Research Report for Importance of Mortgage Downpayment as a Deterrent to Delinquency and Default as Observed in Black Knight (McDash) Servicing History

Research Report for

Importance of Mortgage Downpayment as

a Deterrent to Delinquency and Default as

Observed in Black Knight (McDash)

Servicing History

U.S. Department of Housing and Urban Development

April 2017

U.S. Department of Housing and Urban Development | Office of Policy Development and Research

Research Report for

Importance of Mortgage Downpayment as

a Deterrent to Delinquency and Default as

Observed in Black Knight (McDash)

Servicing History

U.S. Department of Housing and Urban Development

April 2017

Disclaimer

The contents of this report represent the views of the authors and do not necessarily reflect the

views or policies of the U.S. Department of Housing and Urban Development or the U.S.

government.

iii

Preface

The cash downpayment serves the important function of mitigating mortgage credit risk. It also,

however, represents a significant barrier to homeownership for many low- and moderate-income

households. Although potential substitutes for various functions of the cash downpayment exist,

such as mortgage insurance as a protection against lender loss, we still have much to learn about

their effectiveness and how much cash downpayment is needed to mitigate various sources of

credit risk.

This study aspires to advance our learning by using loan-level mortgage origination and

performance data to examine the effectiveness of the cash downpayment as a deterrent to

delinquency and also to serious default in terms of equivalent compensating credit

enhancements. Consistent with previous empirical examination, the study finds that cash

downpayments do mitigate risk; all else equal, lower proportional downpayments were

associated with higher rates of delinquency and default. Compensating tradeoffs can provide an

equivalent level of credit risk mitigation, however. The report quantifies the tradeoff between

lower mortgage downpayments and other loan-level characteristics, such as higher credit score

or lower debt-to-income ratio, that will produce an equivalent level of default risk and also how

loan-level tradeoffs may differ across markets, depending on home price appreciation or

unemployment trends.

This study underscores the importance of the cash downpayment and the potential for balancing

different mortgage downpayment requirements with other relevant compensating factors to

manage mortgage credit risk. It also makes an important contribution to the metrics for

evaluating alternatives to current requirements that balance risk with broadening access to

mortgage markets.

Contents

Introduction ..................................................................................................................................... 1

Literature Review............................................................................................................................ 2

Methodology and Model ............................................................................................................... 11

Model Specification .................................................................................................................. 11

Discussion of Variables ............................................................................................................ 11

Estimation Database...................................................................................................................... 14

Duplicate Observations ............................................................................................................. 14

Outlier Exclusion ...................................................................................................................... 14

Empirical Results .......................................................................................................................... 16

Regression Results .................................................................................................................... 16

Functional Form ........................................................................................................................ 19

Compensating Factors for CLTV .............................................................................................. 20

CLTV Analytics ........................................................................................................................ 22

Implications and Conclusions ....................................................................................................... 30

References ..................................................................................................................................... 32

Additional Reading ....................................................................................................................... 34

Appendix A. Data Analysis .......................................................................................................... 35

Data Quality .............................................................................................................................. 35

Variable Creation and Selection ............................................................................................... 37

Appendix B. Duplicate Observations ........................................................................................... 39

Appendix C. Outlier Exclusions ................................................................................................... 42

Appendix D. Diagnostics Charts ................................................................................................... 44

Appendix E. CLTV Analytics for the Delinquency Model .......................................................... 51

Introduction

The U.S. Department of Housing and Urban Development (HUD) engaged the Integrated

Financial Engineering, Inc. (IFE) group to conduct an independent research project based on the

Black Knight Financial Technology Solutions, LLC McDash™ loan data to determine the

effectiveness of mortgage downpayments as a deterrent to delinquency and default. McDash data

is a loan-level mortgage origination and performance data source maintained by Black Knight

and collected from most major mortgage servicers. The project’s objectives were to (1) form an

analytical database containing performance and economic variables that facilitates empirical

studies and (2) use econometric models to quantify the impact of mortgage downpayment on

mortgage delinquency and default among different market segments and economic conditions.

Most existing literature applies the competing risk model in analyzing loan-level mortgage

performance, which treats prepayments as endogenous and simultaneous with the default

decision. Little has been published, however, on the use of the scorecard-type estimation

approach to investigate the credit quality of individual mortgage loans. One reason scorecards

are not in the public literature is because they are applied on a proprietary and confidential basis

as a tool for competitive advantage by major mortgage banks and mortgage insurers and

guarantors. Consider the well-known and popular FICO score, which is estimated with the

scorecard approach. Even this much-used scorecard does not have public literature that reveals

its structure and estimated coefficients. The point is that scorecard estimation of the type herein

has a time-honored place in mortgage econometrics, just not a public one.

The Literature Review section focuses on empirical estimates of the effect of downpayments on

delinquency and default. The Methodology and Model section presents the scorecard-type model

and its dependent and independent variables. The Estimation Database section describes the

methodology we applied to derive the estimation database, especially in dealing with outliers and

duplicate loan observations. The McDash database does not identify proprietary data, such as

borrowers or the address of the property. We devised an algorithm to identify multiple loans that

may have been originated to support one specific housing transaction. The Empirical Results

section presents the model results. We also computed compensating factors that show how much

the combined loan-to-value must change for a unit change in other explanatory variables in order

to hold the probability of delinquency or default constant. Our research implications and

conclusions are presented in Implications and Conclusions section. Following the References

section, various appendices describe in more detail the McDash data set, the steps taken in

compiling the research sample, and the technique of our analytical models.

Literature Review

The literature reveals that extensive exploration has been dedicated to the factors that drive

mortgage defaults. Default technically is the borrower’s failure to abide by the mortgage contract

provisions. The most common trigger of default is the failure to make required mortgage

payments, and it is this aspect on which we focus this study. The term default is too vague, as it

encompasses temporary or permanent delinquencies. As such, we need to be careful when

comparing the empirical results of various studies, distinguishing initial delinquencies from

foreclosures and settlement; and for foreclosures, distinguishing the start from the completion of

foreclosure proceedings. The completion of foreclosure involves the “ultimate default,” which is

the transfer of the property to the lienholder or to third parties, and, beyond this, to the

disposition of the property and the final accounting of losses.

The ample list of the sources cited in the References section at the end of this report describes the

motivations for all default phases as the willingness-to-pay or the ability-to-pay factors. As a put

option for mortgage buyers, rational defaults can occur when the market value of the collateral is

lower than what is owed to the lender (Kau and Keenan, 1995; Vanderhoff, 1996). That is,

rational borrowers become unwilling to continue paying when what they owe is more than the

value of the purchase price, by an amount that compensates for negative consequences, like

credit damage.

Adverse life events, such as loss of income or wealth, are cited as major factors for the inability

to continue paying a mortgage. The upfront underwriting criteria and analysis, with indicators

such as payment-to-income ratios, attempt to indicate default events based on a borrower’s

ability to pay (Arnone, Darbar, and Gambini, 2007), although underwriting indicators of how a

borrower managed past obligations, measured by credit scores, may predict willingness to pay.

Classifying motivating factors into two categories is not very useful for our purposes, because a

high original loan-to-value (LTV) ratio foreshadows a higher likelihood of the future house price to

become lower than the mortgage debt, but it can reflect a lack of wealth, which, when given adverse

life events, implies that the ability to pay is more likely to be a motivating factor for default.

One major factor of mortgage defaults is the adequacy of the collateral that backs the mortgage

loan (Archer, Ling, and McGill, 1996). The major metric describing collateral risk is the LTV

ratio. Most studies show that, as borrowers put up higher downpayments, the probability of

default risk is lower.

Extensive research has been conducted regarding the effect of the relative amount of the

downpayment, typically measured by the original LTV ratio, on mortgage performance. In this

Literature Review section, we summarize the empirical relationships found in various studies.

Because the focus is on the quantification of the deterrent effect of downpayments on

delinquency and default, our literature review includes only those references that provide such

empirical quantification, with the intention to compare those estimates with the McDash data.

Different empirical approaches typically produce different empirical results, so we point out and

classify the studies according to major differences we observed. For the following major

differences, we accordingly provide estimates of the coefficient of LTV or combined loan-to-

value ratios in this study—and basic information from each of the studies in table 1.

1. Definition of default. This study uses two measures of default, 90 days delinquent in the

first 2 years after origination and the initiation of foreclosure proceedings during the

loan’s observed lifetime. We organize the references in table 1 according to how closely

each reference matches these two measures of default. The table is arranged into two

sections: the first is according to the delinquency measure; and the second is according to

the foreclosure event, with our study being the first in each list. The closer the definition

of default is to ours, the higher up the reference is located on the list. We list some

references in this table more than once, because those have estimates using several

definitions of default.

2. Type of model and estimation technique. Most models are competing risk models. We

found few articles using the mortgage scorecard approach, so we cite several books on

credit-scoring techniques: Siddiqi (2012); Thomas (2009); and Thomas, Edelman, and

Crook (2002); however, we cite many articles using the competing risk model.

Competing risk models estimate the relationship in the put-default option by

simultaneously accounting for the call-prepayment option. Scorecard-type models

estimate the default relationship by itself, with or without factors that are observed after

loan origination. Our model is the latter one. Estimation methods include logistic

regression; different estimators typically produce different estimates of the effects of

downpayment on default. The competing risk approach deals with prepayments by

estimating prepayment equations simultaneously with the default equations. The next

columns list the modeling and estimation techniques and how prepayments are treated.

We attempt to subgroup references into competing risk and scorecard models. For

competing risk models, we show the LTV coefficient in the respective equation and

ignore the simultaneous nature of each respective equation with the others.

3. Other factors held constant. If one factor affecting the default propensity is not

included in a study, it is likely to affect the empirical results of the downpayment-default

relationship, a situation known as the omitted relevant variable problem in the

econometric literature. Most of the literature cited in the text includes the current LTV as

an explanatory variable. Because our focus is on the origination LTV, we do not report

the coefficients of this variable, but the inclusion of LTV as the variable is likely to affect

estimated coefficients of the LTV. Most studies are on competing risk models, applying a

proportional hazard estimation approach. The essence of the proportional hazard

approach is to estimate the probability of delinquency or default in the current period

conditional on the loan status during the previous period. For studies that have the

origination LTV as an explanatory variable, the original LTV becomes less relevant and

the current LTV becomes more relevant as time passes after origination. Therefore, it is

not surprising that the magnitude of the effect of the origination LTV is considerably less

in studies with LTV as an explanatory variable than in scorecard-type studies that do not

use the proportional hazard methodology. In some sense, the current LTV also reflects

the origination LTV, because its current value is due in large part to its first observation,

the origination LTV.

Another reason that the coefficient of the origination LTV in the proportional hazard

models has a much smaller impact on delinquencies and defaults than in scorecard

models is because the effect in the proportional hazard models is per period. In the

scorecard approach, the effect is measured during the time period specified in the

definition of the dependent variable, such as 2 years or as a lifetime in our case. A

comparable coefficient, then, would be to accumulate the per-period effect during the

period specified in the scorecard dependent variable. Because of the multiple reasons

cited previously, the proportional hazard and scorecard approaches produce different

estimation coefficients of the origination LTV.

Table 2 lists other explanatory variables used in the respective equations, because any

differences in the list of variables could affect the estimated LTV coefficient.

4. How Explanatory Variables Are Constructed. In particular, because default is a

borrower put option, a number of studies (see table 2) attempt to measure the estimated

value of the put option as an explanatory variable to indicate to what extent this option is

in the money. These other studies are not directly comparable with ours, so we did not

include them here unless they also have LTV as an explanatory variable. Other studies

have applied indirect measures of LTV as an explanatory variable, for example, by

simply allowing for a nonlinear relationship between LTV and default. We include these

studies in this review.

Our study uses two measures of default, 90 days delinquent in the first 2 years after origination

and the initiation of foreclosure proceedings during the loan’s observed lifetime. The relevant

papers are organized in table 1 based on these two measures. Note that any deviation from either

the selected indicator of default or the time period for which these indicators are observed could

cause the estimated LTV coefficient to differ.

For delinquency measurement, Hwang, Shu, and Van Order (2015) used a competing risk model

to simulate the probability of 5-year 90-day delinquency. Competing risk models are estimated

by multinomial logit, in which at least some measures of default and prepayment both are

endogenous. In table 1, which cites the estimation method, we note three observations: (1) for

cited references, multinomial logit is synonymous with the competing risk model; (2) the

coefficient of the original LTV is not comparable with the binomial coefficient we estimate

because of the simultaneous nature of the equations and the use of the current LTV as an

explanatory variable; and (3) the variable, current LTV, in many of the studies is the LTV

divided by 1 + house price appreciation (HPA) to reflect the house price appreciation, in which

the numerator of the LTV is the amortized and possibly accrued mortgage balance—it is a

different way to include the variable 1 + HPA.

Lam, Dunsky, and Kelly (2013) focused on 90-day delinquency in the first 7 years after

origination. Their study incorporates the LTV variable by a spline function, which allows its

effect to vary by ranges of the LTV. We report the coefficients according to the ranges covered

by the various segments estimated. These are not the individual coefficients that are estimated

for each segment, but rather the cumulative coefficients up to and including each segment. These

values then become comparable with the coefficients of a continuous LTV variable, as in our

study. For example, with linear splines, for LTVs in the range of the third and fourth knot points,

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demonstrates that the probability of 90-day delinquency increases monotonically with the

origination LTV. They also concluded that the default probability is more sensitive to LTV

changes for low FICO scores.

Table 1. Comparison of Different Loan-to-Value Coefficients

Reference

Default

Measure

LTV

Measure

Estimation

Technique

Prepayment

Treatment

Mortgage

Data

Coverage

Time

Period

LTV Coefficient

Delinquency Measurement

McDash

(Ours)

2-year 90-

day

delinquency

Combined

LTV

Binomial

logit

Counted as a

“good” loan

Black Knight

single-family

and condo

for-purchase

2000–

2012

3.4502

Hwang,

Shu, and

Van Order

(2015)

5-year 90-

day

delinquency

Origination

LTV

Multinomial

logit

Endogenous

Freddie Mac

single-family

1999–

2012

2.24**

Lam,

Dunsky,

and Kelly

(2013)

7-year 90-

day

delinquency

Origination

LTV

splines

Multinomial

logit

Endogenous

FHA single-

family

1995–

2008

GSE

<70%: 0.188*

70–80%: 1.191

80–90%: 1.092

90–95%: 1.380

>95%: – 0.211*

FHA

<80%: –

0.291*

80–

90%:

– 0.431*

90–

95%:

2.813

>95%: –

0.350*

Calhoun

and Deng

(2002)

Lifetime 90-

day

delinquency

Origination

LTV

dummies

Multinomial

logit

Endogenous

Fannie Mae,

Freddie Mac

30-year

single-family

1979–

1993

30-year FRM

<60%: – 1.348

60–70%: –

0.090

70–75%: 0.416

75–80%: 0.197

80–90%: 0.309

90–

100%:

0.516

ARM

<60%: –

1.310

60–

70%:

– 0.260

70–

75%:

0.257

75–

80%:

0.209

80–

90%:

0.448

90–

100%:

0.656

Kelly

(2008)

Lifetime 90-

day

delinquency

Origination

LTV

Multinomial

logit

Endogenous

FHA single-

family and

condo for-

purchase

1999–

2006

National sample: – 0.056*

MSA-level samples: –

0.028*

IFE (2014)

Lifetime 90-

day

delinquency

Origination

LTV

dummies

Multinomial

logit

Endogenous

FHA single-

family

1975–

2014

FRM30 90–95%: 0.0701

>95%: 0.0051

FRM15 90–95%: 0.0639

>95%: 0.0626

ARM 90–95%: 0.0734

>95%: 0.0829

Freeman

and

Harden

(2014)

Lifetime

30–90-day

delinquency

Origination

LTV

Multinomial

logit

Endogenous

Community

Advantage

Panel Study

for 30-year

FRMs

1998–

2009

– 0.02

Deng,

Quigley,

and Van

Order

(1996)

Lifetime 30-

day

delinquency

Origination

LTV

Multinomial

logit

Endogenous

Freddie Mac

single-family

1976–

1983

2.491

Garmaise

(2015)

Lifetime 30-

day

delinquency

Origination

LTV

Multinomial

logit

Endogenous

Residential

single-family

2004–

2008

2.616

Deng,

Quigley,

and Van

Order

(2000)

Lifetime

delinquency

Origination

LTV

dummies

Multinomial

logit

Endogenous

Freddie Mac

single-family

1976–

1983

60–75%: 1.327

75–80%: 2.372

80–90%: 3.370

>90%: 3.333

Beem

(2014)

Lifetime

delinquency

Origination

combined

LTV

Binomial

logit

Counted as a

“good” loan

Fannie Mae,

Freddie Mac

30-year

single-family

1999–

2011

0.1**

Foreclosure/Claim Measurement

McDash

(Ours)

Lifetime

foreclosure

Combined

LTV

Binomial

logit

Counted as a

“good” loan

Black Knight

single-family

and condo

for-purchase

first lien

2000–

2012

4.3217

Lam,

Dunsky,

and Kelly

(2013)

7-year

foreclosure

completion

Origination

LTV

splines

Multinomial

logit

Endogenous

FHA single-

family data

1995–

2008

GSE

<70%: – 1.994

70–80%: 1.461

80–90%: 0.520

90–95%: 0.711

>95%: 0.283*

FHA

<80%: –

1.724

80–90%: –

0.105

90–

95%:

4.090

>95%: –

2.045

Freeman

and

Harden

(2014)

Lifetime

90+ day or

foreclosure

Origination

LTV

Multinomial

logit

Endogenous

Community

Advantage

Panel Study

for 30-year

FRMs

1998–

2009

0.04

IFE (2014)

Lifetime

claim

Origination

LTV

dummies

Multinomial

logit

Endogenous

FHA single-

family data

1975–

2014

FRM30 90–95%: 0.1848

>95%: 0.2109

FRM15 90–95%: 0.3962

>95%: 0.6058

ARM 90–95%: 0.1459

>95%: 0.1429

Kelly

(2008)

Lifetime

claim

Origination

LTV

Multinomial

logit

Endogenous

FHA single-

family and

condo

purchase

money loans

1999–

2006

National sample: – 0.057*

MSA-level samples: 0.009*

Ghent and

Kudlyak

(2010)

Default that

ends with

the

borrower

vacating the

home

Origination

LTV &

origination

LTV

dummies

Binomial

logit

Counted as a

“good” loan

Prime and

nonprime

private

securitized

loans,

portfolio

loans, and

GSE loans

1997–

2008

Origination LTV: 1.0**

Origination LTV 80%

dummy: 0.13**

ARM = adjustable-rate mortgage. FHA = Federal Housing Administration. FRM = fixed-rate mortgage. GSE = government-

sponsored enterprise. IFE = Integrated Financial Engineering, Inc. LTV = loan-to-value. MSA = metropolitan statistical area.

* Statistically not significant.

** The coefficients are adjusted to reflect that the LTV ratios were measured as a decimal instead of as a percentage.

Table 2. Comparison of Explanatory Variables in the Literature

Variables

McDash (Ours)

Hwang, Shu, and Van Order (2015)

Lam, Dunsky, and Kelly (2013)

Calhoun and Deng (2002)

Kelly (2008)

IFE (2014)

Freeman and Harden (2014)

Deng, Quigley, and Van Order (1996)

Garmaise(2015)

Deng, Quigley, and Van Order (2000)

Beem (2014)

Ghent and Kudlyak (2010)

LTV at origination

CLTV

CLTV > LTV dummy

Current LTV

Origination LTV dummies

FICO score and MTM LTV

Interaction

Origination LTV = 80% dummy

Source of downpayment

Loan size

Loan grade

FRM

Interest-only loan

Loan type missing

Government loan

Original term can be

divided by 60

Original term

Single-family home

Original credit score

Missing credit score dummy

Prepayment penalty

Primary residence

Documentation type

Jumbo loan

Missing payment status history

Relative property value

Relative loan size

DTI ratio

Yield curve slope

30-year FRM rate

Original interest rate

CMT10/CMT1

Has second loan

Home price volatility

Cumulative HPA

Unemployment rate spread

Mortgage rate spread

Lifetime cumulative HPA

Lifetime unemployment rate spread

Lifetime mortgage rate spread

Mortgage age

Mortgage age squared

Mortgage age square root

Seasonality

Origination cohort

Unpaid principal balance

Spread at origination

Spread at origination dummies

Burnout factor

Credit burnout factor

Census division

Metropolitan location

State laws

Housing structure

Borrower’s ethnic/age/sex

Borrower’s marriage status

Borrower’s education

Borrower’s employment status

Household income

Under water

First-time buyer

Origination year dummy

State dummy

Location dummy

Loan purpose

Unemployment rate

Relative unemployment rate

Lagged unemployment rate

Mortgage premium value

Probability of negative equity

Probability of negative equity squared

Recourse

Fraction of contract value

Fraction of contract value squared

Spread in primary mortgage rate

Number of housing units

Reserve

Builder

Underserved area

Refinance incentive

CLTV = combined loan-to-value. CMT = Constant Maturity Treasury. DTI = debt-to-income. FRM = fixed-rate

mortgage. HPA = house price appreciation. IFE = Integrated Financial Engineering, Inc. LTV = loan-to-value. MTM =

Marked-to-market.

Note: The letter “v” in the data cells indicates that the analysis conducted in the study includes as a control

the variable.

Calhoun and Deng (2002) focused on lifetime 90-day delinquency. They used origination LTV

ratio dummies instead of a continuous variable, separating fixed-rate mortgage (FRM) and

adjustable-rate mortgage (ARM) loans. In table 1, we show the results for both. Calhoun and

Deng observed high default probability for LTV from 70 to 75 percent, attributing it to the less

stringent screening procedures for loans in this LTV range.

Kelly (2008) also focused on lifetime 90-day delinquency probability. Kelly observed negative

LTV coefficients of origination LTV for the nation and for samples of metropolitan statistical

areas (MSAs). The coefficients were not significant, however, because of limited LTV variation

in the sample. They also found that traditional gift assistance for downpayments significantly

increases the delinquency probability.

IFE (2014) estimated a competing-risk model for 90-day delinquencies. Origination LTV

dummies were used in the regression. IFE found that loans with origination LTVs of more than

95 percent have a higher default probability compared with loans with LTVs from 90 to 95

percent for ARM loans. The opposite conclusion was made for FRM loans.

Freeman and Harden (2014) used a lifetime 30-to-90-day delinquency definition. Similar to

Kelly’s (2008) result, a negative significant coefficient was observed; however, the estimated

coefficients are close to zero. One possible reason for this observation is a limited LTV range in

the sample. Of the loans, 90 percent have an LTV ratio of more than 90 percent. The Freeman

and Harden research focused on the impact of downpayment sources on mortgage performance.

Deng, Quigley, and Van Order (1996) focused on lifetime 30-day delinquency. They observe

that default rates for loans with LTV ratios of more than 95 percent are three or four times higher

than default rates for loans with LTV ratios of 90 to 95 percent. The default rates for the latter

loans are, in turn, about five times higher than loans with LTVs of less than 80 percent.

Garmaise (2015) also use lifetime 30-day delinquency. His research examines mainly the impact

of borrowers’ self-reported assets on delinquency probability.

Deng, Quigley, and Van Order (2000) focus on lifetime delinquency of any duration. They

observe that the highest default probability was for loans with LTVs from 80 to 90 percent. They

conclude that borrowers who chose high initial LTV loans are more likely to exercise options in

the mortgage market—prepayment and also default. Their study indicates that the origination

LTV reflects investor preferences for risk in the market.

The second set of studies focuses on foreclosure or claims. Foreclosure is the initiation of

foreclosure proceedings, unless stated otherwise in table 1. The delinquency studies also had

different definitions of the dependent variable in both the time period the delinquency is

observed and the number of days delinquent, so the results are not entirely comparable. These

default studies have more dramatic differences in how the dependent variable is defined,

however, so the estimates are even less comparable with each other.

Lam, Dunsky, and Kelly (2013) analyzed 7-year foreclosure completions. The coefficients of

their LTV spline function can also be converted to comparable values as discussed previously in

the delinquency section.

Freeman and Harden (2014) estimated an equation for lifetime 90-day delinquency to

foreclosure. They observed a positive coefficient of origination LTV; however, the estimated

coefficients are close to zero. It is possible that they found a negative and statistically significant

relationship between LTV and 30-to-90-day delinquency because of the narrow LTV range in

their study.

IFE (2014) also estimated the lifetime claim probability (or, more precisely, log odds) with their

competing risk model. They found loans with origination LTVs of more than 95 percent have a

higher default probability compared with loans with LTVs from 90 to 95 percent. ARM loans

with LTVs from 90 to 95 percent have a foreclosure probability similar to those with LTVs of

more than 95 percent.

Kelly (2008) also estimated the lifetime claim probability. The coefficients of LTV were not

significant for both the national and MSA samples, as was also the case for the 90-day

delinquency equation.

Ghent and Kudlyak (2010) focused on the definition of default that is marked when a borrower

vacates the home, and they used a scorecard-type approach similar to ours. They use a dummy

variable of LTV80 to capture the high likelihood of a second mortgage being present for loans in

which LTV equals exactly 80 percent. The positive coefficient of LTV80 indicated the higher

default option value for these loans and has a strong effect on the probability of default. They

find that lenders have less effective recourse in states that require lenders to go through a lengthy

judicial foreclosure process, rather than a swift nonjudicial foreclosure process to obtain a

deficiency judgment. The reported coefficients in table 1 are adjusted based on the magnitude of

LTV used in the paper.

One important difference between our study and most of the others is the econometric technique.

Ours is a “scorecard” approach similar to Beem (2014), which attempts to predict future relative

performance based on the facts available at the time of origination, possibly controlling for the

future state of the (local) economy. Scorecards have been estimated often but rarely published,

because they are considered proprietary tools for competitive advantage. The primary modeling

and estimation approach in the literature is the competing risk model estimated with multinomial

logit. These are hazard-type models that attempt to explain the probability of (competing)

performance outcomes along the life of the mortgage conditional upon its current status. The

initial LTV becomes a less important factor, because the current LTV over time becomes the

more important factor along this risk dimension. Compared with a scorecard model, then, the

effect of origination LTV is less in the hazard-type models. Another difference is that the

probabilities in the hazard-type models are per period, instead of during the time period specified

in the definition of the delinquency or default, such as the first 2 years. As noted previously,

most coefficients cited in table 1 are for the multinomial logit proportional hazard approach,

making a direct comparison with the logit estimates of a scorecard model difficult.

Another contribution of the current analysis is its inclusion of different mortgage market

segments. Most previous literature (table 1) focused on a specific segment of the mortgage

market. Little discussion occurs among the performance of loans in different programs, such as

Federal Housing Administration, Veterans Affairs, Fannie Mae, Freddie Mac, jumbo, and

subprime markets. The use of the McDash data granted the opportunity to directly compare the

loan credit quality among different mortgage markets and their associated underwriting rules.

Methodology and Model

This section describes the econometric models used to estimate the historical performance of for-

purchase loans from fiscal year (FY) 2000 to FY 2012.

Model Specification

We specified binomial logistic models of the probability of default or foreclosure. The

mathematical expression for the probability of loans to default or foreclose within a specific time

period is given by

 =









Here, we use X to denote the vector of explanatory variables for the probability of default or

foreclosure. We count prepaid loans as “good.”

Discussion of Variables

This section describes some key variables in the model and the intuition behind specifications

and use in the model.

Dependent Variables

We estimate bivariate logistic regressions for performance periods of the first 2 and 3 years after

origination and lifetime and for 90 and 120 days delinquency and the initiation of foreclosure

proceedings. After examining preliminary regression results for these nine different models and

finding similar qualitative results, we selected the following two definitions to demonstrate the

empirical results.

2-year 90-day delinquency. For the delinquency analysis, 90-day delinquency within 2 years is

the dependent variable. Based on industry common practice, early delinquency within 2 years is

an indicator of poor underwriting quality.

Lifetime foreclosure. For the default analysis, foreclosure within the loan’s lifetime is the

dependent variable.

We explain why borrowers do not pay for either 3 consecutive months in the first 2 years or

when a foreclosure proceeding is initiated in a loan’s observed lifetime. Even though cures may

happen, we consider these two conditions to be significant indications of “bad” borrower

behavior. Therefore, we want to discern the underlying factors, particularly the amount of the

downpayment, leading to the decision to stop paying. With our definition of default, the

variability in the duration of foreclosure proceedings and alternative loss mitigation efforts

thereby did not need to be modeled. In the final analysis, it is primarily low or negative HPA that

determines whether an ultimate default occurs and whether a loss is incurred; underwriting a

borrower typically focuses on the borrower decision not to pay, without the complications

accompanying the likelihood of loss in the final default.

Independent Variables

The McDash data set includes an extensive set of variables that we supplement with economic

variables from Moody’s Analytics. We group the available variables for this study into loan-

specific variables and macroeconomic variables. In this section, we define most of the variables

and reserve the results for the Empirical Results section, in which we also discuss the remaining

explanatory variables used in this study.

Loan-specific variables. All static loan-specific variables are generated at the origination of

the loans.

Combined loan-to-value (CLTV) ratio. The sum of the origination primary and second lien

loan amounts, divided by the property value is the calculation to obtain the CLTV ratio. Without

the identity of the borrower and the specific house, only a second loan originated simultaneously

with the primary loan is identified in the McDash data set. In the absence of second loans, CLTV

is equal to the origination loan-to-value ratio.

Borrower credit score. Borrower credit or FICO scores at the loan level are an important

predictor of default and prepayment behavior. We use a dummy variable to identify loans with

missing credit scores.

Household debt-to-income (DTI) ratio. The DTI variable is likely subject to measurement

error, because income, especially for low-documentation loans, is likely to be erroneously recorded.

This variable also has a high degree of missing values, at 46.3 percent. The not-full-documentation

loans have missing DTIs at a rate of 64.9 percent, and full-documentation loans have a rate of 11.1

percent. Extreme outliers also suggest measurement error. In addition to using the numerical

variable, we created two dummy variables to reflect these situations; one variable indicates a missing

value and the other indicates when we censored outlier values. We censored the observations with

DTIs less than 5 percent and more than 70 percent, treating them as if they were missing, and created

a separate DTI outlier indicator to account for this situation. The McDash data set does not include

the total DTI, which includes the payment burden of all household debts.

Spread at origination (SATO). The spread between the mortgage note rate and the prevailing

mortgage rate at the time of origination measures SATO, which is widely regarded as the lender

surcharge for additional borrower risk characteristics not captured by standard underwriting hard

data, such as a FICO score, LTV, DTI ratio, documentation level, and so on. A high SATO loan

is generally riskier, compared with a similar loan with a low SATO (see table 2 for references

using SATO-type variables).

Relative property value. The property value divided by the median house value of the

corresponding MSA provides the relative property value. If the median house price at the MSA

level is not available, then we substitute the state- or national-level median house price.

Grade B and C loans. Grade B and C loan dummy variables indicate grade-B or grade-C

mortgages, which are generally believed to be of poorer credit quality than A-grade loans.

Prepayment penalty clause. Prepayment penalty loans are a special product type. After years of

excluding prepayment penalty clauses, lenders reintroduced them to protect mortgage investors

from multiple solicitations by mortgage brokers to refinance as soon as the market mortgage rate

fell to less than the contract rate. This aggressive solicitation activity produces income for the

brokers and a loss of value for investors. The prepayment penalty is a feature the borrower can

choose when applying for a loan, creating a variable that may reflect self-selection behavior by a

borrower. Loans with prepayment penalty clauses are riskier than those without such a clause in

the contract, at least in part because borrowers are less likely to prepay, which means they may

be exposed to adverse personal and economic events for a longer period of time.

Macroeconomic Variables. Macroeconomic variables are control variables. Some of these

variables are not observed at the time of the underwriting decision but have a very important

influence on whether delinquencies or defaults occur. Macroeconomic variables are typically

explanatory variables in estimating a scorecard and then neutralized, that is, set at specific values

when constructing an underwriting scorecard.

Our data consists of the monthly Federal Housing Finance Agency (FHFA) purchase-only house

price index, along with the Core Based Statistical Area (CBSA) codes for metropolitan areas,

metropolitan divisions, and state or national levels; monthly interest rates, including 1-year and

10-year Department of the Treasury rates and 30-year FRM rates; monthly unemployment rates,

with CBSA codes for metropolitan areas, metropolitan divisions, and state or national levels; and

the state-level census median housing prices for single-family houses and the national level for

condos. All the economic data come from Moody’s Analytics.

We now discuss the three sets of

macroeconomic variables included as control variables.

House price appreciation (HPA). The house price appreciation variable, which measures house

price movements after loan origination, is the main control variable in the possibility that a loan

may become “under water” within the performance observation period. (IFE, 2014).

In our models, HPA is defined based on the dependent variable. For the dependent variable, 90

days delinquent within 2 years, the variable HPA_2yr is calculated as the cumulative HPA during

the first 2 years, measured at the MSA level. If the HPA at the MSA level is not applicable, then we

use the state- or national-level CBSA code. For each property, the measure is:

HPA_2yr =









- 1

where HPI is the price index applicable to each property, based primarily on its MSA. The

source is the FHFA purchase-only index.

For the dependent variable, foreclosure during a loan’s lifetime, we calculate the variable

“HPA_fore_life” as the cumulative HPA up to the initiation of the first time a foreclosure status

occurs or, if there is no foreclosure, up to the end of the observation period, which, in our

estimation data set, is a minimum of 5 years measured at the MSA level. If HPA at the MSA

level is not applicable, then we use state- or national-level price index.

Although we intuitively prefer to measure HPA up to delinquency or default events, because that

is the information borrowers have when making no-payment decisions, measuring the HPA in a

period as short as 2 years appears to be more effective. In the lifetime scenario, a much higher

probability exists for more extreme HPA to occur at different points in time than the cumulative

HPA experienced at foreclosure. The HPA up to the point of foreclosure appears to provide a

better fit in the lifetime scenario.

Yield curve slope. Expectations about future interest rates and differences in short-term and

long-term borrowing rates, associated with the slope of the Treasury’s yield curve, influence the

choice between adjustable-rate mortgage and fixed-rate mortgage loans. We use the spread of the

10-year Constant Maturity Treasury (CMT) yield over the 1-year CMT yield to measure the

slope of the Treasury yield curve.

http://www.economy.com.

Estimation Database

In this section, we describe our methodology to identify and treat duplicate loan observations and

summarize the outlier control process to derive the database used for regressions. Appendix A

includes detailed analyses of the data steps.

The loan information raw data are from the McDash database. McDash loan data is a mortgage

performance database maintained by Black Knight, collected from most major mortgage

servicers. Before our analysis, we screened the loan data using two criteria: (1) the origination

loan calendar year and (2) loan purpose. We first selected loans originated during calendar years

2000 through 2012, focusing on for-purchase loans. After this preliminary screening, the number

of loan observations was reduced from 287,559,201 to 26,642,754.

Duplicate Observations

Approximately 26.5 million loans were originated from 2000 through 2012. We did not have

borrower names or property addresses for those loans, but we suspect, in many cases, that two or

more of the individually reported loans were in fact duplicates of the same mortgage transaction,

and that these multiple reports were because of either (1) one or more servicing transfers, making

them the same loan reported by multiple servicers, or (2) the fact that at least one loan was a

second lien. Approximately 5 million loans had the same origination month, ZIP Code, property

type identification, and original property value as at least one other loan observation. If the

original loan amounts had less than a 10-percent difference, we assumed that these observations

are because of servicing right transfers. A minimal difference in original loan amount may occur

when the new servicer reports the amortized loan amount as of the servicing transfer date instead

of the loan amount at the origination date. We combined the loan payment status histories for

these loans and deleted one of the two loan observations.

If the difference in the original loan amount was more than 10 percent, we assumed that these loans

are two different loans on the same property. The loan with the higher original loan amount was

identified as the primary loan, and only the primary loan performance was used for analysis. If a

foreclosure of the second lien triggered a foreclosure of the primary loan, this would appear in the

performance status of the primary loan. Loans with the lower original loan amount were assumed to

be second liens. We derived the CLTV by dividing the combined loan amount by the original

property value. Loans with a CLTV of more than 125 percent were excluded from our analysis as

outliers. About 3.5 million loans identified as second loans or duplicate servicer-transfer loans were

excluded from the analysis data set. The flowchart describing this process is in appendix B.

After removing second and duplicate loans, we identified 23,189,377 loans as valid for use in

our analysis.

Outlier Exclusion

Our research focuses on first mortgages for single-family homes and condominiums, excluding

an additional 4,075,892 loans and reducing the sample size to 19,113,485 loans. We then

screened the pared sample of loans for outliers, typically thought to be the result of transcription

or data errors. Table 3 shows the data exclusion standards to omit outliers. Details regarding

outlier identification and exclusion are in appendix C.

Table 3. Cutoff Levels for Outlier Exclusion

Variable Name

Data in Model

CLTV ratio

20% ≤ X ≤ 125%

Original credit score

300 ≤ X ≤ 850

DTI ratio

5% ≤ X ≤ 70%

Original property value

10,000 ≤ X ≤ 3,000,000

Original term

60 ≤ X ≤ 480

Loan payment history missing month

X ≤ 3

Original loan amount

10,000 ≤ X ≤ 2,000,000

Original interest rate

1% ≤ X ≤ 25%

CLTV = combined loan-to-value. DTI = debt-to-income.

After excluding all outliers, the total number of observations for the 2-year 90-day delinquency

model is 14,360,593, or 75.13 percent of the loans before outlier exclusions. The total number of

observations for the lifetime foreclosure model is 10,566,442, or 55.28 percent of the loans

before outlier exclusions.

The distributions of the continuous loan origination variables in the final sample set are shown in

table 4.

Table 4. Continuous Variable Distributions of Final Data Set

Variable

Mean

Median

Maximum

Quantiles

Minimum

95%

90%

75%

25%

10%

CLTV

ratio

0.8200

0.8

1.25

0.9921

0.9500

0.7619

0.6250

0.5065

0.2

Original

credit

score

714

722

850

801

791

767

670

624

598

300

DTI ratio

0.34

0.35

0.70

0.54

0.50

0.44

0.25

0.17

0.13

0.05

Original

property

value

284,626

210,000

3,000,000

725,000

550,000

350,000

135,000

90,000

72,000

10,000

Original

term

352

360

480

360

240

Original

loan

amount

217,225

170,259

2,000,000

515,000

400,400

270,750

112,080

76,000

60,000

10,000

Original

interest

rate

0.0610

0.0613

0.161

0.0775

0.0725

0.0663

0.0550

0.05

0.0463

0.01

CLTV = combined loan-to-value. DTI = debt-to-income.

Empirical Results

In this section, we present the regression results and a series of analyses that provide insight into

the extent to which downpayments reduce the probability of delinquency and default, the focus

of this paper. Recall that these are for-purchase loans, single-family home and condominiums,

performance of first mortgages, and from the cohorts 2000 to 2012.

Regression Results

Table 5 presents the estimated logistic regression coefficients and goodness-of-fit statistics for

the delinquency model defined as 90 days delinquent within the first 2 years and for default

defined as initiation of foreclosure proceedings during a loan’s lifetime.

We focus on both factors, delinquency and foreclosure, used in automated underwriting

decisions. In a separate analysis, we test whether a loan with early delinquency leads to a higher

probability of falling into foreclosure during the remainder of its lifetime. The indicator has a

coefficient of 2.52 in the foreclosure equation. This is not a surprising value, because the loan

has to be 90 days delinquent to get to foreclosure status, although not all 90-day delinquencies

result in foreclosure; however, this result suggests that an underwriting focus on the delinquency

equation has merit in its own right, even if the underwriting focus is on foreclosure.

We use the term probability of default (PD) to describe the outcome variable for the analysis

conducted in this study. As mentioned in the literature review section, our definition often differs

from prior studies. The term PD is used for both the delinquency and default equations, unless

the context calls for distinguishing them. A positive coefficient indicates a higher PD.

FRMs have lower PDs than ARMs or balloon mortgages, which is usually thought to reflect

adverse selection of ARMs by the more cash-strapped borrowers. Interest-only loans have higher

PDs. Federal Housing Administration and Veterans Affairs loans have higher PDs than

conventional loans, holding all the other factors constant. If the original term is not divisible by

60 months—that is, if it is not 15, 20, 25, or 30 years—the loan has a higher risk of delinquency.

We suspect that loans with odd terms are mainly modified loans as a result of loss mitigation

efforts. We expect such loans to have higher delinquency rates. In addition, the longer the

original term, the higher the PDs, which likely reflects borrower self-selection: shorter terms

require higher monthly payments, so borrowers with higher incomes and wealth may tend to

select shorter term loans.

Single-family loans have a higher delinquency rate, but a slightly lower default rate, than

condominiums. B and C loans exhibit a higher probability of default than prime loans, the reference

category, and a lower probability of delinquency—although the magnitude is small in absolute

value, and the estimated coefficient is not statistically significant at the 0.0001 probability level.

Government loans tend to have a higher delinquency risk and a higher default risk than conventional

loans. For loans other than government or conventional loans, the delinquency risk is higher

because of the relatively large monthly payments for jumbo loans. On the other hand, the default

risk for other loans is lower than for conventional loans, because credit scores of conventional loan

borrowers are quite good, enabling them to borrow without requirements for insurance.

Furthermore, we experimented with 120-day delinquencies and a 3-year time horizon and found results that are

similar to the 90-day results.

Table 5. Logistic Regression Statistics

Delinquency

Foreclosure

Variable

Coefficient

Pr > ChiSq

Coefficient

Pr > ChiSq

Intercept

1.1164

< 0.0001

– 5.7648

< 0.0001

CLTV

ratio

3.3939

< 0.0001

4.4373

< 0.0001

Has second loan

– 0.0191

0.007

0.0369

< 0.0001

Original credit score

– 0.0127

< 0.0001

– 0.00884

< 0.0001

DTI ratio

1.4891

< 0.0001

0.4105

< 0.0001

DTI ratio is missing

0.3998

< 0.0001

0.5479

< 0.0001

DTI ratio is outlier

0.1608

< 0.0001

0.6734

< 0.0001

Spread at origination

37.9145

< 0.0001

10.9559

< 0.0001

Relative property value

– 0.0207

< 0.0001

– 0.2965

< 0.0001

Primary residence

– 0.0499

< 0.0001

– 0.3378

< 0.0001

Single-family home

0.0951

< 0.0001

– 0.0531

< 0.0001

B or C loan

– 0.0213

0.0016

0.5279

< 0.0001

Jumbo loan

0.138

< 0.0001

0.2018

< 0.0001

Full documentation

– 0.2835

< 0.0001

– 0.3898

< 0.0001

Unknown documentation

– 0.0658

< 0.0001

0.1682

< 0.0001

30-year FRM rate

13.5103

< 0.0001

76.9304

< 0.0001

FRM

– 0.0438

< 0.0001

– 0.4236

< 0.0001

Interest-only loan

0.6205

< 0.0001

0.5122

< 0.0001

Loan type missing

0.194

0.0003

– 0.4749

< 0.0001

Government loan

0.1977

< 0.0001

0.2281

0.0001

Other than government or conventional

0.1606

< 0.0001

– 0.4682

< 0.0001

Has prepayment penalty

0.2771

< 0.0001

0.0567

< 0.0001

Original term

0.00285

< 0.0001

0.00269

< 0.0001

Original term can be divided by 60

– 1.1346

< 0.0001

– 0.1819

< 0.0001

Loan source—correspondent

0.2324

< 0.0001

– 0.2061

< 0.0001

Loan source—whole sale

0.4825

< 0.0001

0.3176

< 0.0001

Loan source—unknown

0.4871

< 0.0001

0.3009

< 0.0001

Payment status history partially missing

0.0349

< 0.0001

0.1246

< 0.0001

Yield curve slope

– 4.0913

< 0.0001

10.0181

< 0.0001

2-year cumulative HPA

– 2.5273

< 0.0001

2-year unemployment rate spread

11.5887

< 0.0001

2-year mortgage rate spread

0.6658

0.0127

Lifetime cumulative HPA until foreclosure

– 3.443

< 0.0001

Lifetime unemployment rate spread until

foreclosure

15.6674 < 0.0001

Lifetime mortgage rate spread until foreclosure

43.4376

< 0.0001

Gini coefficient

0.713

0.701

CLTV = combined loan-to-value. DTI = debt-to-income. FRM = fixed-rate mortgage. HPA = house price appreciation.

Origination credit scores have the expected sign, with a higher score presenting less risk and a

higher magnitude for early delinquency than for lifetime default. This result suggests that the

effect of the credit score measured at origination fades with the passage of time.

We suspect that loans with prepayment penalty clauses are riskier than those without such

contractual clauses, at least in part, because borrowers of loans with prepayment penalty clauses

are less likely to prepay, meaning they are exposed to the possibility of defaulting for a longer

period of time.

Loans for the primary residence have lower PDs than those for second homes or investor

properties. As expected, full-documentation loans have lower PDs than reduced-documentation

loans, and jumbo loans have higher PDs. The loans with some missing payment status history

have higher risk than loans with a complete status history. If the history of missing payments is

longer than 3 months or after the first 3 months, we delete the loan observation.

Wholesale loans and unknown source loans have higher PDs than retail loans, the reference

category. Correspondent loans are more likely to become delinquent, but are surprisingly less

likely to default. During the subprime boom periods, many mortgage brokers actively solicited

troubled borrowers to refinance into subprime loans. As a result, many loans that would have

foreclosed were terminated as if they were fully prepaid, at least for the initial purchase loans.

Relatively higher priced houses within an MSA have lower PDs, possibly reflecting higher

income and wealth of borrowers who can afford more expensive houses and may be less prone to

cashflow issues.

Higher CLTVs have higher PDs.

Higher housing DTI ratios also have higher PDs. Furthermore, if the DTI ratios are missing or

are outliers, the PDs will be higher relative to observations with DTI ratios. For example, the

probabilities of default for a loan with missing DTI, a loan with outlier DTI, and a loan with the

highest acceptable DTI are 2.61, 2.95, and 2.02 percent, respectively, given all other variables

are set at median values in the data set.

The steeper the origination yield curve, the lower the delinquency rate, but higher the default

rate. The steeper the origination yield curve generally suggests that the interest rate will rise

rapidly in the future. ARM borrowers are likely to experience payment shocks at the end of the

initial teaser periods. If a borrower’s income does not rise at the same rate as the origination

yield curve, the borrower may face the inability to pay and enter default. Such payment shocks,

however, tend to occur several years after the origination, thus resulting in limited impact on the

delinquency rate but stronger impact on the default rate.

Higher market rates at origination have higher PDs. The finding is consistent with the default

option theory. When the market interest rate drops, previously originated loans would be priced

at premium. In other words, borrowers would find that they are making higher than market rate

payments. When refinancing is not generally feasible, such as the period after the 2008 financial

crisis, borrowers making higher than market rate payments would have a higher incentive to

default.

If a second lien exists, the primary loan has less delinquency risk, holding constant the LTV for

primary loans without second loans or the CLTV for loans with second loans. The effect

observed in this analysis may be the result of tighter underwriting requirements to qualify for

second liens, so adverse selection exists for those who do not qualify for a second loan. Given

lifetime results, it is probable that the concentration of initial delinquency risk on the smaller

second component of mortgage loans in a short time after origination indirectly reduces the

delinquency risk of loans with a second lien. Second loans mainly cover the risk above an 80

percent LTV; in fact, 95.33 percent of loans with second loans have a primary loan LTV of less

than or equal to 80 percent. Private mortgage insurance is required for Fannie Mae and Freddie

Mac to accept LTVs of more than 80 percent, and private mortgage insurance companies have

complained about these “piggyback” mortgages because they reduce business volume and cause

them to be adversely selected. For the lifetime foreclosure rate, however, primary loans with

second loans perform worse than those without second loans, most likely because a foreclosure

on the more onerous second loan typically triggers a foreclosure on the first loan.

The higher the market mortgage rate SATO, the higher the PDs. Positive SATO stands for the

lender surcharge for additional borrower risk, as described previously.

The next three variables—HPA, the unemployment rate, and market mortgage rate—are not

known at origination, and, if they were included in the development of an automated

underwriting system, these variables would be neutralized. These variables, however, strongly

determine the absolute level of the PDs. They are independent of the credit quality of the

mortgages, so their inclusion should not alter the effects of the fundamental underwriting factors,

and in fact, are required to hold these important factors constant. The higher the HPA, the lower

the PDs. The higher the unemployment rate spread from origination, the higher the PDs. The

higher the SATO during the first 2 years for the delinquency equation and up to foreclosure or

lifetime for the default equation, the higher the PDs.

Functional Form

Notice that the continuous variables are expressed in a linear functional form. We show in

figures 1 and 2 diagnoses for the variables CLTV, FICO, and DTI that indicate whether a linear

form is appropriate. (More diagnostic charts are in appendix D.)

Figure 1. Diagnostics Charts for Combined Loan-to-Value Ratio

Figure 1 shows the predicted and actual PDs along the dimension of the respective variables,

along with the distribution of the observations. It is more important to have the predicted and

actual aligned over the range in which most observations are concentrated and not so much

where data is thin. Figure 1 shows that the higher the CLTV, the higher the PD. When CLTV is

higher than 100 percent, some abnormal behaviors are present in the raw data, but very few

observations are in this range. Both models fit well up to about 110 percent, which is sufficient

for analyses in the current market.

Figure 2. Diagnostics Charts for FICO Score

Figure 2 illustrates that the higher the credit score, the lower the PD. Again, some strange

behaviors occur when a credit score is extremely high or low, but the sample data are thin in

these regions and beyond the range for applicable policy relevance.

Figure 3 shows that the higher the DTI ratio, the higher the PD. A large population is left when

DTI equals 0, because we let DTI equal 0 when it is missing or outside our specified relevant

range of [0.05, 0.7]. In all the previous charts, the linear functional form appears to be

appropriate. For the default equation, the predicted pattern is consistent with actual default rates,

so a nonlinear form is not likely to adjust for a prediction that is considerably less than the actual.

Figure 3. Diagnostics Charts for Debt-to-Income Ratio

Compensating Factors for CLTV

In table 6, we show the percentage point changes in the CLTV that compensate for a one unit change

of each continuous variable, holding other variables constant so that the log-odds ratio, and hence the

PD, are the same. This is simply the variable’s coefficient divided by negative one times the CLTV

coefficient. Note that we use the percent sign (%) in the table, but its meaning is percentage points.

Table 6. Compensating Factors (Continuous Variables)

Variable

Delinquency

(%)

Default

(%)

Original credit score 0.37 0.20

DTI ratio – 43.88 – 9.25

Spread at origination – 1,117.14 – 491.36

Relative property value 0.61 6.68

30-year FRM rate – 398.08 – 1,733.72

Original term – 0.08 – 0.06

Yield curve slope 120.55 – 225.77

2-year cumulative HPA 74.47

2-year unemployment rate spread

– 341.46

2-year mortgage rate spread – 19.62

Lifetime cumulative HPA until foreclosure

77.59

Lifetime unemployment rate spread until foreclosure

– 353.08

Lifetime mortgage rate spread until foreclosure

– 978.92

% = percentage point. DTI = debt-to-income. FRM = fixed-rate mortgage. HPA = house price

appreciation.

For example, in the default equation, if the credit score were to increase by 1.0 (for example,

from 700 to 701), which decreases risk, the combined loan-to-value ratio needs to increase,

which increases risk, by 0.20 percentage points to compensate in the sense of maintaining the

same PD. In more practical terms, if the credit score were to decrease by 100 points (for

example, from 680 to 580), the CLTV would have to decrease by 20 percentage points to

compensate. Note that the linear form of the continuous variables makes the calculation of the

compensating factor straightforward, but also note that this is not the reason for selecting the

linear form, as discussed previously.

Another example highlights that the expression of the variable needs to be accounted for. Debt-to-

income is measured as a decimal in our analysis. Converting it to percentage points requires the

movement of DTI coefficient’s decimal point to the left by two positions. For the delinquency

equation, an increase in the DTI from 40 to 41, which increases risk, requires the reduction of CLTV

by 0.42 percentage points to compensate for the increased risk. An increase of the DTI from 40 to 45

requires a decrease in CLTV of 2.19 percentage points to compensate for delinquencies and a

decrease in CLTV of 0.46 percentage points to compensate for defaults. The finding demonstrates

that DTI is more important for delinquencies but is less important for defaults.

The compensating factors regarding binary variables are shown in table 7. For example, to have

the same probability of default as a prime loan, a B or C loan needs to have a CLTV that is 11.9

percentage points lower than the CLTV of an otherwise identical prime loan.

Another example is that for second and investor-owned homes, which perform worse than

primary residences when all else is held constant, the CLTV needs to be about 7.61 percentage

points lower to maintain the same PD. Conventional mortgage maximum loan-to-value ratios for

second and investor-owned homes traditionally have been lower than those for primary

residences by 5 or more percentage points. Observations from prior research is consistent with

our findings and is an example of how previous manual underwriting requirements, which were

only vaguely based on empirical evidence, applied the compensating factors principle.

Table 7. Compensating Factors (Binary Variables)

Variable

Delinquency

(%)

Default

(%)

Prepayment penalty – 8.16 – 1.28

DTI ratio is missing – 11.78 – 12.35

DTI ratio is outlier – 4.74 – 15.18

Primary residence 1.47 7.61

Single-family home – 2.80 1.20

B or C loan 0.63 – 11.90

Jumbo loan – 4.07 – 4.55

Full documentation 8.35 8.78

Unknown documentation 1.94 – 3.79

FRM 1.29 9.55

Interest-only loan – 18.28 – 11.54

Loan type missing – 5.72 10.70

Government loan – 5.83 – 5.14

Other than government or conventional loan – 4.73 10.55

Has prepayment penalty – 8.16 – 1.28

Original term can be divided by 60 33.43 4.10

Loan source—correspondent – 6.85 4.64

Loan source—whole sale – 14.22 – 7.16

Loan source—unknown – 14.35 – 6.78

Payment status history partially missing – 1.03 – 2.81

DTI = debt-to-income. FRM = fixed-rate mortgage.

CLTV Analytics

In this section we present analytics to examine the CLTV-default relationship. We show these

for the foreclosure equation, but they are similar for the delinquency equation. Charts for the

delinquency equation are in appendix E, which show the PD-CLTV relationship when specific,

interesting explanatory variables change. In the PD-CLTV relationship analyses, all other

variables are set at their median values in the estimation data set.

Figure 4 shows that primary loans without second loans have lower PDs than primary loan with

second loans, at the same levels of LTV or CLTV. This is because the borrowers with piggyback

loans are likely to be riskier, and when a second loan defaults, the corresponding first loan could

be triggered into default.

Figure 4. Effect of Second Loans on Default Probability

Figure 5 shows that very low FICO scores produce very high PDs, compared with high FICO

scores. For a 90 percent CLTV loan, the PD for a FICO score of 500 is nearly 12 times higher

than for a FICO score of 800. As might be expected, the delinquency relationship is even more

exaggerated, as shown in figure 6. At a 90 percent CLTV, the probability of early delinquency is

nearly 35 times higher at a FICO score of 500 compared with a FICO score of 800.

Figure 5. Credit Score Effect on Default Probability

50% 70% 90% 110%

Default Probability

Loan-to-Value

Combined Loan

Non-Combined Loan

10%

15%

20%

25%

30%

35%

40%

45%

50%

50% 60% 70% 80% 90% 100% 110% 120%

Default Probability

Loan-to-Value

FICO=500

FICO=580

FICO=620

FICO=680

FICO=740

FICO=800

Figure 6. Credit Score Effect on Delinquency Probability

Figure 7 shows that higher DTI ratios produce higher PDs. For loans with 90 percent CLTV, the

PD is 1.03 times higher for a 42 percent DTI ratio compared with a 35 percent DTI ratio. Again,

this comparison shows the relatively weak effect DTI ratio has on estimated default probabilities.

Figure 7. DTI Ratio Effect on Default Probability

DTI = debt-to-income.

10%

15%

20%

25%

30%

35%

40%

45%

50% 60% 70% 80% 90% 100% 110% 120%

Delinquency Probability

Loan-to-Value

FICO=500

FICO=580

FICO=620

FICO=680

FICO=740

FICO=800

10%

50% 60% 70% 80% 90% 100% 110% 120%

Default Probability

Loan-to-Value

DTI=0.18

DTI=0.35

DTI=0.42

DTI=0.5

Figure 8 shows that higher-priced houses have lower PDs, likely because of stronger income and

wealth of corresponding borrowers.

Figure 8. Relative Property Value Effect on Default Probability

Figure 9 shows that B and C loans have significantly higher PDs.

Figure 9. B and C Loan Effect on Default Probability

10%

12%

50% 60% 70% 80% 90% 100% 110% 120%

Default Probability

Loan-to-Value

Relative Property

Value=50%

Relative Property

Value=100%

Relative Property

Value=150%

Relative Property

Value=200%

10%

12%

14%

50% 60% 70% 80% 90% 100% 110% 120%

Default Probability

Loan-to-Value

IS B or C

IS NOT B or C

Figure 10 shows that jumbo loans have about a 20-percent higher probability of default rate than

conforming loans.

Figure 10. Jumbo Loan Effect on Default Probability

Figure 11 shows that full-documentation loans have lower PD rates. Full documentation is one

indicator of good underwriting quality, so the PD of loans with full documentation is usually

lower. Full-documentation underwriting can reduce PD about 30 percent.

Figure 11. Full-Documentation Effect on Default Probability

10%

12%

50% 70% 90% 110%

Default Probability

Loan-to-Value

IS JUMBO

IS NOT JUMBO

50% 70% 90% 110%

Default Probability

Loan-to-Value

IS FULL DOC

IS NOT FULL DOC

Figure 12 shows that house price appreciation has a significant effect on PDs. For a loan with 90

percent CLTV, the PD under a -30 percent HPA environment is about three times the PD under

an average 4 percent HPA environment. The finding is only suggestive, because the

measurement of lifetime HPA in our study is complicated by measuring only up to foreclosure

for loans that go into foreclosure.

Figure 12. HPA Effect on Default Probability

HPA = house price appreciation.

Figures 13, 14, and 15 now show the interaction of CLTV, FICO scores, and HPA. Policymakers

might use these types of analyses when selecting combinations of maximum CLTV ratios and

minimum FICO scores. To keep the discussion more tractable, we show only the probabilities of

foreclosure (denoted as PD). The bars represent, for selected FICO score levels as indicated by

the keys on the right side of the next three figures, the change in the PD by moving the maximum

CLTV from 96.5 to 97.0 percent, for example. At a FICO score of 580 and assuming the house

price drops 30 percent, the PD increases 0.3 percentage points if the maximum CLTV increases

from 96.5 to 97.0 percent. This is one demonstration of the cost of relaxing the maximum

allowed CLTV.

10%

15%

20%

25%

30%

50% 70% 90% 110%

Default Probability

Loan-to-Value

HPA= -30% / Lifetime

HPA= -20% / Lifetime

HPA= -10% / Lifetime

HPA= 4% / Lifetime

HPA= 10% / Lifetime

HPA= 20% / Lifetime

Figure 13. Lifetime Foreclosure Probability Change at

House Price Appreciation Equals 4 Percent at Selected FICO Scores

PD = probability of default.

Figure 14. Lifetime Foreclosure Probability Change at

House Price Appreciation Equals –10 Percent at Selected FICO Scores

PD = probability of default.

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

80%-90% 90%-95% 95%-96.5% 96.5%-97%

Lifetime Foreclosure Probability Change

Loan-to-Value Change

PD change for FICO=800

PD change for FICO=740

PD change for FICO=680

PD change for FICO=620

PD change for FICO=580

PD change for FICO=500

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

7.00%

8.00%

80%-90% 90%-95% 95%-96.5% 96.5%-97%

Lifetime Foreclosure Probability Change

Loan-to-Value Change

PD change for FICO=800

PD change for FICO=740

PD change for FICO=680

PD change for FICO=620

PD change for FICO=580

PD change for FICO=500

Figure 15. Lifetime Foreclosure Probability Change at

House Price Appreciation Equals -30 Percent at Selected FICO Scores

PD = probability of default.

Of course, the analysis of changing the maximum LTV or CLTV depends on the economic

environment against which policymakers would want to protect. If private mortgage insurance is

included, they may choose a benign environment such as a positive 4-percent HPA. As an

alternative, policymakers may want to protect against a stressed environment when default losses

may threaten solvency, such as a drop of 30 percent in housing prices.

They would, of course, attempt to balance the cost of higher PD rates with the increase of

origination volume to include a mission to serve low- to moderate-income homebuyers . These

are typical considerations when determining maximum CLTV ratios, and, often, the minimum

acceptable FICO score may be established for different CLTV levels. For example, the minimum

acceptable FICO score may be set at 580 to go to the maximum CLTV; however, the FICO score

can go down to 500 if CLTV ratios are constrained to be no greater than 90 percent. This is an

application of the compensating factors principle.

We observe that the magnitude of deterring PD is relatively high through the CLTV spectrum for

ranges of credit scores in highly negative HPA environments and fairly low across HPA

environments in the higher range of CLTV. The magnitude of deterrence to PD is relatively low

through CLTV spectrum for ranges of credit scores in higher negative HPA environments and

fairly low across HPA environments in the 90-to-97 range of CLTV.

In a similar way, these calculations often also include the selection of the maximum DTI. Note

that, for the default equation, as discussed in the previous compensating factors section, the DTI

has a relatively weak effect.

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

80%-90% 90%-95% 95%-96.5% 96.5%-97%

Lifetime Foreclosure Probability Change

Combined Loan-to-Value Change

PD change for FICO=800

PD change for FICO=740

PD change for FICO=680

PD change for FICO=620

PD change for FICO=580

PD change for FICO=500

Implications and Conclusions

In this research, using a scorecard model and the McDash loan-level performance data, we

quantified the impact of mortgage downpayments (in terms of the CLTV ratio) on mortgage

defaults by controlling for other factors such as loan-specific elements and economic conditions

during the performance period. Our definition of delinquency was 90-days past due within the

first 2 years after origination; our definition of default was the initiation of foreclosure

proceedings during a loan’s lifetime. The estimation sample consisted of for-purchase mortgages

and included government, conventional, and private-sector loans.

Our literature review focused on studies that quantified the effect of the initial downpayment on

delinquency, default, or claims. Very few studies applied the scorecard-type approach. The

literature instead was replete with studies using the competing risk model, which produces

hazard-type estimates and a multinomial logit estimator that make it difficult to compare other

estimates with ours. More reasons for the incompatibility of estimates include different

definitions of delinquency and default, different estimation time periods along with the

explanatory variables selected for inclusion, and the coverage of different mortgage market

segments. We consequently drew no inferences regarding whether our estimates of the absolute

and relative effects of CLTV on the probability of delinquency and default were consistent with

previous literature.

We developed a useable estimation database from the loan performance records in the McDash

loan database that is compiled from the major mortgage servicers Fannie Mae and Freddie Mac.

Our major challenge was that the McDash database does not have borrower names or property

addresses, which created uncertainty when considering multiple reporting incurred by servicing

transfers and second liens. Devising an algorithm to address duplicate entries, we found that 8.58

percent of the loans examined during the 2000-to-2012 period were duplicitous due to servicing

transfers and 6.24 percent to be second liens, distinguishing between the two types based on

reported loan balances. The combined loan-to-value variable, which included the balance of the

second lien when a second lien was identified, accounted for downpayments.

Although we did not create a typical mortgage scorecard, we produced analytics describing how

important the CLTV is relative to other risk factors, such as the FICO credit score and the

housing debt-to-income ratio. The first of these analytics derives from the time-honored tradition

in manual underwriting of assessing creditworthiness by assessing compensating factors. For

example, when a mortgage application reveals a blemished credit record, the application can still

be accepted if accompanied by a greater downpayment to compensate for the credit reputation

deficiency. The advent of mortgage scorecards made the evaluation of compensating factors

implicit. On the other hand, we made the compensating factors explicit, as demonstrated from

our estimated default models, focusing on the CLTV. We computed the amount of percentage

points the CLTV has to decrease in order to offset the change in probability of default when

some other explanatory variable increases. In addition, in the case of binary variables, the

decrease in CLTV needed to offset the credit risk effect when they change from one to zero. For

example, if the loan changes from a prime loan to a subprime loan, holding other factors

constant, the CLTV needs to be lowered by 11.9 percentage points to offset the higher credit risk

of the B or C loan.

We also showed the type of interaction among CLTV, FICO scores, and HPA rates that

policymakers might use and showed tradeoffs when considering combinations of maximum LTV

ratios and minimum FICO scores. Those are, in essence, the types of tradeoffs made within a

scorecard model. Given a specified threshold for default rates and the relevant HPA,

policymakers can choose different combinations of LTV ratios and FICO scores to manage

mortgage credit risks. That is, the LTV ratio and FICO score can serve as compensating factor to

each other to maintain a constant expected default risk.

Analytical inferences from estimated scorecard models evaluate where to set accept or reject cut

points and various override rules, such as the minimum FICO score and the maximum DTI ratio.

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Appendix A. Data Analysis

In this section, we discuss our data source and our data processing procedures, which include

analysis of missing data, outliers, and variable construction.

The source of loan information data is from the McDash loan database. McDash data are the

comprehensive mortgage performance data solutions that Black Knight Financial Technology

Solutions, LLC developed and maintains. The McDash loan data are collected from major

mortgage servicers and from Fannie Mae and Freddie Mac. We screened the loan data using two

criteria: the origination loan calendar year and the loan purpose. We selected loans originating

from 2000 through 2012 and focused on for-purchase loans. This initial screening reduced the

number of loan observations from 287,559,201 to 26,642,754.

Data Quality

Missing Data

Table A1 shows the number of observations with missing values of individual variables. We first

focused on four important variables: (1) original property value; (2) combined loan-to-value

(CLTV) ratio; (3) original credit score, or FICO; and (4) housing debt-to-income (DTI) ratio.

The database did not include the total DTI. Missing data in the variables seriously impair the

ability to conduct empirical analyses.

CLTV is the key variable in this research. Table A1 shows more than 77 percent of the

loans lack information on CLTV; hence, we computed the CLTV for individual loans using

inferences on multiple mortgages on the same property. We present more detail about this

procedure in this section.

Table A1. Loans With Missing Variable Data and Our Resolution

Variable

Total Observation: 26,642,754 Loans

Missing

Observations

Percentage of

Data Missing

Resolution

ZIP Code

785

<0.01

Not used in regression, but used to identify

multiple loans

Property type

580

<0.01

Used missing dummy variable

Original loan amount

619

<0.01

Deleted observations with missing values

Original property value

151,545

0.57

Deleted observations with missing values

CLTV ratio

20,545,263

77.11

Imputed second lien balances

Original credit score

4,408,347

16.55

Used

missing dummy variable

DTI housing ratio

12,338,426

46.31

Used missing dummy variable

Documentation type

6,724

0.03

Used missing dummy variable

Underwriting type

3,098,767

11.63

Used missing dummy variable

Teaser rate

26,579,262

99.76

Not used in regression

CLTV = combined loan-to-value. DTI = debt-to-income.

Data Distributions and Outliers

Outliers are data elements that appear to be erroneously inputted. This analysis begins by

examining the distribution of the numeric data in each year. Table A2 shows the distribution of the

seven numeric variables in our model, which include original interest rate, original loan amount,

original property value, CLTV, original credit score, housing DTI ratio, and original term.

Table A2. Variables Distribution From 2000 Through 2012

Variables Mean Median

Maximum

Quantiles

Minimum

99%

95%

90%

75%

25%

10%

Original interest rate

6.06%

6.00%

75.00%

11.25%

8.74%

7.70%

6.63%

5.25%

4.38%

3.88%

3.13%

<0.01%

Original loan amount

196,638

155,000

90,205,897

785,527

463,200

368,000

245,531

100,000

63,000

44,950

21,480

(85,389)

Original property value

269,561

200,000

99,999,999

1,200,000

665,000

509,000

325,000

131,000

89,000

70,500

44,000

CLTV ratio

255

102

100

Original credit score

714

721

974

812

801

791

767

668

626

601

548

300

DTI ratio

Original term

344

360

999

381

360

342

180

CLTV = loan-to-value. DTI = debt-to-income.

We observe from table A2 that the values of all variables within 1 and 99 percent appear to be

reasonable during the sample period, except for the housing DTI ratio. The analysis suggests that

extreme outliers account for only a very small portion of the data set.

The housing DTI ratio has some particularly high values. For example, the 99th percentile has a

value of 99, indicating that the monthly housing payment is 99 percent of the borrower’s

monthly income. It has been observed in the mortgage industry that the reported payment-to-

income ratio is not particularly reliable across different submarkets, but values as extreme as

these are most likely transcription errors. For estimation purposes, we use not only the variable

DTI but also two dummy variables to indicate missing DTI and outliers. The new DTI variable is

equal to zero (0) if the original DTI is missing or is an outlier. Otherwise, the new DTI is equal

to the original DTI.

Payment Status History Variables

Several variables that measure whether a loan is “good” or “bad” are derived from the payment

history status variable in the delinquency history data set. The payment history status variable is

a string variable containing 1,000 characters. Each character, in sequence, indicates the status of

the loan during each month after loan origination. Thus, the payment history variable provides

the status, and hence, the status transitions of each loan throughout its life, up to the current

observation date. It is critical that the loan status history be complete to determine whether a loan

is bad; that is, the loan has some specified negative event such as a missed mortgage payment

during a time interval. We observed that many loans have missing performance statuses during

their first several months. Table A3 shows the distribution of the first month when a nonmissing

payment performance record appears in the data set since a loan’s origination.

As table A3 shows, loan performance information has become more complete over time. In

recent years, most of the first nonmissing months appear within 2 years of origination.

Table A3. Distribution of the First Month of Nonmissing Payment Performance Record

Loan Percentage by Year

Orig_

Year

First Nonmissing

Payment History

Month Equal to or

Less Than 4 Months

(%)

First Nonmissing

Payment History

Month From

5 Months to 2 Years

(%)

First Nonmissing

Payment Month

From

2 to 5 Years

(%)

First Nonmissing

Payment History

Month From

5 Years to Lifetime

(%)

Missing

Payment

History

(%)

2000

23.61

3.86

59.52

13.01

2001

28.49

4.25

60.74

6.52

2002

31.99

14.90

47.13

5.99

2003

36.05

43.84

18.65

1.46

2004

46.13

45.82

7.70

0.34

2005

76.84

16.94

6.18

0.04

<0.01

2006

79.19

19.08

1.72

0.00

<0.01

2007

88.59

10.98

0.42

0.01

2008

98.04

1.90

0.06

0.00

2009

97.40

2.60

0.00

2010

94.01

4.12

1.86

0.00

2011

96.27

2.95

0.78

0.00

2012

93.47

6.25

0.26

0.08

To improve the data’s performance, we identified duplicate loans originating from servicing

transfers and combined their loan performance history. Appendix B shows detailed methodology

and results. After combining the performance histories of duplicitous loans, we deleted all loan

observations with more than 3 months of missing performance information.

Variable Creation and Selection

Calculating CLTV and Managing Duplicate Loans for Servicing Transfers

The McDash database does not flag primary and secondary loans, nor does it dedupe multiple

servicers reporting the same loans as a result of servicing transfers. We created edits to discern

duplicitous reporting to create a more accurate and vetted data set. These edits work around the

fact that borrowers’ names and property addresses are not part of the data set. For duplicate loan

records entered by multiple servicers, we combined the performance history of incomplete records

to address missing payment history observations. For all loans, we created an original loan-to-

value (LTV) ratio variable and a CLTV for all loans that would be identical to the LTV on loans

without second liens. We used this information to determine whether loans with second loans

perform better or worse than loans without second liens. Appendix B describes the methodology.

Delinquency Variables

To measure the impact of the underwriting process, we conducted analysis of early delinquency,

and we apply the industry practice of 90 days delinquent in the initial 2 years. We also

constructed a performance variable based on the initiation of foreclosure proceedings. Basing our

analysis on the previous examination of the first nonmissing payment history month of each loan

in 2 years and during the observable lifetime, we constructed the following variables:

• First delinquent month variables include the loan age in months during which a loan

becomes 30, 60, 90, and 120 days delinquent for the first time. We also created variables

indicating the first initiation of foreclosure proceedings, using the same method based on

the payment history in the loan’s lifetime.

• Number of delinquent months variables are derived by counting the number of months

when each of the six delinquent statuses is observed during the first 2-year and 3-year

periods after a loan’s origination.

• Default episode month variables are defined in terms of beginning and ending months of

delinquency. The first default episode beginning month is defined as the first month when

a loan becomes 90 days delinquent, and the first default episode ending month is defined

as the last month before the loan cures to the current payment status after the first default

episode beginning month. The same algorithm is used to construct the second, third,

fourth, and fifth default episode beginning and ending months.

Macroeconomic Variables

We prepared four macroeconomic variable data sets for model use. The first data set contained

the monthly Federal Housing Finance Agency purchase-only house price index, with the Core

Based Statistical Area (CBSA) codes for metropolitan areas, metropolitan divisions, and state- or

national-levels. The second data set contained monthly interest rates, including 1-year LIBOR, 1-

year Department of the Treasury rates, 10-year Treasury rates, and the 30-year fixed-rate

mortgage (FRM) rates. The third data set contained monthly unemployment rates, with the

CBSA codes for metropolitan area, metropolitan division, and state- or national-levels. The

fourth data set contained the state-level census median housing prices for single-family houses

and the national-level for condominiums. All the economic data come from Moody’s Analytics.

http://www.economy.com.

Appendix B. Duplicate Observations

Figure B1 details the steps used to deal with suspected duplicate observations for loans on the

same property. Approximately 26.5 million loans originated from 2000 through 2012. We did

not have borrower names or property addresses, but we suspected, in many cases, that two or

more of the individually reported loans were in fact on the same house, and that these multiple

reports were because of either (1) one or more servicing transfers, making it the same loan

reported by multiple servicers, or (2) at least one loan was a second lien. Approximately 5

million loans had the same origination month, ZIP Code, property type identification, and

original property value as at least one other loan observation. These four criteria are cited in the

first row of figure B1. If the original loan amounts had less than a 10-percent difference, we

assumed that these observations are due to servicing transfers. A minimal difference in original

loan amount may occur when the new servicer reports the amortized loan amount as of the

servicing transfer date instead of the loan amount at the origination date. We combined the loan

payment status histories for these loans and deleted one of the two loan observations.

If the difference in the original loan amount was larger than 10 percent, we assumed that these

loans are two different loans on the same property. The loan with the higher original loan amount

was identified as the primary loan, and we used only the primary loan performance for analysis;

if a foreclosure of the second lien triggered a foreclosure of the first, this showed up in the

performance status of the primary loan. Loans with lower original loan amounts were specified

as second liens. We then derived the CLTV by dividing the combined loan amount by the

original property value. Loans with a CLTV larger than 125 percent were excluded from our

analysis as outliers. About 3.5 million loans identified as second loans or duplicate servicer-

transfer loans were excluded from the analysis data set.

Figure B1. Observations Identified as Combined Loans or Servicing Right Transfer Loans

After removing second and duplicate loans, we identified 23,189,377 loans as valid that we used

for our analysis. Table B1 replicates table A3 after the deduping procedure described previously.

Table B1. Distribution of the First Month of Nonmissing Payment Performance Record

Loan Percentage by Year

rig

ination

Year

First Nonmissing

Payment History

Month Equal to or

Less Than 4 Months

(%)

First Nonmissing

Payment History

Month From

5 Months to 2

Years

(%)

First

Nonmissing

Payment Month

From 2 to 5

Years

(%)

First Nonmissing

Payment History

Month

From 5 Years to

Lifetime

(%)

Missing

Payment

History

(%)

2000

23.98

3.84

59.79

12.38

0.00

2001

28.99

4.16

60.96

5.89

0.00

2002

32.63

14.78

47.23

5.36

0.00

2003

37.04

43.75

18.12

1.09

0.00

2004

47.47

45.52

6.73

0.27

0.00

2005

79.00

15.51

5.44

0.05

<0.01

2006

81.20

17.34

1.46

0.00

<0.01

2007

89.81

9.74

0.44

0.01

0.00

2008

98.08

1.86

0.06

0.00

2009

97.39

2.61

0.00

2010

95.35

4.11

0.55

0.00

2011

98.27

1.23

0.50

0.00

2012

94.47

5.26

0.26

0.01

0.00

Compared with table A3, the percentage of the first nonmissing payment history month that is

equal to or less than 4 months increases, after combining the payment history of servicing transfer

loans. Because we measured 90-day delinquencies, we excluded any loan observations with the

first nonmissing payment history that is more than 4 months to avoid uncertain information.

Figure B2. Cumulative Percentage of the First Month of Nonmissing Payment Performance

From the previous chart and after applying the matching methodology, the accumulated

percentage of the first month of nonmissing performance statuses is larger than before in earlier

cohorts due to the combination of payment status histories among servicing transfer loans.

100

0 10 20 30 40

Cumulative Percentage

First Nonmissing Month

Raw Data

Raw Data after Duplication Correction

Appendix C. Outlier Exclusions

Table C1. Outlier Control Process

Outlier

Condition

or Lifetime

Analysis

Number of

Observatio

Excluded

Percentage

Cumulative

Percentage

Outlier

Condition

for 2-Year

Analysis

Number of

Observatio

Excluded

Percentage

Cumulative

Percentage

Any loan

with missing

payment

history

status more

than 3

months

4,483,989

23.46

Any loan

with missing

payment

history

status more

than 3

months

4,483,989

23.46

Any loan

with original

interest rate

less than

1% or more

than 25%

0.00

23.46

Any loan

with original

interest rate

less than

1% or

than 25%

0.00

23.46

Any loan

with original

term less

than 60

months or

more than

480 months

5,204

0.03

23.49

Any loan

with original

term less

than 60

months or

than

480 months

5,204

0.03

23.49

Any loan

with original

loan amount

of more

than

$2,000,000

or less than

$10,000

10,162

0.05

23.54

Any loan

with original

loan amount

of more than

2,000,000

or less than

$10,000

10,162

0.05

23.54

Any loan

with original

property

value of

more than

$3,000,000

or less than

$10,000

21,574

0.11

23.65

Any loan

with original

property

value

than

3,000,000

or less than

$10,000

21,574

0.11

23.65

Any loan

with LTV

more than

125% or

less than

20%

36,240

0.19

23.84

Any loan

with LTV

than

125% or

less than

20%

36,240

0.19

23.84

Any loan

with CLTV

more than

125% or

less than

20%

2,547

0.01

23.86

Any loan

with

CLTV

than

125% or

less than

20%

2,547

0.01

23.86

Any loan

with original

credit score

higher than

850

2,394

0.01

23.87

Any loan

with original

credit score

higher than

850

2,394

0.01

23.87

Any loan

with missing

CLTV

0.00

23.87

Any loan

with missing

CLTV

0.00

23.87

Any loan

with

origination

year of 2010

or later is

excluded for

the lifetime

analysis

3,300,676

17.27

41.14

Any loan

with

payment

status

history of

permanently

missing is

excluded for

lifetime

analysis

684,174

3.58

44.72

Any loan

with

payment

status

history of

permanently

missing

within 2

years.

190,699

1.00

24.87

CLTV = combined loan-to-value. LTV = loan-to-value.

Appendix D. Diagnostics Charts

Here, we show the diagnostic charts for categorical and continuous variables that help to assess

the appropriateness of the functional form of the variable. The left-hand charts are for 90-day

delinquencies in the first 2 years, and the right-hand charts are for lifetime foreclosures.

Figure D1. Diagnostics Charts for Loan Type

Figure D2. Diagnostics Charts for Product Type

Figure D3. Diagnostics Charts for Original Term

Figure D4. Diagnostics Charts for Payment and Interest Frequency

Figure D5. Diagnostics Charts for Occupancy

Figure D6. Diagnostics Charts for Prepayment Penalty Clause

Figure D7. Diagnostics Charts for Documentation

Figure D8. Diagnostics Charts for First Nonmissing Month

Figure D9. Diagnostics Charts for Original Credit Score

Figure D10. Diagnostics Charts for Relative Property Value

Figure D11. Diagnostics Charts for Combined Loan-to-Value

Figure D12. Diagnostics Charts for Yield Curve Slope

Figure D13. Diagnostics Charts for 30-Year Fixed-Rate Mortgage Rate

Figure D14. Diagnostics Charts for 2-Year Cumulative HPA/Lifetime Cumulative HPA

HPA = house price appreciation.

Figure D15. Diagnostics Charts for 2-Year

Cumulative HPA

†

/Lifetime Unemployment Rate Spread

HPA = house price appreciation.

Figure D16. Diagnostics Charts for 2-Year

Cumulative HPA/Lifetime Mortgage Rate Spread

HPA = house price appreciation.

Figure D17. Diagnostics Charts for Debt-to-Income Ratio

Figure D18. Diagnostics Charts for Origination Year

Appendix E. CLTV Analytics for the Delinquency Model

In this appendix, we present analytics to illuminate the combined loan-to-value (CLTV)-2-year

90-day delinquency relationship, to illustrate the delinquency equation. These analytics show the

delinquency probability-CLTV relationship when specific, interesting explanatory variables

change. In these analyses, all other variables are set at their median values in the data set.

Figure E1. Combined Loan Effect on Delinquency Probability

Figure E2. Jumbo Loan Effect on Delinquency Probability

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

4.0%

4.5%

5.0%

50% 70% 90% 110%

Delinquency Probability

Loan-to-Value

Combined Loan

Non-Combined Loan

50% 70% 90% 110%

Delinquency Probability

Loan-to-Value

IS JUMBO

IS NOT JUMBO

Figure E3. Full Documentation Effect on Delinquency Probability

Figure E4. B and C Loan Effect on Delinquency Probability

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

4.0%

4.5%

5.0%

50% 70% 90% 110%

Delinquency Probability

Loan-to-Value

IS FULL DOC

IS NOT FULL DOC

50% 70% 90% 110%

Delinqunecy Probability

Loan-to-Value

IS B or C

IS NOT B or C

Figure E5. Relative Property Value Effect on Delinquency Probability

Figure E6. DTI Effect on Delinquency Probability

DTI = debt-to-income.

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

4.0%

4.5%

5.0%

50% 70% 90% 110%

Delinquency Probability

Loan-to-Value

Relative Property

Value=50%

Relative Property

Value=100%

Relative Property

Value=150%

Relative Property

Value=200%

50% 70% 90% 110%

Delinquency Probability

Loan-to-Value

DTI=0.18

DTI=0.35

DTI=0.42

DTI=0.5

Figure E7. FICO Effect on Delinquency Probability

Figure E8. HPA Effect on Delinquency Probability

HPA = house price appreciation.

10%

15%

20%

25%

30%

35%

40%

45%

50%

50% 70% 90% 110%

Delinquency Probability

Loan-to-Value

FICO=500

FICO=580

FICO=620

FICO=680

FICO=740

FICO=800

10%

12%

14%

50% 70% 90% 110%

Delinquency Probability

Loan-to-Value

HPA= -30% / 2year

HPA= -20% / 2year

HPA= -10% / 2year

HPA= 4% / 2year

HPA= 10% / 2year

HPA= 20% / 2year

Figure E9. 2-Year 90-Day Delinquency Probability Change at

House Price Appreciation Equals 4 Percent at Selected FICO Scores

PD = probability of default.

Figure E10. 2-Year, 90-Day Delinquency Probability Change at

House Price Appreciation Equals -10 Percent at Selected FICO Scores

PD = probability of default.

0.0%

1.0%

2.0%

3.0%

4.0%

5.0%

6.0%

80%-90% 90%-95% 95%-96.5% 96.5%-97%

2-Year 90-

Day Delinquency Probability

Change

Loan-to-Value

PD change for FICO=800

PD change for FICO=740

PD change for FICO=680

PD change for FICO=620

PD change for FICO=580

PD change for FICO=500

0.0%

1.0%

2.0%

3.0%

4.0%

5.0%

6.0%

7.0%

80%-90% 90%-95% 95%-96.5% 96.5%-97%

2-Year 90-Day Delinquency Probability

Change

Loan-to-Value

PD change for FICO=800

PD change for FICO=740

PD change for FICO=680

PD change for FICO=620

PD change for FICO=580

PD change for FICO=500

Figure E11. 2-Year, 90-Day Delinquency Probability Change at

House Price Appreciation Equals -30 Percent at Selected FICO Scores

PD = probability of default.

0.0%

1.0%

2.0%

3.0%

4.0%

5.0%

6.0%

7.0%

8.0%

9.0%

80%-90% 90%-95% 95%-96.5% 96.5%-97%

2-Year 90-

Day Delinquency Probability

Change

Loan-to-Value

PD change for FICO=800

PD change for FICO=740

PD change for FICO=680

PD change for FICO=620

PD change for FICO=580

PD change for FICO=500