University of Southern California Dissertations and Theses

Three essays in United States real estate markets

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Three essays in United States real estate markets

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THREE ESSAYS IN UNITED STATES
REAL ESTATE MARKETS
by
Xiaoxin Zhang

A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(POLICY PLANNING AND DEVELOPMENT)

August 2015

I

Acknowledgments

I would like to give special thanks, beginning with Dr. Richard Green, for his
dedicated guidance and generous support. He stepped in as my Chair after my original
Chair left USC, and helped me to identify research topics. He encouraged me to find
answer for each research question. He brought me to different conferences to develop
presentation skills. He drove me to have a discussion with mortgage product head, in one
of the largest fixed-income companies, to understand secondary mortgage market. He
also helped me find the interests. Thank you.
My gratitude is extended to Dr. Raphael Bostic who had offered the first mortgage
research project in my first year of study in USC. He helped me start from the very
beginning of mortgage-backed securities – the prospectus. I read hundreds of prospectus
to understand the players in the field. His patience and knowledge enables me to find
solution.
I would like to thank Dr. Jin Ma who extended my interest into mathematical finance.
Dr. Jin Ma is one of the best teachers I have had. He supports me to try different classes,
and study with Ph.D. student in Mathematics.
Special thanks are due to Dr. LaCour-Little, who offered some data for my
dissertation. He helped me find my research question. He also provided generous
guidance on my interview.
II

I truly appreciate Dr. Yongheng Deng for this guidance. He supported me to pursue
this degree and understand the fundamental of mortgage. He helped me shape my way of
thinking. He encouraged me to sharpen my research skills with different methods.
I am especially grateful to Dr. Gary Painter and Dr. Christian Redfearn for their
helps during my course of studies. I would give special thanks to my friends – Xudong
An, Minye Zhang, Yiming Wang and Pengyu Zhu. Each of you made my journey in USC
so special.
My deepest gratitude is to my wife, Ling Zhang, and my son, Austin for their endless
love, support and encouragement.
III

Table of Contents
Acknowledgments................................................................................................................ I
List of Tables ..................................................................................................................... V
List of Figures ................................................................................................................... VI
Chapter 1: Prologue ........................................................................................................ 1
Chapter 2: The Effect of Agency on Subprime Mortgage Terminations ....................... 4
2.1 Introduction .......................................................................................................... 4
2.2 The Rise of Mortgage Brokers ............................................................................. 5
2.3 Literature Review ................................................................................................. 7
2.3.1 Agency Theory.............................................................................................. 7
2.3.2 Mortgage Broker Compensation ................................................................. 10
2.3.3 Broker Mortgage Prepayment and Default ................................................. 12
2.4 Competing Risks Hazard Model ........................................................................ 14
2.5 CTSLink Data .................................................................................................... 19
2.6 Empirical Results ............................................................................................... 26
2.7 Conclusions ........................................................................................................ 28
Chapter 3: The Effect of Liquidity on Subprime Terminations ................................... 29
3.1 Introduction ........................................................................................................ 29
3.2 Literature Review ............................................................................................... 32
3.2.1 Securitization .............................................................................................. 32
3.2.2 Liquidity Impact.......................................................................................... 34
3.2.3 Discrete Choice Theory and Multinomial Logit Model ............................. 38
3.3 Empirical Model ................................................................................................. 39
3.4 Data .................................................................................................................... 44
3.5 Empirical Results ............................................................................................... 50
3.6 Conclusions ........................................................................................................ 53

IV

Chapter 4: Trustee Auction Sales Discount on House Prices ....................................... 55
4.1 Introduction ........................................................................................................ 55
4.2 Literature Review ............................................................................................... 57
4.2.1 Negative Effects of Foreclosures ................................................................ 57
4.2.2 Foreclosure Discounts ................................................................................. 60
4.2.3 Arbitrage Pricing Theory ............................................................................ 62
4.3 From Delinquency to Trustee’s Sale .................................................................. 63
4.4 Research Hypotheses.......................................................................................... 65
4.5 Method and Data ................................................................................................ 66
4.6 Regression Results ............................................................................................. 74
4.7 Conclusions ........................................................................................................ 83
References: ........................................................................................................................ 85

V

List of Tables

Table 2-1: Frequency of owner occupied type in full data set .......................................... 20
Table 2-2: Frequency of origination year in full data set .................................................. 21
Table 2-3: Descriptive statistics for mortgage loans – retail versus TPO ......................... 22
Table 2-4: Competing risks hazard estimates with unobserved heterogeneity ................. 25
Table 3-1: Descriptive statistics between sample and all loans ........................................ 46
Table 3-2: Descriptive statistics for mortgage loans ......................................................... 48
Table 3-3: Multinomial Logit (MNL) estimates for mortgage prepayment and default .. 51
Table 4-1: Descriptive statistics for County Records Research data ................................ 71
Table 4-2: Descriptive Statistics for CoreLogic Multiple Listing Service (MLS) data .... 72
Table 4-3: OLS estimates for Sold to Public versus Sold to Beneficiary ......................... 75
Table 4-4: OLS estimates for Auction, REO, Shortsale versus Regular Resale(part a) ... 77
Table 4-4b: OLS estimates for Auction, REO, Shortsale versus Regular Resale (part b)
(cont.) ................................................................................................................................ 78
Table 4-5: Heckman two-stage and OLS estimates for Auction versus Resale (part a) ... 80
Table 4-5b: Heckman two-stage and OLS estimates for Auction versus Resale (part b)
(cont.) ................................................................................................................................ 81
Table 4-6: Heckman two-stage and OLS estimates for Auction versus REO-Sale (part a)
........................................................................................................................................... 82
Table 4-6b: Heckman two-stage and OLS estimates for Auction versus REO-Sale (part b)
(cont.) ................................................................................................................................ 83

VI

List of Figures

Figure 2-1: Freddie Mac Primary Mortgage Market Survey 15 years and 30 years Fixed
Rate Mortgage ................................................................................................................... 24
Figure 3-1: Liquidity chart ................................................................................................ 36
Figure 3-2: Outstanding volume in Asset-Backed Securities ........................................... 47
Figure 3-3: Sample percentage in Census Region ............................................................ 49
Figure 4-1: Los Angeles House Price Index ..................................................................... 73

1

Chapter 1: Prologue

This dissertation contains three independent essays on the real estate market in the
United States. These three papers cover same research timeframe between 2006 and 2012.
The data in this period can illustrate the discrepancy of the outcome, before and after
subprime crisis.
The first two essays focus on residential mortgages with the topics of agency effect
and liquidity effect, respectively. The third essay studies the distressed housing. It
measures the impact of auction sale on housing value, comparing with the other types of
selling options. By looking at the secondary market and the housing market, these essays
capture some missing variables in previous literature. The first essay supports the agency
effect is important in default risk. The second essay finds that mortgage market liquidity
should be used to estimate the termination risks for private-label mortgages. Final essay
shows that auction status would affect the housing price significantly.
Chapter 2 presents an essay which studies the different loan performance originated
by retail lenders and mortgage brokers. Retail lenders and mortgage brokers are two
major types of mortgage originators. Mortgage brokers are less regulated than retail
lenders. They act as agents for both borrowers and lenders. There two facts create
incentives for brokers to increase lending costs to financially unsophisticated borrowers
and also to originate riskier mortgages for investors and homebuyers. Although broker
behaviors have been subject to considerable criticism, there has been little work to show
whether broker originated mortgages perform better or worse than retail mortgages. This
2

paper estimates a competing risk hazard model investigating whether a broker-lender’s
loan performance is worse than a retail lender’s. After measuring this agency effect, the
paper confirms that the performance for broker channel loans is in fact worse.
Chapter 3 presents a multinomial logit model with the same dataset. This section
argues that the supply of mortgage credit has an important impact on mortgage
termination risk. In periods of mortgage expansion, spreads narrow and credit standards,
such as down-payment and documentation requirements, relax. Under such
circumstances, it is easy for mortgagors to prepay their loans and obtain low cost
replacement financing, as well as cash out refinancing. On the other hand, when
mortgage finance is hard to come by, spreads widen and underwriting standards toughen.
Households who would benefit from refinancing are unable to do so. Consequently, the
value of the prepayment option drops, perhaps precipitously.
The estimation shows that after controls for borrower characteristics, the prepayment
hazard was slower and the default hazard faster in 2005-2008 relative to 2002-2004. It
concludes that liquidity shortages by themselves caused credit distress. Limited mortgage
market funding reduced the call option value and therefore reduced the propensity to
prepay, even after controlling for the values of the put and call options. Liquidity in the
mortgage market is thus potentially an important variable for explaining mortgage
termination risks. Linking the option-theory valuation and credit constraint literatures,
this quantitative study introduces a liquidity variable into the multinomial logit model.
Chapter 4 contains the third essay. It points out a major limitation of recent analysis
of foreclosure dynamics - they treat all foreclosure sales as though they are equivalent.
3

Auction theory suggests this should not be the case, and this section treats auction sales
differently from other foreclosure sales. This research seeks to use house transaction data
and public auction data in Los Angeles, California between 2006 and 2012 to determine
if there is a variation in the discounts associated with different foreclosure sale vehicles.
It tests the hypothesis that houses sold in auctions to public are priced at a greater
discount than other types. After controlling for zipcode-level HPI, neighborhood fixed
effects and hedonic housing characteristics; the theory predicts that auction sale discounts
should be higher than non-auction sales, including REO and short sales. The empirical
result further confirms the discount in auction is huge.
The second chapter and third chapter in this thesis involved co-authored work. Both
are co-authored with Professor Richard K Green of University of Southern California. In
both papers, I raised the research question, collected data, reviewed literature, and
performed the empirical research and analysis. The preliminary version of the text was
written by me.

4

Chapter 2: The Effect of Agency on Subprime
Mortgage Terminations

2.1 Introduction

More than two thirds of homeowners in the United States have mortgages. In general,
borrowers find mortgages through two channels: the retail channel or the third-party
originator (TPO) channel. If borrowers use the retail channel, they shop by themselves
among different lenders to find the best mortgage that offer lower coupon, less
origination fee and favorable loan terms. In the TPO channel, the borrower completes a
loan application with the support from TPO. Typically brokers shop around different
lenders for home buyer. Brokers provide assistance with the loan application process, and
offer comprehensive comparison of loan terms among different banks and commercial
banks. This provides time-saving convenience to borrowers, and funnels the loans fund to
those most needed. It reduces search cost and increases efficiency in matching borrower
and lender.
Although brokers reduce transaction cost dramatically, they introduce a serious
principal-agent problem - the conflict of interests among different players (e.g.,
originators, brokers and consumers) in mortgage process. Brokers have received
withering criticism from the public and media, as the delinquencies, defaults, and
foreclosures increased.
This study is an attempt to clarify the linkage between mortgage origination channel
and mortgage termination risk. To do this, this paper delivers an empirical test of the
5

relative performance of two large conduit lenders: one uses the retail channel and the
other uses the TPO channel. It compares the loan performance between different
origination channels. This paper uses a dataset that covers the sub-prime period, and
makes a contribution to re-exam the impact of TPO before and after market crash.
The remainder of this paper is organized as follows. Section 2 illustrates the rise of
mortgage brokers. Section 3 reviews literature on agency theory and mortgage broker
compensation. It specifically focuses on two previous empirical papers on broker
mortgage termination risk analysis. Section 4 elaborates the competing risks hazard
model. Section 5 and 6 describes the data and presents the results of TPO loan
performance. The last section sums up the study.
2.2 The Rise of Mortgage Brokers

Mortgage brokers are intermediaries between mortgagors and mortgagees, providing
service for both sides in a transaction to complete a loan origination. Brokers have access
to different lenders and programs, and are supposed to use their specialized knowledge of
borrowers to search for an appropriate mortgage loan for those borrowers. Although
mortgage brokers are independent from borrowers and lenders, they not only provide
service to both sides, but actually become agents for both sides. In that, there are two
agency relationships among these three players.
On the one hand, borrowers assign brokers a mission to search for the best possible
loan given borrower creditworthiness, income, and wealth. Brokers are compensated by
loan origination fees paid by borrowers. In such a setting, brokers become the agents of
6

borrowers and are expected to act in borrowers’ best interests to find the lower interest
rate and more stable loans.
On the other hand, because lenders benefit from volume (volume allows lenders to
amortize the fixed costs involved in underwriting, securitization, etc.), lenders want to
entice brokers to provide volume in loan origination. Lenders thus reward brokers by
paying yield-spread premiums
1
(YSP). The existence of YSP may let the loans working
in the brokers’ interests instead of the clients. Failing to disclose premium amount also
becomes the center topic on mortgage market.
Thirty years ago, the mortgage market relied on depository institutions. These
institutions “made” mortgage markets by funding mortgage borrowers with money raised
through deposits: they “matched” borrowers and depositors, and earned the difference in
interests. Lenders need to keep the loans on their balance sheet. This limits lenders to
provide more loans. Before secondary mortgage markets taking off in the 1980s, brokers
had a limited but important function. For example, life insurance companies would
invest in home mortgages, and brokers would match borrowers with funds of insurance
company. Once the secondary mortgage market began booming, however, so did the
mortgage brokers’ business. Freddie Mac and Fannie Mae’s market shares grew through
the 1980s and 1990s. When depositories continued to do a large amount of their own
origination, brokers could also connect borrowers with funds from Fannie and Freddie.
LaCour-Little (2009) uses 2006 HMDA dataset and estimates $29 billion revenue in the

1
The YSP is a payment from a mortgage broker receives from a lender in exchange for bringing the lender a borrower
who will pay a rate that is slightly higher than that available directly from the lender.
7

mortgage broker industry, or 1.9 percent of the volume of loan origination in that year.
Bitner (2008) shows that mortgage brokers originated 25 percent of prime loans and
signed up over 50 percent of subprime mortgages in 2003. A more astonishing number,
from the Access Mortgage Research, states that 68 percent of all mortgage lending are
directly or indirectly involved by mortgage brokers in 2004. This number is close to the
National Association of Mortgage Brokers’ claim of 65 percent market share in 2004. It
compares with 52 percent in 1997 (LaCour-Little and Chun 1999). The brokers’ share
increased 3.8 percent annually between 1997 and 2004. Turmoil in the mortgage market
led many brokers to go out of business, and in the first quarter of 2008 broker share
dropped to 49 percent
2
. Nevertheless, brokers have clearly not gone away yet.
2.3 Literature Review
2.3.1 Agency Theory

Ross (1973) shows that even when principals are better at a task than agents,
comparative advantage makes it beneficial for principals to delegate tasks to agents.
Consequently, agents are necessary for economies to reach Pareto-efficiency
3
. The
relationship between borrowers and brokers is clearly a principal-agent relationship.

2
Retail Production Accounted for Over Half Of New Mortgage Originations in Early 2008. Inside Mortgage Finance
25(22), May 30, 2008
3
In Pareto-efficiency, no one can be better without making others worse.
8

This means that the borrower-broker relationship contains two fundamental problems
that Eisenhardt (1989) shows to be common within the principal-agency relationship. The
first agency problem arises from the combination of conflicts of interest and information
asymmetry. Rational choice theory predicts that agents will seek to maximize their own
utility, rather than the principal’s utility. Owing to this conflict of interest, agents will
hesitate to act with a favor for principal’s best interests (Jensen and Meckling 1976).
Even though the agent’s ability to specialize may generate benefits for the principal, the
agent’s own self-interest mitigates and, in certain instances, cost of agency might be
greater than the benefit.
Asymmetric information between principal and agent is another principal-agent
conflict. The principal assigns the agent tasks that may be beyond the competence of the
principal. This can produce two types of problems: 1) Information before assignment:
sometimes, particularly in the absence of licensure, it is difficult for principals to discern
which agents are competent, and which are not. For example, borrowers have little
information to verify whether a particular mortgage broker is competent or not. Until
recently, in many states brokers did not even meet minimal licensing requirements. 2)
Information after assignment: usually principals have insufficient information to
determine whether their agent behaves appropriately.
It is difficult for principal to monitor agent’s effort or honesty, but only a final result.
In mortgage, final loan is even more difficult to tell whether the loan is feasible to the
borrower or not. Some types of loans, such as subprime 228 and subprime 327, have
friendly teaser rates at the beginning, but it suddenly turns to adjusted rate mortgage in 2
or 3 years, and causes a large increase on monthly payment. This is a classic moral
9

hazard problem, a problem that is particularly relevant to the mortgage industry. Because
consumers are often unsophisticated, cannot monitor the “shopping” process, and cannot
easily determine the final real cost of a loan (Kleiner and Todd 2007; LaCour-Little
2009), they are particularly vulnerable to moral hazard. Some scholars (Ambrose and
LaCour-Little 2001; LaCour-Little and Chun 1999) note that similar problems
characterize the investor and broker relationship: brokers can use “churning” to generate
fees, while putting investors in an unexpectedly short duration position.
The second agency problem results from risk sharing. On the one hand, principals
bear most of the risks induced by agents’ behaviors. Indeed, agents can assign risks
without bearing it. At the same time, principals and agents may have endowments that
carry different levels of risk, and therefore have different attitudes toward risk.
(Cadenillas, Cvitanic, and Zapatero 2007). For example, the broker might have an
incentive to risk the borrower’s equity by originating a large loan with a teaser rate. This
gives the borrower substantial optionality: if the value of the house goes up, the borrower
can sell the house and repay the loan having only paid the teaser rate; if the value of the
house goes down, the borrower can walk away. Neither of these results produces a good
outcome for the shareholder. The broker, however, prefers a high loan balance because
such a balance generates higher fees. Because mortgage fees are opaque, it is also
possible that the borrower will obtain a loan (or a house) that is larger than he or she
desires. Both types of agency problems produce risks and costs. The assumptions
underpinning agency theory—that humans are self-interested, bounded-rational and risk
10

averse—provide straightforward explanations for the cost (Eisenhardt 1989)
4
. The
incentives of principals and agents are almost always misaligned. Peterson points out that
“principals virtually never enjoy representation of an agent with the same cost-to-benefit
ratio for expending resources on the completion of a given productive task” (2007: 537).
For example, mortgage brokers do not have adequate incentives to find the lowest cost
mortgage for borrowers, particularly since the complexity of mortgages makes it difficult
for borrowers to know what the lowest cost mortgage might be.
Jensen and Meckling (1976) point out that principals can evaluate the costs and
benefits of the principal-agent relationship by estimating agency cost, which is the sum of
three variables. Their three variables includes the inspection expenditures from principal
necessary to know the status of agent, the bonding costs (an example would be a
guarantee), and the loss that remains even after monitoring and bonding. Principals can
compare these costs to the benefits arising from division of labor, Then they can
determine whether to delegate or not.
2.3.2 Mortgage Broker Compensation

Brokers have an inherent conflict of interests, in that, they work for and are
compensated by both sides - lenders and homebuyers. During the origination process,
brokers charge homebuyers mortgage points and fees. One points is one percent of the

4
Two assumptions include 1) organization has partial goal conflicts among participants and view efficiency as the
effectiveness criterion; 2) information is a commodity which can be purchased
11

loan; points are used to “buy down” interest rates. Loans with higher points usually have
lower interest rate. Brokers also collect fees, including the application fee, mortgage
closing costs, and other brokers’ costs. Normal fees add up to about one percent of the
loan
5
.
Loan origination fees are not regulated—in principle, a broker could charge any
amount they like. Points and fees are relatively transparent, because they must be
disclosed on the HUD-1 Form and Truth in Lending Act (TILA) form. In contrast to this
well-disclosed cost, whole sale mortgage companies compensate brokers through yield-
spread premiums (YSP). YSPs are the commissions earned by brokers for selling a loan
with an interest rate higher than the normal rate. The higher is the spread, the more the
brokers would receive. Many homebuyers were unaware of this side-payment, and
therefore did not know that the more interest they (the homebuyer) paid, the better the
broker was compensated.
LaCour-Little (2009) shows that YSP payments are usually larger than fees charged
to borrowers. The study uses two datasets from different lenders. He finds that borrowers
pay a spread of 20 basis points more for TPO loans than retail loans. LaCour-Little points
out that the premium falls as borrowers have higher income, are better educated, and have
better credit scores. The research defines lower-income as a categorical variable that
captures households with annual incomes of less than $60,000, and so does not capture
very low income households. Woodward (2003) uses a broader dataset which contains

5
See LaCour-Little (2009)
12

households who have a wider range of incomes. It confirms the findings of LaCour-Little
(2009): homebuyers with less education pay higher fees to brokers; minority borrowers
also pay higher fees to brokers. Woodward’s research, however, convers only TPOs, and
so doesn’t cover the difference in outcomes between TPO loans and retail loans. Two
questions worth considering are whether low income households are more prone to use
brokers, and whether the spread between TPO and retail loans increases in education,
income, etc.
2.3.3 Broker Mortgage Prepayment and Default

The increasing market share of TPOs, along with their aggressive marketing
campaign to encourage low-income people to become homeowners mean that brokers’
behavior presumably had an impact on the stability of low-income families and the
broader real estate secondary market. Groups such as the Center for Responsible Lending
argue that brokers pushed low-income families to obtain complicated mortgage products
that generated substantial fees and YSPs. These products, including the most
complicated mortgage, such as the pay-option adjusted-rate mortgages, have
unpredictable payments (although it may begin with interest-only payment, a payment
shock was nearly guaranteed after the first five to ten years), and hence could lead
unsophisticated borrowers to think they had obtained an affordable loan when, in the
longer run, they had not.
LaCour-Little and Chun (1999) are among the first scholars to study the difference
between TPOs and retail lenders. They focus on FHA loans; because they are government
backed, they are immune from default, and so the only risked attached to them is
13

prepayment risk. LaCour-Little and Chun (1999) find that loans from TPOs have higher
prepayment risks than retail lenders. Their explanation is that brokers have easy access to
homebuyers and homeowners, and so have both the means and motive to “churn” loans
through refinancing. Each time brokers consummate a refinance. The refinancing loans
generate income for brokers.
One peculiarity of the broker-lender relationship is the compensation scheme. If
broker compensation was linked to loan performance as well as loan production, the
incentive to churn would be mitigated.
The LaCour-Little and Chun’s study demonstrates the lack of alignment between
brokers and investors, but owing to the fact that it focused on FHA loans was limited to
studying refinance behavior. Non-government backed loans in general, and subprime
loans in particular, carry significant default risk as well. Some borrowers may have little
initial wealth. They can only afford low down-payments. These private labeled loans
usually have a higher Loan-to-Value (LTV). Therefore, even a small drop in house price
might put default option in the money, and affords a large incentive for home owners to
walk away.
Alexander et al. (2002) study competing risks of default and prepayment for loans
originated by one major subprime lending institution in US, a lender that uses both TPO
and retail origination channels. After applying the competing risk model, they find that
the default probability originated through the TPO channel group is higher than the
default probability for loans originated through the retail channel. Alexander et al.’s data,
however, lack an income filed, and so differences in channel may simply proxy for
14

differences in income. The paper does include an ability-to-pay variable, but it is largely
a function of borrower FICO score. The authors find that those with lower ability-to-pay
have higher default probability than those with higher ability-to-pay.
In contrast with the one of LaCour-Little and Chun, Alexander, et al.’s prepayment
result shows different story. The prepayment risk for the TPO group is smaller than the
retail group. The authors posit that the discrepancy may arise from changes in retailers’
marketing strategy. Specifically, lenders as well as brokers began using mass media
solicitations to generate business. Retail lenders also pass-through some loans to the
secondary market, and have a similar funding channel as TPO. It would appear that for a
while, brokers were more likely to “churn,” but ultimately retail lenders, who could also
earn fees through new business, catch up with the same way to ask more homeowner with
retail channel to refinance.
2.4 Competing Risks Hazard Model

The empirical model is based on the contingent claims models of Black-Scholes
(2012), Merton(1973), and Cox, Ingersoll, and Ross (1985). Contingent claims approach
offers a systematic method to value various options. It can be applied to many financial
products that have contingents claim involving uncertainty. For example, debt securities
can be treated as a combination of risk-free assets and contingent claims assets (Merton
1973).
Similar to debt securities, a mortgage asset has several sources of uncertainty: term-
structure risk, default risk (Foster and Van Order 1984), and prepayment risk (Buser,
15

Hendershott, and Sanders 1985). The value of mortgage can therefore be viewed as a
risk-free asset plus a set of contingent claims. The default option is a put option giving
the owner the right, but not the obligation, to sell the underlying asset at a predetermined
strike price. The prepayment option is a call option allowing the homeowner to buy the
mortgage at the par value of the remaining balance.
Series of papers by Brennan and Schwartz (1985), Buser et al. (1985), Dunn and
McConnell (1981, 1981) and Quigley and Van Order (1990) use option theory to provide
theoretical models for valuing prepayment. Other strands of the literature (Ambrose and
Capone 2000; Epperson et al. 1985; Foster and Van Order 1984) use an option
framework to evaluate default risk. Single risk models, however, fail to consider
counterparty risk, and therefore overestimate mortgage value. Kau et al. (1992) points out
the real mortgage value to lender is not as much of the value estimated when considering
a single risk
6
.
Deng, Quigley, and Van Order (1996) and Deng (1997) and offer a unified treatment
on default and prepayment valuation employing McCall (1996)’s proportional hazard
framework. They estimate the jointness of the default and prepayment risks using a
maximum likelihood estimation approach. Deng, Quigley, and Van Order (2000) also
extend this model to consider the unobserved heterogeneity among borrowers. For
example, some borrowers are more “woodhead” or more “ostrich” (Green and LaCour-

6
V= A(r,t)-Joint(H,r,t), where A is present value of the remaining amortizing loan payments, and J is the value of joint
options on prepay and default on a mortgage. Either V=A(r,t)-Call(H,r,t), for default-free mortgage, or V= A(r,t)-
Default(H,r,t), for non-callable loan would overestimate the value of mortgage to lender. (Kau et al. 1992)
16

Little 1999) than others. Deng, Quigley, and Van Order (2000)’s empirical result shows
over forty percent of the borrowers would exercise the prepayment quickly, and about 5
percent are non-sensitive to this call option.
Their study states that the heterogeneity is not trivial among different mortgage
borrowers, particularly concerning prepayment risk. The group of borrowers, who are
sensitive to the change of interest-rate, may quickly act on low interest-rate environment
to prepay and refinance into lower interest-rate loans. As more interest-rate sensitive
borrowers leave the original pool of loan, that loan pool may end up with a majority of
“woodhead” and “ostrich” that would barely refinance even when the call option is deep
in money. Therefore, model without considering heterogeneity in borrowers may
underestimate the prepayment risk.
Owing to the advantages of the approach, this essay adopts the competing risks
hazard model. Using the notation and format of Deng, Quigley, and Van Order (2000),
denote t
p
and t
d
as the random variables that represent the mortgage duration before
default and prepayment. The joint survivor function is specified by:

𝑆 ( 𝑡 𝑝 , 𝑡 𝑑 | 𝑟 , 𝐻 , 𝑌 , 𝑋 , 𝜂 𝑝 , 𝜂 𝑑 )
= ex p ⁡ ( − 𝜂 𝑝 ∑ ex p ( 𝛾 𝑝𝑘
+ 𝛽 𝑝𝑜
′
𝑔 𝑝𝑘
( 𝑟 , 𝐻 , 𝑌 ) + 𝛽 𝑝𝑛
′
𝑋 )
𝑡 𝑝 𝑘 = 1
− 𝜂 𝑑 ∑ ex p ( 𝛾 𝑑𝑘
+ 𝛽 𝑑𝑜
′
𝑔 𝑑𝑘
( 𝑟 , 𝐻 , 𝑌 ) + 𝛽 𝑑𝑛
′
𝑋 )
𝑡 𝑑 𝑘 = 1
)
17

, where g
jk
( r , H , Y )
7
is a vector function for time-varying options-related covariates with
the corresponding parameters β
jo
′
; X is a vector including other non-option-related
variables with the corresponding parameters β
jn
′
; η
j
is an unobservable scale parameter
that generates a rational comparison to differentiate default and prepay hazard functions.
The γ
jk
is a baseline hazard parameter in following general form:
𝛾 𝑗𝑘
= log [ ∫ ℎ
0 𝑗 ( 𝑡 ) 𝑑𝑡
𝑘 𝑘 − 1
] , 𝑗 = 𝑝 , 𝑑 .
This paper uses a nonparametric baseline hazard following the Public Securities
Association (PSA) and Standard Default Assumption (SDA) specifications
8
. The nature
of competing risks means that only the first termination is observable, or one can only
observe min( t
p
, t
d
) for t; the probability of mortgage prepayment in period k is denoted
as F
p
( k | η
p
, η
d
) ; the probability of mortgage default in period k is F
d
( k | η
p
, η
d
) ; the
probability of a mortgage record ending due to right-censoring is F
c
( k | η
p
, η
d
) . The
probability functions is specified by following McCall (1996) and Deng, Quigley, and
Van Order (2000):

7
The input of vector function includes the interest rate (r), property value (H), and other variables (Y).
8
The PSA assumes a gradual rise in termination with a monthly speed of 0.2 percent. The hazard rate would peak in 30
months, and stay the same level after. The SDA assumes a gradual rise in annual default rate that starts at 0.02 percent,
and peak at 0.6 percent in 30months, and remain 0.6 percent until the 60
th
month. It begins to declines by 0.0095
percent each month till 120
th
month, and remains 0.03 percent till the maturity.
18

F
p
( k | η
p
, η
d
) = S ( k , k | η
p
, η
d
) − S ( k + 1 , k | η
p
, η
d
)
−
1
2
( S ( k , k | η
p
, η
d
) + S ( k + 1 , k + 1 | η
p
, η
d
) − S ( k , k + 1 | η
p
, η
d
) − S ( k
+ 1 , k | η
p
, η
d
) )
F
d
( k | η
p
, η
d
) = S ( k , k | η
p
, η
d
) − S ( k , k + 1 | η
p
, η
d
)
−
1
2
( S ( k , k | η
p
, η
d
) + S ( k + 1 , k + 1 | η
p
, η
d
) − S ( k , k + 1 | η
p
, η
d
) − S ( k
+ 1 , k | η
p
, η
d
) )
F
c
( k | η
p
, η
d
) = S ( k , k | η
p
, η
d
)
The unconditional probability for each outcome is given by
F
j
( k ) = p
w
F
j
( k | η
jw
, η
jw
) + p
R
F
j
( k | η
jR
, η
jR
) , j = d , p , c .
, where p
w
and p
R
are the probabilities of being woodhead and being ruthless,
respectively, and η
jw
, and ⁡η
jR
are the scale parameters for each group.
The log likelihood function in competing risks framework is specified by:
log L = ∑ { δ
pi
log (
N
i = 1
F
p
( K
i
) ) + δ
di
log ( F
d
( K
i
) ) + δ
ci
log ( F
c
( K
i
) ) }
In this analysis, g
jk
( r , H , Y ) includes two variables: the call option value (CALL) and
put option value (PUT). Call is defined as:
C A L L
i , ki
=
∑
P
i
( 1 + m
j , τ
i
+ k
i
)
t
TM
i
− ki
t = 1
⁡ − ⁡ ∑
P
i
( 1 + r
i
)
t
TM
i
− ki
t = 1
∑
P
i
( 1 + m
j , τ
i
+ k
i
)
t
TM
i
− ki
t = 1

19

, where TM is the loan term, P is the monthly payment, m is the primary mortgage rate in
terms to different loan term, and r is the mortgage coupon rate at the origination.
The value of the put option is defined as the probability of negative equity
PUT
i , ki
= p r ob ⁡ ( E
i , ki
< 0 )
, where E is equity divided by market value. It assumes that property values follow the
FHFA house price index. E follows the normal distribution with zero mean and state
level property value variance
9
.
2.5 CTSLink Data

This study uses a dataset collected from the Wells Fargo’s CTSLink service. The
data have been collected from www.ctslink.com. It includes 4 million loans from
residential Mortgage-Backed securities issuers for which Wells Fargo serves as trustee.
CTSLink contains information from around 400 private label mortgage-backed securities
issuers, who range from large national banks, such as Citigroup, to small issuers. The
dataset includes 1,205,876 private-label loans. As noted, these loans are not eligible for
GSE purchase, but they are securitized. The issuers of securities are non-agency, but
private institutions. All loans were issued between 1996 and 2008, and the mortgage
history in data ends at December 2010. Each loan has origination date, property type,
loan purpose, FICO score, lien status (i.e., priority), original balance, original appraisal

9
State variance is calculated from Federal Housing Finance Agency (FHFA) state volatility parameters.
20

value, original term, loan-to-value ratio at origination, coupon rate, type of interest rate
(30-year, 15-year, etc.), indicators of default (whether the loan was ever 30-, 60- or 90-
days late), the property zip code and state, and, particularly important, name of originator.
Sample restricts attention to first lien loans for principal residence owner-occupiers
(this makes up 77.1 percent of owners). It is also limited to fixed-rate mortgages, which
comprise 37.5 percent of the CTSLink data. The analysis is further refined to include
only loans originated between 2002 and 2008. After these filters, the data contain a total
of 366,249 loans. Table 2-1 and 2-2 shows the distribution of the owner occupied type
and origination year. 77 percent of the loans are primary residence-type. 19 percent are
for investment. 66 percent were originated in 2006 and 2007.
Table 2-1: Frequency of owner occupied type in full data set
Owner Occupied Type Count Percent
INVESTOR 68,415 18.68%
PRIMARY 282,415 77.11%
SECONDARY 10,585 2.89%
TENANT 806 0.22%
UNKNOWN 4,029 1.10%
Total 366,249

21

Table 2-2: Frequency of origination year in full data set
Year Count Percent
2002 12,892 3.52%
2003 41,093 11.22%
2004 34,904 9.53%
2005 35,013 9.56%
2006 167,962 45.86%
2007 73,909 20.18%
2008 476 0.13%
Total 366,249

Two closely matched national conduit lenders are chosen from hundreds of lenders.
Neither holds mortgages on balance sheet, except for warehousing purposes. This allows
estimation to avoid the lemons problem, because investors will know that the originator is
not holding “good” loans in portfolio (An, Deng, and Gabriel 2011). But the lenders are
different in one respect: Lender A originates 85 percent of loans through the retail
channel, while Lender B originates 95 percent of loans through the TPO channel. Table
2-1 illustrates summary statistics on the two lenders. Surprisingly, the TPO lender has
superior observables: on average its loans have lesser loan-to-value ratios and better
FICO scores than the retail group. The TPO lender does originate larger loans on average.
22

The study adopts the competing risk model described earlier, and includes time
invariant variables, such as categorical variables for loan-to-value, FICO score, and year
of origination.
Table 2-3: Descriptive statistics for mortgage loans – retail versus TPO
Lender A Lender B (TPO)
Variable Mean Std. Dev. Mean Std. Dev.
Original loan balance 314962 245656 331303 239467
Loan term 339.05 56.17 322.48 76.70
Short term indicator (<360 months) 0.13 0.33 0.20 0.40
Coupon Rate 6.26 0.77 6.61 1.19
Origination year
<2005 0.49 0.50 0.43 0.49
2005
0.11 0.31 0.21 0.40
2006
0.15 0.36 0.25 0.43
>= 2007
0.25 0.43 0.12 0.32
Loan to value ratio (LTV) 77.47 17.80 72.79 15.55
LTV less than 70 0.27 0.44 0.30 0.46
LTV between 70 and 80
0.43 0.49 0.59 0.49
LTV between 80 and 90
0.06 0.24 0.06 0.23
LTV greater than 90
0.25 0.43 0.05 0.23
FICO score 706 57 712 47
Percentage of African Americans in zip
code 0.08 0.14 0.09 0.16
Median household Income in zip code 58009 24667 57537 21083
Census Division
New England 0.08 0.28 0.05 0.21
Middle Atlantic 0.28 0.45 0.22 0.41
East North Central 0.11 0.32 0.10 0.30
West North Central 0.08 0.27 0.02 0.15
South Atlantic 0.15 0.36 0.13 0.34
East South Central 0.04 0.19 0.01 0.11
West South Central 0.07 0.25 0.08 0.27
Mountain 0.05 0.22 0.06 0.24
Pacific 0.14 0.34 0.33 0.47
Number of observations 5459 4785

23

Other time-invariant variables include the percentage of African American
population (BLK_PCNT), median household income (MEDIANHI) in the census tract in
which the house is located and dummy variable (SHORTTRM) to indicate loan term is
less than 360 months. To take into account regional economic differences, dummy
variables for the nine census regions are considered.
The time-variant variables include an estimate of the put option value (PUT), an
estimate of the call option value (CALL) and the monthly state unemployment rate
(UNR). CALL is a variable to measure how deep the prepayment option is in the money.
It is defined as the difference between sum of the discounted value of all remaining loan
payments with current interest rate and the sum of the discounted value of all remaining
loan payment with the original mortgage rate. The paper collected the fixed-rate
mortgage rates from Freddie Mac Primary Mortgage Market Survey (PMMS) for
calculating the call options. Figure 2-1 displays the 30-year fixed-rate remained around
6.5% between 2006 and 2007, but gradually declined since the subprime crisis. In a
declining interest rate environment, the call option in the loans originated between 2006
and 2007 would be in the money.

24

0
1
2
3
4
5
6
7
8
200401
200405
200409
200501
200505
200509
200601
200605
200609
200701
200705
200709
200801
200805
200809
200901
200905
200909
201001
201005
201009
201101
201105
201109
201201
201205
201209
201301
201305
201309
15 Year FRM 30 Year FRM
Figure 2-1: Freddie Mac Primary Mortgage Market Survey 15 years and 30 years
Fixed Rate Mortgage

Sources: Mortgage Rates Survey from Freddie Mac
In order to calculate put option value (PUT), or default value, we compare amortized
loan balance to the current home value, which we estimate using quarterly federal
housing finance agency (FHFA) MSA House Price Indexes. State FHFA HPI volatility
parameters in 2010 are used to calculate a probability that the default option is in the
money. From the Bureau of Labor Statistic, state monthly unemployment rate is used as
an explanatory variable to proxy for a “trigger event”.
25

Table 2-4: Competing risks hazard estimates with unobserved heterogeneity

Prepay Default
Parameter Estimate t-stat. Estimate t-stat.
Origination year
2005
0.3305 5.633 *** 0.6511 6.194 ***
2006
0.4731 7.266 *** 0.5578 5.661 ***
>= 2007
0.4432 6.127 *** 0.5856 5.604 ***
Loan to value ratio (LTV)

LTV between 70 and 80
0.0683 1.455 * 0.5918 5.758 ***
LTV between 80 and 90
0.3957 4.421 *** 0.3909 2.622 ***
LTV greater than 90
0.9382 11.493 *** 0.3909 2.715 ***
FICO score
FICO between 620 and 680 0.1366 1.326 * -0.4628 -3.483 ***
FICO between 680 and 740 0.2076 2.019 ** -0.6484 -4.790 ***
FICO greater than 740 0.5132 4.954 *** -1.4195 -9.335 ***
Percentage of African Americans in zip code -0.2431 -1.713 ** -0.0138 -0.073

Short term indicator (<360 months) 0.0254 0.462 -0.3554 -2.753 ***
Median household Income in zip code 0.0305 3.101 *** -0.0693 -3.517 ***
Loan balance in 10,000 (log) 0.1102 3.588 *** 0.1139 2.083 **
Third-Party originated (TPO) loans -0.1142 -2.613 *** 0.2582 3.795 ***
Census Division
New England -0.2075 -2.516 *** 1.0415 6.662 ***
Middle Atlantic -0.3985 -6.892 *** 0.8708 7.778 ***
East North Central -0.2388 -3.248 *** 0.5371 4.665 ***
West North Central -0.2176 -2.323 ** 1.1697 7.245 ***
South Atlantic -0.3788 -5.405 *** 0.7175 6.802 ***
East South Central -0.2052 -1.694 ** 1.1122 5.696 ***
West South Central -0.5273 -6.124 *** 0.465 2.568 ***
Mountain -0.1408 -1.666 ** 0.5814 4.926 ***
Call option value (fraction of loan value) 4.7099 14.868 *** 3.5078 12.998 ***
Put option value (prob. of negative equity) -3.6292 -19.552 *** 1.341 7.740 ***
State unemployment rate -0.0244 -2.372 *** 0.227 12.302 ***
Woodhead 0.0738 6.416 *** 0.0024 3.182 ***
Ruthless 0.7 0 0.0001 0.030
MASS1 0.0253 2.1273 **
Note: Model is estimated by ML approach with PSA baseline hazard function with prepayment and SDA
baseline hazard function with default. Both risks are considered as correlated competing risk and estimated
jointly. LOC1 and LOC2 are locational parameters of the error distribution. LOC2 in prepayment is locked a
0.7. MASS1 is normalized to 1.0 during estimation.
26

2.6 Empirical Results

The model generally performs as expected, in table 2-2. Prepayment gets faster as
vintages become more recent, likely because interest rates fell dramatically in 2008.
Those with higher FICO scores also prepaid more quickly, presumably because the most
credit worthy borrowers have easier access to refinance their mortgage. Census tracts
with higher African-American population prepay more slowly, consistent with the
findings in Clapp, Deng, and An (2006), but the coefficient is not significant. Richer
census tracts have faster prepayment, consistent with the story correlating resources with
access to refinance. The call option variable works as expected, as does the put option—
when households are underwater, they are less able to refinance. Higher unemployment
also produces a lower propensity to refinance; this again is consistent with the
relationship between economic stability and access to refinancing. The one surprise is
that households with higher LTVs at origination are more likely to refinance, but this
does take into account a control for the mark-to-market loan-to-value (i.e., the proxy for
the put option). This study finds, consistent with Alexander, the TPO loans prepay less
frequently than retail loans.
With respect to default, most variables work as expected. Once the value of the put
option is controlled for, the fact that a loan is originated after 2005 (or just before the
house price peak) increases the probability of default. Loans with LTVs above 70
percent at origination are more likely to default, indicating the sunk cost might have an
influence on default behavior. The probability of default decreases with FICO score. It
also increases with unemployment rate. High proportion African-Americans
27

neighborhoods have no more or less frequent than anywhere else. The one large surprise
is that as the prepayment option becomes more valuable, so too does the probability of
default. The fact that default wipes out the prepayment option makes this finding a little
puzzling.
The featured result is that loans originated by the TPO lender do default more
regularly than those originated through the retail channel. The reasons for this might
include Alexander et al. (2002)’s active gaming (broker report exaggerated mortgagee’s
credit or which to increase the approval rate) and passive gaming (apply less due
diligence to the underwriting process).
The termination risks are different between woodhead and ruthless groups. The
ruthless group is 9.5 times more likely to prepay (e.g., 0.700 versus 0.073) than
woodhead group. The result is similar to Deng and Quigley (2004)’s 7 times more risky
in ruthless group. For default, this result shows no significant evidence between two
groups. It is consistent with the result in Deng and Quigley (2004).
Regards to the percentage of ruthless borrowers in this sample, it is about 2.5 percent,
compared with Deng and Quigley (2004)’s 95 percent in prime market and Deng,
Quigley, and Van Order (2000)’s 40 percent in prime mortgages. It is highly possible that
the subprime nature in this sample indicates the borrowers are generally less education
and less financial sensitive to call option value.

28

2.7 Conclusions

This paper performs a “case study” comparing performance outcomes between a
TPO and a retail lender, controlling for the standard set of mortgage underwriting
observables. In general, the TPO lender’s performance was worse than the retail lender.
The result is consistent with the finding of other two previous literatures studying before
sub-prime period. It shows more likelihood to default and less likelihood to prepay for
loans originated through TPO channel.
Although brokers may save homebuyer time and effort to finalize a mortgage and
finally buy a house, homebuyer should not depend on the choice of mortgage brokers.
Since their chosen mortgage product may significantly increase the chance of default. In
an event of default, there would be large loss in homebuyer’s equity and credit.
Investors in RMBS should try to collect more information on the underlying
collaterals of each mortgage-backed securities series. By inspecting the originators, one
should apply different scenario assumptions between TPO loans and retail loans. With
lower conditional prepayment rate (CPR) for TPO loans and high CPR for retail loans,
investors can get a better estimation of the future cash flow, and avoid severe loss.
29

Chapter 3: The Effect of Liquidity on Subprime
Terminations
3.1 Introduction

Residential real estate markets in United States have experienced a liquidity crunch
since 2007. Fund for home mortgages declined by 48 percent between the first quarter of
2007 and the first quarter of 2011
10
. The outstanding issuance of asset-backed securities
funding home mortgages is currently less than half of its peak at the second quarter of
2007. In the meantime, home prices have declined a lot, and residential mortgage
delinquencies have risen sharply.
Recent literature has studied the impact of liquidity shortages on market liquidity and
funding liquidity. Brunnermeier and Pedersen (2009) and Brunnermeier (2009) develop
models of liquidity spirals owing to margin calls and fire-sales that lead prices to
overshoot downward, beyond fundamentals. They emphasize the self-reinforcement
effects of equity/security prices when liquidity dries up. However they do not study the
impact of illiquidity on fundamentals themselves. For example, the absence of mortgage
market liquidity can by itself produce mortgage defaults. This is particularly clear in the
commercial mortgage market, where loans must roll over on a regular basis. In 2009,
companies that were arguably going concerns (General Growth and Forest City, among
them) had trouble acquiring new financing, even though their businesses had substantial

10
See http://ycharts.com/indicators/mortgage_originations/historical_data
30

positive cash flow. In the end, General Growth filed for bankruptcy so it could
reorganize its liabilities. The fact that it was able to emerge from bankruptcy quickly
suggests that it was indeed a going concern.
One could make a similar case for borrowers who are current on their mortgage, but
whose mortgage balance as a present value that is higher than the value of their house,
owing not only to declining house values, but also to the inability to refinance at par.
According to Brunnermeier and Pedersen (2009), market liquidity measures the
thickness of an asset in the market; and funding liquidity denotes as the easiness with
which fund account can liquidate asset to meet redemption. This paper extends the
liquidity concept to mortgage funding. The paper defines mortgage market liquidity as
the available fund for housing market. When available fund in mortgage sector expands,
it would narrow the mortgage spread and ease credit standard. It is easy for homeowner
to refinance the existing mortgage. It increases the value of prepayment option. When
mortgage fund contracts, the opposite would happen - the mortgage spread widens, credit
standard rises, and prepayment falls. This essay studies the funding liquidity from the
macro level (funding from national-wide asset-backed securities sector) to micro level
(funding to borrowers).
This study contributes to the literature on the role of liquidity in asset pricing. It
points out a unique characteristic of pricing mechanism in mortgage-backed security
(MBS) – the implicit call option—is strongly influenced by mortgage fund liquidity. The
call option in turn influences the put option of default. This contrasts with treasuries,
31

which duration is determined contractually. Liquidity hence has little impact on default
probabilities.
The fundamental value of underlying assets in MBS and mortgage funding liquidity
are positively correlated. Liquidity tends to drive down lending standards, and increases
the frequency of homeowners rolling over their loans. Data from Loan Performance
shows that the metropolitan areas with the greatest propensity for exotic loans, including
interest-only (IO) loans and pay-option adjustable rate mortgages, also had the fastest
prepayment rates in the country.
Now consider what happens if lending liquidity dries up. Lenders impose more
screening and exacting underwriting, and credit-constrained borrowers are prevented
from refinancing into lower interest rate loans. The absence of the ability to refinance
could lead owners to default; higher defaults in turn reduce the value of MBS. This
makes investors more cautious, and reluctant to hold mortgage backed securities,
especially, private label MBS. The rise of default risk would trigger compliance guideline
on mortgage risk and force asset manager to sale the securities even in stressed period. In
2008-2009, brokers charged high spread on private label MBS. For some problematic
deals and tranches, brokers even refused to offer price, due to no buy side order to offset
their position. Some bond holders had to ask deal underwriters, but underwriters do not
have the obligation to take the position.
Market was full of sell order, and the demand for new deal disappeared. Since no
participants on new deals, the mortgage market liquidity further dried up. Just as excess
liquidity lead to an upward spiral, so too could insufficient liquidity produce a downward
32

spiral. Even in the absence of liquidity one would have seen financial turmoil
(Brunnermeier 2009; Brunnermeier and Pedersen 2009), but the absence of liquidity
made the turmoil more turbulent.
Section II of chapter reviews broad literature on liquidity and mortgage termination
risk. Section III presents the multinomial logit (MNL) method as empirical model.
Section IV illustrates the data. Section V gives empirical results. Section VI provides a
conclusion.
3.2 Literature Review
3.2.1 Securitization

Securitization creates more liquid real estate markets. By putting loans that were
individually illiquid loans into a trust, issuers argued that they could diversify risk and
hence enhance liquidity. MBS issuers also argued that via charging, they could allow
investors to take on different tailored risk they wanted. Securities usually have a senior-
subordinate structure. Senior tranches were the first recipients of principal. If the senior
tranche received the first 50 percent of cash flow emanating from a mortgage, it was
deemed to be safe, because loans had to suffer expected losses of 50 percent for the
senior tranche to come to harm.
11

11
This paper only discusses the most “vanilla” of tranche structures here. Some highest tranches of Collateralized Debt
Obligations(CDO) that involved “retranching” were often not safe under any circumstances.
33

Securitization began to explode in the prime market during the 1980s and 1990s and
extended to the subprime market between 2002 and 2007. Hess and Smith (1988) argue
that securitization allowed investors from around the world, seeking both yield and the
management of interest rate risk, to fund households who demanded mortgages and who
might not have had access to bank finance. Hess and Smith pointed out that securitization
allowed banks to perform underwriting, short-term funding, and servicing, while
allowing them to avoid the interest rate risk which is inherently difficult for deposit-
funded institutions to manage. Securitization also held out the promise of allowing
financial institutions to focus on their retail services, and reduce the cost of
intermediation. And indeed, the fees associated with mortgages dropped precipitously
for the 25 years following 1981 (Nothaft, Pearce, and Stevanovic 2002).
Many studies have examined securitization’s effect on financial markets and
consumers. Sanders (2002) argues that securitization reduced mortgage rates and offer
liquidity to financial institutional by purchasing loans from them. Financial institutional
can unwind loan position from balance-sheet by securitization, and carry fewer burdens
on fiscal requirement.
Previous research has examined the impact of securitization on mortgage rates.
Woodward (2003) shows that once FHA loans were packaged into Ginnie Mae securities,
spreads between FHA mortgages and Treasuries narrowed. She notes that this had
nothing to do with credit risk, as FHA loans always had the full faith and credit of the US
government behind them. Rather, she argued, the securitization of the loans allowed for
greater liquidity, and Ginnie Mae’s rid borrowers of the need to pay a liquidity premium.
For the “agency loans”, it was liquidity combined with the implicit guarantee from
34

Federal government reduced the mortgage rates. Hendershott and Shilling (1989), in a
heavily cited paper, find that conforming loan rates were lower than non-conforming loan
rates, controlling for risk factors.
More recently, a series of researchers have sought to measures the impact from the
GSEs to change mortgage rates—to say the literature is controversial is an
understatement. While some (Fed bunch and CBO) argue that Fannie and Freddie passed
only a small fraction of their subsidy on to consumers, they did uniformly find that
consumers received some benefit from the GSEs, although it is not clear whether the
benefit arose from liquidity or from a subsidized interest rate. Todd (2001) finds no
evidence that securitization reduced the mortgage rates, but he did show that origination
fees fell as securitization volume increased.
Nothaft, Pearce, and Stevanovic (2002)argue that the GSE funding advantage was
pretty minimal, and therefore consumers benefitted largely from the GSEs liquidity,
rather than their subsidies. Ambrose, LaCour-Little, and Sanders (2004) use loan level
data, and argue that conforming loans had 5.5 percent lower yield spreads than other
loans. Naranjo and Toevs (2002) take a step further, and find a spillover effect from GSE
securities to non-conforming loan rates. The argument is that via securitization, the
GSEs created informational externalities for the non-GSE portion of the market.
3.2.2 Liquidity Impact

The impact of liquidity on the pricing of equities (as opposed to debt instruments
such as mortgages) has long been featured in literature. In a pioneering work, Fisher
35

(1959) studies the impact of liquidity on bond pricing. Using the volume of trading, the
bid-ask spread and the total outstanding volume as measures of marketability for bonds,
he found that bonds with low outstanding volume were less likely to change hands. The
thinness of the market for these bonds produced more uncertainty, which in turn showed
up in the bonds’ prices. Bonds issued in large volumes hence had demonstrably lower
risk premiums. In current practice, many asset management companies use bid-ask
spread as key factor for liquidity. For examples, Blackrock’s Aladdin liquidity risk report,
and Barclays Capital’s liquidity cost score system are both based on bid-ask spread
concept.
Similarly, Garbade and Silber (1976) use total outstanding bond volume to draw
associations between liquidity and pricing. Ambrose and Warga (1995) produce one of
the first papers designated to study the liquidity of agency bonds. Specifically, they look
at the difference in Fannie Mae and Treasury issues, and derive how the difference in
issues contributed to spread. Gonzalez-Rivera (2001) find that one basis point (bp)
increase in the spread, between the yield of a 30-year agency MBS and that of a 10-year
constant-maturity Treasury was associated with a difference of $554 million funding to
the agency secondary market.
When capital for mortgage lending is abundant, in that there is less risk of finding
investors willing to purchase securities, liquidity premium spread is so tightened that
market liquidity becomes insensitive to the funding liquidity (Brunnermeier and Pedersen
2009). But when losses cause funding liquidity to plummet, funding illiquidity will
trigger the loss of market liquidity. Brunnermeier (2009) and Brunnermeier and Pedersen
36

(2009) point out two liquidity-price spirals arising from the subprime crisis: the loss
spiral and the margin spiral.
1. Losses – funding problems for MBS -> investors in current MBS reduce position
-> securities price drop -> more losses -> loop again
2. Initial loss – funding problems for MBS -> investor reduce position -> securities
price drop -> increasingly high margin requirement -> fire-sales -> loop again

Figure 3-1: Liquidity chart

(revised from Brunnermeier and Pedersen (2009))
This paper proposed the third liquidity–price spiral in private label RMBS market as
follows:
3. Initial loss – mortgage funding problems for MBS -> investor reduce position ->
less funding for mortgage -> tighten underwriting standard -> increase default
risk of underlying loans -> lower fundamental value -> securities price drop ->
loop again
37

This third price spiral is part of by-products from securitization process. The
“originate to distribute” model of mortgage market provided liquidity and reduced
mortgage costs. The abundant liquidity might cause lax underwriting and less screening
to increase mortgage origination volume. Retail lenders, such as banks, only bear short
term (3-6 months) “pipeline risk” - the risk of holding the loans before securitization.
Loan originators tend not to face the consequences of default risk, and thus they have few
incentives to screen and monitor borrowers. Because they could shed credit risk, retail
lenders found that even shaky loans produced positive expected return, and therefore
approved loans even when credit models suggested that they shouldn’t.
12

Because third-party originators do not even finish pipeline risk, they hold even less
risk than retailer lenders. Exotic loans, such as pay-option adjustable rate mortgages,
teaser-rate adjustable rate mortgages, high loan-to-value ratio loans, piggyback loans and
home equity lines, as well as low- and no-documentation loans, tended to be originated
by brokers. LaCour-Little and Chun (1999), in an analysis of FHA loans, found that
broker-originated loans performed worse than others, in that they were more likely to
prepay, perhaps reflecting churning. Alexander et al. (2002) look at the competing risks
of default and prepayment for a subprime lender. With controlling for loan quality, their
data include both brokerage and retail origination channels. They find default probability
originated through the brokerage channel is higher than that for loans originated through
the retail channel.

12
The lemon’s problem, ironically, should have ameliorated this issue, as investors should have known that retails
would sell their worst loans, and hence should have only purchased them at a discount. This did not appear to happen,
however.
38

In the time of liquidity crunch, the above distribute model would suddenly dry up the
mortgage fund due to limited investors on non-agency RMBS. Issuers might have
difficulty to find the buyers for new deal, and expect high spread or lower price on new
deal.
3.2.3 Discrete Choice Theory and Multinomial Logit
Model

Regarding the mortgage termination, continuous-time methods is preferred given the
accuracy to estimate the coefficients, since people are making decision on a continuous
time basis. Borrowers are making decision about their mortgages anytime. However
mortgage performance data can only observe and record that decision on a monthly basis,
especially at the monthly due date. When home buyers continue on the mortgage
payment, one knows the mortgage would remain current. In the case of default, mortgage
would miss one scheduled payment. The default status would be recorded at the past due
date. Prepayment is similar. In discrete choice theory, Allison (1982)points out the
repeated events model can be constructed as a single event model, and one can break up
each event history into multiple discrete time units which would be treated independently.
This discrete time nature fits to the framework of multinomial logit model (MNL). In
MNL model, the logit of prepayment and default is estimated jointly. In each period, the
sum of three probability of default, prepay and current is always one. MNL requires
independent probability is offset by the reduction of other choices. It has a competing risk
nature for each condition.
39

3.3 Empirical Model

MNL model has been adopted in mortgage termination risk in various empirical
studies. Clapp et al. (2001) obtain maximum-likelihood estimators for binary
regression models in prepayment risk only. Calhoun and Deng (2002) expand the MNL
model into competing risk framework and more aggressively they suggest to use MNL
model for adjusted-rate mortgage. Clapp et al. (2006) propose a mass point mixed MNL
framework to estimate with unobserved heterogeneity. Although the advantage to
estimate with unobserved heterogeneity is being able to deal with different type of
borrowers, the results of Clapp et al. (2006)’s MNL and mass-point MNL have similar
significant coefficients and signs. They suggest the traditional MNL can be used to
estimate mortgage termination without unobserved heterogeneity.
The likelihood function and log-likelihood function for an MNL model can be
expressed as:
𝐿 ( 𝛽 ) = ∏ ∏ ∏ Pr ( 𝑦 𝑖𝑡
= 𝑗 )
𝐷 𝑖 𝑡 𝑗 2
𝑗 = 0
𝑁𝑡
𝑖 = 1
𝑇 𝑡 = 1
,
ln ( L ) = ∑ ∑ ∑ 𝐷 𝑖 𝑡 𝑗 ln ⁡ ( Pr ⁡ (
2
𝑗 = 0
𝑁𝑡
𝑖 = 1
𝑦 𝑖𝑡
= 𝑗 )
𝑇 𝑡 = 1

, where j = 0 for current, 1 for default, and 2 for prepay; Ditj is the status indicator for
loan i in time t with j status.
Define:
Pr ( 𝑌 𝑖𝑡
= 0 ) =
1
1 + ∑ ex p ⁡ (
𝐽 𝑘 = 1
𝑍 𝑖𝑡
‘
𝛽 𝑘 )
, ⁡ ⁡ ⁡ ⁡ j = 0 ,
40

Pr ( 𝑌 𝑖𝑡
= 𝑗 ) =
ex p ( 𝑍 𝑖𝑡
‘
𝛽 𝑗 )
1 + ∑ ex p ⁡ (
𝐽 𝑘 = 1
𝑍 𝑖𝑡
‘
𝛽 𝑘 )
, ⁡ ⁡ ⁡ ⁡ j = 1 , 2 ,

Where in each vector Z
it
is a vector of loan conditions for loan i, at the time t. It
includes time variables and time-invariant variables.
Using maximum likelihood method, it is easy for commercial software to finish the
estimation. It is able to cover large number of loan data, comparing to a much smaller
dataset in competing risk hazard model. Furthermore, MNL model is quickly to reach
convergence. The convergence is no guaranteed in competing risk hazard model. This
dataset has been sent to competing risk hazard framework, and cannot reach the
maximum likelihood estimators.
A long series of studies have focused on mortgage termination risk. Mortgages have
two embedded options - a call (prepayment) option and a put (default) option. The call
option value is the difference between the non-callable and callable mortgage. Using the
Cox, Ingersoll, and Ross (CIR) (1985) mean-reverting term structure, Buser et al. (1985)
find that on a mortgage with an 80 percent LTV, the value of the call option to the
borrower is about 30 basis points.
Dunn and McConnell (1981) find a similar option spread, although Buser at al. (1985)
point out that in principal, valuing mortgage options is very dependent on assumed
parameters. For instance, a higher speed of adjustment (k) in CIR, would reduce the
interest rate quickly. In turn, it would increase the prepayment likelihood, and increase
the call premium. When interest rates adjust quickly to their long term mean rates, deep
incentives to refinance would happen less frequently, hence reducing the likelihood of a
41

call being exercised and thus reducing the call premium (Buser, Hendershott, and Sanders
1985).
Moreover, Dunn and McConnell (1981) and Green and LaCour-Little (1998) show
borrowers often exercise options sub-optimally. Borrowers would at times refinance
when market rates are higher than the coupon on their mortgages; at other times they
would not refinance even when there is a large incentive to do so. This “suboptimal”
behavior makes mortgages more valuable to investors.
Green and Shoven (1986) introduce the proportional hazards model in mortgage
valuation. The hazard model is well-suited to handling the censoring problem endemic to
mortgage data. At the time they wrote the paper, mortgages were often assumable, and
thus their innovation was to show that the due-on-sale clauses would reduce the
prepayment probabilities significantly. The empirical result shows that the trigger time in
prepayment is highly correlated with the interest rate.
These insights seem obvious now, but were innovative at the time, Quigley and Van
Order (1990) estimate a hazard function of prepayment based on 6,375 loans. Like Green
and Shoven (1986), Quigley and Van Order (1990) find that the value of the call option
(the difference between the market and mortgage interest rates) is a significant and
sufficient determinant of prepayment. Quigley and Van Order (1990) also show that high
42

initial loan-to-value (LTV) reduces the possibility of prepayment, probably because of
liquidity constraints
13
.
Standing along the literature on the call option is literature on the put option (Foster
and Van Order, 1984; Epperson et al. 1985 and Cunningham and Hendershott, 1986).
The default option can use proxy by introducing the house price, H, into the formula for
calculating the mortgage value.
Mortgage X(r, H, t) is considered as derivative assets, and valued by a risk-adjusted
expected present value as follows:
𝑋 ( 𝑟 , 𝐻 , 𝑡 ) = 𝐸 ̅
[ 𝑋 ( 𝑟 ( 𝑇 ) , 𝐻 ( 𝑇 ) , 𝑇 ) 𝑒 − ∫ 𝑟 ( 𝑠 ) 𝑑𝑠
𝑇 𝑡 ]
Foster and Van Order (1984), and Cunningham and Hendershott (1986) point out the
dispersion on the underlying assets and the interest rate are the major determinates of
default. Foster and Van Order consider “ruthless” default, meaning the borrowers would
default whenever the present value of remaining mortgage payments is greater than the
value of property (i.e., the option is “in the money”). Cunningham and Hendershott (1986)
criticize this frictionless default framework because it ignores the reputational cost of loss
of credit rating.
Even though the ruthless default assumption is unrealistic, Quigley and Van Order
(1995)’s simulation result suggests that observed data proves the frictionless model is
valid assumption. However they point out that 1) ruthless model exaggerates the variation

13
See also Schwartz and Torous (1989).
43

when the default rate is high over time; 2) loss severities is positive related to initial loan-
to-values ratios, which is different to the mortgage literature; 3) the spread between
default likelihood for high LTV and low LTV loans is too high. Since the transaction cost
to exercise the option cannot account for these inconsistencies, they imply that there are
other transactions costs beyond reputational loss in trading houses. These costs are likely
idiosyncratic. Vandell (1995) proposes an agenda on the development of theoretic and
empirical models to translate transaction cost variables into the terms in option-price
model. Kau and Slawson (2002) attach four transaction costs into an option-pricing
model, and allow sub-optimal termination.
Pinoeered by Kau et al. (1992) and Kau et al. (1995), researchers focus on the
jointness of the default and prepayment risk. Kau et al. (1992) point out the real value of
the mortgage to lender (V) is less than the value arising from single risk. Particularly
important is that the prepayment and default options influence each other, and so
empirical models that focus on only on one option or the other will be mis-specified.
Kau and co-authors overcome this limitation by adopting a state space analysis, in
which the term structure of interest rate and home value patterns are estimated and the
state path is divided into prepayment, default and continuation regions. They also
consider nonfinancial prepayment and default motivations in the model. Their striking
finding is that the nonfinancial (or “suboptimal’) default, although rare, always lower V,
and the nonfinancial prepayment always raise V.
As discussed in the chapter 2, literature (Deng et al. 1996 and Deng 1997) begins to
extend the single risk framework to handle multiple risks with competing nature. Deng et
44

al. (2000) also divide the borrowers into subgroup with different responds to home price
and interest rate. This heterogeneity among borrowers is documented.
Recent studies have extended the competing risk model to incorporate homeowner
mobility. Clapp et al. (2001) separate prepayments triggered by refinancing and by
moving. Archer, Ling, and McGill (1997) and more recently An, Clapp, and Deng (2010)
show that mobility characteristics affect the probability of moving, and therefore
prepayment. The data, described below, prevent from identifying the impact of mobility
on prepayment.
A boom in structured finance arguably led to aggressive lending practices and lower
lending standards. Keys et al. (2010) use a discontinuity design to show that loans that
qualified for securitization defaulted about ten to twenty percentage points more than
loans that did not qualify for securitization. Mian and Sufi (2009) show that credit growth
grew rapidly relative to income growth. Demyanyk and Van Hemert (2011) show that
after controlling for measurable characteristics, vintage 2006 and 2007 loans had higher
delinquency rates than loans of earlier vintage.
This discrepancy is consistent with the hypothesis that liquidity by itself has an
impact on termination risk. This study extends the literature by examining the effects of
liquidity on both types of termination risk: prepayment and default.
3.4 Data

This chapter uses same data as previous chapter, but focuses on different scope. This
chapter focuses on full data set by looking at different originators. This is different from
45

last chapter in which only two originators are selected to conduct the analysis. The
dataset was collected from the Wells Fargo’s CTSLink service. Most loans are non-
conforming loans, which mean that they do not meet the requirements of government-
sponsored enterprises (GSEs). These loans are acquired by private parties. In contrast to
conforming loans, which are guaranteed by the GSEs, senior investors in non-agency
loans are protected through subordination. In periods of severe house price declines,
however, subordinate securities can be eaten through, putting senior securities at risk.
Even the most senior securities should be somewhat price sensitive to changes in default
probability.
The dataset includes 1.2 million private-label securitized loans which were originated
between 1996 and 2008. 16 percent of loans were originated before 2004. 14 percent of
loans were originated in 2005. Majority of the loans, or 53 percent of the loans were
originated in 2006 or the year right before subprime crisis. The mortgage history in data
ends in December 2010. The individual loan data include origination date, property type,
loan purpose, FICO score, lien status (i.e., priority), original balance, original appraisal
value, original term, loan-to-value ratio at origination, coupon rate, type of interest rate
(30-year, 15-year, etc.), indicators of default (whether the loan was ever 30-, 60- or 90-
days late), property zip code and state.
Using the same treatment of previous chapter, the data exclude non-first lien loans,
investor loans, and adjusted-rate mortgages. Because the vast majority of the loans in the
data were originated between 2002 and 2008, the empirical research is restricted to
analyzing loans originated in this period. After these filters, data contain a total of
366,249 loans. Owing to the computational complexity of estimating a competing risk
46

model with heterogeneity, the estimation is based on a random draw of 20,000 loans from
the pool of loans. As demonstrated in Table 3-1, the characteristics of the sample
represent the population of mortgages for full sample.
Table 3-1: Descriptive statistics between sample and all loans
Sample All loans
Variable Mean
Std.
Dev.
Mean
Std.
Dev.
Original loan balance

208,803

215,198

208,940

212,328
Loan term

310.8

80.7

310.8

81.0
Coupon rate

8.0

2.5

8.0

2.5
LTV

63.3

29.2

63.1

29.2
FICO score

677.7

67.0

688.0

67.3
Percentage of African Americans in zip
code

0.1

0.2

0.1

0.2
Median household income in zip code

50,956

19,039

51,091

19,223
Observations 20,000 366,249

By collecting data from the Federal Reserve Board, we obtain home mortgages level
(ABS_L) in asset-backed securities (ABS). The data represent the quarterly level of
outstanding volume for ABS in home mortgages. The home mortgage presents about 40
percent of total financial assets in asset-backed securities. Different asset classes in asset-
backed securities change in the same way. They peaked at the second quarter of 2007 and
declined since then. The outstanding volume represents the market supply and demand
for each sector. If the investors are more likely to participate in ABS, the issuers are more
47

-
500,000
1,000,000
1,500,000
2,000,000
2,500,000
3,000,000
3,500,000
4,000,000
4,500,000
5,000,000
2005Q1
2005Q2
2005Q3
2005Q4
2006Q1
2006Q2
2006Q3
2006Q4
2007Q1
2007Q2
2007Q3
2007Q4
2008Q1
2008Q2
2008Q3
2008Q4
2009Q1
2009Q2
2009Q3
2009Q4
2010Q1
2010Q2
2010Q3
2010Q4
2011Q1
2011Q2
2011Q3
2011Q4
2012Q1
2012Q2
2012Q3
2012Q4
2013Q1
2013Q2
2013Q3
2013Q4
USD Millions
Issuers of asset-backed securities; total financial assets
Issuers of asset-backed securities; total mortgages; asset
Issuers of asset-backed securities; home mortgages; asset
likely to pool the loans and issue more series of tranches to fit the need of investors.
Apparently, after the sub-prime crisis, investors are running away from this sector.
Figure 3-2: Outstanding volume in Asset-Backed Securities
Source: Federal Reserve Board 2014
In order to better estimate the effect of LTV, FICO and seasonal-effect, these
variables are further designed into categorical variables. Here is a list of other time-
invariant variables: percentage of African American population (BLK_PCNT), and
median household income (MEDIANHI) in the zip code in which the house is located, as
well as dummy variables for the nine census regions.
48

Figure 3-3 demonstrates the concentration of the loans within each census division.
24.6 percent of sample located in Pacific Division (Alaska, California, Hawaii, Oregon
and Washington) and 22.5 percent located in South Atlantic (Delaware, District of
Columbia, Florida, Georgia, Maryland, North Carolina, South Carolina, Virginia and
West Virginia).
Table 3-2: Descriptive statistics for mortgage loans
Variable Mean Std. Dev.
Original loan balance 208,003 215,198
Loan term 310.77 80.69
Short term indicator (<360 months) 0.30 0.50
Coupon rate 8.00 2.50
Origination year
2005 0.14 0.35
2006 0.53 0.50
>= 2007 0.17 0.37
Loan to value ratio (LTV) 63.30 29.20
LTV between 70 and 80 0.28 0.45
LTV between 80 and 90 0.10 0.30
LTV greater than 90 0.16 0.37
FICO score 667.70 67.00
Percentage of African Americans in zip code 0.13 0.20
Median household income in zip code 50,956 19,039
Census Division
New England 0.043 0.202
Middle Atlantic 0.119 0.324
East North Central 0.120 0.325
West North Central 0.044 0.205
South Atlantic 0.225 0.418
East South Central 0.035 0.183
West South Central 0.090 0.286
Mountain 0.078 0.268
Pacific 0.246 0.430
Number of observations 20,000

49

Figure 3-3: Sample percentage in Census Region
50

Different from previous chapter, this chapter includes one more time-variant variable
(the outstanding issuance of ABS_L) into the model. It would be estimated with the put
option value (PUT), an estimate of the call option value (CALL) and the monthly state
unemployment rate (UNR). We also try to estimate the model using ABS_Flow, which
measures the market flow in outstanding issuance of asset-backed securities.
𝐴 𝐵 𝑆 _ 𝐹𝑙𝑜𝑤 𝑡 = 𝐴 𝐵 𝑆 _ 𝐿𝑒 𝑣𝑒 𝑙 𝑡 − 𝐴 𝐵 𝑆 _ 𝐿𝑒𝑣𝑒𝑙 𝑡 − 1

But ABS_Flow variable does not receive significant estimation for most models.
3.5 Empirical Results

The table 3-3 reports the result of MNL using a random sample of 20,000 loans
described above. The result is consistent with option theory. The call option variable has
substantial explanatory power for the prepayment decision. When the value of call option
is “in the money”, homeowners are more likely to exercise the ability to refinance into
the lower interest rate.

51

Table 3-3: Multinomial Logit (MNL) estimates for mortgage prepayment and
default
Prepay Default
Parameter Estimate
Std.
Er.
Estimate
Std.
Er.
intercept -9.348 0.251 *** -4.958 0.382 ***
Original loan balance 0.106 0.019 *** 0.281 0.030 ***
Short term indicator (<360 months) 0.496 0.028 *** -0.186 0.060 ***
Origination year
2005 -0.135 0.042 *** 2.169 0.107 ***
2006 -0.052 0.038 2.586 0.100 ***
>= 2007 -0.281 0.048 *** 2.542 0.103 ***
Loan to value ratio (LTV)
LTV between 70 and 80 -0.296 0.036 *** 0.353 0.051 ***
LTV between 80 and 90 -0.496 0.053 *** 0.259 0.061 ***
LTV greater than 90 -0.042 0.035 0.194 0.061 ***
FICO score
FICO between 620 and 680 0.179 0.032 *** -0.172 0.044 ***
FICO between 680 and 720 0.261 0.037 *** -0.427 0.054 ***
FICO greater than 720 0.510 0.041 *** -1.205 0.084 ***
Percentage of African Americans in zip code 0.018 0.066 -0.063 0.091
Median household income in zip code 0.496 0.028 *** -0.186 0.060 ***
Census Division
New England -0.119 0.061 * 0.116 0.102

Middle Atlantic -0.209 0.043 *** 0.072 0.070

East North Central -0.318 0.043 *** 0.290 0.070 ***
West North Central -0.143 0.060 ** 0.110 0.104

South Atlantic -0.149 0.036 *** -0.039 0.056

East South Central -0.285 0.070 *** 0.283 0.105 ***
West South Central -0.421 0.053 *** -0.299 0.860 ***
Mountain 0.059 0.045 0.038 0.077
Call option value (fraction of loan value) 4.800 0.116 *** 2.034 0.130 ***
Put option value (prob. Of negative equity) -0.161 0.054 *** 0.991 0.056 ***
Unemployment rate in zip code 0.076 0.005 *** -0.146 0.005 ***
ABS home mortgage level 0.001 0.000 *** -0.003 0.000 ***
Number of loans 20,000

52

Original loan-to-value (LTV) matters as an explanatory variable even after
controlling for the value of the put option. The explanation for this might be loss
aversion as shown in Green, Rosenblatt, and Yao (2011) or the existence of asymmetric
information between borrowers and lenders as shown in Deng et al. (2000). Loans with
LTV at origination of over 70% are more likely to default than those with lower LTV.
The impact of LTV at origination on prepayment choice is negative. As LTV rises,
prepayment propensity falls. In contrast with others’ findings, Green, Rosenblatt, and
Yao (2011) find that, after controlling for mark-to-market LTV, LTV at origination has
no impact on prepayment. The effect in this estimation does attenuate the prepayment
speed, as LTV rises.
Higher FICO score borrowers prepay more quickly, likely owing to their easier
access to credit. Homeowner with high FICO score can get qualified again to take
advantage of lower interest rate in different market conditions.
Not surprisingly, high FICO borrowers are less likely to default. The result finds that
minority borrowers are neither more nor less likely to prepay or default. Loans with
maturities of less than 30 years prepay more quickly, and default less. The estimate also
shows that median household income in neighborhood and unemployment variables have
the expected impacts on prepayment and default. Higher original loans balances produce
higher prepayment and default risks.
With respect to regions, the result finds the Pacific and Mountain regions have the
fastest prepayment rates. Within these regions include California, Arizona and Nevada,
brokers were engaged in substantial churning. In terms of default, there is considerable
53

variation across regions. Finally, the proxy for liquidity – outstanding ABS issuance
levels, performs as expected. Prepayment gets faster as more credit is available in the
home mortgage market. Homeowners are also less likely to default in the face of
abundant liquidity. Again, these results hold even after controlling for the call and put
options.
3.6 Conclusions

This chapter presents evidence that termination risks are influenced by mortgage
market liquidity. In a credit-friendly environment, borrowers can obtain loans with
relaxed underwriting through both retail and broker channels. Homeowners can easily
refinance their loans, and this by itself makes them less likely to default. But the recent
credit crunch has reversed this. Banks tightened their underwriting standards and brokers
found it more difficult to shop around loans among the wholesale lenders, as the private
label market has largely shut down. The estimate shows in such an environment, people
default at a faster speed, and refinance less often. This increases the default termination
risk for the underlying assets for MBS.
To the extent illiquidity raises the risk of default, it causes house prices to drop,
which in turn destabilizes the loans that at one time were stable, and which can produce a
negative feedback loop. Not including liquidity in empirical models poses a potential
challenge to the accuracy of termination models and the valuation of mortgages. The
empirical results also support the possibility of a Brunnermeier and Pedersen (2009) type
54

liquidity-price spiral. We claim that a liquidity-price spiral on mortgage market amplifies
the recent financial turmoil.

55

Chapter 4: Trustee Auction Sales Discount on
House Prices
4.1 Introduction

The mortgage foreclosures in the United States increased rapidly between 2008 and
2013. It is widely accepted that home foreclosures impose great costs on lenders and
borrowers, and on community and society. In most cases, home foreclosures are ended
with distressed sale. During delinquency, lenders are likely to accept short-sales from
delinquent borrowers even the sales of proceeds cannot repay mortgage obligations and
fees. Similar to short-sales, in foreclosure, the final auction price might be less than the
outstanding balance of the loan. Lenders can avoid repossessing the home and reduce
maintenance costs and legal fees.
Distressed sales have been studied extensively. Recent studies (Clauretie and
Daneshvary 2009) find significant foreclosure discount associated with distressed
property, although the level of discount is different. They treat foreclosure sales as equal,
but this essay shows that the different foreclosure vehicles may influence the lenders’
reclaim on defaulted properties.
Following the foreclosure procedure, the lender can grant the short sales before a
public auction. If there is no short-sale on the property, a public auction usually would be
processed. During the auction, the property can be sold to cash buyer, or can be sent/sold
back to the beneficiary (the lender). Lenders then acquire the property, changing the
status of the house to real estate owned (REO). Lenders are reluctant to hold those
56

properties on their books, and finally, those properties would be sold at discounted prices.
Although the sellers for auction and REO are more likely to reduce the reservation prices
for exchange of quick sales, the competition among buyers may still bid up the price, and
keep the auction discount at a reasonable level.
Single-family foreclosure rate has increased significantly since the subprime crisis.
Accordingly, the number of REO sales, short sales and auctions sales increased by 40
percent between 2006 and 2012. Given the difference on market segments, straight-
forward auction procedure and cash requirement, this paper tries to solve the following
question, “Is there different discount rates between trustee auction sales and other types
of sales?” This essay uses the Los Angeles County as an example and compares the sales
of different foreclosure vehicles used by lenders. It adopts a hedonic model with housing
characteristics and neighborhood characteristics. The model compares the trustee auction
sales against REO sales, short sales and regular re-sale.
The remainder of the paper is organized as follows. Section II of this paper reviews
the broad literature on foreclosure studies and auction theory. Section III describes the
process after house is defaulted. Section IV presents a standard hedonic model and my
hypotheses. Section V describes the data collected from multiple listing service (MLS)
data and County Records Research. Section VI presents the empirical result. Section VII
gives summary.
57

4.2 Literature Review
4.2.1 Negative Effects of Foreclosures

The literature on the negative effects of foreclosures includes direct impact on the
individual in default and negative externalities to the society. The direct impact on the
borrowers is straightforward to demonstrate. Foreclosures not only take away existing
home, a wealth-building asset, but also cause moving expenses and deterioration on
credit. Mortgage delinquencies reduce creditworthiness, which increases the likelihood of
increase on current payment for consumer credit (such as auto loan and credit card loans).
It is more difficult and more expensive to access to new credit. Using credit bureau
records, Brevoort and Cooper (2013) study the credit experience after foreclosure. They
point out that the restricted access to credit has a long duration, and credit scores recovery
comes slowly. The economic shocks that leads to foreclosure would remain and their
wave effect persist over time. Although the national delinquency remains high for a
record of seven years, Brevoort and Cooper show that the lower credit score derives more
from the elevated delinquency rates on different types of consumer credit along with
mortgage delinquency in subsequent years. They find post-foreclosure effects are
remaining regardless of creditworthiness before delinquency.
In terms of household consumption, Hayashi (1985) documented that credit-
constrained households consume less in credit stress period. Although foreclosures cause
the delinquent household to move, it doesn’t mean that living conditions would get
substantially worse. Molloy and Shan (2013) show that the delinquent migrants in
58

general do not move to less-desirable neighborhoods; and the housing unit quality of next
rental place remains similar. Foreclosure does not severely reduce housing consumption.
The neighborhood externalities of foreclosures have been fully explored. Foreclosed
properties usually end up with a distressed sale. The presence of foreclosed properties
also reduces the prices of neighboring houses. Some empirical studies measure the effect
of foreclosures on surrounding property values. Immergluck and Smith (2006) use
hedonic model to estimate the impacts of the foreclosure of single-family units on other
single-family units in Chicago. They show an eighth of a mile of a single-family home
might reduce 0.9 percent in home value. Using the home sales and foreclosure data in
Dallas County in 2006, Leonard and Murdoch (2009) indicate an additional foreclosure
within 250 feet is associated with a decrease of a sale price of $1,666.
Schuetz, Been, and Ellen (2008) have reported foreclosure starts have negative
impact on the sale of surrounding house. The price discount has a positive relationship
with the number of nearby foreclosures. They also show the evidence of a threshold
effect; the price discount is not significant when the nearby foreclosures are small. But
their data only covers 2000 to 2006, a pre-crisis period. According to CoreLogic’s
national foreclosure report
14
, the number of mortgaged homes per foreclosure fell from
1,600 in 2005 to 500 in 2012, representing a decrease of 68.75 percent. The foreclosure
inventory is almost triple. Given the triple foreclosures in the New York City, it might
lead either to over- or under-estimates of the discount effects.

14
National Foreclosure Report, CoreLogic, Oct 2013
59

During appraisal process, appraiser or broker would adopt a relative price by
studying recent sales of similar properties in nearby neighborhood. Since this evaluation
would not take all sell as equal, Lin, Rosenblatt, and Yao (2009) assume the foreclosed
properties would be sold at a discount, and the reduced price would lead to reduce
appraised value of neighboring property. They indicate the spillover effect is significant
within a radius of 2,700 feet, within five years prior to the sale. Their empirical study in
the Chicago PMSA between 2003 and 2006 projects the worst effect is 8.7% discount.
Foreclosures increase the population of turnover and vacant building. The decline of
neighborhood and lack of social control in the neighborhood might lead to elevated crime
rates. A handful of recent studies have examined the hazard that foreclosed property
might place on neighborhood stability. Using data in Glendale, Arizona between 2003 to
2008, Katz, Wallace, and Hedberg (2011) show foreclosures do not have long term effect
on crime. But they find foreclosed properties have short-term (no more than 3 or 4
months) negative effect on crime.
Use rates of acquisitive crime and data on rates of foreclosure during 2007 at the
county level, Ellen, Lacoe, and Sharygin (2013) show a foreclosed property reduces
maintenance, increase residential turnover and vacancy. These increase the pay-off to
commit crime and reduce the likelihood to be caught. They find that addition foreclosures
contribute to higher rate of total crimes, violent crimes and public order crimes.
Arnio, Baumer, and Wolff (2012) show a non-linear effects of foreclosure on crime:
1) the crime rates is stable when foreclosure rates are lower or close to historically
60

average level; 2) when foreclosure rates increase from average foreclosure rates to high
foreclosure rates, this change of status finally causes an increase of crime rates.
4.2.2 Foreclosure Discounts

Clauretie and Daneshvary (2009) summarize six empirical research studies on
foreclosure sales. Those six papers report varying foreclosure discounts associated with
different regions and distressed properties. Shilling, Benjamin, and Sirmans (1990) focus
on the condominium units. They compare with regular residential condominium the
distressed units in Baton Rouge, Louisiana. Lenders would like to lower reservation price
and anticipate a sale within a short time after acquisition. According to Shilling et al.,
lenders give up the premium in order for a quick sale for foreclosed property, in exchange
of less cost of ownership, development, operation and sale of the property. In the end,
their empirical model indicates a 24 percent discount on liquidated REO properties.
Consistent with Shilling, Benjamin, and Sirmans’s finding, Forgey, Rutherford, and
Springer (1996) study single-family houses in Arlington, TX and get a 23 percent
discount on foreclosed single-family houses. They also document a cash discount of 16.5
percent. Sellers are more likely to accept lower price to insure that the deal can be
completed without further interruption in financing.
Later Carroll, Clauretie, and Neill (1997) comment on Forgey, Rutherford, and
Springer’s research, and point out their bias on the 23 percent discount, since they
mistakenly use zipcode as continuous variables, and the coefficient of zipcode would not
make any empirical sense. Instead, Carroll, Clauretie, and Neill (1997) carry out a similar
61

study with Las Vegas data, with a set of location dummy to control for location. They
find an insignificant foreclosed discount.
Hardin and Wolverton (1999) use income-generated apartment property in Phoenix,
Arizona, and find 22 percent foreclosure discount compared to non-foreclosure apartment
sales. They suggest this is due to the seller motivation to avoid carrying costs as well as a
need to satisfy regulatory capital requirements. The financial condition would enhance
credit rating and maintain seller’s stock price.
Springer (1996) studies the selling strategies against different motivated sellers. He
compares three groups of sellers who have relocated, vacant house and foreclosure in
Arlington, Texas. His empirical result estimates the impacts of seller motivation on
selling prices and time on market. Only foreclosure houses have significant impact on
marketing time.
In contrast to previous literature, Pennington-Cross (2006) uses repeat-sale approach
to eliminate housing characteristics effect during two sale periods. He compares the
appreciation rates between normal – foreclosed property and normal – normal property.
After controlling for state fixed effect and housing characteristics, the result shows a 22
percent less appreciation in foreclosed property than its counter property.
The above literature confirms the discount on distressed properties. But none of the
research differentiates different types of distressed sale. This paper not only confirms the
discount on foreclosed properties, but also shows the different distressed sale vehicles
have different discount.
62

4.2.3 Arbitrage Pricing Theory

Arbitrage pricing theory indicates that even with the insufficient real estate market,
the expected return of similar properties should remain close. The asset price should
equal the cash flow discounted with the expected return. However a huge discount of
foreclosed properties has been documented in these papers, one can speculate in this
market by buying the properties at discount, and selling it to general market. This makes
an arbitrage profit and realizes a high excess return. According to Forgey, Rutherford,
and Springer (1996), such excess return can reach 40 percent (24 percent foreclosed
discount and 16.5 percent cash discount), if speculators use cash to finish a deal.
In theory, this arbitrage opportunity would attenuate more buyers into the distressed
market, and competition effectively bids up the price, and eliminates price deviations and
finally mitigate or reduce the discount. Clauretie and Daneshvary (2009) criticize the
missing of time on market (TOM) among all pervious papers. They carry out an
empirical research with TOM variable (defined as the dummy of whether the property is
on market for over 30 days). They argue that although such arbitrage opportunity may be
less, the stigma effect on distressed peoperties would still cause some discount, but not a
huge one. They control for other nagative property characteristics and TOM, and report a
7.5 percent of true discount caused by foreclosure per se.
Similar to arbitrage opportunity theory, common-value auction theory (i.e., auction
theory based on the idea that all bidders have a common view of what they are bidding
for) shows that number of bidders in an auction has an ambiguous effect on prices. On
the one hand, more competition should produce more aggressive bidding. On the other
63

hand, more competition adds severity to the winner’s curse, and therefore would lead
rational bidders to bid less aggressively.
4.3 From Delinquency to Trustee’s Sale

This paper focuses in Los Angeles County, California, a power-of-sale or non-
judicial state. Power-of-sale clause in deed of trust entitles the lender to foreclose a
property without court oversight. This simplifies the study to avoid considering legal
issues of lender and unexpected timing regarding court decision.
Delinquency starts with borrower failed to make mortgage payment on the collateral.
After several months of miss scheduled payments, the lenders or mortgage servicers
would file default status on the county recorder’s office. Lenders would notice the
homeowner through mail or public notice. In next three-month period, the property
owners still have options to keep the properties – either reinstate the loans or sell the
property. The lenders or mortgage servicers may restrucuture the loan, work out a plan
with defaulted home owner. In order to reduce the cost and time delay, lenders encourge
the owners to sell the property and avoid default on their credit report. When the proceeds
from the pre-foreclosure sales is less than the remaining outstanding balance, accrual
interest and late fees, the sales become short-sale. During the process, borrower can get
the approval of lender to process a short-sale. In general, a granted short-sale would
elimiate the balance difference between outstanding loan amount and short-sale proceed.
Lenders usually would stop collect the remaining balance in pre-foreclosure sales.
64

If borrower cannot complete short sales of the property in this limited time, a
trustee’s sale (foreclosure auction) would be processed through public auction at an
advertised place and period. The owner has another minmum 21 days to sell the property
before public aution.
In the auction, about 80-90 percent of auctions have no outside bidders show up to
bid
15
. Lender would try to prevent under price auction. If the auction price is much less
than market value, or the recovered amount is much less than the defaulted amount,
lender would acquire the property as REO with a higer bid and manage the property with
lender’s fund. This can be easily showed that in auction data, the price of acution are
rational without unexpected discount.
All bids in trustee’s sale are in the form of cash or cashier’s check. The auction
would wipe out all trust deeds (loans) junior to the foreclosing loan. The bid winner
would receive the property rights through power-of-sale clause in deed of trust.
During foreclose preocess, a property can end up in many different paths. Although
the majority of them end up in REO, there are still many other outcomes such as short-
sales and auction sales. Previous literature discuss about the foreclosed sale, which are
more related to REO sales. They neglects the acution section. Therefore they are unable
to investigate the discount related to auction sales. This paper would be the first empirical
study to discuss the auction sales discount on house price.

15
Source from http://www.countyrecordsresearch.com
65

4.4 Research Hypotheses

Many differences between auction sales and other foreclosure sales might lead to a
further discount for auction sales. First, the sequence of foreclosure sales is in order.
Trustee’s sale is after pre-foreclosure sale and before REOs. Lenders might experience
less cost in trustee’s sale than pre-foreclosure sale. Lenders are also reluctant to acquire
REOs, since the cost of keeping property and sale the distressed property is huge. Most
lenders have to meet the regulatory requirements related to risk asset. Lenders are more
likely to let the property off their book by auction.
Second, trustee’s sale is straightforward compared to pre-foreclosure sale. It involves
less complex procedure and fewer parties. Most legal issue has been taken care before the
auction. The auction result only depends on the number of bidders and the availability of
the property before the auction
16
.
In pre-foreclosure sale, property owners have 3 months and 21 days to negotiate a
sale or short-sale (sale price < outstanding) with potential buyers. Short sale transactions
are time-consuming. The process includes the cooperation among buyer, seller, agent,
and lenders. It takes time for seller and buyer to reach a short sale agreement. It takes
months for lenders to responds short sale offers. From the buyer side, buyer may find a
comparable or similar priced deal during this long period. Although it is a good
opportunity for defaulted owners or sellers to get rid of property without damage to their

16
The owner can still reinstate the loans or sale the property, after the notice of public auction.
66

credit, the sellers might have less time and knowledge to sale the property. Also the
potential buyers worry about the lien status. If the property has multiple liens status, the
short-sale requires more lenders to approve the transaction. Due to the complexity of this
sale, real estate agents are less experienced in short sales deals. The success of pre-
foreclosure sale is quite low and highly depends on the skills of owners, buyers, agent,
and the loan condition.
Third, it might due to market segment. Short sales can get financing from lender, but
trustee’s sale is cash-bid. It requires all cash payment up front. This requirement
significantly reduces a lot of bidders, since it suddenly increases home buyer‘s budget
constraint by 4 times (given one can get a 80% LTV loan from lender) or 9 times (for a
90% LTV loan). Currently, the main method to finance real property is by borrowing
money from banks or mortgage brokers. It usually requires 10-20 percent down payment,
depends on the creditworthiness, and the loan terms. Without mortgage, potential buyers
in auction are some passive investors who hold large cash and plan to exchange short or
zero duration cash to long duration wealth-building asset.
As parts of foreclosure sale vehicles, auction sales, short sales and REOs are
expected to sell at a discount. Because of the above differences, auction sale houses
might sell at further discount, when compared to non-auction residential sales.
4.5 Method and Data

This paper would follow same approach of other papers on foreclosed discount. It
uses a hedonic regression model to estimate the effect of auction status on the final sale.
67

A commodity can embody various attributes. Hedonic model assume the price of these
bundled attributes, or a house in this study, is the inner product of attributes and
equilibrium value for each unit of attribute (Yezer, Phillips, and Trost 1994; Pennington-
Cross and Ho 2010). Rosen (1974) provides a theoretical framework for integrated
treatment of hedonic prices. The price function can be estimated by the demand and
supply function of differentiated products.
The price function follows a log-linear hedonic regression:
Ln(P)=H(Xp,Xs,Xa)
, where Ln(P) is the natural log of the price of the property,
Xp = a vector incorporating physical house characteristics,
Xs = a vector for spatial neighborhood characteristics (location variables),
Xa = a dummy variable for the sale category.
The physical house characteristics vector Xp includes the unit age, square footage of
building, dummy variable for two stories or up, number of bedrooms. The spatial
neighborhood characteristics Xs include the zipcode level unemployment rate in
percentage, African American population in percentage, and median household income in
the zipcode.
Due to the data nature, the sample in this essay only considers the sold properties,
and doesnot consider the characteristics of unsold properties. It is possible that the result
in the above hedonic regression is biased due to sample selection bias, and the result
cannot extend to all housing unit including sold and unsold. In order to solve this,
68

Heckman (1979)’s two stage estimation procedure is used in the following one on one
comparision.
It starts with two equation model, with regession equation:
𝑃 𝑖 = 𝑋 𝑖 ′
𝛽 + 𝜀 𝑖
, and selection equation
𝑆 𝑖 = 𝑍 𝑖 ′
𝛾 + 𝜔 𝑖
where the dependent variable 𝑃 𝑖 is the sold amount of house i which is recorded only
when the house successfully sold; 𝑋 𝑖 is a vector ofthe housing characteristics and
neighorhood condition; 𝛽 is a vector of shadow prices for hedonic characteristics; 𝜀 𝑖 is the
error term in regression euqation; 𝑆 𝑖 is the unobserved propensity to final sell in the
market; 𝑍 𝑖 is the vector of common components in 𝑋 𝑖 ; the errors 𝜀 𝑖 and 𝜔 𝑖 follows joint
distribution:
(
𝜀 𝜔 ) ~ 𝑁 [ (
0
0
) , (
𝜎 2
𝜌𝜎
𝜌𝜎 1
) ]
,where N denotes the normal distribution.
The final sold amount 𝑃 𝑖 is only observerable when 𝑆 𝑖 is equal 1; and remain
observerable when 𝑆 𝑖 is equal 0;
E [ 𝑃 𝑖 | 𝑍 𝑖 = 𝑃 𝑖 , 𝑆 𝑖 = 1 ] = [ 𝑋 𝑖 ′
𝛽 | 𝑆 𝑖 > 0 ] + 𝐸 [ 𝜀 𝑖 | 𝑍 𝑖 , 𝑆 𝑖 > 0 ] = 𝑋 𝑖 ′
𝛽 + 𝐸 [ 𝜀 𝑖 | 𝜔 𝑖 > − 𝑍 𝑖 ′
𝛾 ]
= 𝑋 𝑖 ′
𝛽 + 𝜌𝜎 𝜆 ( 𝜀 𝑖 )
69

Where 𝜆 ( 𝜀 𝑖 ) = (
𝜙 ( 𝑍 𝑖 ′
𝛾 )
𝛷 ( 𝑍 𝑖 ′
𝛾 )
) is the inverse Mills ratio, with 𝜙 is the density function of
the standard normal, and 𝛷 is the distribution fucntion;
In order to obtain unbiased estimate of ⁡ 𝛽 , the model regresses 𝑃 𝑖 on 𝑋 𝑖 and the
inverse Mills ratio with observed home price. The first step of Hechman producedure is
to estimate a probit model to obtain the estimates of inverse Mills ratio. The probit model
includes sold properties, list without final sale and removed list. The seccond step
estimate 𝑋 𝑖 ′
𝛽 + 𝜌𝜎 𝜆 ( 𝜀 𝑖 ) by OLS for home price observed. The final regression is
Ln(P)=H(Xp,Xs,Xa, IMR),
, where Ln(P) is the natural log of the price of the property.
Xp = a vector incorporating physical house characteristics,
Xs = a vector for spatial neighborhood characteristics (location variables),
Xa = a dummy variable for the sale category,
IMR = inverse Mills ratio estimated from probit model.
This paper utilizes two separate data sets, whose coverage both includes Los Angeles,
Califoria with the priod of 2006 to 2012. The first data set was obtained from County
Records Research, a company that collects all auction information on foreclosed
properties in California. Each auction record contains the basic information of ten-digit
Assessor's Identification Number (AIN), address, city, zipcode, trustor, name of owner,
and beneficiary. The data also contains the loan details, such as loan lien, loan amount,
and loan date. The property physical conditions include year of built, number of stories,
70

number of bedrooms, number of bathrooms, lot square footage, and building square
footage.
The acution information includes auction date and auction time. In terms of auction
results, the data record opening bid, sold amount and auction status. Auction status
includes sold to public, sold to beneficiary, cancelled, and postponed. This paper would
focus on the differece between sold to public and sold to beneficiary. The other auction
statuses including postpone, cancelled, none(due to missing report), and invalid sale were
eleminiated from the data for clean up purpose. All of these four acution statuses
comprise 0.08% of the auctions in the data set.
For all acution sales, there is no financing. They must be paid with cash. In order to
control for neighnorhood quality, the data were joined with a vector of neighborhood
characteristcs comprising of percentage of Africa American, unemployment rate, and
median household income.
The original dataset comes with some miscoded data. The data of the properties with
following conditions were elminated: bedrooms or bathrooms over 8, sales price less than
$100,000 or greater than $2,000,000, building square footage less than 500 or greater
than 5,000, and lot square footage less than 1,000 or greater than 45,000.

71

Table 4-1: Descriptive statistics for County Records Research data

Sold to
beneficiary
Sold to public
Variable Mean Std Dev Mean Std Dev
Sold amount 316,783 177,941 262,298 144,928
Unit age 50.05 23.833 52.75 22.831
Store indicator for stories are 2 or up 0.039 0.195 0.045 0.208
Number of bathrooms 1.941 0.565 1.743 0.522
Number of bedrooms 2.981 0.865 2.845 0.847
Building square footage 1,487 616 1,545 619
Lot square footage 6,720 4,807 7,032 4,482
Unemployment rate in zip code 0.091 0.035 0.087 0.034
Percent of African American in zip code 0.129 0.166 0.121 0.166
Median household income in zip code 44,065 15,132 45,208 15,497
Number of observations 33,815 10,198

On average, the properties sold to public are $54,000 less than those back to beneficiary
and thus becoming REO. In contrast to the lower price for properties acquired by public,
Table 4-1 shows those properties, in fact, have larger living space and lot square footage.
Furthermore, those neighorhoods have less unemployment rate, less population of Afrian
American and higher median household income. It indicates that bidders in auction prefer
better quality houses, and expect lower home prices per square foot.
Second data in this essay is multiple listing service (MLS) data in Los Angeles
County and covering residential property listing from 2006 to 2012. Like County Records
Research, MLS includes the housing characteristics of built-year, living square footage,
land square footage, number of bedrooms and total rooms, and number of stories. In
72

terms of sale category, this paper includes resale, REO-sale, and shortsale
17
. After same
procedure of data cleaning up, the data set has 218,207 resales and 55,156 reo-sales, and
31,187 shortsales.
Table 4-2: Descriptive Statistics for CoreLogic Multiple Listing Service (MLS) data

RESALES REOSALE SHORTSALE
Variable Mean
Std.
Dev.
Mean
Std.
Dev.
Mean
Std.
Dev.
Sold amount
580,04
0
322,07
8
324,55
6
168,60
5
349,88
8
177,70
5
Unit age 57.54 15.85 58.60 15.80 58.42 15.21
Store indicator for stories are 2 or up 0.15 0.35 0.10 0.30 0.11 0.32
Number of bedrooms 3.06 0.84 3.04 0.83 3.03 0.81
Number of total rooms 5.77 1.25 5.56 1.17 5.62 1.18
Building square footage 1,608 632 1,436 522 1,470 539
Lot square footage 8,180 5,227 7,376 4,515 7,641 4,773
Unemployment rate in zip code 0.07 0.03 0.08 0.03 0.08 0.03
Percent of Africa American in zip
code
0.08 0.14 0.11 0.17 0.09 0.14
Median household income in zip
code
52,258 18,591 45,647 13,802 48,095 14,821
Number of observations 218,207 55,156 31,187

Out of the total 304,550 sample sales, 18% were REO sale and 10% were short-
sale samples. On average, selling price in these two types of distressed property was
about $240,000 less than regular resales. Different from the County Records Research
data, distressed properties in MLS data have lower quality. Living and property space
were less than regular sales. Furthermore, the neighborhood conditions were worse with

17
Sample data set excludes new construction (6.8 percent of total).
73

higher unemployment, higher Africa American propulation, and lower median household
income.
One possible explanation for this discrepency is that in auction sample, homebuyers
can choose better quality house and neighborhood among distressed properties. But in
MLS sample, distressed properties are already located in worse condition neighborhood
with worse property conditions. Eventhough homebuyers would try to select better one
out of the distressed sample, the distressed sample has already lower quality than regular
sales.
Figure 4-1: Los Angeles House Price Index

Source: CoreLogic Zipcode level HPI
Between 2006 and 2012, housing market in Los Angeles went down about 30
percentage (see Figure 4-1). In order to capture the housing market impact on the price,
this study adjusts the final selling price with zipcode level HPI (Jan, 2006 HPI=100).
0
20
40
60
80
100
120
January 2006
April 2006
July 2006
October 2006
January 2007
April 2007
July 2007
October 2007
January 2008
April 2008
July 2008
October 2008
January 2009
April 2009
July 2009
October 2009
January 2010
April 2010
July 2010
October 2010
January 2011
April 2011
July 2011
October 2011
January 2012
April 2012
July 2012
October 2012
74

4.6 Regression Results

Log-linear multiple regression models are applied in this paper with following form:
Log(Price_HPI)=f(STATUS DUMMY,AGE, AGE2,STORY2UP,BDMNBR,
SQFT,UNEMPLOYMENT,AFRICAN_PERCENT,MEDIANHI,MONTH,YEAR,ZIPCODE,
IMR)
,where:
Variable Description
Dependent variable

Log(Price_HPI)
Log(dollar amount of sold properties), dollar amount has been
adjusted with zipcode level HPI (HPI Jan, 2006 = 100);
Independent variables
STATUS_DUMMY Dummy variables for sell type;
Hedonic housing characteristics
AGE Unit age;
AGE2 Unit age squared;
STORY2UP Store indicator for stories are 2 or up;
BDMNBR Number of bedrooms;
SQFT Square feet of building;
Hedonic neighborhood characteristics (zip code level)
UNEMPLOYMENT Unemployment rate in the zip code;
AFRICAN_PERCENT Percentage of African Americans in zip code;
MEDIANHI Median household income in the zip code;
Fixed effects

Month_i Dummy variables for month of sell;
Year_i Dummy variables for year of sell;
Zip_i Dummy variables for each zip code group;

IMR
Inverse Mills ratio is calculated from the probit model and
inserted into the hedonic regression;

75

Before examining the discount of auction status on sale price, the discount of
different status within each data was tested. In other word, the impact of selling to public
versus selling to beneficiary on final sell price was tested, with STATUS_DUMMY
(AUCTION)=1 if sold to public, and 0 if sold to beneficiary.
Table 4-3: OLS estimates for Sold to Public versus Sold to Beneficiary
Linear Model Log-Linear Model
Parameter Estimate t-stat Estimate t-stat
intercept 89636.00 12.23 *** 12.1619 596.03 ***
Unit age 1603.72 14.19 *** 0.0074 23.53 ***
Unit age squared 3.04 2.66 *** 0.0000 -4.95 ***
Store indicator for stories are 2 or up 67900.00 20.07 *** 0.1602 17.01 ***
Number of bedrooms 2241.16 1.89 * 0.0127 3.85 ***
Building square footage 127.90 114.36 *** 0.0003 109.04 ***
Unemployment rate in zip code -1243759.00 -35.97 *** -5.2587 -54.63 ***
Percent of African American in zip code -43348.00 -9.21 *** -0.1076 -8.21 ***
Median household income in zip code 1.35 18.43 *** 0.0000 1.89 *
Auction to public -74160.00 -48.15 *** -0.2337 -54.52 ***
R-squared 0.39

0.40

Adjusted R-squared 0.39

0.40

Number of observations 44013

44013

***significant at 0.01 level, ** significant at 0.05 level, * significant at 0.1 level

Table 4-3 presents the linear regression and log-linear regression for sample of
44,014 properties in auction data. Age of the property has a quadratic relationship with
property price, with peak at 46 years in log-linear model. Properties with 2 stories or up
are 16% more expensive than the ones without. Social economic variables show that
neighorhood influences house price significantly. High unemployment draws the price
down. High concentration of Afrian American population reduces the home value.
Properties with higer median household income are more expensive.
76

Regarding the auction effect inside auction data, there is a 23 percent discount over
property sold to public than ones sold to beneficiaries. Considering the loss of $74,160
for each property, the lenders are willing to let the property go out of balance sheet. The
possible reason is that the estimated costs of holding the property in REO are more than
23 percent of the property.
Pennington-Cross (2006) summarizes the costs for lender to maintain the property as
follows. Firstly, there is a direct cost of maintaining the physical property: gardening
under some city requirement, keep the property current for later sale, and so on. As time
goes by, the costs would go up even more in the case of major maintainance needed
during the holding period. Secondly, the regulatory capital requirements would force
lenders to reduce those property holding. Thirdly, the fund in physical property cannot be
used for other lending. This would limit lender’s income. Furthermore, for large
institutions, funds may not be lent out right away. From the accounting point of view,
those funds can still generate decent income for lender through some overnight financial
vehicle. Lastly, the properties would eventually be sold in some other ways, in which, it
costs lender to market the properties.
During the financial crisis and house price downturn, many properties are in the
auction vehicle, most lender are facing the same decision and have the same incentives to
sell the properties at lower price. It has been proved in previous reviewed studies that
foreclosed properties are sold with less value. But this study further investigates into the
auction properties. Table 4-3 shows that auction property would take further discount,
such as 23 percent, against other foreclosed property.
77

Since the County Records Research data is just a foreclosed set of the whole real
estate market, it is worthwhile to test this result in a data set with regular sale and to also
compare auction sales with others such as short-sales and REO sales.
Table 4-4: OLS estimates for Auction, REO, Shortsale versus Regular Resale(part a)
Parameter
Estimate Std.Err.
intercept 11.9000 0.0111 ***
Sale status

Trustee's Auction -0.3852 0.0032 ***
REO -0.2190 0.0019 ***
Short sale -0.1853 0.0022 ***
Unit age
0.0091 0.0002 ***
Unit age squared -0.0001 0.0000 ***
Number of bedrooms -0.0194 0.0011 ***
Building square footage 0.0004 0.0000 ***
Unemployment rate in zip code
-5.7213 0.0460 ***
Percentage of African Americans in zip code -0.5540 0.0068 ***
Median household income in zip code 0.0000 0.0000 ***
Store indicator for stories are 2 or up -0.0173 0.0025 ***
Zip code group

zip code start with 900 0.3621 0.0043 ***
Zip code start with 902 0.0272 0.0042 ***
Zip code start with 903 0.1317 0.0113 ***
Zip code start with 904
0.8049 0.0124 ***
Zip code start with 905 0.0715 0.0063 ***
Zip code start with 906 -0.2655 0.0044 ***
Zip code start with 907 -0.1173 0.0046 ***
Zip code start with 908
0.0182 0.0047 ***
Zip code start with 910 0.0364 0.0049 ***
Zip code start with 911 0.2290 0.0062 ***
Zip code start with 912 0.1232 0.0061 ***
Zip code start with 913
-0.2355 0.0040 ***
Zip code start with 915 0.0439 0.0072 ***
Zip code start with 916 0.1378 0.0055 ***
Zip code start with 917 -0.1873 0.0040 ***
Zip code start with 918
0.1836 0.0103 ***
Zip code start with 935 -1.0497 0.0068 ***
(to be continued)
78

Table 4-4b: OLS estimates for Auction, REO, Shortsale versus Regular Resale (part
b) (cont.)
Parameter
Estimate
Std.
Err.

Sale month

January -0.0108 0.0038 ***
February -0.0110 0.0037 ***
March -0.0201 0.0036 ***
April -0.0142 0.0036 ***
May -0.0032 0.0036

June 0.0032 0.0036

July 0.0043 0.0036

August 0.0034 0.0036

September 0.0022 0.0037

October 0.0070 0.0036 *
November 0.0046 0.0037

Sale year

2010 0.0239 0.0021 ***
2011 -0.0848 0.0021 ***
2012 -0.0445 0.0020 ***
R-Squared 0.7607

Adjusted R-Squared 0.7606

Number of observations
164731
***significant at 0.01 level, ** significant at 0.05 level, * significant at 0.1 level

Column 2 of Table 4-4 contains the linear regression with 3 dummy variables,
AUCTION, REO, and SHORTSALE, comparing with the regular resale properties.
Housing physical have a similar relationship with this first result and other empirical
studies: AGE is quadratic function of home price; number of bedrooms is negative; total
square footage is postivie. Neighberhood effects on home value remain: higher
unemployment reduces the property value; Afrian American population has a negative
association with the sale prices; higher median household income increases the sold
amount.
79

Seasonal effects are signficiant for Janauary, Febrary, March, April and October. It
may indicate people are more likely to move in Spring. Sales in 2010 are 2 percent higher
than sales in 2009. But the trend goes down in 2011 and 2012.
The estimated parameter for Auction shows that holding all other housing physical
characteristics and the neighborhood condition constant, properties sold to public in
auction are traded for on avearage 38.5 percent less than regular resale in the sample.
REO properties and short-sale properties have discounts of 21.9 percent and 18.5 percent
respectively. All statistics for status dummy in the model are significant at the 0.01 level.
To take care of the sample selection problem in this study, the inverse Mills ratio is
also included in the following pair comparision between different sale type. All the
inverse Mills ratio is also signicant in pair comparision, indicating that sample selection
matters. Between Heckman two-stage model with inverse Mills ratio and OLS without
inverse Mills ratio, Table 4-5 compares Auction sale to resale; Table 4-6 compares
Auction sale to REO-Sale. Both result shows a positive inverse Mills ratio parameter
estimate. This indicates that the houses in the sample are more expensive than the houses
excluded from the sample. Most coeffeicients remain same sign and significant level. The
coeffeicient of auction sale reduces from -37.7 to -38.1. It indicates the final discount on
auction sales would be slightly higher with inverse Mills ratio.
Given the cash requirement in auction sale, one can derive the excess auction
discount by deducting 16.5 percent cash discount from the result of Forgey, Rutherford,
and Springer (1996).

80

Table 4-5: Heckman two-stage and OLS estimates for Auction versus Resale (part a)
Heckman two-stage OLS
Parameter
Estimate
Std.
Err.
Estimate
Std.
Err.

intercept
12.074 0.018 *** 11.995 0.014 ***
Trustee's Auction
-0.381 0.003 *** -0.377 0.003 ***
Unit age
-0.002 0.001

0.008 0.000 ***
Unit age squared
0.000 0.000 ** 0.000 0.000 ***
Number of bedrooms
-0.049 0.004 *** -0.022 0.001 ***
Building square footage
0.000 0.000 *** 0.000 0.000 ***
Unemployment rate in zip code
-5.345 0.130 *** -6.159 0.060 ***
Percentage of African Americans in zip
code
-0.555 0.012 *** -0.610 0.009 ***
Median household income in zip code
0.000 0.000 *** 0.000 0.000 ***
Store indicator for stories are 2 or up
-0.111 0.014 *** -0.012 0.003 ***
Zip code group

zip code start with 900
0.363 0.006 *** 0.387 0.006 ***
Zip code start with 902
0.065 0.006 *** 0.055 0.006 ***
Zip code start with 903
0.121 0.017 *** 0.118 0.017 ***
Zip code start with 904
0.702 0.018 *** 0.788 0.014 ***
Zip code start with 905
0.035 0.008 *** 0.057 0.008 ***
Zip code start with 906
-0.277 0.008 *** -0.311 0.006 ***
Zip code start with 907
-0.126 0.008 *** -0.158 0.006 ***
Zip code start with 908
-0.023 0.006 *** -0.019 0.006 ***
Zip code start with 910
0.053 0.006 *** 0.053 0.006 ***
Zip code start with 911
0.179 0.009 *** 0.219 0.008 ***
Zip code start with 912
0.085 0.008 *** 0.082 0.008 ***
Zip code start with 913
-0.226 0.007 *** -0.260 0.005 ***
Zip code start with 915
-0.006 0.009

0.003 0.009

Zip code start with 916
0.123 0.008 *** 0.145 0.007 ***
Zip code start with 917
-0.173 0.006 *** -0.194 0.005 ***
Zip code start with 918
0.105 0.013 *** 0.139 0.012 ***
Zip code start with 935
-1.056 0.010 *** -1.073 0.009 ***
(to be continued)

81

Table 4-5b: Heckman two-stage and OLS estimates for Auction versus Resale (part
b) (cont.)
Heckman two-stage OLS
Parameter
Estimate
Std.
Err.
Estimate
Std.
Err.

Sale month

January
0.019 0.007 *** -0.018 0.005 ***
February
0.010 0.006 -0.014 0.005 ***
March
-0.002 0.005 -0.017 0.005 ***
April
0.004 0.005 -0.010 0.005 **
May
0.014 0.005 *** 0.005 0.005
June
-0.007 0.005 0.009 0.005 **
July
-0.004 0.005 0.008 0.005 *
August
0.002 0.005 0.007 0.005
September
0.001 0.005 0.005 0.005
October
0.003 0.005 0.009 0.005 **
November
0.002 0.005

0.004 0.005

Sale year

2010
0.026 0.004 *** 0.009 0.003 ***
2011
-0.093 0.003 *** -0.103 0.003 ***
2012
-0.129 0.012 *** -0.050 0.003 ***
Inverse Mills ratio
0.158 0.022 ***

R-Squared
0.754

0.754

Adjusted R-Squared
0.754

0.754

Number of observations
103660

103660

***significant at 0.01 level, ** significant at 0.05 level, * significant at 0.1 level

82

Table 4-6: Heckman two-stage and OLS estimates for Auction versus REO-Sale
(part a)
Heckman two-stage OLS
Parameter
Estimate
Std.
Err.

Estimate
Std.
Err.

intercept 11.685 0.020 *** 11.705 0.019 ***
Trustee's Auction
-0.219 0.004 *** -0.218 0.004 ***
Unit age
0.006 0.001 *** 0.011 0.000 ***
Unit age squared
0.000 0.000 *** 0.000 0.000 ***
Number of bedrooms -0.023 0.004 *** -0.008 0.002 ***
Building square footage 0.000 0.000 *** 0.000 0.000 ***
Unemployment rate in zip code -4.662 0.088 *** -4.739 0.085 ***
Percentage of African Americans in zip code -0.410 0.012 *** -0.397 0.011 ***
Median household income in zip code 0.000 0.000 *** 0.000 0.000 ***
Store indicator for stories are 2 or up -0.082 0.018 *** -0.016 0.005 ***
Zip code group

zip code start with 900 0.250 0.009 *** 0.234 0.008 ***
Zip code start with 902 -0.022 0.008 *** -0.031 0.007 ***
Zip code start with 903 0.113 0.018 *** 0.106 0.018 ***
Zip code start with 904 0.804 0.049 *** 0.774 0.048 ***
Zip code start with 905 0.064 0.015 *** 0.057 0.015 ***
Zip code start with 906 -0.190 0.008 *** -0.195 0.008 ***
Zip code start with 907 -0.051 0.008 *** -0.061 0.008 ***
Zip code start with 908 0.078 0.009 *** 0.072 0.008 ***
Zip code start with 910 -0.002 0.010

-0.010 0.010

Zip code start with 911 0.238 0.014 *** 0.232 0.014 ***
Zip code start with 912 0.275 0.013 *** 0.262 0.013 ***
Zip code start with 913 -0.199 0.007 *** -0.197 0.007 ***
Zip code start with 915 0.180 0.015 *** 0.172 0.015 ***
Zip code start with 916 0.124 0.010 *** 0.125 0.010 ***
Zip code start with 917 -0.168 0.007 *** -0.173 0.007 ***
Zip code start with 918 0.319 0.026 *** 0.297 0.026 ***
Zip code start with 935 -0.935 0.011 *** -0.912 0.010 ***
(to be continued)

83

Table 4-6b: Heckman two-stage and OLS estimates for Auction versus REO-Sale
(part b) (cont.)
Heckman two-stage OLS
Parameter
Estimate
Std.
Err.

Estimate
Std.
Err.

Sale month
0.025 0.007 *** 0.016 0.006 **
January
0.031 0.007 *** 0.021 0.006 ***
February
0.002 0.006

-0.005 0.006

March
0.019 0.006 *** 0.011 0.006 *
April
0.036 0.006 *** 0.031 0.006 ***
May
0.024 0.006 *** 0.028 0.006 ***
June
0.023 0.006 *** 0.025 0.006 ***
July
0.022 0.006 *** 0.017 0.006 ***
August
0.014 0.006 ** 0.008 0.006

September
0.024 0.006 *** 0.018 0.006 ***
October
0.024 0.007 *** 0.016 0.006 **
November

Sale year

2010
-0.043 0.017 *** -0.104 0.003 ***
2011
-0.162 0.015 *** -0.217 0.003 ***
2012
-0.156 0.006 *** -0.173 0.004 ***
Inverse Mills ratio
0.094 0.025 ***

R-Squared
0.6272

0.6271

Adjusted R-Squared
0.6270

0.6269

Number of observations
60590

60590

***significant at 0.01 level, ** significant at 0.05 level, * significant at 0.1 level

4.7 Conclusions

Auction sales have grown dramatically in current market, and reached its peak in
2009. It has becomes one significant way for financial institutions to sell troubled real
estate assets and for potential homeowners to take advantage of the foreclosure
environment and become homeowners. It is worth comparing the different outcomes
between trustee auction sales and non-auction sales. The paper uses standard liner and
log-linear hedonic price regressions to estimate the difference in sale prices between
84

trustee auction and non-auction sales. It shows a discount of 23 percent between property
sold to public and property that are back to beneficiary, resulting in REO. The final data
includes four types of sales: regular resale, REO sale, short-sale and auction sale to public.
The empirical result records an average 37 percent discount of auction sale to public.
The high discount of auction sales shows a great opportunity for potential home
buyers to take advantages of the current housing market. Even after controlling housing
characteristics and social economic conditions, property discount remains. However the
auction sales do not accept financing, and require cash payment, which prevents the
families with finance shortage from getting involved.
There are some limitations on this study. Like many other hedonic literature, the
physical condition of house is not included in empirical study. It is possible that the
physical condition of the house results in this huge discount. County Records Research
data contains Assessor's Identification Number and address. Given the large foreclosures
in Los Angeles, it might be impossible to locate the house and record the physical quality.
The other method is to use repeat sale data. Assumed the condition of the same house
would no change much, repeat sale data could reduce the effect of physical condition and
other untangable factors. Auction sales barely have repeat sale. Or the chance to have two
auctions on the same house between 2006 and 2012 is small. Corelogic data does not
include address and can’t be used to match with auction sales for repeat sale observation.

85

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Abstract (if available)

Abstract This dissertation contains three independent essays on the real estate market in the United States. These three papers cover same research timeframe between 2006 and 2012. The data in this period can illustrate the discrepancy of the outcome, before and after subprime crisis. ❧ The first two essays focus on residential mortgages with the topics of agency effect and liquidity effect, respectively. The third essay studies the distressed housing. It measures the impact of auction sale on housing value, comparing with the other types of selling options. By looking at the secondary market and the housing market, these essays capture some missing variables in previous literature. The first essay supports the agency effect is important in default risk. The second essay finds that mortgage market liquidity should be used to estimate the termination risks for private-label mortgages. Final essay shows that auction status would affect the housing price significantly.

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Asset Metadata

Creator Zhang, Xiaoxin (author)

Core Title Three essays in United States real estate markets

School School of Policy, Planning and Development

Degree Doctor of Philosophy

Degree Program Policy, Planning, and Development

Publication Date 07/24/2015

Defense Date 05/26/2015

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag agency,auction discount,liquidity,mortgage,OAI-PMH Harvest,Real estate

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Green, Richard K. (committee chair), Bostic, Raphael (committee member), Ma, Jin (committee member)

Creator Email xiaoxinz@usc.edu,zhang_xiaoxin@hotmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-605562

Unique identifier UC11300262

Identifier etd-ZhangXiaox-3685.pdf (filename),usctheses-c3-605562 (legacy record id)

Legacy Identifier etd-ZhangXiaox-3685.pdf

Dmrecord 605562

Document Type Dissertation

Format application/pdf (imt)

Rights Zhang, Xiaoxin

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA