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Federal Reserve Bank of Chicago

Complex Mortgages
Gene Amromin, Jennifer Huang,
Clemens Sialm, and Edward Zhong

November 24, 2010
WP 2010-17

Complex Mortgages∗

Gene Amromin
Federal Reserve Bank of Chicago

Jennifer Huang
University of Texas at Austin

Clemens Sialm
University of Texas Austin and NBER

and Edward Zhong
University of Wisconsin-Madison

November 24, 2010

∗
We thank Ethan Cohen-Cole, Serdar Dinc, Pete Kyle, Jay Hartzell, Jeongmin Lee, Robert McDonald,
Laura Starks, Sheridan Titman, Michelle White and seminar participants at the 2010 Financial Economics and
Accounting Conference, the Federal Reserve Bank of Chicago, the University of Lausanne, the University of
Texas at Austin, and the University of Zurich for helpful comments and suggestions. Gene Amromin is at the
Federal Reserve Bank of Chicago, 230 South LaSalle Street, Chicago, IL 60604. Email: gamromin@frbchi.org;
Jennifer Huang is at the McCombs School of Business, University of Texas at Austin, Austin, TX 78712.
Email: jennifer.huang@mccombs.utexas.edu; Clemens Sialm is at the McCombs School of Business, University of Texas at Austin, Austin, TX 78712. Email: clemens.sialm@mccombs.utexas.edu; and Edward
Zhong is at the Department of Economics, University of Wisconsin-Madison, Madison, WI 53715. Email:
edzhong@gmail.com.

Complex Mortgages

Abstract
Complex mortgages became a popular borrowing instrument during the bullish housing market of the early 2000s but vanished rapidly during the subsequent downturn.
These non-traditional loans (interest only, negative amortization, and teaser mortgages)
enable households to postpone loan repayment compared to traditional mortgages and
hence relax borrowing constraints. At the same time, they increase household leverage
and heighten dependence on mortgage reﬁnancing to escape changes in contract terms.
We document that complex mortgages were chosen by prime borrowers with high income
levels seeking to purchase expensive houses relative to their incomes. Borrowers with
complex mortgages experience substantially higher ex post default rates than borrowers
with traditional mortgages with similar characteristics.

“The availability of these alternative mortgage products
proved to be quite important, and, as many have recognized,
is likely a key explanation of the housing bubble.”
–Ben S. Bernanke

Introduction

Over the last decade, the residential mortgage market has experienced a signiﬁcant increase
in product complexity, followed by a rapid reversion back to simple products. In this paper,
we study the mortgage contract choice of individual households and their subsequent default
behavior.
The menu of household mortgage choices in the United States was dominated for decades by
fully-amortizing long-term ﬁxed rate mortgages (FRM) and, to a lesser extent, by adjustable
rate mortgages (ARM) that locked in the initial interest rate for the ﬁrst ﬁve to seven years of
the contract. From the vantage point of the borrower, FRM contracts preserve contract terms
established at origination for the lifetime of the loan. For practical purposes, the same can
be said of the prevailing ARM contracts, given the average borrower tenure at a particular
house of about seven years. Knowing the monthly servicing costs and amortization schedules
simpliﬁes the household budgeting problem.
The mortgage market has experienced a signiﬁcant increase in product complexity in the
early 2000s. The products that gained prominence during the period of rapid house price
appreciation featured zero or negative amortization, short interest rate reset periods, and very
low introductory teaser interest rates. We term these “complex mortgages” (CM). Figure 1
shows the proportion of ﬁxed rate, adjustable rate, and complex mortgage products originated
over the period between 1995 and 2009, as reported by LPS Applied Analytics (our primary
data source described in detail below). The share of complex products in the U.S. remained

below 2% until the second half of 2003 before jumping to about 30% of mortgage originations
just two years later. In some geographic areas complex mortgages accounted for more than
50% of mortgage originations. The complex products faded almost as quickly, declining to
less than 2% of originations in 2008.
Complex mortgages appear to be at the core of the recent rise and decline in housing
prices. To obtain an impression of the relation between risk levels and mortgage complexity,
we aggregate the loan-level data into 366 Metropolitan Statistical Areas (MSAs) and then
sort all MSAs into quintiles according to the proportion of complex mortgage loans in 2004 –
the ﬁrst year of substantial originations of complex loans. Figure 2 summarizes the average
quarterly changes in house prices for the bottom, the middle, and the top MSA quintiles.
We observe that MSAs in the top complexity quintile experience stronger house appreciation
before 2006 and faster depreciation after 2006. This result provides an indication that house
price changes were more pronounced in MSAs with high proportion of complex loans. It also
suggests the importance of understanding the reasons for CM usage and the drivers of their
eventual performance.
The deﬁning feature of complex mortgages is the deferral of principal repayment. As a
result, complex mortgages are characterized by low mortgage payments during the ﬁrst few
years of the contract, which relaxes household liquidity and borrowing constraints and enables
households to take large exposures in housing assets. The lack of mortgage amortization
inevitably produces two eﬀects: a higher loan-to-value (LTV) ratio for any given path of
house prices and a greater reliance on reﬁnancing to escape increases in payments once a
contract enters the amortization phase.
Complex mortgages can be optimal borrowing instruments if households expect their income levels or housing prices to increase over time, as discussed by Piskorski and Tchistyi
(2010). They can also be optimal instruments for lenders concerned with their exposure in
2

an asset bubble environment (Barlevy and Fisher (2010)). In addition, complex mortgages
might also be rationally chosen by households that exhibit relatively high labor income risk
and live in areas with volatile house prices. These households have an incentive to minimize
the initial mortgage payments and to keep the mortgage balance relatively high because they
have the option to default in case of adverse income and house price shocks. These incentives
to rationally default should be particularly pronounced in non-recourse states, where lenders
do not have access to the non-collateralized assets of households in case of delinquency. In
this case, complex mortgages should be a hallmark of sophisticated borrowers keenly aware
of the value of the default option.
On the other hand, the low initial payments of complex mortgages might obfuscate the
long-term borrowing costs for households, as suggested by Carlin (2009) and Carlin and Manso
(2010). Lenders might have an incentive to introduce complex products to hide the actual
fees embedded in ﬁnancial products. Whereas it is relatively easy for a household to compare
the costs of plain-vanilla ﬁxed rate mortgages across diﬀerent lenders, it is more diﬃcult to
compare complex loans that often include intricate reset schedules, prepayment penalties, and
short-lived teaser interest rates. Lenders might be particularly eager to oﬀer these products
if they are conﬁdent that they can securitize these loans. In this case, we should observe
that complex mortgages are taken out primarily by unsophisticated investors that do not
understand the speciﬁc features of their mortgage contracts.
To study the mortgage choices of households and the default experiences, we make extensive use of the LPS Analytics data. The database, described in detail in Section 2, contains
loan level information for a large sample of mortgages in the United States. Of particular
relevance for our analysis is the ability to identify precise contract terms, both at the time of
origination and over the lifetime of the loan.
Our main result indicates that complex mortgages are taken out by well-educated house3

holds with relatively high income levels and with prime credit scores. We ﬁnd that households borrowing complex mortgages earn signiﬁcantly higher annual incomes ($141,998) than
households borrowing ﬁxed rate mortgages ($88,642) or adjustable rates mortgages ($101,005).
Furthermore, only 7% of borrowers using complex loans have credit scores below 620 (commonly considered subprime credit scores), whereas 10% of ﬁxed rate borrowers and 23% of
adjustable rate borrowers fall into this subprime category. We also ﬁnd that a higher proportion of the population in neighborhoods with a high propensity of complex loans tend to
have a college degree. Finally, complex loans are more prevalent in non-recourse states, where
non-collateralized assets of the households are protected. Thus, these results indicate that
complex loans are not primarily originated to naive households that are fooled by lenders into
inappropriate mortgage contracts.
Nonetheless, these households are stretching to purchase more expensive houses relative to
their incomes, as indicated by their higher value-to-income (VTI) ratios. Higher VTI ratios
are associated with greater propensity to use complex contracts even after controlling for
MSA-level income and VTI measures. This suggests that at least a part of the relationship is
due to households using complex mortgages to get more expensive houses within high housing
price areas. We also ﬁnd that areas with higher past house price appreciation and higher
population growth have more complex mortgages, whereas areas that experienced sustained
house price decreases in the past ten years have fewer complex mortgages. This evidence
suggests that the expectation of continued house price appreciation is a likely driving force
behind the popularity of complex mortgages.
Next, we study the default behavior of borrowers of complex mortgages. The focus on
initial loan aﬀordability might motivate households to borrow too extensively and to underestimate reﬁnancing risk, which is exacerbated by historically short reset periods and recasting
of negative amortization loans. After controlling for observable characteristics that include
4

the FICO credit score and income, we ﬁnd that households with complex mortgages are more
likely to default. This holds true after the set of controls is expanded to include time-varying
loan-to-value ratios, which suggests that higher CM defaults are not due exclusively to higher
ex post leverage. Since complex mortgages typically have lower monthly payments relative
to their ﬁxed rate counterparts during the ﬁrst years after origination, the higher default
rates suggest that either CM households are more likely to default strategically, or that these
households have more volatile income streams. Overall, our ﬁndings suggest that in addition
to the well-documented impact of subprime mortgages, households with complex mortgages
might be a signiﬁcant driving force behind the mounting defaults during the recent crisis.
While the extension of credit to subprime borrowers and mortgage securitization has received much attention following the ﬁnancial crisis of 2007-2009, the choice and impact of
mortgage complexity remains largely unexplored. Mian and Suﬁ (2009) show that the sharp
increase in mortgage defaults in 2007 is signiﬁcantly ampliﬁed in geographic areas with a high
density of subprime loans that experienced an unprecedented growth in mortgage credit prior
to 2007. Keys, Mukherjee, Seru, and Vig (2010) focus on the role of mortgage securitization
process, ﬁnding that securitization lowered the screening incentives of loan originators for their
subprime borrowers. Jiang, Nelson, and Vytlacil (2010b) study the relation between mortgage
securitization and loan performance and ﬁnd that the lender applies lower screening eﬀorts
on loans that have higher ex ante probabilities of being securitized.1 Our paper contributes
to this literature by suggesting an additional and important channel linking mortgage market
1

Additional papers on securitization and the expansion of credit to subprime borrowers include Adelino,
Gerardi, and Willen (2009), Bond, Musto, and Yilmaz (2009), Keys, Mukherjee, Seru, and Vig (2009), Loutskina and Strahan (2009), Mayer, Pence, and Sherlund (2009), Stanton and Wallace (2009), Agarwal, Ambrose,
Chomsisengphet, and Sanders (2010), Bajari, Chu, and Park (2010), Barlevy and Fisher (2010), Berndt, Holliﬁeld, and Sandas (2010), Campbell, Giglio, and Pathak (2010), Corbae and Quintin (2010), Demyanyk and
Hemert (2010), Garmaise (2010), Gerardi, Rosen, and Willen (2010), Glaeser, Gottleb, and Gyourko (2010),
Goetzmann, Peng, and Yen (2010), Jiang, Nelson, and Vytlacil (2010a), Piskorski, Seru, and Vig (2010),
Purnanandam (2010), Rajan, Seru, and Vig (2010), Stanton and Wallace (2010), and Woodward and Hall
(2010).

innovations to the ﬁnancial crisis of 2007-2009.
A few recent papers have investigated the role of non-traditional mortgage contracts in the
recent crisis. Piskorski and Tchistyi (2010) study optimal mortgage design in an environment
with risky privately observable income and costly foreclosure and show that the features of the
optimal mortgage contract are consistent with an option adjustable rate mortgage contract.
Corbae and Quintin (2010) present a model where heterogeneous households select from a set
of mortgage contracts and have a choice of defaulting on their payments. Using their model,
they ﬁnd that the presence of subprime mortgages with low down payments substantially
ampliﬁes foreclosure rates in the presence of a large exogenous shock to house prices. In a
contemporaneous paper, Barlevy and Fisher (2010) describe a rational expectations model in
which both speculators and their lenders use interest-only mortgages when there is a bubble
in house prices. They provide evidence that interest only mortgages were used extensively in
cities where inelastic housing supply enables pronounced boom-bust cycles. Our paper studies
empirically the characteristics and the default experiences of borrowers of complex loans.
The remainder of this paper is structured as follows. Section 2 describes our data sources
and reports summary statistics. In Section 3 we study the mortgage choice of households and
describe the main features of mortgage contracts. In Section 4 we study the delinquency of
diﬀerent contract types.

Data Sources and Summary Statistics

Our study relies on several complementary data sources that cover various aspects of the housing market during the period between 2003 and 2007. In particular, the micro level analysis
of mortgage contract choice and performance relies heavily on the proprietary mortgage-level
database oﬀered by Lender Processing Services (LPS) Applied Analytics (formerly known as
McDash Analytics). LPS collects data from some of the nation’s largest mortgage servicers
6

that report contract and borrower details at the time of loan origination, as well as monthly
information on mortgage performance. The LPS data coverage has grown steadily over time,
with 9 out of 10 largest servicers reporting to the database by 2003. Our database covers
about 10 million mortgages with a total loan value of more than $2 trillion between 2003 and
2007.
For the purposes of our study, the availability of granular information on mortgage contract
terms is of particular importance. For each of the loans, LPS provides information on the
loan interest rate, the amortization schedule, and the securitization status. For adjustable rate
mortgages (ARMs), we know the rate at origination, the frequency of resets, the reference rate,
and the associated contractual spread. For loans that do not amortize steadily over their term,
we know the horizon of the interest-only period, whether negative amortization is allowed and
if so, to what extent and over what period of time. This information allows us to precisely
categorize loan contracts.
The LPS data also contains key information on borrower and property characteristics
at the time of origination. These include the appraised property value, the loan-to-value
ratio (LTV), property type (single family or condominium), whether the property was to be
occupied by the borrower, and the borrower’s creditworthiness as measured by their FICO
(Fair Isaac Corporation) credit score.2
An important feature of the LPS database is that unlike some other data sources, it is
not limited to a particular subset of the loan universe. The LPS data cover prime, subprime,
and Alt-A loans,3 and include loans that are privately securitized, those that are sold to
2

As Bajari, Chu, and Park (2010) emphasize, an important feature of the FICO score is that it measures
a borrower’s creditworthiness prior to taking out the mortgage. FICO scores range between 300 and 850
Typically, a FICO score above 800 is considered very good, while a score below 620 is considered poor. As
reported on the Fair Isaac Corporation website (www.myﬁco.com), borrowers with FICO scores above 760 are
able to take out 30-year ﬁxed rate mortgages at interest rates that are 160 basis points lower, on average, than
those available for borrowers with scores in the 620-639 range.
3

Alt-A loans are a middle category of loans, more risky than prime and less risky than subprime. They

Government Sponsored Enterprises (GSEs), and loans that held on banks’ balance sheets.
Although this allows for a broad set of mortgage contracts, the coverage is somewhat skewed
in favor of securitized loans that are more likely to be serviced by large corporations reporting
to LPS. The relative scarcity of portfolio loans is relevant to us since some of the contracts
of interest, such as option ARMs, are commonly held in lenders’ portfolios. Still, the large
overall size of the data ensures that we have ample coverage of all contract types.
We complement borrower information in LPS with household income data collected under
the Home Mortgage Disclosure Act (HMDA). Doing so allows us to compute some of the key
measures of loan aﬀordability, such as the ratio of house value to income (VTI). We further
augment the loan-level data with information on trends in local home prices. Quarterly data
on home prices is available by metropolitan statistical area (MSA) from the Federal Housing
Finance Agency (FHFA)-an independent federal agency that is the successor to the Oﬃce
of Federal Housing Enterprise Oversight (OFHEO) and other government entities.4 We use
the FHFA House Price Index (HPI) including all transactions that is based on repeat sales
information. We use a house price index to construct borrower-speciﬁc variables on cumulative
growth in local house prices.
At the more aggregate level, we utilize zip code level information from the 2000 U.S.
Census to control for broad demographic characteristics, such as education levels. We also
make use of the annual per capita income and unemployment rate data at the MSA level from
the Bureau of Economic Analysis (BEA).
are generally made to borrowers with good credit scores, but the loans have characteristics that make them
ineligible to be sold to the GSEs-for example, limited documentation of the income or assets of the borrower
or higher loan-to-value ratios than those speciﬁed by GSE limits.
4
As part of the Housing and Economic Recovery Act of 2008 (HERA), the Federal Housing Finance
Regulatory Reform Act of 2008 established a single regulator, the FHFA, for GSEs involved in the home
mortgage market, namely, Fannie Mae, Freddie Mac, and the 12 Federal Home Loan Banks. The FHFA
was formed by a merger of the Oﬃce of Federal Housing Enterprise Oversight (OFHEO), the Federal Housing
Finance Board (FHFB), and the U.S. Department of Housing and Urban Development’s government-sponsored
enterprise mission team (see www.fhfa.gov for additional details).

To determine whether lender recourse has an impact on mortgage choices and mortgage
defaults we follow Ghent and Kudlyak (2010) and classify U.S. states as recourse or nonrecourse states. In non-recourse states, recourse in residential mortgages is limited to the
value of the collateral securing the loan. On the other hand, in recourse states the lender may
be able to collect on debt not covered by the proceedings from a foreclosure sale by obtaining
a deﬁciency judgment.5
The summary statistics on these variables are presented in Table 1 and we will discuss
diﬀerences in these variables across mortgage types in more detail in Section 3.2. All of the
variables discussed above are summarized in Table 9.

Mortgage Choice

This section describes in detail the diﬀerences in characteristics of the main mortgage contracts
oﬀered in the U.S. during the last decade and the determinants of the mortgage choice.

3.1

Mortgage Contract Design

In this section we illustrate the diﬀerent payment patterns of some popular U.S. mortgage
contracts. We classify all mortgage products into three groups: (1) Fixed Rate Mortgages
(FRM); (2) Adjustable Rate Mortgages (ARM); and (3) Complex Mortgages (CM).6
Fixed rate mortgages are level-payment fully-amortizing loans with maturities that generally last for 15 or 30 years. For example, a household borrowing $500,000 on a 30-year ﬁxed
rate mortgage with a 5% interest rate will be required to make equal monthly payments of
$2,684 for 360 months. After 30 years the mortgage will be paid oﬀ completely. Borrowers
5

Ghent and Kudlyak (2010) classify the following states as non-recourse: Alaska, Arizona, California, Iowa,
Minnesota, Montana, North Dakota, Oregon, Washington, and Wisconsin.
6

Additional information on various mortgage contracts can be obtained from the website of Jack M. Guttentag at http://www.mtgprofessor.com.

generally have the option to prepay the mortgage if they sell the property or if they reﬁnance
their loan due to a decrease in mortgage interest rates.
Adjustable rate mortgages are fully-amortizing loans where the interest rate changes after
an initial period according to a preselected interest rate index. The initial period with a
ﬁxed interest rate typically lasts between two and seven years. The mortgages exhibit caps
and ﬂoors that prevent the interest rates from changing too much over the lifetime of the
loan. Interest rates on ARMs generally are lower than those on FRMs due to the increasing
term structure of interest rates and the availability of the prepayment option in FRMs.7 For
example, a 5/1 ARM with a 30-year maturity, a $500,000 initial balance, and a 4.5% initial
interest rate will have initial mortgage payments of $2,533 per month for the ﬁrst 60 months.
Subsequently, the payments can increase or decrease depending on the level of interest rates.
If the interest rate increases to 7%, then the monthly payment in the sixth year will increase
to $3,221.8
Complex mortgages include a variety of back-loaded mortgage contracts. Most complex
mortgages are adjustable rate mortgages and exhibit time-varying payments. The most popular contract is an Interest Only (IO) mortgage. IO borrowers only need to pay the mortgage
interest for an initial time period that typically lasts between ﬁve and ten years. Subsequently,
the mortgage becomes a fully-amortizing loan. For example, a 5-year IO adjustable rate loan
with a 30-year maturity, a $500,000 initial balance, and a 4.5% initial interest rate will have
initial mortgage payments of $1,875 per month for the ﬁrst 60 months. Subsequently, the
payments reset according to the future interest rates. If the interest rate increases to 7%,
7

Fixed rate mortgages can be reﬁnanced when interest rates decrease, which is a very valuable option that
is priced in the initial interest rate. There are numerous papers on prepayments. See for example, Dunn and
McConnell (1981), Schwartz and Torous (1989), Stanton (1995), Dunn and Spatt (1999), Longstaﬀ (2005),
Campbell (2006), Amromin, Huang, and Sialm (2007), Gabaix, Krishnamurthy, and Vigneron (2007), and
Schwartz (2007).
8

Several papers study the tradeoﬀ between FRMs and ARMs (e.g., Campbell and Cocco (2003), Vickery
(2007), and Koijen, Van Hemert, and Van Nieuwerburgh (2009)).

then the monthly payment in the sixth year will almost double to $3,534. Even if interest
rates remain at 4.5%, the mortgage payment will increase to $2,779 per month at the end of
the initial interest-only period. The payments increase even more for mortgages with longer
interest-only periods.
A second type of a complex mortgage is a Negative Amortization Mortgage (NEGAM),
such as an Option ARM. These mortgages give borrowers the option to initially pay even
less than the interest due. The diﬀerence between the interest due and the actual mortgage
payment is added to the loan balance. These mortgages carry the risk of larger increases
in mortgage payments, when the mortgage is recast to become a fully amortizing loan after
5-10 years or when the loan balance exceeds the initial balance at origination by more than a
certain amount (typically 10-25%).
Finally, a third type of a complex mortgage is a Teaser Rate Mortgage (TRM). For TRMs,
the initial interest rate is signiﬁcantly below the fully indexed rate. Teaser rate loans typically
charge investors interest rates of between 1-2% during the ﬁrst 1-12 months. Most teaser rate
mortgages also feature negative amortization.
In sum, complex mortgages are back-loaded products with limited amortization during
the ﬁrst years after origination. As mentioned in the introduction, complex mortgages can
be optimal if households expect their income levels or housing prices to increase over time
(Piskorski and Tchistyi (2010)). However, the low initial payments of complex mortgages
also carry a number of risks, from obfuscating the long-term borrowing costs of households
( Carlin (2009), Carlin and Manso (2010)) to greater reliance on reﬁnancing to avoid increases
in payments. This obfuscation might be particularly pronounced for teaser rate mortgages,
whose low payments only apply for a relatively short initial period.

3.2

Summary Statistics by Mortgage Type

Table 2 reports statistics for our broad mortgage categories – fully-amortizing ﬁxed rate
(FRM), fully-amortizing adjustable rate (ARM) and complex (CM) mortgage types. Our
data contain in excess of 10 million loan contracts originated between 2003 and 2007. In
our sample, 69 percent of mortgages are ﬁxed rate mortgages, 12 percent are adjustable rate
mortgages, and the remaining 19 percent are complex mortgages.
Complex mortgages, on average, are associated with higher loan amounts relative to the
traditional ARM and FRM mortgages, and are used to ﬁnance more expensive houses. For
example, the average home value for complex loans is $513,728, whereas the average home
values for FRMs and ARMs are $264,878 and $309,465, respectively. Counter to some of the
commonly made assertions about complex mortgages, they are extended to borrowers with
high income levels. Indeed, the mean income of a complex mortgage borrower is about 60%
higher than that of a borrower with a traditional plain-vanilla ﬁxed rate mortgage.
Nevertheless, the average ratio of house value to income (VTI) – a measure of aﬀordability
– is considerably higher in complex mortgage contracts, suggesting that complex mortgage
borrowers are purchasing more expensive houses relative to their income. Yet, this higher
spending on houses is not reﬂected in the loan-to-value (LTV) ratio, as all mortgage types
have similar ﬁrst lien LTV values.9 Panel A of Figure 3 depicts the cumulative distribution
function of the VTI ratio for borrowers with diﬀerent mortgage contracts. The ﬁgure indicates
that CM borrowers tend to have substantially higher VTI ratios than both ARM and FRM
borrowers. Median households using FRMs, ARMs, and CMs have value-to-income ratios
of 3.0, 3.1, and 3.7, respectively. Put diﬀerently, for a given level of income CM borrowers
9
LPS data is collected at the loan and not property level, which limits one’s ability to construct an accurate
estimate of the total debt secured by the house. In particular, we are unable to account for second-lien
mortgages loans (the so-called “piggyback loans”) used to ﬁnance the house. Primarily for this reason, we do
not emphasize the importance of LTV in our empirical analysis and instead focus on the VTI ratio.

purchased houses valued at about 20% more. The lower initial payments on complex mortgages
thus appear to enable households to purchase expensive homes relative to their income levels.
We also ﬁnd that borrowers of complex mortgages have better credit scores than ARM
borrowers and similar credit scores as FRM borrowers. Whereas 23% of ARM borrowers
have FICO credit scores below 620, the same can be said of only 10% of FRM and 7%
of CM borrowers. Panel B of Figure 3 summarizes the entire distribution of FICO scores
for diﬀerent mortgage contracts. Whereas many borrowers using ARMs tend to have subprime credit scores, the credit quality of borrowers using CMs is fairly similar to that of the
FRM borrowers. These results emphasize that the clientele for complex mortgages diﬀers
signiﬁcantly from that for subprime loans.
Several other loan characteristics are diﬀerent for complex mortgages. CM borrowers are
more likely to live in a condominium and are slightly more likely to use the property they
are ﬁnancing for investment purposes. We also ﬁnd signiﬁcant diﬀerences in the frequency of
prepayment penalties across mortgage types. Unlike FRMs, a signiﬁcant fraction of ARMs
and CMs face penalties if the loans are prepaid within the ﬁrst two or three years. Around
40% of the mortgages in our sample are from reﬁnancing transactions, whereas the remaining
proportion is from new home purchases. Complex mortgages have a slightly higher share of
reﬁnancings compared to new purchases.
Since complex loans are particularly popular for expensive homes, they are also more likely
to exceed the conforming loan limit (i.e be jumbo loans). Hence, although 79% of FRMs are
securitized by government-sponsored enterprises (GSEs, such as Fannie Mae, Freddie Mac,
amd Ginnie Mae), only 24% of CMs go through the GSEs. Private securitization partially
oﬀsets the lack of GSE involvement in the ARM and CM markets.
Complex mortgage borrowers receive signiﬁcantly lower initial interest rates than FRM or
ARM borrowers. The mean initial interest rate on complex mortgages of 5.12% is signiﬁcantly
13

lower than the rates on FRMs (6.16%) and ARMs (5.97%). This result is primarily caused
by teaser rate mortgages that charge, on average, an initial interest rate of only 1.30%. For
each ARM and CM loan we impute the rate such borrowers might have received had they
chosen a conventional 30-year ﬁxed rate mortgage instead. We deﬁne such hypothetical rate
as the average interest rate on all 30 year FRMs originated in the same month, state, with
similar loan size (whether or not above the conforming limit), LTV ratio, and FICO score.
The hypothetical FRM interest rate is similar across the various contracts.
Whereas the variables above are available at the loan level, we also report some additional
variables observed at the MSA or the state level. We ﬁnd that CM borrowers tend to live in
cities with higher income levels and with higher VTI ratios. Thus, some of the variation in
income levels and VTI ratios is driven by diﬀerences in these characteristics across cities.
From a spatial standpoint, complex mortgages are more common in geographic areas that
experienced high house price appreciation. The average 3-year cumulative price appreciation
among complex borrowers amounted to a staggering 44%, as compared with 30% among
traditional FRM borrowers. We also document that only 12% of complex mortgages were
originated in areas that had experienced four quarters of declines in house prices over the
preceding 10 years, as opposed to 13% of FRMs and 16% of ARMs.
Unfortunately, we do not observe the education level of borrowers directly. However, we
can compute the proportion of people in zip codes with a college education. Households
using complex mortgages tend to live in areas with a higher proportion of college graduates.
Finally, the population growth rate and the unemployment rate, which capture macroeconomic
conditions at the MSA level, are similar in areas with diﬀerent mortgage compositions.
Complex mortgages were substantially more popular in non-recourse states, where the
lender cannot access assets of the defaulting households beyond the value of the collateral
securing the loan. Whereas only 22% of FRMs are in non-recourse states, 44% of CMs are
14

originated in such states.
Table 3 breaks out the key summary characteristics among diﬀerent complex mortgage
types. Teaser loans, on average, appear to be used to ﬁnance more expensive homes and are
associated with higher loan values. They also display the highest VTI ratios. It is worth
noting that few of the teaser contracts are oﬀered to subprime borrowers. As expected,
teaser loans commonly carry prepayment penalties. Finally, even among complex products,
teaser loans are taken out in areas with higher house price appreciation, often to reﬁnance
an existing mortgage obligation. Finally, IO contracts appear to have been subject to stricter
underwriting criteria. Whereas only 11% of IOs were underwritten on the basis of less than
full documentation, more than 40% of NEGAM and TRM loans were issued in this manner.

3.3

Geographic Distribution of Mortgages

Figure 4 shows the concentration of complex mortgages in diﬀerent counties across the United
States in 2002, 2005, and 2008. Consistent with Figure 1, we ﬁnd that complex mortgages were
fairly uncommon in 2002. The distribution of complex mortgages looks dramatically diﬀerent
in 2005, when multiple counties in California, Colorado, Florida, and Nevada had CM shares
in excess of 40%. In some zip codes in these states more than half of mortgage originations
were complex loans. While this pattern looks suggestive, numerous areas with high house
price appreciation had few complex mortgages even at the peak of the housing boom. For
example, CM contracts accounted for only about 5% of loans in the Albany, NY metropolitan
area where house prices rose by more than 80% between 2001 and 2007. In contrast, CMs
proved to be very popular in the Detroit MSA, where nominal house prices remained ﬂat
during this period. It is also worth noting that in some areas rapid price increases preceded

the surge in CM contracts, whereas other areas had the opposite relationship.10

3.4

Aﬀordability of Diﬀerent Mortgage Contracts

Complex mortgage products have relatively low payments during their ﬁrst years and thereby
enable households to purchase more expensive homes. Figure 5 depicts the ratio between
the monthly payments of ARMs and CMs relative to fully-amortizing FRMs originated in
the same month for borrowers with similar characteristics (i.e., loans originated in the same
states with similar FICO scores and loan-to-value ratios). We observe that 64.5% of ARMs
and 85.6% of CMs have payments that are less than those of comparable FRMs during the
ﬁrst year. Furthermore, 9.0% of ARMs and 49.8% of CMs have payments that are more than
20% lower. Panels B and C show that the payments on the vast majority of CMs remain
lower than those on FRMs even three or ﬁve years after the origination. For example, we
ﬁnd that ﬁve years after origination the payment ratio is less than one for 87.6% of CMs, and
less than 0.8 for 62.5% of CMs. Thus, a relatively small fraction of complex mortgages have
substantial resets of mortgage payments during the ﬁrst ﬁve years that cannot be managed
by reﬁnancing into a new contract.11 This result indicates that CM borrowers continued to
have relatively low payments throughout the mortgage crisis of 2007-2009. Mortgage defaults
during the crisis would likely have been signiﬁcantly higher if complex mortgages had reset
their minimum payments after a shorter introductory time period.
The ﬁnding that ARMs and CMs payments were lower than those for comparable FRMs for
an extended period of time can be explained by several factors. First, short-term interest rates
have decreased over our sample period thereby reducing the payments on ARMs and CMs,
10
Granger causality tests carried out at the MSA level present mixed evidence of the relationship between
changes in house prices and CM shares. The results are also highly sensitive to the choice of evaluation period.
This subject is discussed in greater detail in a concurrent paper by Barlevy and Fisher (2010).
11
Unfortunately we do not have suﬃciently long time series available to study the resets in more detail since
most of the complex mortgages in our sample are originated between 2004 and 2006.

which are generally tied to such rates. Second, Figure 5 only shows the payments of mortgages
that survived and were not previously reﬁnanced. Households that obtain mortgages with
lower interest rates and lower total payments are less likely to reﬁnance a loan, resulting in a
tendency of the actual payments on surviving ARMs and CMs to decrease over time relative
to the FRMs.
By virtue of their amortization structure, complex loans largely maintain a high leverage
ratio over time. Figure 6 depicts the distribution of the remaining mortgage balance one, three,
and ﬁve years after mortgage origination relative to the original balance for the three mortgage
contract types. Even ﬁve years after origination (Panel C) around 51% of complex mortgages
are within 2.5% of their initial loan balance and around 16% of borrowers increased their loan
balance by more than 2.5%. This creates a sharp contrast with FRM and ARM borrowers
who gradually pay down their mortgages. Thus, CM borrowers tend to keep substantially
higher debt levels than households with more traditional mortgage products. This makes
CM borrowers more susceptible to economic shocks. This dynamic deterioration in relative
leverage ratios becomes particularly dramatic in the event of slower house price appreciation,
as experienced during the housing crisis of 2007-2009.12

3.5

Determinants of Mortgage Choice

In this section we analyze the determinants of mortgage choice more systematically. In particular, we estimate the likelihood of selection of a particular mortgage contract type (ARM
or CM) relative to a baseline contract, which we take to be an FRM. These relative likelihoods are estimated as a function of loan- and borrower-level covariates, as well as MSA-level
12
The higher long-term loan-to-value ratios of complex loans may have contributed to a further deterioration
in housing markets, as suggested by the leverage eﬀect of Stein (1995) and Lamont and Stein (1999). Additional
papers that study the macro-economic aspects of housing prices include Lustig and Van Nieuwerburgh (2005),
Ortalo-Magne and Rady (2006), Piazzesi, Schneider, and Tuzel (2007), Brunnermeier and Julliard (2008),
Favilukis, Ludvigson, and Van Nieuwerburgh (2010), Landvoigt, Piazzesi, and Schneider (2010), and Van
Nieuwerburgh and Weill (2010).

aggregates. Formally, we use maximum likelihood to estimate the following multinomial logit
regressions:
P rob(Yi = m)
State
Y ear
= eβm Xi +F Ei +F Ei + i ,
P rob(Yi = F RM)

(1)

where P rob(Yi = m)/P rob(Yi = F RM) is probability of obtaining an ARM or CM relative
to a FRM, X is a vector of mortgage-speciﬁc covariates, F E Y ear are indicator variables for
the origination years, and F E State are geographic indicator variables.
Table 4 reports the estimated coeﬃcients. The ﬁrst two columns use only individual
household level characteristics to explain the mortgage choice and the last two columns include
MSA level aggregates and state ﬁxed eﬀects. All regressions include time ﬁxed eﬀects and
the standard errors are clustered by MSA. Since some of the MSA level variables are not
available for the full sample, the corresponding speciﬁcations include fewer observations than
the overall sample summarized in Table 2.
We ﬁnd that households with higher income levels are signiﬁcantly more likely to obtain
a complex mortgage than to take out a more traditional FRM loan. Despite their higher
income, these households are stretching to purchase more expensive homes, as indicated by
their higher estimated coeﬃcients on value-to-income (VTI) ratios. Although ARM loans are
also more likely in higher VTI transactions, the economic eﬀect of VTI is stronger for CM
contracts. Households with lower FICO scores are signiﬁcantly more likely to choose an ARM
or a CM contract, although the coeﬃcient estimate is substantially smaller for CMs than for
ARMs.
The theme of complex mortgages as “aﬀordability products” for households with preferences for relatively expensive homes relative to their incomes is reﬂected in several other
coeﬃcients. For instance, we ﬁnd that CM contracts are much more prevalent for mortgages

above the GSE conforming loan limit. Such mortgages are subject to the so-called jumbo
spread, which increases the relative appeal of payment-shrinking CM products. Most strikingly, however, CM borrowers are much more likely to provide incomplete documentation for
their loans. The greater reliance of CM contracts on low-documentation underwriting is consistent with borrower eﬀort to inﬂate their income to qualify for a higher loan amount needed
for an expensive house. Overall, there is little evidence that a typical complex mortgage is
taken out by a relatively poor and naive household.
We ﬁnd that the type of property has an impact on mortgage contract choice. Mortgages
used to ﬁnance condominiums and investment properties are more likely to be ARMs or
CMs. Complex mortgages might be particularly attractive for such types of properties, since
owners of condominiums and investment properties have potentially fewer indirect costs of
strategically defaulting on their properties. They might therefore have an incentive to pay
down their mortgage balance relatively slowly to increase the option value of strategic default.
We also ﬁnd that households in non-recourse states are signiﬁcantly more likely to obtain
a complex mortgage than households in recourse states. This might also be caused by the
higher option value of defaulting in non-recourse states. Households in such states have smaller
incentives to pay down their mortgages as they can simply walk away in case of default without
worrying about the lender accessing their other assets. However, it is interesting that lenders
did not curtail to a more signiﬁcant degree the prevalence of complex loans in non-recourse
states.
It is possible that the positive association between CM contract choice and both VTI and
income reﬂects the propensity of CMs to be concentrated in high income and high house price
MSAs. However, speciﬁcations that incorporate MSA-level controls and state ﬁxed eﬀects
preserve these relationships. Although some of the coeﬃcients are attenuated in those speciﬁcations, they remain highly signiﬁcant. This suggests that within individual geographies,
19

complex mortgage choice is favored by the relatively well-oﬀ that are stretching their budget
ﬂow constraints to aﬀord more expensive houses.
Complex mortgages are backloaded contracts in which reduced mortgage payments are
followed by higher payments needed to catch up on the delayed principal repayment. There
are several explanations justifying this preference for an increasing payment path. First,
individual households might anticipate future income growth, due either to favorable local
economic conditions or to their personal wage proﬁle, especially for younger households. For
these households it makes sense to purchase expensive homes relative to their incomes under
the permanent income hypothesis (Gerardi, Rosen, and Willen (2010) and Cocco (2010)).
Second, households might expect house prices to appreciate in the future, which enables them
to reﬁnance their loans to meet the higher future payments (Barlevy and Fisher (2010)). Third,
the popularity of these backloaded products might be an outcome of lax lending standards
due to agency issues, in which lenders care only about the fees generated from originating the
loans and not about future defaults when they sell the loans via securitization (Carlin (2009),
Keys, Mukherjee, Seru, and Vig (2010) and Jiang, Nelson, and Vytlacil (2010a)).
We cannot perfectly separate these three explanations. However, results in Table 4 shed
some light on their relative importance in the choice of mortgage contracts. Since we cannot
observe household expectations for their income and house price growth, we use the prior three
years’ house price appreciation and an indicator variable for whether the area experienced
an annual decline over the prior ten years as proxies for expected income and house price
growth rates. These two variables capture the extent to which households extrapolate past
local experiences to build their expectations about future house price dynamics. Borrowers
and lenders in areas which experienced a recent decline in house prices might have been
more cautious in choosing instruments that exhibit low or even negative amortization. On
the other hand, borrowers and lenders in geographic areas where appreciation was substantial
20

might have been more willing to accept non-amortizing loans if they expected the appreciation
to continue in the future. In addition, we include the prior one-year population growth rate
in the MSA as a proxy for expected income and house price growth. Geographic areas with
signiﬁcant population growth might be areas where households expect signiﬁcant house price
and income growth.
We ﬁnd that the price decline indicator variable and the population growth rate signiﬁcantly aﬀect the choice of CM. In particular, CM contracts are more popular in areas that did
not experience an annual house price decline over the prior ten years and in areas with high
population growth. This evidence suggests that the expectations of continued house price and
income growth are likely a driving force behind the popularity of complex mortgages.
Finally, if complex mortgages are aﬀected by agency conﬂicts and are pushed to naive
households to maximize the commissions for loan oﬃcers, then we might expect these loans
to be concentrated in low income areas with poorly educated households. We do not ﬁnd
support for this hypothesis. Cities with lower proportions of college educated households and
with lower median incomes do not exhibit higher proportions of complex loans.
Table 5 reports the coeﬃcients of multinomial logit regressions that further diﬀerentiate
between various types of complex contracts. The estimates are consistent with the univariate
results in Table 2. In particular, we see that NEGAM and especially TRM contracts were
used by high-income borrowers to reﬁnance their high-priced primary residences, often on the
basis of only limited income and asset documentation. It is likely that such reﬁnancings were
serial in nature, which would further underscore the fragility of such contracts in environments
where the reﬁnancing markets freeze up.

Mortgage Delinquencies

In this section we study the delinquency of diﬀerent types of mortgages. A mortgage is
delinquent if the borrower is at least 60 days late in making the mortgage payments.

4.1

Reasons for Mortgage Delinquencies

Delinquencies might diﬀer across mortgage types for various reasons. First, ARMs and CMs
are generally adjusted according to short-term interest rates and might have higher delinquency rates because their mortgage payments increase in a rising interest rate environment.
Over our sample period the interest rates have not risen substantially, suggesting that this
channel is likely not of signiﬁcant importance.
Second, CMs generally exhibit an increasing payment trend over the life of the loan since
the initial payments are not fully amortizing as described previously. Mortgage delinquencies
might become more likely after the various resets when the payments suddenly increase.
On the other hand, CMs might exhibit lower delinquency rates during the initial period
when mortgage payments are relatively low. Some complex mortgage contracts (e.g., Option
ARMs) give borrowers the ﬂexibility to adjust their mortgage payments as their income levels
ﬂuctuate, which might reduce the probability of defaults. As we observe in Figure 5, most
complex mortgages have lower mortgage payments than corresponding FRMs or ARMs over
the ﬁrst ﬁve years since origination.
Third, CMs pay down their mortgage balance at a slower rate than FRMs and ARMs
as summarized in Figure 6. Therefore, borrowers of complex loans have a bigger incentive
to default on their loans in case of cash ﬂow diﬃculties or for strategic reasons. Whereas a
borrower with a complex mortgage might just walk away from their mortgage contract if they
experience ﬁnancial diﬃculties, a borrower with a FRM or an ARM might be more likely to

sell their home since the embedded equity is higher for fully amortizing mortgage contracts.
Fourth, borrowers that are attracted to ARMs and CMs might diﬀer in their preferences.
Borrowers that are willing to bear interest-rate risk might be more risk-tolerant as shown by
Campbell and Cocco (2003). Finally, borrowers using traditional mortgage products might be
more inﬂuenced by ethical norms that motivate them to pay back their debt even if it would
be more economical to default on a mortgage contract, as discussed by Guiso, Sapienza, and
Zingales (2009).

4.2

Summary of Mortgage Delinquency

Panel A of Table 6 reports the proportion of mortgages that are delinquent after one, three,
and ﬁve years by mortgage type. We observe that FRMs have the lowest delinquency rates at
all horizons, CMs have lower delinquency rates than ARMs at a one year horizon but higher
delinquency rates at longer horizons. For example, 22.75% of CMs, 18.48% of ARMs, and
11.95% of FRMs are delinquent at a 5-year horizon. Thus, at longer horizons the probability
of delinquency increases for CMs.
Figure 7 shows the proportion of mortgage delinquencies for FRMs, ARMs, and CMs for
the ﬁrst ﬁve years after origination. In each month we depict the proportion of remaining
mortgages that become delinquent for the ﬁrst time. We observe that complex mortgages
have strictly higher delinquency rates than ﬁxed rate mortgages at all horizons. Mortgage
delinquencies of complex loans reach peaks of 1.3% and 1.2% of surviving loans after 27 and
39 months since origination. These peaks occur three months after common reset intervals,
since delinquency begins when a mortgage payment is at least 60 days late. We observe a
similar peak for ARMs after a horizon of 27 months.
Whereas ARMs have slightly higher rates of delinquency at short horizons, CMs have
substantially higher rates at longer horizons. It must be kept in mind that borrowers of
23

complex loans have relatively high delinquency propensities despite having signiﬁcantly higher
credit scores than ARM borrowers, as summarized in Table 2. It is also insightful that the
delinquency rate increases substantially even before the minimum loan payments are reset
after two or three years, indicating that some borrowers of complex loans do not even make
the relatively low initial mortgage payments.

4.3

Hazard Rate Model

To investigate the determinants of mortgage delinquencies, we run the following Cox proportional hazard model:
Y ear +F E Y ear +F E State +
t
i

h(i, t) = h0 (t)eβXi,t +F Ei

(2)

where the hazard rate h(t) is the estimated probability of ﬁrst time 60 day delinquency
at time t conditional on surviving to time t− , h0 (t) is the baseline hazard rate, X is a vector
of household-speciﬁc covariates, and F EiY ear and F EtY ear are two indicator variables for the
origination year and calendar years to control for diﬀerent vintage eﬀects and macroeconomic
conditions. In some speciﬁcations, we also include F E State to control for state ﬁxed eﬀects.
The loan sample is expanded to a loan-year level so that time-varying covariates can be included. Also, time is scaled so that the ﬁrst observation date is the calendar year of origination
(time 0), and subsequent calendar years are measured relative to the year of origination. Implicitly, loans of diﬀerent vintages are compared with each other, so that the baseline hazard
represents the probability of delinquency for a borrower with covariates of 0 at t years after
origination. In some speciﬁcation we split up complex mortgages into the three sub-types (IO,
NEGAM, and TRM).
Table 7 reports the estimated coeﬃcients of the propensity of ﬁrst time 60 day delinquency,
24

so that the change in probability of delinquency can be read as odds ratios. For example, in
column 1, the coeﬃcient of 0.792 for CM means that the ratio of the probability of delinquency
for a borrower with a complex mortgage and the probability of delinquency for a borrower
with similar characteristics but a ﬁxed rate mortgage is e1×0.792 /e0×0.792 = 2.2; or the complex
borrower is about 2.2 times more likely to be delinquent.
In the ﬁrst two columns, we use only borrower characteristics at the time of loan origination to estimate the delinquency probability. In last two columns, we include time-varying
characteristics and state ﬁxed eﬀects. The current LTV ratio is deﬁned as the mortgage loan
amount at the end of the prior period divided by the current home value. The current home
value is estimated by adjusting the home value at origination by the house price appreciation
at the MSA level since the origination. Households with complex loans will pay down their
mortgages at a slower pace (as illustrated in Figure 6) and will have higher current LTV ratios.
In addition, areas with house price declines will have higher current LTV ratios. Households
with LTV ratios exceeding 100% will have higher incentives to default on their loans since they
do not have any home equity at stake. Thus, including the current LTV ratio in the hazard
model controls for dynamic leverage levels, which diﬀer across mortgage types. Finally, the
unemployment level captures the proportion of unemployed in an MSA and the income growth
is deﬁned as the growth rate of income at the MSA level since the mortgage was originated.
We ﬁnd that CMs have signiﬁcantly higher delinquency rates than FRMs in all speciﬁcations. Delinquency rates are particularly high for teaser rate mortgages, which are presumably
the least transparent mortgage contract we analyze. Households that borrow using ARMs also
have signiﬁcantly higher propensities to be delinquent, although the coeﬃcient estimate is substantially smaller than the coeﬃcient on complex mortgages. The propensity to be delinquent
decreases with the income level at origination. Furthermore, borrowers with lower credit
scores, subprime borrowers, loans originated with low or no documentation, loans above the
25

conforming limit, and investment properties are signiﬁcantly more likely to be delinquent.
The last two columns consider the impact of the additional MSA level variables and state
ﬁxed eﬀects. We ﬁnd that households in areas with high unemployment and depressed income growth since the origination of the loan are more likely to be delinquent, suggesting
that the diﬃculty to meet cash ﬂow payment is certainly a driver of mortgage delinquency.
However, local income shocks are likely to aﬀect borrowers of diﬀerent mortgages similarly.
To investigate the impact of house price appreciation and diﬀerent amortization schedules,
we include the current LTV ratio. We ﬁnd that households with higher current LTV ratios
are signiﬁcantly more likely to default, suggesting that strategic default is likely a contributor to mortgage delinquency as well. This source of delinquency is also likely to explain the
signiﬁcantly higher delinquency rate for CMs over time, since the LTV for CMs increases signiﬁcantly over time relative to ARMs or FRMs due to the low or even negative amortization
in the ﬁrst few years.
It is also remarkable that the coeﬃcients on CMs remain highly statistically signiﬁcant
even after controlling for the current LTV ratio, the local income growth rate, the local unemployment rate, and state ﬁxed eﬀects, suggesting that CM borrowers might be fundamentally
diﬀerent from FRM borrowers. They might be more risk seeking in general, as revealed by
their choices for CM contracts. They might have riskier income or might be more receptive to
the idea of strategic default. Additional work is needed to fully disentangle the various sources
of delinquency. These results are consistent with the structural model of Corbae and Quintin
(2010), who ﬁnd that the presence of nontraditional mortgages ampliﬁed the foreclosure crisis
between the ﬁrst quarter of 2007 and the ﬁrst quarter of 2009.

4.4

Bankruptcy

The decision to default on a mortgage is related to the decision to declare bankruptcy. Contrasting the determinants of personal bankruptcy with the determinants of mortgage delinquency gives us important insights about the motivation of the delinquency behavior. It is
not necessary that households that default on their mortgages are also declaring bankruptcy.
Nor is it necessary that households that declare bankruptcy default on their mortgages. For
example, in our sample only 13% of households that are delinquent on their mortgage also declare bankruptcy. Furthermore, only 29% of households that declare bankruptcy also default
on their mortgage loans.13 Bankruptcy is signiﬁcantly less common than mortgage defaults.
In our sample, 13% of mortgages become delinquent at any time during their life, whereas
only 2% of mortgage borrowers also declare bankruptcy.
Panel B of Table 6 shows the proportion of households with diﬀerent mortgage types that
declare bankruptcy. We observe that FRMs have the lowest bankruptcy rate at all horizons.
Households borrowing using CMs have higher bankruptcy rates than ARMs at a ﬁve year
horizon. For example, 3.18% of CMs, 2.94% of ARMs, and 2.15% of FRMs households declare
bankruptcy within a ﬁve year horizon after they originate a mortgage.
Table 8 reports the propensity of households to declare personal bankruptcy and contrasts
it with those that are delinquent on their mortgage. Not surprisingly, most coeﬃcients have
the same signs in both regressions. For example, higher income and higher FICO scores reduce
the propensities of both delinquency and bankruptcy.
It is interesting that some variables show up with diﬀerent signs in the two regressions.
For example, although investment properties have higher mortgage delinquency rates, households with investment properties are less likely to ﬁle for personal bankruptcy. This evidence
13

See Li, White, and Zhu (2010) for a discussion of the relationship between bankruptcy laws and mortgage
defaults.

suggests that owners of investment properties are more likely to walk away from the property
when it is economical to do so, even if they can aﬀord to continue the mortgage payment.
Moreover, loans with low documentation are more likely to be delinquent, but that variable
does not predict personal bankruptcy, suggesting that these households might be more likely
to strategically default.

4.5

Prepayment

Another reason that households go into delinquency is that they cannot reﬁnance their previous mortgage when they have a high LTV ratio or experience a bad income shock. Panel C
of Table 6 summarizes the proportion of mortgages that are prepaid. Mortgages are prepaid
if the borrowers pay-oﬀ their loan before maturity either by reﬁnancing the loan or by paying
oﬀ the mortgage using the proceeds from selling the house or through other means. We ﬁnd
that ARMs are more likely to be prepaid than FRMs, while CMs have intermediate levels of
prepayments. Unfortunately, we do not observe whether households prepay their mortgages
to reﬁnance their loan or whether they prepay their mortgages because they sold their homes.
The last column of Table 8 reports the propensity of households to prepay. Many variables
have the opposite sign for the delinquency and the prepayment regressions, since variables that
increase the probability of prepayment likely will decrease the probability of delinquency. For
example, loans with high current LTV are less likely to be prepaid and more likely to go into
delinquency. However, there are some exceptions. For example, CMs and ARMs are both
more likely to be prepaid and more likely to go into delinquency. Loans that were used to
reﬁnance another loan are both less likely to be prepaid and less likely be delinquent.

Conclusions

The recent housing crisis brought the extension of credit to subprime borrowers and agency
problems inherent in mortgage securitization to the forefront of academic research. This paper
focuses on a diﬀerent aspect of credit markets during this time – namely, the proliferation of
non-amortizing mortgages. In addition to variable interest rates, such mortgages also featured
changes in amortization schedules set oﬀ by a variety of triggers. These complex mortgage
contracts became extremely popular during the mid 2000s and vanished almost completely
after the housing crisis of 2007-2009.
We ﬁnd that complex mortgages were the contract of choice for relatively high credit quality
and high-income households seeking to purchase houses that were expensive relative to their
incomes. We further ﬁnd that CM contracts were not simply an inevitable outcome of high
house prices. Even within high house price areas these contracts are associated with households
stretching to aﬀord more expensive houses, often on the basis of stated income alone. We
document that complex mortgages experienced substantially higher defaults, controlling for a
variety of borrower and loan characteristics, as well as macroeconomic shocks. Higher default
rates cannot be attributed solely to greater leverage of complex mortgages and the onset of
amortization resets brought about by inability to reﬁnance complex loans. That complex loans
were more likely to be underwritten using stated income may also indicate greater inherent
earnings variability of CM borrowers, which would make them more susceptible to economic
shocks.

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Table 1: Summary Statistics
This table reports means, standard deviations, medians, and ﬁrst and third quartiles for our data
sample.

Loan Amount
House Value
Income
VTI
First Lien LTV
FICO
FICO less than 620
Subprime
Low Documentation
Condo
Investment Property
Reﬁnance
With Prepayment Penalty
Prepayment Penalty Term (in Months)
Above Conforming Limit
Government Securitized
Private Securitized
Initial Interest Rate (in %)
Hypothetical FRM Interest Rate (in %)

Mean
218,065
317,294
100,211
3.54
0.75
707
0.11
0.07
0.14
0.13
0.10
0.41
0.13
30.17
0.11
0.64
0.25
5.94
6.19

Std. Dev.
181,464
297,950
88,251
1.94
0.18
67
0.31
0.26
0.34
0.34
0.30
0.49
0.34
13.48
0.31
0.48
0.43
1.44
0.45

1st Quart.
108,300
145,000
50,000
2.22
0.67
662
0
0
0
0
0
0
0
24.00
0
0
0
5.50
5.88

Median
168,000
234,000
75,000
3.18
0.79
715
0
0
0
0
0
0
0
36.00
0
1
0
6.00
6.13

3rd Quart.
268,918
388,000
117,000
4.41
0.86
762
0
0
0
0
0
1
0
36.00
0
1
1
6.50
6.50

MSA level variables
Median Income
Median VTI
House Price Change Prior 3 Years
Decrease in House Prices Prior 10 Years
College or More
Population Growth (in %)
Unemployment Rate (in %)
Non-Recourse State

77,641
3.28
0.33
0.13
0.35
1.10
5.03
0.27

20,689
0.82
0.21
0.34
0.16
1.43
1.40
0.44

62,000
2.60
0.14
0
0.22
0.29
4.10
0

74,000
3.15
0.29
0
0.32
0.82
4.80
0

88,000
3.80
0.46
0
0.45
1.74
5.70
1

Number of Observations

10,208,522

Table 2: Summary Statistics by Mortgage Type
This table reports summary statistics for Fixed Rate Mortgages (FRM), Adjustable Rate Mortgages
(ARM), and Complex Mortgages (CM).
All

FRM

ARM

Loan Amount
House Value
Income
VTI
First Lien LTV
FICO Credit Score
FICO less than 620
Subprime
Low Documentation
Condo
Investment Property
Prepayment Penalty
Prepayment Penalty Term (in Months)
Reﬁnance
Above Conforming limit
Government Securitized
Private Securitized
Initial Interest Rate (in %)
Hypothetical FRM Interest Rate (in %)

218,065
317,294
100,211
3.54
74.17
707
0.11
0.07
0.14
0.13
0.10
0.13
30.17
0.41
0.11
0.64
0.25
5.94
6.19

179,415
264,878
88,642
3.40
73.88
710
0.10
0.03
0.11
0.11
0.09
0.06
37.39
0.41
0.05
0.79
0.15
6.16
6.17

220,374
309,465
101,005
3.46
77.01
684
0.23
0.24
0.09
0.17
0.11
0.25
27.57
0.34
0.13
0.43
0.41
5.97
6.20

357,887
513,728
141,998
4.07
73.45
710
0.07
0.10
0.26
0.18
0.11
0.33
27.85
0.45
0.33
0.24
0.54
5.12
6.23

77,641
3.28
0.33
0.13
0.35
1.10
5.03
0.27

74,105
3.13
0.30
0.13
0.33
1.11
5.04
0.22

76,530
3.28
0.32
0.16
0.36
1.12
5.21
0.26

91,254
3.84
0.44
0.12
0.39
1.08
4.87
0.44

10,208,522

7,071,317

1,202,383

1,934,822

Number of Observations

Table 3: Summary Statistics of Complex Loans by Mortgage Type
This table reports summary statistics for diﬀerent types of complex mortgages including InterestOnly Mortgages (IO), Negative Amortization Mortgages (NEGAM), and Teaser Rate Mortgages
(TRM).
All CM

NEGAM

TRM

357,887
513,728
141,998
4.07
73.45
710
0.07
0.10
0.26
0.18
0.11
0.33
27.85
0.45
0.33
0.24
0.54
5.12
6.23

352,757
501,394
141,348
4.03
74.05
720
0.05
0.08
0.11
0.20
0.14
0.14
28.01
0.34
0.32
0.31
0.53
5.99
6.24

343,059
497,894
135,024
4.02
74.18
689
0.16
0.23
0.42
0.17
0.06
0.39
28.28
0.54
0.29
0.22
0.51
6.03
6.31

393,023
571,770
153,249
4.27
70.67
710
0.03
0.00
0.49
0.15
0.08
0.83
27.38
0.64
0.42
0.06
0.57
1.30
6.10

91,254
3.84
0.44
0.12
0.39
1.08
4.87
0.44

89,390
3.75
0.43
0.11
0.40
1.18
4.72
0.39

92,525
3.86
0.43
0.11
0.36
0.98
5.03
0.49

95,133
4.07
0.49
0.16
0.39
0.93
5.08
0.55

1,934,822

1,087,058

484,574

363,190

Number of Observations

Table 4: Mortgage Choice Multinomial Logit Regressions
This table reports the coeﬃcients of multinomial logit regressions for mortgage choice. The coeﬃcients are measured relative to FRM. The signiﬁcance levels are abbreviated with asterisks: One,
two, and three asterisks denote signiﬁcance at the 10, 5, and 1% level, respectively.
Individual-level Covariates
ARM
CM
Log(Income)
Value-to-Income
FICO/100
Subprime
Low Documentation
Above Loan Limit
Condo
Investment Property
Reﬁnance
Non-Recourse States

0.440∗∗∗
(0.024)
0.080∗∗∗
(0.013)
−0.379∗∗∗
(0.013)
2.304∗∗∗
(0.040)
−0.006
(0.037)
0.718∗∗∗
(0.053)
0.664∗∗∗
(0.054)
0.283∗∗∗
(0.025)
−0.535∗∗∗
(0.022)
0.153∗∗
(0.078)

0.773∗∗∗
(0.034)
0.126∗∗∗
(0.016)
−0.054∗∗∗
(0.020)
1.481∗∗∗
(0.069)
0.892∗∗∗
(0.047)
1.382∗∗∗
(0.064)
0.742∗∗∗
(0.049)
0.110∗∗∗
(0.040)
−0.021
(0.043)
0.720∗∗∗
(0.090)

College or More
House Price Change
Decrease in House Prices
MSA Median Income
MSA Median VTI
MSA Population Growth

Origination Year Dummies
State Dummies
Observations

Yes
No
10,166,582

State Fixed Eﬀects
ARM
CM
0.274∗∗∗
(0.015)
0.028∗∗∗
(0.006)
−0.405∗∗∗
(0.014)
2.306∗∗∗
(0.040)
0.036
(0.031)
0.707∗∗∗
(0.041)
0.483∗∗∗
(0.037)
0.346∗∗∗
(0.017)
−0.560∗∗∗
(0.020)

0.507∗∗∗
(0.028)
0.041∗∗∗
(0.009)
−0.053∗∗
(0.022)
1.448∗∗∗
(0.077)
0.914∗∗∗
(0.043)
1.306∗∗∗
(0.044)
0.453∗∗∗
(0.027)
0.072∗∗
(0.029)
−0.116∗∗
(0.050)

0.871∗∗∗
(0.058)
−0.152
(0.152)
−0.072∗∗
(0.036)
0.276∗∗
(0.120)
0.264∗∗∗
(0.050)
2.673
(1.650)

0.110
(0.086)
0.317
(0.194)
−0.212∗∗∗
(0.036)
1.006∗∗∗
(0.161)
0.248∗∗∗
(0.058)
4.398∗∗
(1.852)

Yes
Yes
8,944,872

Table 5: Mortgage Choice Multinomial Logit Regressions for Detailed Classiﬁcation
This table reports the coeﬃcients of multinomial logit regressions for mortgage choice. The coeﬃcients are measured relative to FRM. The signiﬁcance levels are abbreviated with asterisks: One,
two, and three asterisks denote signiﬁcance at the 10, 5, and 1% level, respectively.
State Fixed Eﬀects
IO
NEGAM

ARM
Log(Income)
Value-to-Income
FICO/100
Subprime
Low Documentation
Above Loan Limit
Condo
Investment Property
Reﬁnance
College or More
House Price Change
Decrease in House Prices
MSA Median Income
MSA Median VTI
MSA Population Growth

0.277∗∗∗
(0.015)
0.029∗∗∗
(0.006)
−0.410∗∗∗
(0.014)
2.291∗∗∗
(0.041)
0.082∗∗
(0.032)
0.699∗∗∗
(0.042)
0.481∗∗∗
(0.036)
0.340∗∗∗
(0.017)
−0.548∗∗∗
(0.020)
0.853∗∗∗
(0.057)
−0.192
(0.153)
−0.072∗∗
(0.036)
0.312∗∗∗
(0.120)
0.253∗∗∗
(0.050)
2.560
(1.610)

0.433∗∗∗
(0.029)
0.056∗∗∗
(0.010)
0.113∗∗∗
(0.020)
1.316∗∗∗
(0.052)
−0.067
(0.041)
1.362∗∗∗
(0.047)
0.473∗∗∗
(0.032)
0.243∗∗∗
(0.032)
−0.435∗∗∗
(0.057)
0.439∗∗∗
(0.098)
0.331∗
(0.183)
−0.185∗∗∗
(0.051)
0.761∗∗∗
(0.176)
0.277∗∗∗
(0.058)
4.882∗∗
(2.031)

Origination Year Dummies
State Dummies
Observations

0.520∗∗∗
(0.022)
0.007
(0.006)
−0.303∗∗∗
(0.018)
2.213∗∗∗
(0.097)
1.742∗∗∗
(0.060)
1.114∗∗∗
(0.040)
0.472∗∗∗
(0.031)
−0.330∗∗∗
(0.038)
0.166∗∗∗
(0.042)
−0.342∗∗∗
(0.076)
−0.300
(0.256)
−0.292∗∗∗
(0.049)
1.699∗∗∗
(0.209)
0.082
(0.099)
1.807
(1.708)

Yes
Yes
8,944,873

TRM
0.725∗∗∗
(0.038)
0.016∗∗
(0.007)
−0.304∗∗∗
(0.035)
−2.771∗∗∗
(0.204)
1.901∗∗∗
(0.049)
1.376∗∗∗
(0.053)
0.306∗∗∗
(0.048)
−0.120∗∗
(0.048)
0.685∗∗∗
(0.076)
−0.640∗∗∗
(0.097)
0.712∗∗
(0.285)
−0.298∗∗∗
(0.046)
1.677∗∗∗
(0.247)
0.133∗
(0.076)
4.677∗
(2.729)

Table 6: Mortgage Delinquencies, Household Bankruptcies, and Prepayment Decisions
This table reports the proportion of mortgages that are at least 60 days delinquent, the proportion
of households with mortgages that declare bankruptcy, and the proportion of mortgages that are
prepaid after one, three, and ﬁve years. Mortgages are prepaid if a borrower reﬁnances the loan or
pays back the loan completely before maturity.
Panel A: Proportion of Mortgages that are Delinquent
FRM
ARM
CM
1 Year
3 Years
5 Years
Number of Loans

2.65
9.31
11.95

6.43
15.63
18.48

4.02
17.56
22.75

6,895,047

1,174,328

1,917,719

Panel B: Proportion of Households Declaring Bankruptcy
FRM
ARM
CM
1 Year
3 Years
5 Years
Number of Loans

0.25
1.51
2.15

0.52
2.28
2.94

0.26
2.20
3.18

6,895,047

1,174,328

1,917,719

Panel C: Proportion of Mortgages that are Prepaid
FRM
ARM
1 Year
3 Years
5 Years
Number of Loans

7.66
28.32
37.29

15.10
47.12
59.98

12.05
38.33
45.34

6,895,047

1,174,328

1,917,719

Table 7: Hazard Model of Mortgage Delinquency
This table reports the hazard rate for mortgage delinquency. The signiﬁcance levels are abbreviated with asterisks: One, two, and three asterisks denote signiﬁcance at the 10, 5, and 1% level,
respectively.

CM
IO
NEGAM
TRM
ARM
Log Income
Value to Income (VTI)
FICO/100
Subprime
Low Documentation
Above Loan Limit
Condo
Investment Property
Reﬁnance
Non-Recourse State

Individual-level Covariates
0.792∗∗∗
(0.020)
0.761∗∗∗
(0.026)
0.774∗∗∗
(0.021)
0.964∗∗∗
(0.027)
0.346∗∗∗
0.343∗∗∗
(0.013)
(0.013)
−0.249∗∗∗
−0.250∗∗∗
(0.018)
(0.018)
−0.030∗∗∗
−0.030∗∗∗
(0.008)
(0.008)
−1.108∗∗∗
−1.106∗∗∗
(0.016)
(0.016)
0.408∗∗∗
0.422∗∗∗
(0.016)
(0.016)
0.052∗∗∗
0.039∗∗∗
(0.015)
(0.013)
0.395∗∗∗
0.403∗∗∗
(0.038)
(0.038)
−0.086∗∗
−0.084∗∗
(0.041)
(0.041)
0.289∗∗∗
0.290∗∗∗
(0.033)
(0.033)
−0.152∗∗∗
−0.160∗∗∗
(0.009)
(0.009)
0.108∗
0.112∗
(0.061)
(0.061)

College or More
Current LTV
Unemployment Level
Income Growth since Origination
Calendar Dummies
Orig. Year Dummies
State Dummies
Observations

Yes
Yes
No
32,960,513

State Fixed Eﬀects
0.689∗∗∗
(0.014)
0.664∗∗∗
(0.019)
0.687∗∗∗
(0.014)
0.800∗∗∗
(0.022)
0.326∗∗∗
0.324∗∗∗
(0.012)
(0.012)
−0.164∗∗∗
−0.165∗∗∗
(0.017)
(0.016)
−0.014∗
−0.014∗
(0.008)
(0.008)
−1.058∗∗∗
−1.057∗∗∗
(0.018)
(0.018)
0.421∗∗∗
0.430∗∗∗
(0.011)
(0.011)
0.053∗∗∗
0.043∗∗∗
(0.012)
(0.010)
0.442∗∗∗
0.438∗∗∗
(0.026)
(0.026)
−0.064∗∗
−0.063∗∗
(0.026)
(0.026)
0.283∗∗∗
0.284∗∗∗
(0.030)
(0.030)
−0.164∗∗∗
−0.170∗∗∗
(0.013)
(0.013)
−1.415∗∗∗
(0.061)
0.762∗∗∗
(0.066)
0.037∗∗∗
(0.008)
−0.040∗∗∗
(0.004)
Yes
Yes
Yes
26,019,616

−1.411∗∗∗
(0.062)
0.761∗∗∗
(0.066)
0.037∗∗∗
(0.008)
−0.040∗∗∗
(0.004)
Yes
Yes
Yes
26,019,616

Table 8: Hazard Models of Mortgage Delinquency, Personal Bankruptcy, and Mortgage Prepayment
This table reports the hazard rate for mortgage delinquency, personal bankruptcy, and prepayment
decisions. The signiﬁcance levels are abbreviated with asterisks: One, two, and three asterisks denote
signiﬁcance at the 10, 5, and 1% level, respectively.
Delinquency
CM
ARM
Log Income
Value to Income (VTI)
FICO/100
Subprime
Low Documentation
Above Loan Limit
Condo
Investment Property
Reﬁnance
College or More
Current LTV
Unemployment Level
Income Growth from Origination
Calendar and Orig. Year Dummies
State Dummies
Observations

Bankruptcy

Prepayment

0.689∗∗∗
(0.014)
0.326∗∗∗
(0.012)
−0.164∗∗∗
(0.017)
−0.014∗
(0.008)
−1.058∗∗∗
(0.018)
0.421∗∗∗
(0.011)
0.053∗∗∗
(0.012)
0.442∗∗∗
(0.026)
−0.064∗∗
(0.026)
0.283∗∗∗
(0.030)
−0.164∗∗∗
(0.013)
−1.415∗∗∗
(0.061)
0.762∗∗∗
(0.066)
0.037∗∗∗
(0.008)
−0.040∗∗∗
(0.004)
Yes
Yes
26,019,616

0.631∗∗∗
(0.017)
0.208∗∗∗
(0.013)
−0.358∗∗∗
(0.024)
−0.171∗∗∗
(0.011)
−0.763∗∗∗
(0.012)
0.075∗∗∗
(0.022)
−0.006
(0.011)
0.408∗∗∗
(0.040)
−0.193∗∗∗
(0.030)
−0.200∗∗∗
(0.023)
0.232∗∗∗
(0.015)
−1.373∗∗∗
(0.070)
0.707∗∗∗
(0.062)
0.046∗∗∗
(0.010)
−0.032∗∗∗
(0.004)
Yes
Yes
25,851,519

0.372∗∗∗
(0.019)
0.545∗∗∗
(0.011)
0.079∗∗∗
(0.012)
0.001
(0.002)
−0.091∗∗∗
(0.013)
0.289∗∗∗
(0.017)
−0.008
(0.008)
−0.099∗∗∗
(0.020)
−0.051∗∗∗
(0.011)
−0.270∗∗∗
(0.011)
−0.116∗∗∗
(0.010)
0.123∗∗∗
(0.045)
−0.634∗∗∗
(0.063)
−0.037∗∗∗
(0.008)
0.012∗∗∗
(0.004)
Yes
Yes
25,989,417

LPS
LPS
LPS
LPS
LPS
LPS
LPS
LPS
LPS
FHFA
FHFA
Census
Ghent and
Kudlyak (2010)
LPS and FHFA

BLS
BEA

Reﬁnance
Condo
Investment Property
Subprime
Prepayment Penalty
Prepayment Penalty Term
Percentage above Conforming
Share Government Securitized
Share Private Securitized
House Price Change Prior 3 Years
Decrease in House Prices Prior 10 Years

Share College or More
Non-Recourse

Unemployment Level
Income Growth from Origination

Current LTV

Data Source
LPS
LPS
HMDA
LPS
LPS
LPS
LPS

Variable
Loan Amount
Home Value
Income
FICO
VTI
First Lien LTV
Hypothetical FRM Interest Rate

CBSA-Qtr
CBSA-Qtr

Individual

Zip (static)
State

Individual
Individual
Individual
Individual
Individual
Individual
Individual
Individual
Individual
CBSA-Qtr
CBSA-Qtr

Aggregation
Individual
Individual
Individual
Individual
Individual
Individual
Individual

Description
Loan amount
Appraised home value at origination
Reported Income from loan application
FICO at origination
Appraisal value divided by income from loan application
Loan amount divided by appraised value of home
Average interest rate on 30-yr FRM within month, state,
conforming, LTV, and FICO buckets
Reﬁ or not
Condo property or not
2nd home or investment
Subprime indicator as the servicer believes; does not include Alt-A
Flag for prepayment penalty along
Length in months of prepayment penalty
Flag for conforming loan.
Securitization ﬂag after 1yr of loan life
Securitization ﬂag after 1yr of loan life
House price change in the past 3 years
Indicator variable for whether there were 4 quarters
of house price depreciation in the past 10 years
Proportion of 2000 population with college education or better
States where recourse in residential mortgages is limited by
the value of the collateral securing the loan.
The mortgage loan amount at the end of the prior period divided
by the current home value. The current home value is estimated
by adjusting the home value at origination by the house price
appreciation at the MSA level since the origination.
Unemployment rate
Growth rate of per capita personal income

This table reports the description of the variables used and the corresponding data sources.

Table 9: Variable Descriptions

1.00

0.90

0.80

0.70
Cumulative Proportion

FRM
0.60

0.50

0.40
ARM

0.30

0.20
CM

0.10

0.00
1995

1997

1999

2001

2003

2005

2007

2009

Figure 1: Composition of Mortgage Products.
The ﬁgure depicts the composition between Fixed Rate Mortgages (FRM), Adjustable Rate
Mortgages (ARM), and Complex Mortgages (CM) over the period between 1995 and 2009.

0.06

0.04

Quarterly House Price Appreciation

Q3
0.02
Q1
0
1998

2000

2002

2004

2006

2008

-0.02

-0.04

Q5
-0.06

Figure 2: Quarterly House Price Changes by Complexity Quintile
This ﬁgure depicts the quarterly house price changes of MSAs quintiles sorted according
to the proportion of complex mortgages in 2004. Q1, Q3, and Q5 correspond to the mean
appreciation levels of MSA in the ﬁrst, third, and ﬁfth quintile according to the complex
share.

Panel A: Value-to-Income Ratio
1
0.9
0.8

Cumulative Distribution

0.7
0.6
0.5

FRM

ARM

0.4
0.3
0.2
0.1
0
0

4
5
Value to Income Ratio

Panel B: FICO Credit Score
1

0.9

0.8

Cumulative Distribution

0.7

FRM

0.6

0.5
ARM

0.4

0.3

0.2

0.1

0
500

550

600

650
FICO Score

700

750

800

Figure 3: Cumulative Distribution Functions by Mortgage Type
These ﬁgures depict the cumulative distribution functions of the value-to-income ratio (VTI)
and FICO credit scores for Fixed Rate Mortgages (FRM), Adjustable Rate Mortgages
(ARM), and Complex Mortgages (CM) over the period between 1995 and 2009.

Panel A: Complex Mortgages in 2002

Panel B: Complex Mortgages in 2005

Panel C: Complex Mortgages in 2008

Figure 4: Geographic Distribution of Complex Mortgages
These ﬁgures depict the geographic distribution of complex mortgages in 2002, 2005, and
2008.

Panel A: Mortgage Payment After One Year Relative to FRM
0.05
ARM

0.045
0.04
0.035

Distribution

0.03
0.025
CM

0.02
0.015
0.01
0.005
0
0

0.2

0.4

0.6

0.8

1.2

1.4

1.6

1.8

Actual Mortgage Payment after 1 Year Relative to FRM

Panel B: Mortgage Payment After Three Years Relative to FRM
0.06
ARM
0.05

Distribution

0.04

0.03

0.02

0.01

0
0

0.2

0.4

0.6

0.8

1.2

1.4

1.6

1.8

Actual Mortgage Payment after 3 Years Relative to FRM

Panel C: Mortgage Payment After Five Years Relative to FRM
0.08
ARM
0.07

0.06

Distribution

0.05
CM

0.04

0.03

0.02

0.01

0
0

0.2

0.4

0.6

0.8

1.2

1.4

1.6

1.8

Actual Mortgage Payment after 5 Years Relative to FRM

Figure 5: Mortgage Payment Relative to FRM
These ﬁgures depict the actual mortgage payments for Adjustable Rate Mortgages (ARM)
and for Complex Mortgages (CM) one, three, and ﬁve years after origination relative to the
mortgage payments of a Fixed Rate Mortgages (FRM) with similar borrower characteristics.

Panel A: Remaining Balance After One Year
0.8
FRM

0.7

Cumulative Distribution

0.6

0.5
CM
0.4

0.3

0.2

ARM

0.1

0
0.8

0.85
0.9
0.95
1
1.05
Remaining Mortgage Balance After One Year Relative to Original Balance

1.1

Panel B: Remaining Balance After Three Years
0.4
FRM
0.35
CM

Cumulative Distribution

0.3

0.25

ARM

0.2

0.15

0.1

0.05

0
0.8

0.85
0.9
0.95
1
1.05
Remaining Mortgage Balance After Three Years Relative to Original Balance

1.1

Panel C: Remaining Balance After Five Years
0.25

FRM
CM
ARM

Cumulative Distribution

0.2

0.15

0.1

0.05

0
0.8

0.85
0.9
0.95
1
1.05
Remaining Mortgage Balance After Five Years Relative to Original Balance

1.1

Figure 6: Remaining Mortgage Balances
These ﬁgures depict the remaining mortgage balances after one, three, and ﬁve years relative
to the initial balances for Fixed Rate Mortgages (FRM), Adjustable Rate Mortgages (ARM),
and Complex Mortgages (CM).

0.014

0.012

0.01

Hazard Rate

0.008
ARM
0.006

0.004
FRM
0.002

0
0

30
Months After Origination

Figure 7: Proportion of Mortgage Delinquencies by Month After Origination
The ﬁgure depicts the proportion of surviving loans that are delinquent by month after orignation for Fixed Rate Mortgages (FRM), Adjustable Rate Mortgages (ARM), and Complex
Mortgages (CM) over the period between 2003 and 2009.

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Full text of Working Papers (Federal Reserve Bank of Chicago) : Complex Mortgages, Working Paper 2010-17

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