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
ii

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.
iv

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
1

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 McDashTM 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. 
2

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-tovalue ratios in this study—and basic information from each of the studies in table 1. 
3

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 
4

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, 

LLLLLLssssssssssss3 and LLLLLLssssssssssss4, the contribution of LTV is equal to β1 × LLLLLLssssssssssss1 + β2

× (LLLLLLssssssssssss2 − LLLLLLssssssssssss1) + β3 × (LLLLLLssssssssssss3 − LLLLLLssssssssssss2) + β4 × (LLLLLL − LLLLLLssssssssssss3). If 

we take only significant coefficients into consideration, the Lam, Dunsky, and Kelly study 

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.
5

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 singlefamily

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 singlefamily and 

condo forpurchase 

1999–

2006

National sample: – 0.056*

MSA-level samples: –

0.028*

IFE (2014)

Lifetime 90-

day 

delinquency

Origination 

LTV 

dummies 

Multinomial 

logit Endogenous FHA singlefamily

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
6

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 singlefamily 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 singlefamily 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 singlefamily 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 = governmentsponsored 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.
7

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 v v v v v v v

CLTV v v

CLTV > LTV dummy v

Current LTV v v

Origination LTV dummies v v v

FICO score and MTM LTV 

Interaction

v

Origination LTV = 80% dummy v

Source of downpayment v v v v

Loan size v v

Loan grade v

FRM v v v v

Interest-only loan v v

Loan type missing v

Government loan v

Original term can be 

divided by 60

v

Original term v

Single-family home v v

Original credit score v v v v v v v v v

Missing credit score dummy v v

Prepayment penalty v v

Primary residence v v

Documentation type v

Jumbo loan v v

Missing payment status history v

Relative property value v

Relative loan size v v

DTI ratio v v v v v v v

Yield curve slope v v v

30-year FRM rate v

Original interest rate v

CMT10/CMT1 v

Has second loan v v

Home price volatility v

Cumulative HPA v v v

Unemployment rate spread v v v v
8

Mortgage rate spread v v v

Lifetime cumulative HPA v

Lifetime unemployment rate spread v

Lifetime mortgage rate spread v

Mortgage age v v v v v

Mortgage age squared v

Mortgage age square root v

Seasonality v v v

Origination cohort v

Unpaid principal balance v v v

Spread at origination v v v

Spread at origination dummies v

Burnout factor v v v

Credit burnout factor v

Census division v

Metropolitan location v

State laws v v

Housing structure v v

Borrower’s ethnic/age/sex v

Borrower’s marriage status v v v v

Borrower’s education v

Borrower’s employment status v

Household income v v

Under water v

First-time buyer v v v

Origination year dummy v v v

State dummy v

Location dummy v

Loan purpose v v

Unemployment rate v v v v

Relative unemployment rate v

Lagged unemployment rate v

Mortgage premium value v

Probability of negative equity v v v

Probability of negative equity squared v v

Recourse v

Fraction of contract value v

Fraction of contract value squared v

Spread in primary mortgage rate v

Number of housing units v v

Reserve v

Builder v

Underserved area v

Refinance incentive v

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 
9

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. 
10

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. 
11

Methodology and Model

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

PPPP = α+XXβ

1+ α+XXβ

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-
12

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. 
13

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.1 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 = HHHHHH24

HHHHHH0

 - 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. 

 

1 http://www.economy.com. 
14

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.
15

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% 5%

CLTV

ratio

0.8200 0.8 1.25 1 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

352 360 480 360 360 360 360 360 240 60

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.
16

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.2

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.

 

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

similar to the 90-day results.
17

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. 
18

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 
19

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.
20

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. 
21

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-toincome 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 
22

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. 
23

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

0%

1%

2%

3%

4%

5%

6%

7%

8%

9%

50% 70% 90% 110%

Default Probability

Loan-to-Value

Combined Loan

Non-Combined Loan

0%

5%

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
24

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.

0%

5%

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

0%

1%

2%

3%

4%

5%

6%

7%

8%

9%

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
25

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

0%

2%

4%

6%

8%

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%

0%

2%

4%

6%

8%

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
26

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

0%

2%

4%

6%

8%

10%

12%

50% 70% 90% 110%

Default Probability

Loan-to-Value

IS JUMBO

IS NOT JUMBO

0%

1%

2%

3%

4%

5%

6%

7%

8%

9%

50% 70% 90% 110%

Default Probability

Loan-to-Value

IS FULL DOC

IS NOT FULL DOC
27

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.

0%

5%

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
28

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
29

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
30

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. 
31

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. 
32

References 

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Constraints on Residential Mortgage Terminations,” Regional Science and Urban Economics 26: 

235–261. 

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Quality and Governance.” Working paper 07/82. Washington, DC: International Monetary Fund. 

Beem, Richard H., Jr. 2014. “Residential Mortgage Delinquency Rates: The Determinants of 

Default,” Issues in Political Economy 23: 59–75.

Calhoun, Charles A., and Yongheng Deng. 2002. “A Dynamic Analysis of Fixed- and 

Adjustable-Rate Mortgage Terminations,” The Journal of Real Estate Finance and Economics

24 (1): 9–33. 

Deng, Yongheng, John M. Quigley, and Robert Van Order. 1996. “Mortgage Default and Low 

Downpayment Loans: The Costs of Public Subsidy,” Regional Science and Urban Economics 26 

(3–4): 263–285. 

———. 2000. “Mortgage Terminations, Heterogeneity and the Exercise of Mortgage Options,” 

Econometrica 68 (2): 275–307. 

Freeman, Allison, and Jeffrey J. Harden. 2014. “Affordable Homeownership: The Incidence and 

Effect of Downpayment Assistance,” Housing Policy Debate 25 (2): 308–319. 

Garmaise, Mark J. 2015. “Borrower Misreporting and Loan Performance,” The Journal of 

Finance 70 (1): 449–484. 

Ghent, Andra C., and Marianna Kudlyak. 2010. “Recourse and Residential Mortgage Default: 

Theory and Evidence from U.S. States.” Working paper 09–10R. Richmond, VA: The Federal 

Reserve Bank of Richmond.

Hwang, Min, Binzi Shu, and Robert Van Order. 2015. Understanding the Underwriting in Prime 

Markets: the GSE Case. Working paper. Washington, DC: George Washington University. 

Integrated Financial Engineering, Inc. (IFE). 2014. Actuarial Review of the Federal Housing 

Administration Mutual Mortgage Insurance Fund Forward Loans for Fiscal Year 2014. 

Washington, DC: U.S. Department of Housing and Urban Development. 

Kau, James B., and Donald Keenan. 1995. “An Overview of Option-Theoretic Pricing of 

Mortgages,” Journal of Housing Research 6: 217–244. 

Kelly, Austin. 2008. “Skin in the Game: Zero Downpayment Mortgage Default,” Journal of 

Housing Research 17 (2): 75–99. 

Lam, Ken, Robert M. Dunsky, and Austin Kelly. 2013. Impacts of Down Payment Underwriting 

Standards on Loan Performance: Evidence from the GSEs and FHA Portfolios. Working paper 

13–3. Washington, DC: Federal Housing Finance Agency. 

Siddiqi, Naeem. 2012. Credit Risk Scorecards: Developing and Implementing Intelligent Credit 

Scoring. Hoboken, NJ: John Wiley & Sons, Inc.

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Oxford University Press. 
33

Thomas, Lyn C., David B. Edelman, and Jonathan N. Crook. 2002. Credit Scoring and Its 

Applications. Philadelphia: Society for Industrial and Applied Mathematics. 

Vanderhoff, James. 1996. “Adjustable and Fixed Rate Mortgage Termination, Option Values 

and Local Market Condition: An Empirical Analysis,” Real Estate Economics 24 (3): 379–406. 
34

Additional Reading

Ambrose, Brent W., and Richard J. Buttimer, Jr. 2000. “Embedded Options in the Mortgage 

Contract,” The Journal of Real Estate Finance and Economics 21 (2): 95–112. 

Campbell, Tim, and J. Kimball Dietrich. 1983. “The Determinants of Default on Conventional 

Residential Mortgages,” The Journal of Finance 38 (5): 1569–1581. 

Caplin, Andrew, Charles Freeman, and Joseph Tracy. 1997. “Collateral Damage: Refinancing 

Constraints and Regional Recessions,” Journal of Money, Credit and Banking 29 (4): 497–516. 

Deng, Yongheng. 1997. “Mortgage Termination: An Empirical Hazard Model with a Stochastic 

Term Structure,” The Journal of Real Estate Finance and Economics 14 (3): 310–331. 

Dunn, Kenneth B., and Chester Spatt. 2005. “The Effect of Refinancing Costs and Market 

Imperfections on the Optimal Call Strategy and the Pricing of Debt Contracts,” Real Estate 

Economics 33 (4): 595–618. 

Elmer, Peter, and Steve Seelip. 1999. “Insolvency, Trigger Events, and Consumer Risk Posture 

in the Theory of Single-Family Mortgage Default,” Journal of Housing Research 10 (1): 1–25. 

Findley, M. Chapman, and Dennis Capozza. 1977. “The Variable Rate Mortgage: An Option 

Theory Perspective,” Journal of Money, Credit and Banking 9 (2): 356–364. 

Foster, Charles, and Robert Van Order. 1984. “An Options-Based Model of Mortgage Default,” 

Housing Finance Review 3 (4): 351–372. 

Kau, James B., Donald Keenan, and Taewon Kim. 1994. “Default Probabilities for Mortgages,” 

Journal of Urban Economics 35 (3): 278–296. 

Kau, James B., and Taewon Kim. 1994. “Waiting to Default: The Value of Delay,” Journal of 

the American Real Estate and Urban Economics Association 227: 195–207. 

Pavlov, Andrey D. 2000. “Competing Risks of Mortgage Prepayments: Who Refinances, Who 

Moves, and Who Defaults?” The Journal of Real Estate Finance and Economics 23 (2): 185–212.

Peristiani, Stavros, Paul Bennett, Gordon Monsen, Richard Peach, and Jonathan Raiff. 1997. 

“Credit, Equity, and Mortgage Refinancings,” Economic Policy Review 3 (2): 83–99. 

Phillips, Richard A., Eric Rosenblatt, and James H. Vanderhoff. 1996. “The Probability of FixedAnd Adjustable-Rate Mortgage Termination,” The Journal of Real Estate Finance and 

Economics 13 (2): 95–104. 

Quercia, Roberto G., and Michael A. Stegman. 1992. “Residential Mortgage Default: A Review 

of the Literature,” Journal of Housing Research 3 (2): 341–379. 

Quigley, John M. 1987. “Interest Rate Variations, Mortgage Prepayments, and Household 

Mobility,” The Review of Economics and Statistics 69 (4): 636–643. 

Schwartz, Eduardo, and Walter Torous. 1993. “Mortgage Prepayment and Default Decisions: A 

Poisson Regression Approach,” Journal of the American Real Estate and Urban Economics 

Association 21: 431–449. 

Von Furstenburg, George. 1969. “Default Risk on FHA-Insured Home Mortgages as a 

Function of the Terms of Financing: A Quantitative Analysis,” The Journal of Finance 24: 459–

477.
35

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 <0.01Not used in regression, but used to identify 

multiple loans

Property type 580 <0.01Used missing dummy variable

Original loan amount 619 <0.01Deleted observations with missing values 

Original property value 151,545 0.57Deleted observations with missing values 

CLTV ratio 20,545,263 77.11Imputed second lien balances

Original credit score 4,408,347 16.55Used missing dummy variable

DTI housing ratio 12,338,426 46.31Used missing dummy variable

Documentation type 6,724 0.03Used missing dummy variable

Underwriting type 3,098,767 11.63Used missing dummy variable

Teaser rate 26,579,262 99.76Not used in regression

CLTV = combined loan-to-value. DTI = debt-to-income. 
36

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% 5% 1%

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 196,638155,000 90,205,897 785,527 463,200 368,000 245,531 100,00063,00044,95021,480 (85,389)

Original property value 269,561200,000 99,999,999 1,200,000 665,000 509,000 325,000 131,00089,00070,50044,000 0

CLTV ratio 87 90 255 102 100 99 97 80 74 62 40 21

Original credit score 714 721 974 812 801 791 767 668 626 601 548 300

DTI ratio 37 37 99 99 63 52 45 26 18 13 5 1

Original term 344 360 999 381 360 360 360 360 342 180 180 1

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-toincome 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. 
37

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 0

2001 28.49 4.25 60.74 6.52 0

2002 31.99 14.90 47.13 5.99 0

2003 36.05 43.84 18.65 1.46 0

2004 46.13 45.82 7.70 0.34 0

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 0

2008 98.04 1.90 0.06 0.00 0

2009 97.40 2.60 0.00 0.00 0

2010 94.01 4.12 1.86 0.00 0

2011 96.27 2.95 0.78 0.00 0

2012 93.47 6.25 0.26 0.08 0

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-tovalue (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.
38

• 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.3

 

3 http://www.economy.com. 
39

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 servicertransfer loans were excluded from the analysis data set. 
40

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. 
41

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

Loan Percentage by Year

Origination

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 0.00

2009 97.39 2.61 0.00 0.00 0.00

2010 95.35 4.11 0.55 0.00 0.00

2011 98.27 1.23 0.50 0.00 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. 

30

40

50

60

70

80

90

100

0 10 20 30 40

Cumulative Percentage 

First Nonmissing Month

Raw Data

Raw Data after Duplication Correction
42

Appendix C. Outlier Exclusions

Table C1. Outlier Control Process

Outlier 

Condition 

for Lifetime 

Analysis

Number of 

Observatio

ns 

Excluded

Percentage Cumulative 

Percentage

Outlier 

Condition 

for 2-Year 

Analysis

Number of 

Observatio

ns 

Excluded

Percentage Cumulative 

Percentage

Any loan 

with missing 

payment 

history 

status more 

than 3 

months

4,483,989 23.46 23.46

Any loan 

with missing 

payment 

history 

status more 

than 3 

months

4,483,989 23.46 23.46

Any loan 

with original 

interest rate 

less than 

1% or more

than 25%

35 0.00 23.46

Any loan 

with original 

interest rate 

less than 

1% or more 

than 25%

35 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 

more 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 of 

more 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 

more 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 

more than 

125% or 

less than 

20%

2,547 0.01 23.86
43

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

48 0.00 23.87

Any loan 

with missing 

CLTV

48 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. 
44

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 
45

Figure D3. Diagnostics Charts for Original Term

Figure D4. Diagnostics Charts for Payment and Interest Frequency

Figure D5. Diagnostics Charts for Occupancy
46

Figure D6. Diagnostics Charts for Prepayment Penalty Clause 

Figure D7. Diagnostics Charts for Documentation

Figure D8. Diagnostics Charts for First Nonmissing Month
47

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
48

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.
49

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
50

Figure D18. Diagnostics Charts for Origination Year
51

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

0%

1%

2%

3%

4%

5%

6%

50% 70% 90% 110%

Delinquency Probability

Loan-to-Value

IS JUMBO

IS NOT JUMBO
52

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

0%

1%

1%

2%

2%

3%

3%

4%

4%

5%

5%

50% 70% 90% 110%

Delinqunecy Probability

Loan-to-Value

IS B or C

IS NOT B or C
53

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%

0%

1%

2%

3%

4%

5%

6%

50% 70% 90% 110%

Delinquency Probability

Loan-to-Value

DTI=0.18

DTI=0.35

DTI=0.42

DTI=0.5
54

Figure E7. FICO Effect on Delinquency Probability

Figure E8. HPA Effect on Delinquency Probability

HPA = house price appreciation.

0%

5%

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

0%

2%

4%

6%

8%

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
55

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
56

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