significant default risk. Traditional option pricing models, where default is
endogenous and determined only by interaction of house value and interest rates, find that
the default option value is significant when the LTV is greater than 100%.1 As a result,
high-LTV loans are usually junior debt with lower priority of claim on the asset, with the
majority of high-LTV loans originated for the purpose of debt consolidation.
Furthermore, high debt levels are also correlated with the probability of bankruptcy.
Thus, high-LTV loans are often like unsecured debt or credit cards, and as a result, the
equilibrium tradeoff between borrower credit signals, debt amount and cost, and
regulatory environment should be most apparent in this market.
1See Kau and Keenan (1995) and Quercia and Stegman (1992) for an overview of the option-pricing modelas applied to mortgages and mortgage default.
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The goal of this study is to examine the pricing of high-LTV debt and determine
whether state-specific default laws have an impact on the availability and cost of that
debt. Thus, we begin with a review of the theoretical models of borrower choice of credit
and credit availability. From this review, we develop a simple theoretical model that
provides predictions concerning borrower and lender choice of mortgage terms under
differing assumptions regarding state default regulations. Using the predictions as a
guide for the empirical analysis, the study has three main objectives. This first is to
determine whether lenders rationally price loans to higher risk borrowers. The second is
to determine the impact of borrower protection laws on the price of credit and the third is
whether borrowers in states that limit lender ability to seek default remedies pay higher
credit costs.
The empirical findings will provide insights into the role of state specific default
and foreclosure laws on the equilibrium supply of credit and its costs. These insights
should enable policy makers to better assess the adequacy of current borrower protection
laws with respect to the evolving high-LTV debt market. Furthermore, by recognizing
the general equilibrium nature of the credit market, the analysis will provide policy
makers with a solid framework for assessing the validity of the accusations of predatory
lending within this market.
II. High LTV Mortgages
A variety of mortgages are originated in the U.S. that have different
characteristics in terms of priority (first and home equity loans), loan-to-value ratio
(LTV) and credit quality of the borrower (A-rated and B/C-rated borrowers). We would
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expect that the different mortgages would have different default rates as well as different
prepayment rates.
For illustrative purposes, we compare the prepayment rates and 90-day
delinquency rates for three mortgage products. The first mortgage product is a senior
mortgage with low LTVs (80% and less). The second mortgage product is a home equity
loan (which is junior in priority to the first mortgage). The third mortgage product is a
high LTV second mortgage which is junior to the first mortgage and can have aggregate
LTVs up to 125% of house value.
Chart 1 presents the prepayment rates on the three different mortgage products
(based on pool-level prepayments on mortgage-backed securities). The prepayment on
the first mortgage is represented by a Residential Funding Corporation mortgage-backed
security (RFMSI 1997-S5) which had a weighted-average coupon (WAC) of 8.16% and a
weighted-average LTV (WALTV) of 74.30% as of May 1997. The prepayment on the
home equity loan is represented by a Money Store mortgage-backed security (TMSHE
1996-D) which had a WAC of 11.15% and a WALTV of 72.60% as of May 1997. The
prepayment on the high LTV loan is represented by a Firstplus Financial mortgage-
backed security (Firstplus 1997-1) which had a WAC of 14.11% and a WALTV of
114.00% as of May 1997. All three mortgages had approximately the same weighted-
average maturity (WAM) as of May 1997.
The RFMSI 1997-S5 first mortgage deal had the highest prepayment rates of the
three mortgages. The Firstplus 1997-1 125 LTV loan deal had the lowest prepayment
rates of the three mortgages. The TMSHE 1996-D home equity loan deal was in the
middle of the other two loans in terms of prepayment speeds. Clearly, the Firstplus 1997-
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1 125 LTV had the desirable feature of having the highest interest rate (WAC = 14.11%)
and the lowest prepayment speed (which would give investors a greater number of
coupon payments at the highest rate of the three mortgages). The only negative to the
Firstplus 1997-1 125 LTB loan deal would be delinquencies and default.
Chart 2 depicts the 90-day delinquency rates on the three mortgages over the
same period of time. In terms of delinquencies, the RFMSI 1997-S5 first mortgage deal
experienced the lowest 90-day delinquency of the three mortgage types during the
December 1997 through August 2000 period. This is not surprising given that
Residential Funding has very high credit standards for the mortgages in their pool. The
TMSHE 1996-D home equity loan deal, on the other hand, had the highest 90-day
delinquency rate among the mortgage types while Firstplus 1997-1 125 LTV loan deal
had delinquencies somewhere in between. While it seems perplexing that the 125 LTV
deal (with a WLTV of 114.00%) actually had lower 90-day delinquencies than the home
equity loan deal (with a WLTV of 72.60%), it is not really surprising. In order to
convince investors to purchase mortgage-backed security deal with a WALTV of
114.00%, the 125 LTV loans usually require better credit scores for the borrowers in
order to quell investor concerns regarding potential defaults.
Given that the Firstplus Financial 125 LTV mortgage has a higher interest rate
than the Money Store home equity loan (and substantially higher aggregate LTV) yet a
lower incidence of ex-post delinquencies, it is of interest to examine the role that the
borrowers credit scores and LTV play in the determination of the 125 LTV interest rate.
In the next section, we develop a model that provides predictions concerning second
loans amounts and costs given differences in state specific laws and regulations.
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III. The Model
We begin by assuming a two-period model where the borrower has an initial
income endowment of W0with an expectation that income in period one will be 1~
W . For
simplicity, we assume that the borrower utilizes period zero income and debt to finance
consumption and enters into debt contracts to maximize period one total wealth (income
plus assets). Lenders can verify the initial income endowment but are only able to
observe an imperfect credit quality signal () of the expectation of period one income.2
We assume that is distributed over the interval [0,1] where larger values of signal
higher expectations of period one income.3 The borrower purchases a housing unit for V0
at time 0 utilizing secured debtMto partially fund the purchase whereMM.5
2Verification of borrower wealth at loan origination through examination of tax returns and bank accountsis common practice.3Typical credit quality signals (such as those compiled by Fair, Isaac & Co.) combine informationregarding borrower income, assets, debts, and payment history into a numeric score that is predictive of
borrower potential to default on future debt payments.4For high LTV levels (M/V0> 0.80), lenders require that borrowers purchase mortgage insurance effectively raising the cost of borrowing.
5The condition that 1~V + 1
~W>Massumes that lenders believe that strategic default can be limited through
enforcement of borrower deficiency judgments. We explicitly allow for this in the analysis below.
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The borrower also finances non-housing consumption (C0) by borrowing
unsecured debt (P) that is also due in period 1 with the amount due denoted as
P=P(1+rp). Since P is unsecured, the lender looks to expected period one income for
repayment, and thus, the amount of unsecured debt available at period 0 is based on the
expectation of income ( 1~
W ) and the borrowers credit score. Since the credit score
provides a signal of expected period 1 income, the higher the borrowers credit signal (),
the greater the amount of unsecured debt made available. Given that mortgage debt has a
senior claim to the period 1 assets and income, the interest rate on secured debt is lower
than unsecured debt (rm
M, and 0
)(>
P.6 If realized period 1 income and
house values (W1and V1) are greater thanPandM, respectively, then all debts are paid
in full and the borrowers period 1 net wealth position is W1-P+V1-M>0.
Turning to the conditions under which the borrower would default, we recognize
that uncertainty is captured in the model via period 1 income and house values.
Furthermore, state-level regulations regarding borrower rights and responsibilities can
have considerable impact on expected default losses (or recovery rates) and as result
would impact borrower credit costs in equilibrium. For example, Ambrose, Buttimer,
and Capone (1997) document that a significant delay can exist between borrower default
(missed payment) and lender foreclosure. Ambrose and Buttimer (2000) then show that
this delay introduces a number of potential options to the borrower with respect to curing
6Ambrose, LaCour-Little, and Sanders (2002) empirically verify this prediction by demonstrating thatborrower credit risk is negatively related to the credit spread on first mortgages.
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default prior to the lender foreclosing on the property. Using these concepts, Ambrose
and Pennington-Cross (2000) discuss how state laws that define the foreclosure process
and establish creditor rights can impact the supply of mortgage credit.7 For example,
state default laws can impact the credit supply by defining how foreclosure is
accomplished and whether creditors may pursue other borrower assets in the event that
the collateral sale does not discharge the debt. Furthermore, state bankruptcy laws and
regulations allow borrowers to protect a portion of their housing equity and non-housing
property via homestead and personal property exemptions.8 In order to introduce state
level default costs to the analysis, we define as the probability that the lender will be
able to recover default losses through foreclosure sale or deficiency judgments. Thus,
lies on the interval (0,1] where =1 denotes states with strong lender protection laws and
0 denotes states with strong borrower protection laws. If =0, then the borrower has no
incentive to repay the debt and will default in every case with the uninteresting
equilibrium result that no lender would enter into a loan contract.
We now consider the various borrower and lender period 1 payoff conditions
assuming extreme values for . Figure 1 shows the payoff conditions for the secured and
unsecured lenders as well as the borrower. In Panel A, we assume that =1 implying that
the lenders are able to foreclose on the borrowers assets to satisfy an outstanding claim.
Case 1 shows the payoff positions when the total value of all assets is greater than the
debt outstanding. In this situation, the borrower obviously pays off all loans and has a
7Pence (2002) confirms this finding using HMDA loan level data.8As discussed by Berkowitz and Hynes (1999) and Lin and White (2001), Federal bankruptcy law providesa homestead exemption of $7,500 but each state is allowed to set its own exemption level.As a result,individual state homestead exemption levels vary widely with some being unlimited and others being veryrestricted. Lin and White (2001) note that personal property exemptions have smaller variation acrossstates.
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positive wealth position. In Case 2, we show the payoff when the value of the house is
greater than the secured mortgage debt, but period one wealth is less than the unsecured
debt (W1
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Panel C shows the period one outcomes assuming that Pis now financed with a
secured second mortgage. The payoff conditions in Case 2 are altered to reflect the
ability of the junior secured lender to seize part of the borrowers housing equity. Since
V1-M>0, the payoff to the secured second lender is greater than the payoff to the
unsecured lender ([V1+W1-M]> [W1]). The secured second lenders gain is directly
offset by the borrowers loss; and, as a result, in states where borrower default costs are
low, the unsecured lender has an incentive to entice the borrower to switch from
unsecured debt to secured debt by offering more generous loan terms for junior secured
debt than for unsecured debt.
The implications of our model with respect to borrower quality and loan amount
contrast with the model predictions of Brueckner (1994, 2000), who develops a simple
two-period model of borrower default that examines the impact of borrower risk on
choice of loan amount. Brueckners model is based on default being triggered by
declines in the underlying collateral asset value and his analysis implies that low risk
borrowers self-select smaller loans while high-risk borrowers select larger loans. This
result is based on the observation that default costs appear to be important in
understanding the empirical incidence of default. Brueckners model follows from the
information asymmetry arguments first applied to the insurance market by Rothschild
and Stiglitz (1976). Rothschild and Stiglitzs (1976) analysis of the insurance market
demonstrated that when insurers cannot discern risky applicants from non-risky
applicants, the safe applicants signal their risk profile by applying for less insurance
than the risky applicants. Similarly, Brueckners model indicates that, in the presence
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of non-trivial default costs, only high-risk borrowers are willing to pay the premium for a
high LTV ratio.9
However, our predictions are consistent with those presented by Harrison, et al
(2002), who modify Brueckners model to examine the impact of borrower income on
default. Borrower income is not explicitly considered in the original Brueckner model
where default is motivated by changes in house value. Rather than allow default to be
motivated by uncertain future asset values, Harrison, et al (2002) motivate default based
on uncertainty regarding the borrowers future income (holding the asset value fixed).
Thus, default occurs if the borrowers future income is insufficient to repay the debt in
the presence of a decline in asset value. With default conditional on income, their model
shows that when default costs are high, risky borrowers choose low LTV ratios to
minimize default costs. However, their model provides additional insights by indicating
that when default costs are low, risky borrowers may actually choose higher LTV ratios.
To summarize, our analysis implies that borrowers in states with low default costs
will have higher secured second loan amounts relative to borrowers in states with high
default costs. Furthermore, our model also implies that secured junior loan amounts
should be directly correlated with borrower credit quality since the lender looks to both
the underlying collateral as well as future income for loan repayment. That is, our model
predicts that higher quality borrowers will have higher loan amounts relative to lower
quality borrowers. This is consistent with the predictions of Harrison et al (2002) and
directly counters to the predictions of Brueckner (1994, 2000). In addition, to the extent
9Brueckners model is consistent with models corporate borrowering. For example, Bolton andScharfstein (1996) develop a model of debt issuance that predicts that low-risk firms should borrower froma greater number of creditors while high-risk firms will only borrower from a few creditors. Their modelalso implies that low risk borrowers will have larger second loans relative to high-risk borrowers.
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that lenders are able to differentiate borrower quality based on credit scores, we expect
that loan costs should be negatively related to borrower credit scores.
IV. Data
In order to test the predictions from our model, we employ a dataset of 132,184
second mortgage loans originated for securitization between 1995 and 1999. This dataset
is unlike most other mortgage datasets in that these mortgages represent second loans that
are secured by the underlying property. However, in many cases, when the original
mortgage loan balance is combined with 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 designation denotes the fact that the maximum LTV ratio
is normally 125 percent of the property collateral value. In order to make the dataset as
clean as possible, we include only subordinate loans with single-family residential
collateral. The dataset contains information regarding the borrowers reason for desiring
the mortgage, allowing a test of whether loans originated for the purpose of debt
consolidation differ from loans originated for other purposes (home improvement,
refinancing, etc.).
Table 1 shows the distribution of the loans by origination year. We note that the
majority of the mortgages (50%) were originated in 1997. The mortgages were
originated across the US, but have significant concentration in California (21.5%) with
the next highest concentration in Florida (7.8%).10 Consistent with Texas banking laws
10A table detailing the geographic distribution of mortgages originations is available from the author uponrequest.
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regarding second mortgages, there were only 206 loans originated in Texas.
Furthermore, consistent with the findings of Ambrose, LaCour-Little, and Sanders
(2002), we find that the origination spread for high credit quality borrowers is
significantly lower than the origination interest rate spread for low credit quality
borrowers (Table 2).11
In order to estimate the impact of state-specific default laws, we follow the
analysis of Ambrose and Pennington-Cross (2000) who categorize the states based on
whether creditors must use judicial or non-judicial foreclosure and whether the states
have anti-deficiency judgment statutes.
12
From the lenders perspective, this
classification system defines a high default cost state as one that requires judicial
foreclosure proceedings but does not allow deficiency judgments. Similarly, a low
default cost state is one that does not require judicial foreclosure and allows lenders to
obtain deficiency judgments against borrower assets.
Given that deficiency judgments increase the risk to the borrower, the theory
proposed by Harrison et al (2002) suggests that borrowers in states that allow deficiency
judgments should self select lower debt amounts than borrowers in states that limit
deficiency judgments, all else being equal. As a preliminary test of this hypothesis, we
report in Table 3 the mean total debt loan-to-value ratio and senior debt loan-to-value
ratios based on whether or not the borrower lives in a state that allows deficiency
judgments. We find that borrowers in states that have do not allow deficiency judgments
11The origination interest rate spread is defined as the mortgage contract rate at origination less the 10-yearTreasury rate at date of origination.12Judicial foreclosure proceeding are more costly and time-consuming than non-judicial proceedings sincecreditors are required to obtain a court order to foreclosure on the property to satisfy the debt. Anti-deficiency judgment statutes prohibit creditors from attaching other assets or garnishing future wages tosatisfy losses that occur due to default.
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carry significantly higher senior debt amounts but lower total debt amounts than
borrowers in states that allow deficiency judgments.
Since judicial foreclosure has the perception of providing greater borrower
protection than non-judicial foreclosure proceedings, total debt amounts and junior loan
amounts in states that require judicial foreclosure should be higher than in states that
allow non-judicial foreclosure. Thus, Table 3 also reports the mean total loan-to-value
ratios and senior loan-to-value ratio classified by state law regarding foreclosure.
Contrary to expectations, we find that mean senior loan-to-value ratios are significantly
lower in states that require judicial foreclosure.
13
However, total debt loan-to-value ratios
are higher in states that require judicial foreclosure. Since default costs are in general a
zero sum game (borrower protections limit lender default recovery and pro lender
regulations increase potential borrower losses), one possible explanation for this result is
that lenders may ration credit in states where legal regulations limit lender abilities to
quickly recover assets in case of default. Since most borrowers in default do not have
other assets to attach, lenders may view deficiency judgments as less important than the
ability to utilize non-judicial foreclosure proceedings.
When factoring borrower credit and information signaling, Harrison et al (2002)
suggest that holding default costs constant, high quality borrowers in high default cost
states self-select higher loan amounts while low quality borrowers self select lower loan
amounts to minimize the potential cost of default. Therefore, we test whether higher risk
borrowers select larger loans and whether higher risk borrowers in high default cost states
select lower loan amounts, holding all else constant. Table 4 shows the differences in
mean loan-to-value ratios based on whether the borrowers FICO score is greater than or
13This is consistent with the findings of Pence (2002).
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less than the average FICO score in the sample. Consistent with our theory, higher
quality borrowers do have significantly higher senior loan amounts. However, lower
quality borrowers have higher loan-to-values based on total debt. This finding is
inconsistent with the debt-signaling hypothesis proposed by Bolton and Scharfstein
(1996). Holding all else constant, Bolton and Scharfsteins (1996) theory is that lower
risk borrowers will have larger second loans as they are in a position to take on more
debt.
In the regression analysis discussed below, we test whether lenders price loans
based on borrower risk and default costs. Merton (1974) predicts that borrower yield
spreads are a positive function of total debt. In contrast, the model predicts that lenders
will offer borrowers lower spreads to entice them to switch from unsecured personal debt
to secured mortgage debt. This last test should provide insight into the question of
whether lenders engage in predatory lending practices by charging interest rates unrelated
to borrower credit risk.
V. Empirical Modeling
One of the primary problems with analyzing the impact of state level default costs
on the availability of credit is the endogenous relationship between the mortgage loan
terms, the loan amount, the collateral quality, and the borrowers credit quality. This
endogenous relationship is widely recognized in the literature that examines borrower
choice concerning loan amount and housing consumption. For example, Ambrose,
LaCour-Little, and Sanders (2002) employ a simultaneous equations system to recognize
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the well-known endogenous relationship between LTV and house value.14However, our
analysis is more complicated in that we examine the borrowers choice of junior loan
debt and the impact of default costs on the availability and cost of that debt. In this
context, the amount of housing consumption is already determined. Thus, the
endogenous terms are related to the amount of the second loan, its costs (interest rate
spread), and loan term, assuming that the borrowers house (collateral) value, credit
quality and income are exogenous to the decision. Therefore, to control for this
endogenous relationship we estimate the following system via non-linear three-stage least
squares regression (3SLS):
( )
i
k
ik
j
ij
r
iiiii
treasmktiiii
QtrDUMYrDUM
adcreditspreyieldcurve
improvecashoutdebtconsolDJ
rrFICOTermloanamtSpread
treas
+++
+++
+++++
++++=
==
19
17
16
13
121110
98765
43210 )log(
(1.)
( )
i
k
ik
j
ij
iiii
iiii
QtrDUMYrDUMimprovecashout
debtconsolDJFICOhouse
lfirstmtgbaTermSpreadloanamt
+++++
+++++
+++=
==
17
15
14
11
109
87654
3210log
(2.)
i
k
ik
j
iji
iiiii
QtrDUMYrDUMD
JFICOloanamtSpreadTerm
++++
++++=
==
12
10
9
6
5
43210 )log(
(3.)
14See Ling and McGill (1998) for an example of a simultaneous equation model where mortgage demand isa function of borrower income, nonhousing wealth, desired housing consumption, and demographiccharacteristics, and housing consumption is a function of the level of mortgage debt as well as economicand demographic factors.
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where Spreadiis the second mortgage origination spread, loanamtiis the second (junior-
secured) loan amount, Termiis the term of the second loan, rmktis the current mortgage
rate as proxied by the Freddie Mac 30-year fixed-rate mortgage rate, rtreasis the 10-year
constant maturity treasury rate, yieldcurve is the market yield curve (10-year constant
maturity treasury rate less the 1-year constant maturity treasury rate), creditspread is the
bond market credit risk spread as proxied by the difference in the BAA and AAA
corporate bond rates,FICOiis borrower iscredit score at origination, houseiis the value
of the house at second loan origination,firstmtgamtiis the first (senior) mortgage amount,
debtconsoli is the percent of the second loan used for debt consolidation purposes,
cashoutiis the percent of the second loan that is taken as cash at closing, improveiis the
percent of the second loan used for home improvement purposes,D is a dummy variable
denoting states that allow lenders to pursue deficiency judgments against borrowers in
default, J is a dummy variable denoting states that require judicial foreclosure
proceedings, YrDUM is a series of dummy variables denoting the year of origination
(1996-1999 with 1995 being the reference year), and QtrDUMis a series of three dummy
variables denoting the origination quarter (the first quarter is the reference).
The origination Spread is calculated as the effective yield assuming a 10-year
holding period less the 10-year constant maturity treasury rate. In calculating the
effective yield, we include the impact of closing costs and points. Approximately 10% of
the sample had missing or incorrectly coded closing cost amounts. Thus, we imputed the
closing costs on loans with missing data using the mean closing cost amount for the top
75 percent of the sample. The dataset does not contain actual information about the
points charged to borrowers; however, discussions with lender representatives indicate
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that the lender uniformly charged 8 points on all loans originated. Thus, in estimating the
effective yield we also assume that 8 points were charged at origination.
Given the large number of observations available, we segmented the sample into
an estimation subsample and a holdout subsample. The estimation subsample was
created by randomly drawing 75 percent of the full sample with the remaining 25 percent
held as the holdout sample. The mortgage spread system was estimated using the
estimation subsample with the holdout subsample used for testing model fit and accuracy.
Table 6 presents the non-linear 3SLS parameter estimates for the mortgage spread
system. As expected, the estimated coefficients for loan spread, term, and loan amount
indicate a negative relationship between loan amount and cost (loan amounts decline as
the cost increases) and a positive relationship between cost and term and loan amount and
term.
Consistent with the model developed above, the parameter estimates show that
borrower credit quality (FICO score) is negatively related to credit cost and loan amount.
That is, higher quality borrowers (higher FICO scores) have lower second loan
origination spreads all else being equal. In addition, borrower credit quality is positively
related to the mortgage term with higher quality borrowers selecting longer-term loans.
This is counter to the debt-signaling hypothesis discussed by Flannery (1986) that higher
quality borrowers are less susceptible to financial shocks and can thus borrower over
shorter terms. However, our result is consistent with the Diamonds (1991) theory that
low quality borrowers are unable to issue longer-term debt since lenders are unwilling to
lend longer term. Furthermore, after controlling for other factors, the model parameter
estimates indicate that higher quality borrowers actually have lower second loan amounts.
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This is counter to the simple comparison of means reported earlier. However, this result
is consistent with Brueckners (2000) theory that, in equilibrium, higher quality
borrowers do not request larger loan amounts.
The model coefficients provide strong support for a positive relationship between
borrowers in states that require judicial foreclosure proceedings and the second loan
terms. The parameter estimates indicate that borrowers in states that require judicial
foreclosure have higher second loan amounts, pay more for the loan (origination spread is
larger), and borrower over a shorter term. However, we find the opposite effect for states
that limit borrower deficiency judgments. The negative coefficients for deficiency
judgments in the spread and loan amount equations indicate that borrowers in states that
prevent lenders from seeking deficiency judgments have lower spreads and loan amounts.
This is consistent with the theory that lenders tradeoff loan costs with loan amounts. The
results are also consistent with the theory that lenders restrict credit in states with
regulations that limit their ability to recover losses (anti-deficiency judgment statutes)
whereas lenders do not restrict credit in states that simply increase the costs associated
with default (require judicial foreclosure) but do not limit the lenders ability to recover
losses.
The coefficients regarding the use of funds do not reveal a significant relationship
between loan amount or cost and the percentage of funds used to consolidate other debts.
However, we do find that that the cost of second loan debt is significantly lower as the
percentage of the loan amount used for home improvements or cash out increases. At the
same time, borrowers seeking loans for home improvements or to cash out also have
lower amounts.
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Examining the other macro economic and borrower specific factors, we see that
borrowers with higher house values have higher second loan amounts while borrowers
with larger first mortgages have lower second mortgages. We also find that the cost of
second loans is positively related to the mortgage market interest rate spread and the
overall market credit risk premium (corporate bond credit risk spread). This is consistent
with a number of previous studies who find that the mortgage market is integrated with
the larger capital markets.15
VI. Model Predictions
In Table 7 we report the mean and median spread, second loan amount, and loan
term prediction errors for the estimation sample using the parameter estimates reported in
Table 6. Since the mean prediction errors can be skewed by extreme outliers, we chose
to focus on the median values. The first row reports the mean and median prediction
errors (residuals) for the full sample. The median values indicate that the model tends to
underfit the spread and overfit the loan amount and term. We next divide the sample
based on borrower FICO score and note that the spread prediction error appears to be
smaller for the low FICO sample (FICO scores less than 684). For the high FICO
subsample, the predicted spread is 25 basis points lower than the actual while the median
error for the low FICO subsample is only 0.76 basis points lower. We also estimate the
impact of the borrowers reason for the originating the second loan. Analysis of the
residuals indicates that the prediction error is highest for borrowers using at least 90% of
the loan amount for debt consolidation (123 basis points for high FICO borrowers and 94
basis points for low FICO borrowers).
15For example, see Gonzalez-Rivera (2001) and Kolari, Fraser, and Anari (1998) for example.
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We also examine the prediction errors for high quality and low quality borrowers
based on their state default regulations. We classify high default cost states (from the
lenders perspective) as states that require judicial foreclosure proceedings (J=1) but do
not allow deficiency judgments (D=1). Low default cost states are classified as those that
do not require judicial foreclosure (J=0) but allow deficiency judgments (D=0).
Interestingly, we find that the spread prediction error is uniformly negative (model over
predicts the spread) across all state default regulation categories for the high quality
borrower subsample. However, the model appears to uniformly under predict loan costs
for the low FICO subsample (errors are positive). In the final section of Table 7, we
highlight the prediction errors for high and low default cost states based on borrower
quality assuming funds used for debt consolidation. The model errors are slightly greater
for states with high default costs.
In Table 8 we assess the estimated systems predicted accuracy using the hold-out
sample as an out-of-sample test. Predicted spread, loan amount, and term were estimated
via Newtons method for each observation in the holdout sample using the parameter
coefficients reported in Table 6. Since this is an out-of-sample test, the mean
prediction errors for the full sample are no longer zero. The results indicate that the
system has a relatively high predictive accuracy. The mean spread error is 0.1 basis
points and the median spread error is 12 basis points. As in Table 7, we find that the
model tends to over estimate the spread for high quality borrowers and under predict the
spread for low quality borrowers. However, the degree of error is larger for high quality
borrowers than for low quality borrowers.
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By controlling for borrower risk characteristics, interrelated loan terms, market
conditions, and state-level default laws, we are able assess the degree of under- or over-
pricing of junior secured mortgages. We create a series of hypothetical borrowers
differentiated by risk and location. For example, we segment the holdout sample into
very high and very low quality borrowers where very high quality is defined as any
borrower with a FICO score above the 75thpercentile of the whole sample (FICO>706)
and very low quality is defined as any borrower with a FICO score below the 25 th
percentile of the whole sample (FICO < 658). Next we calculate the independent
variable means for these high and low quality subsamples further segmented by whether
their state requires judicial foreclosure (J=1) or does not allow deficiency judgments
(D=1). Using the relevant mean values of these hypothetical borrowers, we then estimate
predicted loan spreads, term, and amounts. Comparing these predicted values to the
actual means for each borrower segment will allow us to quantify the degree of lender
under or over pricing.
Table 9 shows the comparison for borrowers living in high default cost and low
default cost states. Consistent with the prediction errors reported above, we see that
predicted as well as actual spreads are lower in low default cost states. However, it is
interesting to note that low quality borrowers are consistently over-charged relative to the
model predictions. For example, the interest rate charged on a loan to a low quality
borrower living in a high cost state was, on average, 64 basis points higher than the
predicted value. On the other hand, high quality borrowers living in states with high
default costs were consistently under charged by 18 basis points, on average.
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VII. Summary and Conclusions
The high LTV mortgage examined in this paper is an interesting twist on the
home equity loan contract in that it has a higher interest rate and aggregate LTV than
traditional home equity loans. As the market continues to grow for the various
permutations of home equity loans, the impact of credit on mortgage rates becomes quite
important (particularly when compared to conforming first mortgages purchased by the
government sponsored agencies where credit risk is of little concern).
In this paper, we examine the pricing of high-LTV debt and determine whether
state-specific default laws have an impact on the availability and cost of that debt. First,
we find that lenders rationally price loans to higher risk borrowers for the most part;
however, when we focus on smaller and smaller FICO scores buckets, the results indicate
that the mean actual loan rates are higher than those predicted by our model. Second, we
examine the impact of borrower protection laws on the price of credit and if borrowers in
states that limit the lenders ability to seek default remedies pay higher credit costs; we
find that states that do not require judicial foreclosure and allow deficiency judgments on
high LTV loans have lower lending rates (by about 33 basis points) than loans in states
that require judicial foreclosure and do not allow deficiency judgments. Third, we find
that there is a greater degree of error in the pricing of high LTV loans to low FICO
borrowers than to high FICO borrowers. Stated in a different way, it is more difficult to
explain the rate charged to lower credit risk borrowers in that the rates charged are higher
than those predicted by our rational model of loan pricing.
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REFERENCES
Ambrose, B.W., and R.J. Buttimer, Jr. Embedded Options in the Mortgage Contract.TheJournal of Real Estate Finance and Economics21:2 (2000), 95-111.
Ambrose, B.W., R.J. Buttimer, Jr., and C.A. Capone, Jr. Pricing Mortgage Default andForeclosure Delay.Journal of Money, Credit, and Banking29:3 (1997), 314-325.
Ambrose, B.W., and A. Pennington-Cross. Local Economic Risk Factors and the Primaryand Secondary Mortgage Markets.Regional Science and Urban Economics30:6 (2000),683-701.
Ambrose, B.W., M. Lacour-Little, and A. Sanders. Credit Spreads and Capital Structure:Evidence from the Mortgage Market, Ohio State University Working Paper (2002).
Berkowitz, J. and R. Hynes. Bankruptcy Exemptions and the Market for MortgageLoans.Journal of Law and Economics42 (1999), 809-830.
Bolton, P. and D. Scharfstein. Optimal debt structure and the number of creditors.Journal of Political Economy104:1 (1996), 1-25.
Brueckner, J.K. Mortgage Default with Asymmetric Information. Journal of RealEstate Finance and Economics20 (2000), 251-275.
Brueckner, J.K. Unobservable Default Propensities, Optimal Leverage, and EmpiricalDefault Models: Comments on Bias in Estimates of Discrimination and Default inMortgage Lending: The Effects of Simultaneity and Self-Selection. Journal of RealEstate Finance and Economics 9:3 (1994), 217-222.
Diamond, D. Debt Maturity Structure and Liquidity Risk. Quarterly Journal ofEconomics (1991), 709-737.
Flannery, M. Asymmetric Information and Risky Debt Maturity Choice. Journal ofFinance41 (1986), 18-38.
Gonzalez-Rivera, G. Linkages Between Secondary and Primary Markets forMortgages.Journal of Fixed Income(2001), 29-36.
Harrison, D.M., T.G. Noordewier, and A. Yavas. Do Riskier Borrowers BorrowMore?. Pennsylvania State University Working Paper (2002).
Kau, J.B. and D.C. Keenan. An Overview of the Option-Theoretic Pricing ofMortgages.Journal of Housing Research6:2 (1995), 217-244.
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Kolari, J.W., D.R. Fraser, and A. Anari. The Effects of Securitization on Mortgagemarket Yields: A Cointegration Analysis.Real Estate Economics26:4 (1998), 677-693
Lin, E.Y., and M.J. White. Bankruptcy and the Market for Mortgage and HomeImprovement Loans.Journal of Urban Economcis50 (2001), 138-162.
Ling, D.C., and G.A. McGill. Evidence on the Demand for Mortgage Debt by Owner-Occupants. Journal of Urban Economics44 (1998), 391-414.
Merton, R.C. Theory of Rational Option Pricing. Bell Journal of Economics4 (1974),141-183.
Pence, K.M. Foreclosing on Opportunity: State Laws and Mortgage Credit. Board ofGovernors of the Federal Reserve System working paper (2002).
Quercia, R., and M.A. Stegman. Residential Mortgage Default: A Review of the
Literature.Journal of Housing3 (1992), 341-380.
Rothschild, M. and J. Stiglitz. Equilibrium in Competitive Insurance Markets: An Essayon the Economics of Imperfect Information. Quarterly Journal of Economics90 (1976),629-649.
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Chart 1. Historical Prepayments for Three Mortgage Products.
Historical Prepayment
0.00%
10.00%
20.00%
30.00%
40.00%
50.00%
60.00%
70.00%
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)
CPR
FIRSTPLUS 125 LTV97-1 Money Store Home Equity 1996-D RFMSI Whole Loan
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Chart 2. Historical 90-day Delinquency for Three Mortgage Products.
Historical 90 Day Delinquency
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
12.00%
14.00%
16.00%
18.00%
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)
90DayDelinquency
FIRSTPLUS 125 LTV97-1 Money Store Home Equity 1996-D RFMSI Whole Loan
Source: Bloomberg.
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Figure 1: End of Period 1 Net Payoff Positions for the Borrower and Lenders.
Panel A: High Default Cost State (=1)Period 1 Outcome
Condition Borrower
Action
Secured
Lender
Unsecured
Lender
Borrower
Case 1: V1 > MW1 > P
Payoff AllDebt
M P V1+W1-M-P
Case 2: V1> MW1 < PV1-M< P
Default onUnsecured
Debt
M W1 V1-M
Case 3: V1< MW1 < P
Default onAll Debt
V1+C1 0 0
Panel B: Low Default Cost State (0 P
Payoff AllDebt
M P V1+W1-M-P
Case 2: V1> MW1 < PV1-M< P
Default onUnsecured
Debt
M [W1] (1-)[W1]+ [V1-M]
Case 3: V1< MW1 < P
Default onAll Debt
[V1+W1] 0 (1-)[V1+W1]
Panel C: Low Default Cost State (0 P
Payoff AllDebt
M P V1+W1-M-P
Case 2: V1> MW1 < PV1-M< P
Default on2ndLoan
M [V1+W1-M] (1-) [V1+W1-M]
Case 3: V1< MW1 < P
Default onAll Debt
[V1+W1] 0 (1-)[V1+W1]
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Table 1: Distribution by Origination Year
Year Frequency Percent
1995 495 0.4
1996 14,212 10.8
1997 65,977 49.9
1998 50,929 38.51999 571 0.4
Total 132,184 100.0
Table 2: Mean Loan Origination Spread by Borrower FICO Score
(Standard Deviations in parentheses)
Borrower Fico Range mean std dev
[0, 658) 15.38 2.29
[658, 682) 14.09 2.06
[682, 706) 13.07 1.88
[706+) 12.50 1.89
Table 3: Mean Loan Amounts Classified by State Foreclosure Laws.
(Standard Deviations in parentheses)
Deficiency Judgments Judicial Foreclosure
AllowedNot
Allowed t-stat. RequiredNot
required t-stat.
Senior Debt LTV 79.28 82.71 43.7***
77.78 81.84 46.1***
(14.54) (13.60) (15.03) (13.88)
Total Debt LTV 111.28 109.84 -19.9*** 111.48 110.39 -14.1***
(12.45) (13.01) (12.65) (12.70)N 79,831 52,353 93,167 39,017
Note: t-statistic test for equality of means under assumption of unequal variance.***significant at the 1% level.
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Table 4: Mean Loan Amounts Classified by Borrower FICO Score.
(Standard Deviations in parentheses)
FICO ScoresHighFICO
LowFICO t-stat.
Senior Debt LTV 79.63 51.82 24.0***
(14.53) (13.99)
Total Debt LTV 110.08 111.26 16.8***
(13.10) (12.31)
N 61,473 70,711
Note: t-statistic test for equality of means under assumption of unequal variance.High 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 FICOscore for the sample.
***significant at the 1% level.
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Table 5: Descriptive Statistics
Variable Label N Mean Std Dev
Original_Interest_Rate Junior Mortgage Interest Rate 132184 13.60 1.50
Loanamt Junior Mortgage Loan Amount 132184 $31,699.92 $12,095.56
Yield Junior Mortgage Effective Interest Rate 132184 19.629 2.302Spread Junior Mortgage Origination Spread 132184 13.746 2.307
Firstmtgbal First Mortgage Loan Amount 132184 $94,231.82 $45,891.29
Value House Value (Appraised) 132184 $114,695.56 $49,883.17
Loan_To_Value Loan_To_Value (total debt) 132184 110.709 12.693
FICO Borrower FICO Score 132184 683.314 35.590
rmkt 30 - Fixed Conventional Market Rate 132184 7.396 0.417
Yieldcurve 10 year Treasury - 1 year Treasury 132184 0.514 0.317
treasr Standard Deviation of 10-year Treasury 132184 0.305 0.085
Creditspread Baa - AAA Bond Spread 132184 0.627 0.065
J 1=require judicial 132184 0.295 0.456
D 1=allows deficiency 132184 0.604 0.489
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Table 6: Non-linear Three-Stage Least Squares Estimation
of Mortgage Origination Terms
(t-statistics reported in parentheses)
Spread log(loanamt) Term
Intercept 61.496***
7.553***
-325.231***
(81.25) (26.28) -(23.81)
Spread -0.098*** 4.211***-(14.39) (13.64)
log(loanamt) -6.139*** 43.803***
-(38.83) (121.03)
Term 0.118***
0.022***
(31.41) (111.41)
FICO -0.014*** -4.30E-04* 0.016*
-(20.58) -(1.84) (1.60)
debtconsol 4.40E-04 0.001
(0.02) (0.44)
homeimprove -0.920*** -0.011***
-(15.23) -(2.96)
cashout -1.048*** -0.013***-(15.65) -(3.31)
J 0.278*** 0.045*** -1.951***
(7.29) (4.29) -(4.16)
D -1.266*** -0.227*** 10.036***
-(26.27) -(22.53) (22.34)
(rmkt-rtreas) 0.349***
(7.37)
treas -0.576***
-(3.95)
yieldcurve 0.751***
(5.53)
creditspread 3.584***
(13.73)
firstmtgbal -5.61E-08*
-(1.62)
Value 1.07E-07***
(4.36)
Yr96 -2.841*** -0.363*** 16.074***
-(9.96) -(5.09) (4.99)
Yr97 -4.899***
-0.807***
35.723***
-(16.29) -(11.37) (11.20)
Yr98 -8.063*** -1.513*** 67.279***
-(23.35) -(20.94) (21.10)
Yr99 -7.106*** -1.169*** 52.136***
-(14.00) -(9.56) (9.56)
Qtr2 0.095 0.165**
-7.551***
(0.35) (2.23) -(2.26)
Qtr3 -0.519* 0.010 -0.595
-(1.93) (0.14) -(0.18)
Qtr4 -1.478***
-0.220***
9.712***
-(5.49) -(3.01) (2.94)
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***significant at the 1% level.**significant at the 5% level.*significant at the 10% level.
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Table 7: Mean (Median) Prediction Errors (Estimation Sample)(Actual Predicted)
Number ofObservations Spread Log(Amount) Term
Full Sample 99,128 0.0000 0.0000 0.0000
-(0.1266) (0.0264) (21.4125)
High Fico Borrower 47,155 -0.1335 0.0016 -0.3102
-(0.2500) (0.0303) (21.6336)Low FICO Borrower 51,973 0.1211 -0.0015 0.2815
-(0.0076) (0.0233) (21.2488)High FICO Borrower
Debt Consolidation 4,891 -1.1518 -0.1316 -20.6670
-(1.2313) -(0.0929) -(4.0076)
Home Improvement 984 -0.0740 0.0723 6.0451
-(0.4612) (0.1725) (12.8743)
Cash Out 1,134 -0.2369 0.2444 5.2756
-(0.3230) (0.2867) (10.3322)
Low FICO BorrowerDebt Consolidation 6,508 -0.9254 -0.0998 -11.4102
-(0.9373) -(0.0534) (8.2084)
Home Improvement 1,569 -0.1870 0.1901 8.1556
-(0.5444) (0.2878) (15.9529)
Cash Out 132 -0.7798 0.1540 -3.8320
-(0.7495) (0.1385) (4.5451)High FICO Borrower
Judicial=0, Deficiency = 0 14,983 -0.1815 0.0162 1.0175
-(0.2951) (0.0334) (26.3948)
Judicial=0, Deficiency = 1 18,864 -0.0667 -0.0178 -1.9679
-(0.2221) (0.0301) (14.7209)
Judicial=1, Deficiency = 0 12,287 -0.1835 0.0016 0.3964 -(0.2550) (0.0165) (27.8560)
Judicial=1, Deficiency = 1 1,021 -0.0615 0.1462 2.3289
-(0.0334) (0.1395) (30.5895)
Low FICO Borrower
Judicial=0, Deficiency = 0 17,839 0.1803 0.0000 -0.4268
(0.0291) (0.0205) (23.1725)
Judicial=0, Deficiency = 1 18,183 0.0419 0.0052 1.6218
-(0.0874) (0.0460) (17.0591)
Judicial=1, Deficiency = 0 14,859 0.1183 -0.0177 -0.8415
(0.0180) -(0.0043) (24.5719)
Judicial=1, Deficiency = 1 1,092 0.5123 0.0852 4.8119
(0.3769) (0.0950) (27.3471)High FICO Borrower,Debt Consolidation
Low Cost (J=0, D=0) 1,751 -1.1267 -0.1076 -17.9652
-(1.1466) -(0.0851) -(3.0290)
High Cost (J=1, D=1) 69 -1.3798 -0.0603 -32.0205
-(1.1720) -(0.0260) -(30.2281)Low FICO Borrower,Debt Consolidation
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Low Cost (J=0, D=0) 2,494 -0.8270 -0.0854 -12.3726
-(0.8542) -(0.0410) (6.3782)
High Cost (J=1, D=1) 83 -0.8566 -0.0459 -13.8616
-(0.9305) -(0.0601) (14.4214)
Note: High FICO borrower sample include all borrowers with FICO scores greater thanor equal to 684 and the low FICO borrower sample include all borrowers with FICOscores less than or equal to 683. Fund utilization samples are all borrowers utilizinggreater than 90% of funds for the purpose identified.
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Table 8: Mean (Median) Prediction Errors (Random Holdout Sample). Predictions
obtained from coefficients estimated on 75% random sample. High FICO Borrower
sample have FICO scores greater than or equal to 684 and the low FICO Borrower
sample have FICO scores less than or equal to 683.
(Actual Predicted)
Number ofObservations Spread Log(Amount) Term
Full Sample 33,056 -0.0010 0.0051 0.3406 -(0.1203) (0.0269) (20.9147)
High Fico Borrower 15,867 -0.1355 0.0064 -0.0897 -(0.2497) (0.0328) (21.8026)Low FICO Borrower 17,189 0.1233 0.0039 0.7378
(0.0069) (0.0229) (20.1700)High FICO Borrower
Debt Consolidation 1,656 -1.1091 -0.1429 -18.8407
-(1.2117) -(0.0934) (2.7961)
Home Improvement 311 0.0413 0.0787 6.5076
-(0.3991) (0.2049) (19.3227)
Cash Out 335 -0.3111 0.1954 7.0499
-(0.4818) (0.2805) (7.9445)
Low FICO Borrower
Debt Consolidation 2,163 -0.9747 -0.1013 -10.1066
-(0.9709) -(0.0522) (9.9774)
Home Improvement 481 -0.1593 0.3707 19.2671
-(0.7301) (0.2568) (16.0577)
Cash Out 39 -0.9877 0.2099 6.2720
-(1.0412) (0.2963) -(8.7189)High FICO Borrower
Judicial=0, Deficiency = 0 5,020 -0.1481 0.0267 -0.1111
-(0.2807) (0.0397) (25.8882)
Judicial=0, Deficiency = 1 6,341 -0.1018 -0.0179 -0.8099
-(0.2471) (0.0238) (16.0214)
Judicial=1, Deficiency = 0 4,187 -0.1648 0.0080 0.9720
-(0.2283) (0.0264) (28.7814)
Judicial=1, Deficiency = 1 319 -0.2254 0.1484 0.6268
-(0.1959) (0.1575) (26.2334)
Low FICO Borrower
Judicial=0, Deficiency = 0 5,775 0.1557 0.0011 1.3329
(0.0715) (0.0275) (23.3103)
Judicial=0, Deficiency = 1 6,162 0.0482 0.0178 1.5119
-(0.1189) (0.0354) (15.4308)
Judicial=1, Deficiency = 0 4,881 0.1608 -0.0193 -0.6048
(0.0462) -(0.0065) (24.1994)
Judicial=1, Deficiency = 1 371 0.3733 0.1216 -3.7221
(0.4573) (0.1147) (24.0928)High FICO Borrower,Debt Consolidation
Low Cost (J=0, D=0) 574 -1.2218 -0.1009 -18.8487
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-(1.2058) -(0.0567) (4.7627)
High Cost (J=1, D=1) 28 -1.4715 0.0495 -34.7247
-(1.6136) (0.0716) -(11.0780)Low FICO Borrower,Debt Consolidation
Low Cost (J=0, D=0) 766 -0.8823 -0.0948 -10.1004
-(0.9507) -(0.0507) (9.0993) High Cost (J=1, D=1) 38 -1.4532 0.1127 -13.1733
-(1.0207) (0.1019) -(20.1656)
Note: Estimation sample created by drawing a 75% random sample of the full samplewith the remaining 25% used to test the model fit. High FICO borrower sample includesall borrowers with FICO scores greater than or equal to 684 and low FICO borrowersample includes all borrowers with FICO scores less than or equal to 683. Fundutilization samples are all borrowers utilizing greater than 90% of funds for the purposeidentified.
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Table 9: Actual versus Predicted Loan Terms
Mean Values Predicted Values
Spread Log(Amount) Term Spread Log(Amount) Term
High FICO Borrower
Low Cost (J=0, D=0) 12.67 10.32 240.81 12.59 10.30 240.62
High Cost (J=1, D=1) 12.75 10.36 242.65 12.93 10.20 250.12
Low FICO Borrower
Low Cost (J=0, D=0) 15.53 10.18 239.51 15.06 10.20 237.78
High Cost (J=1, D=1) 15.86 10.21 250.30 15.22 10.15 251.69
High FICO Borrower subsample includes all borrowers with FICO scores in the 75thpercentile. Low FICO Borrower subsample includes all borrowers with FICO scores inthe 25thpercentile. Predicted values are estimated using mean values of the independent
variables in each respective subsample.