ANALYSIS OF THE FACTORS USED BY VALUATION MODELS FOR

MORTGAGE-BACKED SECURITIES

By

Bhawani Singh

A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science

in Management and Systems Stern School of Business

New York University

2015

Table of Contents Table of Tables ................................................................................................................................. v

Table of Figures............................................................................................................................... vi Acknowledgements ........................................................................................................................ vii A Declaration ................................................................................................................................ viii Abstract ............................................................................................................................................ ix

Chapter 1 - Introduction ................................................................................................................. 1

1.0 Introduction .............................................................................................................................. 1

1.1 Purpose of Research ................................................................................................................. 3

1.2 Problem Definition .................................................................................................................. 6

1.3 Research Question ................................................................................................................... 7

1.4 Conclusion ............................................................................................................................... 7

Chapter 2 - Literature Review ........................................................................................................ 9

2.1. Introduction ............................................................................................................................. 9

2.2 Types Of Risks That Effect the Valuation Of a Mortgage Backed Security ........................... 9

2.3 Prepayment and Default Risk Models ................................................................................... 10

2.3.1 Perfect Payer (Refinance Activity). ............................................................................. 13

2.3.2 Perfect Payer (Age of the Mortgage Assets). ............................................................... 13

2.3.3 Loan Balance. .............................................................................................................. 14

2.3.4 FICO score. .................................................................................................................. 14

2.3.5 Geographic. .................................................................................................................. 15

2.4 Interest Rate Risk Models ...................................................................................................... 16

2.4.1 Vasicek model. ............................................................................................................. 16

2.4.2 Cox, Ingersoll and Ross (CIR) Model. ........................................................................ 17

2.4.3 Black–Derman–Toy Model.......................................................................................... 17

2.4.4 Ho–Lee Model. ............................................................................................................ 18

2.4.5 Hull–White Model. ...................................................................................................... 19

2.4.6 The Black–Karasinski Model. ..................................................................................... 19

2.5 Other Models ......................................................................................................................... 20

2.5.1 Heath–Jarrow–Morton (HJM) Model. ......................................................................... 20

2.5.2 LIBOR Market Model. ................................................................................................. 20

2.6 Subprime and Prime Mortgages ............................................................................................ 21

2.7 Foreclosure Process ............................................................................................................... 22

2.7.1 Judicial Foreclosure. .................................................................................................... 23

2.7.2 Power of Sale. .............................................................................................................. 23

2.7.3 Strict Foreclosure. ........................................................................................................ 23

2.8 Conclusion ............................................................................................................................. 23

Chapter 3 - Research Methodology And Design ......................................................................... 25

3.1 Introduction ............................................................................................................................ 25

3.2 Research Question and Hypothesis ........................................................................................ 25

3.3 Relevance of Topic ................................................................................................................ 26

3.4 Research Methodology .......................................................................................................... 27

3.5 Research Design: Variables Identified .................................................................................. 28

3.5.1 FICO Score. ................................................................................................................. 29

3.5.2 Geography of Loan. ..................................................................................................... 29

3.5.3 Loan Balances. ............................................................................................................. 30

3.5.4 Perfect payers. .............................................................................................................. 30

3.6 Conclusion ............................................................................................................................. 30

Chapter 4: Data Collection ........................................................................................................... 31

4.1 Introduction ............................................................................................................................ 31

4.2 Database Description: Population and Sample ...................................................................... 31

4.3 Database Description: Reliability and Validity ..................................................................... 34

4.4 Conclusion ............................................................................................................................. 38

Chapter 5 - Results and Analysis .................................................................................................. 40

5.1 Introduction ............................................................................................................................ 40

5.2 Data Analysis and Interpretation ........................................................................................... 40

5.3 Conclusion ............................................................................................................................. 67

Chapter 6 – Conclusions and Recommendations ........................................................................ 68

6.1 Introduction ............................................................................................................................ 68

6.2 Conclusion: Hypothesis Holds True ...................................................................................... 68

6.3 Recommendations .................................................................................................................. 68

6.5 Contribution of This Study .................................................................................................... 71

6.6 Limitations of the Study ........................................................................................................ 72

6.8 Conclusion ............................................................................................................................. 72

iii

References ....................................................................................................................................... 74

Appendix A – FEFUO Letter ........................................................................................................ 82

Appendix B – Glossary .................................................................................................................. 83

iv

Table of Tables

Table 3-1. Models Used in the Industry and Their Component Variables ................................... 23

Table 5-1. R2 Explanatory Power ................................................................................................. 37

Table 5-2. Statistical Analysis for pool BCAP 2007-AA2 22A1 ................................................. 38

Table 5-3. Statistical Analysis for pool BOAA 2005-1 2A1 ........................................................ 41

Table 5-4. Statistical Analysis for Pool B0AA 2005 10 5A1 ....................................................... 43

Table 5-5. Statistical Analysis for pool BCAP 2007-AA2 33A1……………….. ....................... 43

Table 5-6. Statistical Analysis for pool BOAA 2005-6 7A1 ........................................................ 46

Table 5-7. Statistical Analysis for pool BOAA 2005-1 2A1 ........................................................ 47

Table 5-8. Statistical Analysis for pool AMAC 2003-12 2A ....................................................... 49

Table 5-9. Statistical Analysis for pool AHM 2005-2 3A ............................................................ 50

Table 5-10. Statistical Analysis for pool AMAC 2003-12 2A ..................................................... 60

Table 5-11. Statistical Analysis for pool AHM 2005-1 8A1 ........................................................ 60

Table 5-12. Statistical Analysis for pool AHM 2005-1 6A .......................................................... 61

Table 5-13. Statistical Analysis for pool AHM 2004-1 1A .......................................................... 61

v

Table of Figures

Figure 5-1. Change in Median and Mean Incomes 2001-2010 ................................................... 52

Figure 5-2. Change in Median and Mean Net worth 2001-2010 ................................................. 52

Figure 5-3. Change in real GDP .................................................................................................. 53

Figure 5-4. Monthly Change in Nonfarm Employment............................................................... 53

Figure 5-5. Unemployment Rate ……………….. ....................................................................... 54

Figure 5-6. Long Term Unemployment ....................................................................................... 54

Figure 5-7. Before Tax Family Income 2001-2004 ...................................................................... 55

Figure 5-8. Before Tax Family Income 2007 - 2010 ................. Error! Bookmark not defined.56

Figure 5-9. Before Tax Family Income 2007 – 2010 Continued .................................................. 57

Figure 5-10. Amount Before Tax Family Income ........................................................................ 58

Figure 5-11. U.S. Wages ............................................................................................................... 58

vi

Acknowledgements

I sincerely thank Nouriel Roubini for his service as my Thesis Supervisor. I also thank Dr.

Sandra Marshall and Dr. Jeffery Keefer for the Research Project and Research Process and

Methodology (RPM), which prepared me for my thesis research. Additionally, I would like to

thank Dr. Nitya Singh for the guidance to pursue my studies at NYU. My thanks also go to all

the instructors at Stern , from whom I learned a great deal.

vii

A Declaration

I grant powers of discretion to the Department, SPS, and NYU to allow this thesis to be

copied in part or in whole without further reference to me. This permission covers only copies

made for study purposes or for inclusion in Department, SPS, and NYU research publications,

subject to normal conditions of acknowledgement.

viii

Abstract

Since 2007, a greater emphasis has been placed on the valuation of mortgage-backed securities (MBS), especially because of the systematic risk that they pose to financial institutions in particular and the whole economy in general. The thesis, therefore, evaluated the various methodologies presently used by rating agencies such as S&P and banks such as JP Morgan for inhouse valuation to calculate the value of a mortgage-backed portfolio. Given that there are multiple models to value prepayment, default, and interest rate risk for mortgage-backed securities, the thesis examined the level of correlation between the main input factors used in the various models and the foreclosure rates. Using hypothesis testing the result findings go on to suggest that there is a relationship between the dependent variable (foreclosure rates) and independent variables (credit score, perfect payer, balance and geography), the relationship is not a static one, but a dynamic once. This relationship suggests that the correlation between the dependent variable and independent variable changes over time. Another major finding of this thesis was to suggest that the input variables which compose a Mortgage Backed Security (MBS) have an explanatory power over the foreclosure rates. The period of study in this thesis was a seven year longitudinal study between the years 2008 and 2014.

Keywords: Mortgage-backed securities, valuation, prepayment model, credit risk model,

interest risk model.

ix

Chapter 1 - Introduction

1.0 Introduction

Securitization in the United States began during the 1970s with US government-sponsored

National Mortgage Association funding programs for residential mortgages, followed by private

financings. Gaining popularity beginning of the 1980s, securitization has become a common

financing tool on the global level (Bakri, 2014). “Securitization of Mortgage-backed securities

(MBS) are debt obligations that represent claims to the cash flows from pools of mortgage loans,

most commonly on residential property. Mortgage loans are purchased from banks, mortgage

companies, and other originators and then assembled into pools by a governmental, quasi-

governmental, or private entity. The entity then issues securities that represent claims on the

principal and interest payments made by borrowers on the loans in the pool, a process known as

securitization.” (Fast Answers,2015).

By 2006, the securitization market has grown to $1.480 trillion of issuance (Ashcraft &

Schuermann,2014). Since the Great Recession in 2007, one of the main culprits widely blamed

for the downturn was the inaccurate valuation of distressed mortgage-backed securities (MBS)

held by major banks and financial institutions. These instruments were also widely held outside

of the United States. This lent even greater impetus to the contagion process. This was reflected

in the extensive write offs by financial institutions at both their own capital level, and also within

investment funds which they managed. These events have been a key contributing factor in calls

for greater supervision of financial institutions and setting of risk appropriate capital

requirements. (Reilly, 2009)

The pricing of such complex structures, structured in various tranches (a piece, portion or

slice of a deal or structured financing. This portion is one of several related securities that are

1

offered at the same time but have different risks, rewards and/or maturities. "Tranche" is the

French word for "slice"), and requiring complex calculations to estimate cash flows assuming

various defaults rates, made it difficult to accurately value them on their own merits after the

collapse of Lehman Brothers. With no active market to trade in the secondary market, the banks

were unable to accurately value the MBS, thus leading to issues with valuation, balance sheet

liabilities, and ultimately the dreaded margin call from counter parties. The losses booked by the

banks forced them to write down capital, while margin calls drained liquidity from the financial

markets. These losses reduced the capacity of the banks to act as purveyors of credit in an

economy already shaken by the collapse of a large swathe of the housing market. The resulting

contraction in credit ultimately caused the US economy to implode in 2007.

DiMartino and Duca (2007) suggest that, “in the early and mid-2000s, high-risk

mortgages became available from lenders who funded mortgages by repackaging them into pools

that were sold to investors. New financial products were used to apportion these risks, with

private-label mortgage-backed securities (PMBS) providing most of the funding of subprime

mortgages. The less vulnerable of these securities were viewed as having low risk either because

they were insured with new financial instruments or because other securities would first absorb

any losses on the underlying mortgages” (DiMartino & Duca, 2007, p. 47). This enabled more

first-time homebuyers to obtain mortgages, and homeownership rose. (Duca, Muellbauer, &

Murphy, 2011)

The resulting demand bid up house prices, more so in areas where housing was in

tight supply. This induced expectations of still more house price gains, further increasing

housing demand and prices (Case, Shiller, & Thompson, 2012). Investors purchasing PMBS

profited at first because rising house prices protected them from losses. When high-risk mortgage

2

borrowers could not make loan payments, they either sold their homes at a gain and paid off their

mortgages, or borrowed more against higher market prices. Because such periods of rising home

prices and expanded mortgage availability were relatively unprecedented, and new mortgage

products’ longer-run sustainability was untested, the riskiness of PMBS was not well-

understood. On a practical level, risk was “off the radar screen” because many gauges of

mortgage loan quality available at the time were based on prime, rather than new, mortgage

products.

While sub-prime lending was not new, two key factors helped precipitate the disaster:

The lack of sufficient estimates on which to base default probabilities, and the assumption that

there could not be a nationwide housing collapse. When house prices peaked, mortgage

refinancing and selling homes became less viable means of settling mortgage debt, and mortgage

loss rates began to rise for lenders and investors. In April 2007, New Century Financial Corp., a

leading subprime mortgage lender, filed for bankruptcy. Shortly thereafter, large numbers of

PMBS and PMBS-backed securities were downgraded to high risk, and several subprime lenders

closed. As the bond funding of subprime mortgages collapsed, lenders stopped making subprime

and other nonprime risky mortgages. This lowered the demand for housing, leading to sliding

house prices that fueled expectations of still more declines, further reducing the demand for

homes. Prices fell to such low levels that it became difficult for troubled borrowers to sell their

homes to fully pay off their mortgages, even if they had provided a sizable down payment (Duca,

2010).

1.1 Purpose of Research

Much research has focused on the valuation of MBS, and these valuation methods have

been reinvented and developed since 2007. The main impetus for such a change came from the

Federal Reserve, pushing the banks and major financial institutions to accurately value their

3

exposure to the MBS portfolio they are holding and meet the capital requirements. To accurately

measure the foreclosure risk, pre-payment risk, value at Risk (VAR); various models have been

developed that value these performing and non-performing MBS Pools. The concept of

performing pools implies that the borrower is paying on time and non-performing implies that

the buyer has missed several payments. The concept of foreclosure risk implies to the risk in a

MBS pool that the borrower will not pay, and default on his loan, leading to a bank foreclosure.

Pre-payment risk is the risk in a MBS pool that a borrower will pay ahead of time, causing the

pool to have lower interest payments thus lower return. VAR is the total risk of a MBS portfolio

that may be at risk given a macro-economic event, such as rise in interest rate. Some institutions

have taken a lead on this and are the industry leaders. One such market leader in this segment is

Blackrock. The company was invited by the Federal Reserve to independently value the banks’

MBS holdings, and also by the Greek government to advise them on their exposure. Their

propriety valuation system is called “Alladin” and is considered the industry standard (Goliath,

2011).

Presently the MBS market is $8.7 trillion, while the total outstanding public and private

bond market is $39.9 trillion in the USA, which include treasuries, MBS, auto loans, credit cards,

etc. (Campbell, 2014). The mortgage-backed security market is crucial to the economy not only

because there are large sums of money involved, but also because it is a very crucial and direct

link to the economy. The consumer accounts for two-thirds of the spending in the United States

economy; therefore, taking out a mortgage is the single biggest investment an average person

makes in his life. This is also important because many borrow against the unrealized capital gain

in their home to finance consumption. The collapse in home prices therefore had a negative

“multiplier” effect on consumption.

4

This trend drives not only the mortgage industry but also various other industries that are

dependent on the housing market such as construction, heating, appliances lumber etc. The

housing market not only creates jobs and consumes resources during the construction, but also

plays an important role in stimulating the economy through numerous associated activities such

as ongoing home maintenance, gardening, repairs and home improvements. Businesses such as

Home Depot depend on these types of activities to survive. Thus, given the far-reaching effect of

the housing sector on the economy, the mortgage-back security industry is critical to the

economy. However, since the bubble burst in 2008, housing is now seen as playing a lesser role

in economic growth. There has been a relatively moderate recovery which, despite record low

interest rates, continues to be hampered by difficult access to credit for non-prime borrowers.

The core logic of the models used within the MBS is based on the cash-flow of the

mortgages. The system works as follows: once a mortgage is issued by a bank it is collected by

the bank and combined in a pool. The pool may range from as little as 25 loans to a few thousand

individual loans. In previous asset backed securitizations there was an assumption of “safety in

number, with over-collateralization seen as a means of ensuring sufficient cash flows for debt

repayment. This may have been the case in the case of MBS (mortgage backed securities) backed

by strong credits. However, as investors discovered, over collateralization cannot compensate for

risks that were not viable at inception. “The process of posting more collateral than is needed to

obtain or secure financing. Overcollateralization is often used as a method of credit enhancement

by lowering the creditor's exposure to default risk.” (Investopedia, 2003) The criteria for forming

the pool are based on various circumstances or investor needs, such as maturity of the pool

which might be a 15 years period or a 30 years period, Another criteria is required return. A 15%

required return will have riskier mortgages where as a 6% required return will have a less risky

5

loans. Once a pool is created, it is given to a rating firm such as Moody’s or S&P. The rating

firm does its due diligence and assigns an investment grade to the pool based on the risk metrics

they have identified. Some risk metrics used by rating companies are loan to value (LTV), i. e

how much is being borrowed vs the value of the property, credit scores etc. The bank either

holds the pool on its own balance sheet or sells it to investors. (Tatom, 2009)

1.2 Problem Definition

The mechanics of mortgage backed securities are based on payments by the individual

borrowers. The borrower makes monthly payments and the servicing firm i.e. the bank, collects

the payments and amortizes the loan with part payment to interest and remaining to principal till

the balance becomes zero. The most common types of mortgages are 30 year fixed rate, and 15

year fixed rate mortgages. The problem with such complex instruments is that they are made of

several moving pieces, such as tranches, which react differently to macro-economic events.

They are also very susceptible to changes in interest rates – which may cause an extension, in the

event that rates should rise, of the original maturity or, in the event that rates fall, prepayments.

In this last case, the best borrowers, who can access refinancing at lower rates shall prepay. This

is tantamount to “adverse selection”. The pool generally tends to be comprised increasingly of

lower rated credits. In the event of a recession and fall in borrower income, this may lead to an

increased foreclosure rate. Thus the way to predict the effect is to use proxies. In the case of

mortgage backed security, the proxies are FICO score, geography of the loan and payment

history. The decision to use a proxy is based on each individual company’s fund manager, and

the model they plan to use, as well as the variables that they seem fit to include or drop from the

model. There is no industry standard established for this. It is essential therefore, that such

proxies are relevant measures. However, there is a paucity of research which aims to establish

whether such proxies are relevant indicators or not (Fabozzi, 1998). Since there is no industry or

6

government standard each firm is left to design a model that it likes based on the proxies the

research team decides to use.

1.3 Research Question

This thesis, therefore, investigated the various methodologies and models that are used to

calculate the value or price of a distressed MBS security. A distressed MBS security is a pool

that has a high rate of foreclosures. A correlation analysis was conducted between the main

inputs into the models (credit score, geography, loan balances and perfect payer percentage) with

the foreclosure rates. Such an analysis enabled us to developing a comprehensive understanding

of whether the input variables into the models had a high explanatory potential or not; and

whether the models were using the correct factors or not. The thesis therefore answered the

research question: What is the nature of correlation between the factors used by the most

common risk models (e.g. FICO score, geography, loan balance and perfect payer) used to

predict foreclosure rate of the pool?

1.4 Conclusion

The primary goal of this thesis was to develop an understanding of the various models

that are used to analyze mortgage backed securities, and identify which model is the optimum

model for financial professionals to use. In order to answer the research question, I conducted an

extensive literature review in Chapter 2. This set the stage of developing an understanding of

what is the existing work in the field, as well as enabling me to identify the numerous research

gaps. In Chapter 3, I then went ahead and identified the research methodology to be followed, as

well as developed the research design that I used to answer the research question. Once the

research methodology was established in Chapter 4, I then enumerated how the data would be

collected and processed. The data was tested in Chapter 5, and as identified in the research

7

methodology, I used numerous techniques to answer the research question. Finally, in Chapter 6,

I summarized the research and put forward my recommendations and conclusion.

8

Chapter 2 - Literature Review

2.1. Introduction

In order to evaluate the relevance of this research topic, I conducted a comprehensive

literature review and approached the ideas from different viewpoints. The objective of this

review was to establish the theoretical background on which I based my thesis. I used existing

scholarly works to first of all identify the various types of risks that effect the valuation of a

mortgage backed security. Once the various types of mortgage backed securities were identified,

I then reviewed the various prepayment and default risk models. I also evaluated the literature on

various interest rate models and risk models. An analysis of the existing work was necessary to

establish the argument that the variables identified by me are variables that are the primary basis

of calculation in all of the models.

2.2 Types Of Risks That Effect the Valuation Of a Mortgage Backed Security

A study done by Dunn and McConnell (1981) on the various methods used by banks to

value the portfolio of mortgage-backed securities on their balance sheet came to the conclusion

that there is no model that can be considered as being superior over the other, as well as can be

considered as the benchmark model that the rest of the industry should follow. However, it is

significant to note that in spite of the usage of more than six different types of models in the

industry, none of the models were able to predict the problem in the industry that triggered the

financial debacle. This fact highlights the limits of credit enhancement capacities of structuring

when dealing with situations, where at inception debt repayments were contingent on asset sales

by the borrowers (Hung & Lin, 2007).

During the 1980’s, MBS were simple in their structure, unlike today, where

computational power and complexity of the MBS structure have greatly increased. Currently

9

with many counter parties involved, tracing the loan’s deal and exposures to off-balance-sheet

entities is almost impossible (Dunn & McConnell, 1981). Mortgage-backed securities are

financial instruments that are backed by the house as the collateral, thus the premise is that the

holder of the note is assured that on default, the payment of the remaining balance will definitely

come through. In reality however, the house value turns out to be in many cases lower than the

residual debt, leading to losses for both the lenders as well as for the bond holders, with regard to

fixed income instruments. The key support is that the cash flows from the borrowers were

secured for payment of capital and interest; this is of little avail when the foreclosure rate

explodes. However, the risk is that the borrower will pay faster. Thus, the investor has to find

another security to invest the money to meet his long-term investment target. In such a scenario,

the investor faces risk of not finding similar investment opportunities, or has to the take

additional risks. The second risk that the investor faces is that the interest rate will change

causing reinvestment risk. Based on this, it can be argued that the main risks that need to be

modeled are the prepayment risk, the interest rate risk, and the default risk (Becketti, 1989).

2.3 Prepayment and Default Risk Models

There are four major factors influencing the prepayment models (Stanton, 1995). The

first is the refinancing incentive, which is the incentive a borrower has when the rates go down

below the current mortgage rate. The second factor is the age of the mortgage, technically called

seasoning. The term seasoning refers to a phenomenon in which a new pool of mortgages pays

the balance faster, both as in prepayments and full payments. This can be attributed to the fact

that, in the new pool, the borrowers find better rates and refinance or move and sell the property.

This can also lead to investors needing to simultaneously contend with lower than expected cash

flows and ‘adverse selection’ as remaining cash flows are contingent on payments by the higher

10

credit risk. These are the borrowers who were not deemed sufficiently creditworthy to access

refinancing and remain in the pool by default (Stanton, 1995).

However, as time goes by this activity becomes lower and somewhat fixed to a low

percentage of the total mortgages. The third factor is the month of the year also known as

seasonality. On an average, mortgages are paid off more often in the summer months than in the

winter months. Fourth factor is also known as premium burnout. As different households have

different cost bases for the mortgages they have taken out, the interest rates for some households

may need to fall further than other households, for the aforementioned households to be

financially profitable to refinance or prepay (Stanton, 1995).

An analysis of the literature suggested that there are three main categories of prepayment

models presently used in the industry:

1. Econometric approach: This model is the projection of cash flow based on

prepayment models that are fine-tuned to historical data (Schwartz & Torous,

1989).

2. Option-based Approaches: These models are built upon projection of cash flow

based on option-based theory and the value of the underlying call options of the

MBS (Stanton,1995).

3. Reduced-form Approaches: These models focus on intensity models as used in

credit risk modelling (Kau, Keenan & Smurov, 2004).

Prepayment risk is the key to determining the MBS value. This was the traditional

assumption posited on an acceptable credit standing of the underlying collateral. With the market

focused on the stronger credits, credit issues were deemed manageable via over-collateralization.

Prepayment risk models can be broken down into two approaches. The first approach is the

11

statistical approach. In this approach statistical tools are used to predict the probability of

prepayment in term of Conditional Prepayment Rate (CPR). The reduced form models are

widely used, as they are highly customizable and depend on the parameters defined by the user.

This flexibility makes reduced form models easy to develop and use by regular users, and do not

require programming or mathematical skills to accurately model the historical data. However,

given recent experience, historical data are not always a good predictor of the future. The model

works well when dealing with historical data, but the forecasting validity of such models is

suspect, as it was evident during the 2007 crisis (Dowing, Stanton, & Wallace, 2003).

Predominantly in the case of mortgage cash flows the unscheduled cash flows result from

prepayments, not from scheduled amortization. Therefore, the choice of an accurate prepayment

factor is the main driver to calculate the liquidity and valuation metrics. There are numerous

sources of commercial or third-party prepayment models. One of the most popular models is the

Bloomberg median estimates. This model is an average of the mortgage rate via a survey of the

research departments of several Wall Street broker/dealers. BondEdge is a tool also on

Bloomberg, widely used as a fixed income portfolio analytics system by many banks and

financial institutions (Bloomberg, 2009). Another model that is popular is the Andrew Davidson

Co. (ADCO) model. (Bloomberg, 2009). This proprietary model is different from the above two

as it provides a loan level detail and is also available via Bloomberg. The third model is the

Applied Financial Technologies (AFT) model. This proprietary model is also available via

Bloomberg and can be used at the loan or MBS level inside several advanced Asset Liability

Management (ALM) models (Fan, Sing, & Ong, 2012).

Aside from the above mentioned statistical approaches, another approach used in the

industry is the mathematical approach. In this process the model is based on mathematical

12

finance and is sub-classed into option-based approach or structural approach, which is predicting

prepayment via credit risk modeling. Majority of the prepayment models are based on multi-

factor regression and/or optimization models using the below mentioned factors (Nakamura,

2011).

2.3.1 Perfect Payer (Refinance Activity). This has a direct effect on the factor perfect

payer, if a loan is refinanced , the old loan is pain in full and thus perfect pay percentage

increases in the pool. Under this factor, the market loan interest rate is lower than the original

term, thus the borrower refinances to a new lower-rate loan. According to Guttentag (2004), “to

repay a loan by taking out another loan, refinancing can allow one to secure a lower interest rate;

for example, one can replace a loan at an 8.5% rate with one at 5.5%. In the case of a balloon

loan, refinancing can repay the principal if one does not have sufficient funds to do it. This

implies that if one has made only interest payments over the life of the loan and has not reduced

the principal amount when the loan comes due, refinancing can prevent bankruptcy. There are

two main drawbacks to refinancing. First, there is no certainty that one will be approved for it.

One thus takes a risk every time one decides to make only interest payments on a loan or

mortgage. Secondly, refinancing generally resets the repayment period; that is, if one refinances

six years into a 10 year loan, the one generally repays the new loan over 10 years instead of the

remaining four” (Guttentag, 2004,p.18).

2.3.2 Perfect Payer (Age of the Mortgage Assets). The industry standard is to use the

Public Securities Association (PSA) approach to ramp up prepayments over the first 30 months

of a mortgage, and then the prepayments are assumed to be stable.

The main rational is that when a pool is new, borrowers who have good credit will move

out sooner when they get good offers, similarly, borrowers who are not credit worthy but

13

somehow got the loan will default, thus during the first 30 months the outliers, both good and

bad borrowers will exit the pool early. But newer models are factoring in other factors such as

buyer laziness or lack of opportunistic behavior even when there are economic advantages of

doing so after the initial year or so have passed.

2.3.3 Loan Balance. It has been observed using historical data that loan balances with

lower balances prepay slower; this is assumed that the borrower has less incentive as the dollar

advantage of a refinance is minimal. “The general loan limits for 2015 are unchanged from 2014

(e.g., $417,000 for a 1-unit property in the continental U.S.) and apply to loans delivered to

Fannie Mae in 2015 (even if originated prior to 1/1/2015).” (Mortgage Refinance Financial

Glossary, 2011).

2.3.4 FICO score. It has been observed that loans with lower FICO scores than the

national average tend to prepay slower, perhaps because they cannot get favorable loan terms

thus the incentive to refinance is not there. The lower prepayment risk was however not

sufficient compensation for the higher repayment risk. Bhardwaj & Sengupta (2011) in their

paper suggested that “FICO score is a simple yet effective measure for evaluating the

performance of credit scoring. As mentioned earlier, the advantage of using such a measure is

twofold. First, it lends itself to both non-parametric and parametric estimation. Second, it

minimizes the impact of situational factors on this measure of credit score performance. Using

this measure, we find that credit score performance is robust to both high and low default

environments. However, evidence suggests that some of the increase in credit scores over the

cohorts can be explained as adjustment for the increased riskiness in other attributes on the

originations. This was particularly true for low levels of credit scores resulting in a sharp

deterioration of credit score performance in terms of our nonparametric measure. Significantly,

14

once we control for other (riskier) attributes in the origination, our parametric credit score

performance shows improvement over the cohorts. This would suggest an over-reliance on credit

scoring not only as a measure of credit risk but also as a means to set risk on other origination

attributes. In part, this reliance led to deterioration in loan performance even though average

credit quality as measured in terms of credit scores actually improved over the year” (Bhardwaj

& Sengupta, 2011).

2.3.5 Geographic. Longstaff (2005) conducted an empirical analysis and observed that

certain parts of the country prepay faster than the others. This is a function of job mobility,

younger demographics, etc. Regardless of the method or model of prepayment estimates, it is

advised to back-test projected prepayments versus actual prepayment. Seasonality, historical data

have shown that mortgages prepay faster during the summer months than during winter months

in most parts of the country (Longstaff, 2005).

Valuing MBS requires that a model takes into consideration both the behavior and the

prepayment of the mortgages in the pool. After the economic crisis of 2008, the renewed focus

on this sector has increase significantly. This has resulted in us developing a better understanding

of MBS, however several challenges remain. “These challenges include the persistence of

model-based MBS pricing errors (option adjusted spread, or OAS), the observed variance in bids

for MBS derivative auctions” (Bernardo & Cornell, 1997).

Another prepayment model approach is the option-based model. Here a no-arbitrage

pricing theory is used but in a discrete time setting. Kariya and Kobayashi (2000), formulated a

framework for pricing a mortgage-backed security (MBS) that predicted the burnout effect based

on a one-factor valuation model. However, this option-based approach implicitly and usually

assumes homogeneous mortgagors. This is a serious short-coming since it is very rare to have a

15

pool of mortgagors that are homogeneous. The mortgagors in an MBS pool are typically

heterogeneous, with different incomes, FICO scores, geographic locations (Ushiyama & Pliska,

2011). This was however not the case with the sub-prime mortgage ABS, which were composed

of largely credit homogenous mortgages. Geographical diversification, if any, brought little

solace to the investors.

2.4 Interest Rate Risk Models

The other major source of uncertainty in MBS valuation is the use of interest rates.

Different models are used to value that segment, thus making the one-factor-model valuation less

accurate. A large decrease in the mortgage rate that follows a decrease in the short-term rate

tends to lower the value of an MBS due to the refinancing activity. On the other hand a decrease

in the short-term rate also has an opposite effect thereby increasing the value of an MBS by

increasing the discount factors. Therefore, it is important to balance the two and incorporate their

separate roles (Ushiyama & Pliska, 2011). In a recent study, Tahani and Li (2011), came to the

conclusion that the interest rate behavior is not Gaussian but Brownian in nature, as evidenced by

the changing volatility of the interest rates (Tahani & Li, 2011). Brownian motion refers to the

motion of gas particles as they move about randomly. Using this concept Vervaat (1979), has

shown that interest rates mimic the random behavior of the gas particles. Thus, financial models

that incorporate the random walk are more accurate. The literature discussed above goes on to

show that there are various approaches that can be adopted to calculate and develop interest rate

models. Some of the major models following the earlier mentioned approached are:

2.4.1 Vasicek model. The Vasicek model is a mathematical model used in finance

predicting how interest rates effect fixed-income valuation, such as that of a mortgage-backed

security. The Vasicek model is a one-factor model where short-term rates are the main driver, as

it contributes interest rate movements as driven by only one source of market risk, which in this

16

model is the short-term interest rate (Vasiçek,1977). The significance of this model is that it was

the first of its kind and subsequent models are based on it.

2.4.2 Cox, Ingersoll and Ross (CIR) Model. The Cox–Ingersoll–Ross model (or CIR

model) is used to model interest rates in the valuation of MBS. The CIR model is a one-factor

model mostly factoring in short-term interest rates, and the interest rate fluctuations are driven by

only one source of market risk. CIR model was introduced in 1985 by John C. Cox, Jonathan E.

Ingersoll and Stephen A. Ross as an extension of the Vasicek model. The extension that this

model added was time-varying functions that replaced the factors and they can be introduced in

the model to make it sync with a set of predetermined term structure and volatility of interest

rates (Cox, Ingersoll, & Ross, 1985).

2.4.3 Black–Derman–Toy Model. The Black–Derman–Toy model (BDT) is a popular

short-rate one-factor model used in the pricing mortgage-backed securities. The short-term rate is

the single most important stochastic factor that determines the predictions of the model. This

model is extremely popular within the industry, and used widely, as it was the first model to

combine the mean reverting behavior of short-term interest rates with lognormal distribution.

This model was developed in-house by Goldman Sachs in the 1980’s by Fischer Black, Emanuel

Derman, and Bill Toy (Black, Derman, & Toy, 1990).

The popularity of this model stems from the fact that it is used by one of the most

influential player in the MBS market. Another salient feature of the BDT model is that it uses a

binomial lattice. The model is calibrated using balance and fit of the volatility of interest rates

caps, and the current yield curve or the interest rates structure. Thus once we have the calculated

or calibrated lattice, then it is easier to value the complex interest-rate sensitive MBS.

17

The model was developed by its originator for a lattice-based environment; however the

model has shown it is the following continuous stochastic differential

equation:

where,

= short-term rate at a given point t

= value of the asset

= short-term rate volatility at a given time t

= Brownian motion under a risk-neutral probability measure

Black, Derman, & Toy (1990).

2.4.4 Ho–Lee Model. The Ho–Lee model was developed in 1986 by Thomas Ho and

Sang Bin Lee (1986). It was the first arbitrage-free model of interest rates. An arbitrage-free

model is a financial engineering model that calculates prices or valuation in such a way that it is

impossible to construct arbitrages between two or more of those prices. Thus, the profit of

buying from one seller and simultaneously selling to another buyer, and making a profit, is not

there.

Under this model, the short rate follows a normal process:

The Ho–Lee model adds values since it is fine-tuned to the market data thus the valuation

is essentially the fair market price. The Ho–Lee model can therefore accurately calculate the

price of the bonds with the market yield curve. The model calculates the yields based on a

binomial lattice based method (Ho & Lee,1986). However, one of the weaknesses of the model is

18

that it does not incorporate mean reversion. Additionally it generates bell-shaped distribution of

rates in the future that makes it unpredictable as with this distribution negative rates are possible.

2.4.5 Hull–White Model. The Hull–White model is a model used to calculate future

interest rates. The Hull–White model is based on the principles of no-arbitrage models, which are

more practical given the present-day interest-rate term structure. The model easily translates the

mathematical description of the future interest rates for a binominal tree; hence derivatives such

as Bermudan swaptions can be valued in the model.

The first Hull–White model is still popular today and was introduced in 1990 by John C.

Hull and Alan White (Hull & White, 2001).

The model is a short-rate model.

There are disagreements among the users about to the exact time-dependent parameters,

but the most commonly accepted hierarchy has

θ and α constant – the Vasicek model

θ has t dependence – the Hull–White model (Hull & White, 2001).

2.4.6 The Black–Karasinski Model. The Black–Karasinski model is used for the

calculation of the term structure of interest rates. This model is also from the family of no-

arbitrage models and uses a one-factor model for predicting interest rate movements influenced

by a single source of randomness. The model is a good fit for today’s market, as in its most

generic form, for the calculation of the call options on the underlying loans of the MBS. The

main driving factor of the model is the short-term rate. The short-term rate is assumed to follow

the following stochastic differential equation (under the risk-neutral measure):

19

In the above equation dWt is a standard Brownian motion. The short-term interest rates

are assumed to be log-normal distribution (Black & Karasinski, 1991).

2.5 Other Models

In addition to the earlier mentioned models, other models used in the industry are as

follows:

2.5.1 Heath–Jarrow–Morton (HJM) Model. Heath–Jarrow–Morton (HJM) model

negates an assumption that is the core of the models above, i.e., no drift estimation is needed.

The HJM model is different from other models as, this model captures the full dynamics of the

entire forward rate curve; whereas the other models incorporating drift only capture dynamics of

one point of the curve, or short rate. HJM frameworks are usually non-Markovian with infinite

dimensions. But recent research has shown that they can be computed in a finite manner, making

it computationally feasible (Heath, Jarrow, & Morton, 1990).

2.5.2 LIBOR Market Model. The LIBOR market model is used for predicting the future

curve of interest rates. In the LIBOR model, the quantities are modeled to get the interest rate

risk, rather than the individual LIBOR forward rates. This method offers a better understanding

of the volatilities that are directly linked to the underlying contracts and can be observed easily in

the market. In the LIBOR model a lognormal process is used to model the individual forward

rate. Black model leads to a Black formula for interest rate caps, that tells us what maximum

value an option can have a , in other words what is the cap on it. The most popular formula is the

Black formula for interest rate caps, this formula is the market standard to quote cap prices in

terms of implied volatilities, hence the term "market model".

The LIBOR market model in a simple explanation is a collection of forward LIBOR of

different forward rates. The LIBOR Market Model (LMM) differs from short-rate models as it

20

uses the lognormal LMM for each forward rate, in that it evolves a set of discrete forward rates.

Specifically,

where

dW is an N-dimensional geometric Brownian motion with

The LMM relates the drifts of the forward rates based on no-arbitrage arguments.

Specifically, under the Spot LIBOR measure, the drifts are expressed as the following:

Nekrasov, (n.d.).

Definitions

2.6 Subprime and Prime Mortgages

“The main difference between prime and subprime mortgages lies in the risk profile of

the borrower; subprime mortgages are offered to higher-risk borrowers. Specifically, lenders

differentiate among mortgage applicants by using loan risk grades based on their past mortgage

or rent payment behaviors, previous bankruptcy filings, debt-to income (DTI) ratios, and the

level of documentation provided by the applicants to verify income. Next, lenders determine the

price of a mortgage in a given risk grade based on the borrower’s credit risk score, e.g., the Fair,

Isaac, and Company (FICO) score, and the size of the down payment.” (Agarwal & Ho, 2007).

“Subprime loans, which are loans to borrowers with relatively low credit scores and

records of poor credit performance or little credit experience, have become an increasing share of

all mortgages in this decade and currently make up about 13 percent of such loans. In 2000 and

earlier, subprime loans were negligible. Other higher risk mortgages today include credit

21

extended by the Federal Housing Administration (FHA) and so-called "alt-?" loans, which are

loans to borrowers usually with prime credit scores, but who do not provide any documentation

("no-doc") of income or wealth or ability to service pay the loan, or very little documentation

("low-doc"). They have been reported to constitute over 10 percent of all mortgages. When all

three categories are added together, nearly 30 percent of loans outstanding are estimated to be in

the high-risk category. Subprime loans have foreclosure rates that are much higher than that for

prime loans” (Tatom, 2009).

2.7 Foreclosure Process

“Foreclosure processes are different in every state. Differences among states range from

the notices that must be posted or mailed, redemption periods, and the scheduling and notices

issued regarding the auctioning of the property. In general, mortgage companies start foreclosure

processes about 3-6 months after the first missed mortgage payment. Late fees are charged after

10-15 days; however, most mortgage companies recognize that homeowners may be facing

short-term financial hardships. It is extremely important that you stay in contact with your lender

within the first month after missing a payment. After 30 days, the borrower is in default, and the

foreclosure processes begin to accelerate. If you do not call the bank and ignore the calls of your

lender, then the foreclosure process will begin much earlier.

Three types of foreclosures may be initiated at this time: judicial, power of sale and strict

foreclosure. All types of foreclosure require public notices to be issued and all parties to be

notified regarding the proceedings. Once properties are sold through an auction, families have a

small amount of time to find a new place to live and move out before the sheriff issues an

eviction notice.

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2.7.1 Judicial Foreclosure. All states allow this type of foreclosure, and some require it.

The lender files suit with the judicial system, and the borrower will receive a note in the mail

demanding payment. The borrower then has only 30 days to respond with a payment in order to

avoid foreclosure. If a payment is not made after a certain time period, the mortgage property is

then sold through an auction to the highest bidder, carried out by a local court or sheriff's office

(Foreclosure Process/U.S. Department of Housing and Urban Development, 2015).

2.7.2 Power of Sale. This type of foreclosure, also known as statutory foreclosure, is

allowed by many states if the mortgage includes a power of sale clause. After a homeowner has

defaulted on mortgage payments, the lender sends out notices demanding payments. Once an

established waiting period has passed, the mortgage company, rather than local courts or sheriff's

office, carries out a public auction. Non-judicial foreclosure auctions are often more expedient,

though they may be subject to judicial review to ensure the legality of the proceedings

(Foreclosure Process/U.S. Department of Housing and Urban Development, 2015).

2.7.3 Strict Foreclosure. A small number of states allow this type of foreclosure. In strict

foreclosure proceedings, the lender files a lawsuit on the homeowner that has defaulted. If the

borrower cannot pay the mortgage within a specific timeline ordered by the court, the property

goes directly back to the mortgage holder. Generally, strict foreclosures take place only when the

debt amount is greater than the value of the property” (Foreclosure Process/U.S. Department of

Housing and Urban Development, 2015).

2.8 Conclusion

In conclusion, the literature indicated that there are several models that have been

developed over the years for the purpose of valuation of mortgage-backed securities. Each model

is valuable and correct in its methodology as shown by its authors. However, different

23

circumstances and priorities make one model better than the other. There is no one model that is

the industry standard and superior to the other. However, each of the models relies on input

factors that are similar. The major factors are FICO score, loan balances, geography of the loans,

perfect payee. In the following sections, I used the variables identified by the literature, as a part

of my model, and developed an understanding of the level of efficiency of each of the models

identified above, in understanding Mortgage Backed Securities.

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Chapter 3 - Research Methodology And Design

3.1 Introduction

In the section related to research methodology and design, I clearly identified the

research question, and enumerated on the research design, adopted by me to test my research

question. I also identified the research methodology as well as the various variables that I used to

test the research question.

3.2 Research Question and Hypothesis

The primary goal of this thesis was to investigate the various methodologies and models

that are used to calculate the value or price of a distressed MBS security, and conduct a

correlation analysis between the main inputs into the models (FICO score, geography, loan

balances) with the foreclosure rates. Such an analysis enabled us to understand whether the input

variables into the models have a high explanatory potential or not; and whether the models are

using the correct factors or not. The thesis therefore answered the following research question,

R.Q.: Does a correlation exist between the foreclosure rate of the pool and the factors

used by the most common risk models used to predict foreclosure rates?

In order to answer this research question, I used existing literature to develop the

following hypotheses:

H0: There exists no correlation between the foreclosure rate of the pool, and variables such as

Credit Score, Perfect Payer, Balance and Geography; which are used to predict foreclosure rates.

H1: There exists a correlation between the foreclosure rate of the pool, and variables such as

Credit Score, Perfect Payer, Balance and Geography; which are used to predict foreclosure rates.

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3.3 Relevance of Topic

This thesis is intended to benefit the mortgage-backed security professionals, bank and

valuation experts, who utilize numerous methods to value their risk or portfolio on a daily basis,

without the knowledge whether one methodology is superior to other. As there are numerous

models, and all of them have a sound logical and mathematical basis, there is no one model that

may be considered superior in all instances compared to others. The thesis, therefore, provided a

brief introduction to various models used to value MBS, and established a correlation between

the main inputs that drive the model, and the foreclosure rate. Additionally, this thesis provided

recent graduates entering into the MBS structure finance field with a summary of the valuation

methods, and a reference of how valuation is done for such products.

Table 3-1. Models Used in the Industry and Their Component Variables

Factor used FICO Geography Loan balance Perfect payer

Vasicek model

Cox, Ingersoll and Ross

(CIR) model

Black–Derman–Toy model

Ho–Lee model

Black–Karasinski (B-K)

model

Heath–Jarrow–Morton

(HJM) model

LIBOR market model

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The thesis did not try to analyze the internal logic of all the models mentioned (Table 3-

1), as this stream of research has been extensively studied by numerous scholars (Vasiçek,1977;

Black, Derman, &Toy,1990).

3.4 Research Methodology

To answer the research question enumerated above, a quantitative method approach was

adopted using a longitudinal study over seven years from 2008 to 2014 focusing on the factors

that are used in the model. The use of a longitudinal study as a methodology, instead of surveys

and interviews, was adopted as this approach is more robust and prevents individual biased from

impacting the final result. For example, if a survey of finance professionals was conducted on the

correlation between FICO score and foreclosure rate, then the results would have a personal bias

experience component. This would result in the data not being homogeneous, and call into

question the validity of the data. Similarly, if a regression analysis were based on survey, the

results would be skewed. In the case of interviews, the same issues would persist making the

analysis unreliable.

The longitudinal study used here evaluated four input variables. These factors are FICO

score, loan balance, geography of the location of the house that make up the pool of loan in the

mortgage backed security, and the payment history of the borrowers. These variables were

evaluated over a 7-year period from 2008 to 2014 to identify whether there is a significant

correlation between the factors and foreclosure rate. The major emphasis of the thesis was to

identify the correlation between the dependent variable and the independent variables. The

nature of the correlation, i.e., if it is positive or negative, is outside the scope of the study. The

main reason a period between the years 2008 and 2014 was chosen was, because it was during

this time frame that the largest collapse in the housing market in the history or modern

economics took place. The epic-center of such a housing crisis was also based in the mortgage

27

backed securities market, making it the ideal time frame to study (Goliath, 2011). The rational

for picking the period was that if we were to see the nature of relationship between the dependent

variable and the four independent variables we have chosen for the study. Then the period of

extreme change and foreclosures and recovery would be better than using a period where there is

little change in the macro economic situation of the country in general and the borrowers in

particular.

The foreclosure rate was the metric chosen as a benchmark, rather than price, as default is

a major risk event in a mortgage-backed security. It would make price meaningless if there is

going to be no future cash flow. With the longitudinal survey, the study investigated if there is a

correlation between the main factors the models use, and the foreclosure rate. The reason

correlation with the foreclosure rate and input factors as a method was chosen, because the

greater the correlation the higher the reliability level of the models.

3.5 Research Design: Variables Identified

The method used in the thesis was a longitudinal study using a 7-year time frame. The

main independent variables are FICO score, geography of the loans in the pool, loan balances,

and perfect payers (see Table 1). The dependent variable is the foreclosure rate. It is defined as

the mortgage foreclosure rate: the dollar value of 1–4 family mortgages that are delinquent by 30

days or more or are in foreclosure, divided by the dollar value of all 1–4 family mortgages. For

example, if we assume there are 100 loans in the pool of a mortgage back security, of the 100

loans, 10 are not making payments for over 30 days and five are in foreclosure. Then the

foreclosure rate for this pool is 15%. In the research design, it is important to not only identify

the constructs, but also to clearly explain them so that when I test my research question, I am

able to ensure robustness. The independent variables or constructs are as follows:

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3.5.1 FICO Score. FICO score is a credit score based on a mathematical formula using

payment history, debt balance, and length of credit history, types of credit used, and recent

inquiries. The score ranges from 300 to 850. The score is used by mortgage lender to access the

borrowers’ credit worthiness and risk. ‘A FICO Score is a three-digit number calculated from the

credit information a credit report. Lenders use these scores to estimate their credit risk, which is,

how likely is the borrower to pay his credit obligations as agreed. A FICO Score assesses the

information in a borrowers credit report at a particular point in time. It helps lenders evaluate

credit risk reliably, objectively, and quickly. And it helps the borrower obtain credit based on his

actual borrowing and repayment history, filtering out extraneous details such as race or religion’

(What’s in My FICO Score. 2014).

3.5.2 Geography of Loan. This metric classifies where the collateral/home is located.

Since a mortgage-backed security has a large number of loans, they tend to be a mixture from all

over the country. For example, some pools are only from one state such as Florida; while some

are a mixture of various states such as California, New York and Michigan. “Geographic

diversification does not guarantee diversification in housing market returns. To the extent that

the housing market is associated with the probability of loan default, a relevant measure of loan

diversification is the correlation between the returns in housing markets of the loan collateral. As

an illustration of this point consider that despite the geographic distance, returns on a California

house price index have a correlation coefficient of 0.87 with returns on an index measuring

house price returns in Washington DC. We construct a Herfindahl index of the geographic

concentration in each deal as follows. For each deal, we calculate the percentage of the deal

principal that is concentrated in each of the 50 states, plus Washington, DC. The deal-level

29

Herfindahl index is then calculated as the sum of the squared weights” (Nadauld,& Sherlund,

2009).

3.5.3 Loan Balances. This metric provides the unpaid balance (UPB) information. The

UPB is defined as the amount owned by the borrower on the loan. The loan balance is not a fixed

amount. The original balance is reduced as payments are made based on an amortization

schedule. The payments are applied to both interest and principal and over time the balance

becomes zero. Thus the higher the balance the greater the effect the loan has on the pool as the

default of a high-balance loan will have more impact on the pool than a low-balance loan. This

behavior of this variable makes it an ideal candidate to be included in the research as one of the

factors that helps us identify the level of correlation with the foreclosure rate.

3.5.4 Perfect payers. This metric reflects the percentage of people in the pool who have

been paying on time over a period of time. There are several sub categories within this. The first

sub-category is the 24 month payer, which is comprised of individuals who have not missed a

payment in the past 24 months. The second sub-category is the 60 month perfect payer, which is

comprised of borrowers who have paid on time for the past 60 months. The category we are

benchmarking in this study is the perfect payer, which is individuals who have not missed a

single payment at all.

3.6 Conclusion

Based on the literature review in Chapter 2, we were able to identify the research

question, and how it fits within the overall literature on the topic. This chapter took the study

further and clearly identified the research question, the research design, as well as the dependent

and independent variables. The next chapter identified how the data was collected and analyzed.

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Chapter 4: Data Collection

4.1 Introduction

The data collected in this study was a time series date. Most of the data covered a 10-year

period of mortgage-backed securities issued before 2004, and was active with payments being

made by the underlying cash flow. To add diversity to the data, the study also included some

mortgage-backed securities that either collapsed or were paid out. The main data source was the

Bloomberg terminal that was accessed through the NYU library. Specifically, using the

Bloomberg fixed-income section, and sorting for active pools of mortgage-backed securities

issued before 2004, the database collected pools of data that includes MBS with both active

payments, as well as mortgage-backed securities that either collapsed or were paid out. The

database consisted of a total of 1000 such unique securities. For the study we choose 10 pools

that had more than 1,000 individual mortgages inside then, so the N in the regression analysis

would be large and no outlier would have minimal effect on the results. The pools have not been

modified and the regression analysis was performed on the original data. These pools are

existing pools and have been chosen to give a diverse representation. The pools were chosen

from different banks and not from one single bank. Additionally, care was taken that the pools

represented different geography and cont concentrated from one area, such as New York or

Texas.

4.2 Database Description: Population and Sample

The population of the data set comprised of all mortgage-backed securities issued in the

United States of America prior to 2004. The mortgage-backed securities range from FICO scores

of 400 to 800, geographically they represent all 50 states, and have loan balances ranging from

$10 million to $2 billion. The total population of such loans is over 1,000. The sample that I

31

chose from this population is around 300. These randomly chosen MBS have a diverse loan

balance, FICO score, and geography and payment histories. The choice of a sample size of 300 is

apt, as it is sufficient to resolve any issues arising from missing data or presence of outliers. The

sample is large enough to resolve any self-selection biases and other statistical errors that are

commonly observed in datasets with a low sample sizes. The method of identifying samples is

based on the criteria defined earlier in the study. Once I was able to identify the population set, I

randomly picked 300 pools that have all the four independent variables. This pool of 300

securities, of different vintages and characteristics, was subjected to statistical tests to answer the

research question. Results of 10 pools from the 300 tested are discussed in detail. The reason we

discussed 10 pools in detail was we wanted to elaborate the relationship how the dependent

variable is affected by the independent variable. We discussed the macro economic, political,

business environment impacting the variables in details so the reader can understand in details

the relationship between the independent variable and dependent variables.

At this stage it is important to point out that the loans chosen consist of prime

loans and, not sub-prime loans, but the prime loans are distressed given the rescission in the

chosen period of 2008 to 2014. The aim of the thesis was to test the relationship of the input

factor to the foreclosure rate, thus having sub-prime mortgages might have had given us

unreliable data. The study of MBS in the sub-prime mortgage is the subject of another study, but

beyond the scope of this thesis. The primary reason why the sub-prime mortgage was because

they are biased towards default, especially given the credit and income profile of the borrower,

and also not geographically dispersed. “Subprime originations appear to be heavily concentrated

in fast-growing parts of the country with considerable new construction, such as Florida,

California, Nevada, and the Washington DC area. Subprime loans were also heavily

32

concentrated in zip codes with more residents in the moderate credit score category and more

black and Hispanic residents. Areas with lower income and higher unemployment had more

subprime lending.” (Mayer & Pence, 2008). The economic recovery since 2009 has been unlike

any other, and this slow recovery has caused wages to be depressed. Additionally, there is the

concept of shadow unemployment, where people are working part-time or working jobs they are

more qualified for. This may be causing substantial drift in the credit standing of loans

previously deemed non sub-prime. This trend may be further accentuated by continuing

restrictions on credit to non- perfect credit score borrowers.

Thus, having sub-prime pools might have had resulted in the identification of spurious

result between the foreclosure rate and the input variables. The major drawback would be a self-

selection bias, i.e. bad pools being tested for default. My objective is to keep the data as close to

the source as possible without having to amend it. Having sub-prime pools would require us to

adjust for locations, or greater default, to normalize it with other pools. In short the pool of data

would not be homogeneous, and therefore not comparable.

The data collection design mostly leveraged the resources of the Bloomberg fixed-

income section available at NYU libraries, to gain access to the data. Sample securities were

identified using the criteria enumerated above, and then saved in an Excel format. The data

analysis plan adopted a two-step methodology. The first step was sorting the securities in Excel

based on the year of maturity, FICO score average, loan balance average, and average payment

history. Since these are our independent variables, such a process helped weed out securities that

were too similar. For, example, if two pools were made by a bank using similar mortgages from

a common larger pool, then we can see that the pools are too similar and we would take only one

pool for our study not the other. This would help us minimize any biases .The second step of the

33

analysis involved conducting a regression analysis using each independent variable, and the

dependent variable as the foreclosure rate.

The focus of the study was to find the level of dependence between the independent

variables and the dependent variable. For example, does a low FICO score pool result in a high

default among borrowers, or does a high FICO score pool have a high foreclosure rate too? Thus,

using correlation and regression analysis through the SPSS software version 23 was a perfect

tool to identify such a relationship.

4.3 Database Description: Reliability and Validity

According to Morse and Davidshofer (2005), “Joppe (2000) defines reliability as: The

extent to which results are consistent over time and an accurate representation of the total

population under study is referred to as reliability and if the results of a study can be reproduced

under a similar methodology, then the research instrument is considered to be reliable.” Validity

is defined as the statistical measure that a writer employees to show that the test in this case the

regression analysis is measuring what the test intends to measure (Murphy & Davidshofer,

2005). There are numerous methods to measure validity. For this study, we adopted the concept

of construct validity; which is a measure of how well observed relationships between test

constructs, match those predicted by some theory (Cronbach & Meehl, 1955). According to

Morse and Davidshofer (2005), “Kirk and Miller (1986) identify three types of reliability

referred to in quantitative research, which relate to: (1) the degree to which a measurement,

given repeatedly, remains the same (2) the stability of a measurement over time; and (3) the

similarity of measurements within a given time period.” Charles (1995) adheres to the notions

that consistency with which questionnaire [test] item are answered or individual’s scores remain

relatively the same can be determined through the test-retest method at two different times. This

34

attribute of the instrument is actually referred to as stability. If we are dealing with a stable

measure, then the results should be similar. A high degree of stability indicates a high degree of

reliability, which means the results are repeatable” (Morse & Davidshofer, 2005)

To establish a relationship between the input factors and foreclosure rate, it is important

to use the correct data from a non-biased source. The study, therefore, used data available in the

public domain. By public domain, we mean data that is available academically, that is not

proprietary, and data that is not cleaned to remove any markers or identifiers. The rational for

using such a data is to keep the study transparent, and remove any data biases that maybe

inherent in proprietary data. Such a data source allows for easy replicability of my conclusions,

adding to further robustness of the research method. If we were to primarily use only proprietary

data, such as data from Goldman Sachs, then there is a possibility that the data may be biased.

This is true for the data made available by Goldman Sachs, as it tends to be biased towards high

FICO scores, primarily because they refuse to deal in loans that have a high foreclosure rate.

Using proprietary data will also defeat the purpose of the study, which was to establish a

relationship between both high and low FICO score and foreclosure rate. The study therefore

incorporated pools that were diverse and structurally different from each other. The criteria for

different sources was based on the independent variables that the study has identified for the

study, i.e. the FICO score, the location of the mortgages, loan balances and payment history.

According to Morse et al. (2004); “Joppe, (2000) detects a problem with the test-retest

method which can make the instrument, to ascertain degree, unreliable. She explains that test-

retest method may sensitize the respondent to the subject matter, and hence influence the

responses given. We cannot be sure that there was no change in extraneous influences such as an

attitude change that has occurred. This could lead to a difference in the responses provided”.

35

Similarly, Crocker and Algina (1986) noted that when a respondent answers a set of test items,

the score obtained represents only a limited sample of behavior. As a result, the scores may

change due to some characteristic of the respondent, which may lead to errors of measurement.

These kinds of errors will reduce the accuracy and consistency of the instrument and the test

scores. Hence, it is the researchers’ responsibility to assure high consistency and accuracy of the

tests and scores. Crocker and Algina (1986) suggested that, "test developers have a responsibility

of demonstrating the reliability of scores from their tests." Morse et al. (2004). Thus, after

evaluating several sources of data, the dataset from Bloomberg was identified as the most viable

source.

The decision to use Bloomberg data source, over others available sources, was guided by

numerous factors. The first reason to use the Bloomberg data is the ease of availability. It is

available for NYU student and faculty via Bloomberg terminal. Secondly, Bloomberg has data

on mortgage-backed securities for almost all securities that were issued by almost all parties

dating back to the 1970s. This is important for the study because we conducted a longitudinal

study over a 10 year period, and used pools issued by several banks. The rational in evaluating

data spread over a seven year period was to lower the possibility of a bad year or cyclical

macroeconomic events having a bias effect on the data. For example, interest rates, employment

level etc. may have an impact on the pool for a particular given year, but by using a 10 year

period, we minimized the effect of business cycle on the data. We need to however bear in mind,

that the last 10 years have not been representative of the business cycles since 1945.

The third reason for using Bloomberg data was because it was used by a majority of

finance firms, and is considered as the industry standard. Therefore, the data made available

through the Bloomberg terminal on mortgage-backed pools is current. Bloomberg has access to

36

almost all the major issuers of mortgage backed securities. This is evidenced by the fact that my

initial search resulted in over a 1,000 such pools with different FICO scores, loan balances,

payment history. Therefore, the breadth of data available helps us address and test input factors

that is hardest to decipher, i.e. geography. Usually a mortgage-backed issuance is heavily loaded

with mortgages from one region. Thus using different pools of mortgage-backed securities

enabled us to ensure that there existed a valid relationship between the geography of the loans in

the pool, and foreclosure rate. For example, if we were to use a pool that has mortgages

originating from mostly Florida, then our regression analysis would show a spurious relationship

between geography and foreclosure rates. Therefore, it was necessary to have a dataset that is

geographically dispersed to ensure that the correlations identified are meaningful and valid.

According to Moorse (2004), “the traditional criteria for validity, finds their roots in a

positivist tradition, and to an extent, positivism has been defined by a systematic theory of

validity. Within the positivist terminology, validity resided amongst, and was the result and

culmination of other empirical conceptions: universal laws, evidence, objectivity, truth, actuality,

deduction, reason, fact and mathematical data to name just a few” ( page?)

Based on the above developed arguments, the study adopted regression analysis

techniques, specifically the R2 functionality in SPSS, to develop a reliable parameter and show

that the independent variables have an effect on the dependent variable, and it is not a random

correlation or a relation.

A common tendency for quantitative researchers is to focus on the tangible outcomes of

the research , a single figure or a number to explain the research question, rather than

demonstrating what verification strategies were used in the research. According to Morse et al.

(2004), “While strategies of trustworthiness may be useful in attempting to evaluate rigor, they

37

do not in themselves ensure rigor. While standards are useful for evaluating relevance and utility,

they do not in themselves ensure that the research will be relevant and useful.” Therefore, it is

time to reconsider the importance of verification strategies used by the researcher in the process

of inquiry so that reliability and validity are actively attained, rather than proclaimed by external

reviewers on the completion of the project.

“These strategies to include rigor include investigator responsiveness, methodological

coherence, theoretical sampling and sampling adequacy, an active analytic stance, and saturation.

These strategies, when used appropriately, force the researcher to correct both the direction of

the analysis and the development of the study as necessary, thus ensuring reliability and validity

of the completed project” Morse et al. (2004).

Based on the above guidelines, it can be argued that the research methodology of

adopting a longitudinal study over a seven year period, with data available from a third party

(Bloomberg), is the correct manner in which the research question can be empirically tested and

verified. Therefore, the method of testing adopted in the thesis was a combination of regression

analysis and interpretation of result tables. This was accomplished by using the SPSS/excels

software. The research design therefore enumerated by me, and the research methodology

identified, helped make the study parsimonious, verifiable and reliable; as they meet all the

criteria discussed by Morse necessary in any research.

4.4 Conclusion

The main objective of this thesis was to identify the relationship between the four input

factors and the foreclosure rate, quantifying it by adopting regression analysis. Additionally, the

thesis attempted to provide an economic/business analysis between the main inputs into used in

various models (FICO score, geography, loan balances), and its relationship with foreclosure

rates. Such an analysis enabled us to understand whether the input variables into the models have

38

a high explanatory potential or not, and whether the models are using the correct factors or not.

The thesis therefore answered the question, what is the nature of correlation between the factors

used by the most common risk models (e.g. FICO score, geography, loan balance, etc.) used to

predict foreclosure rates and the foreclosure rate of the pool? The research design and

methodology enumerated earlier in the chapter played an important role in helping us identify the

road map to be followed in order to answer the research question.

39

Chapter 5 - Results and Analysis

5.1 Introduction

In the earlier sections, not only has the research question been clearly identified, but also

it was highlighted how the question fits within the overall literature on the topic of MBS.

Subsequently, the research methodology was identified, and the research design was enumerated.

Following the research methodology identified in chapter 4, the data was collected, and a time

series database was developed. Both regression analysis and ANOVA tools were used to

deconstruct the data and develop a better understanding of how the data answers the research

question. This chapter deals with the analysis of the data, the subsequent interpretation of the

data, and how it helped answer the research question.

5.2 Data Analysis and Interpretation

The regression analysis presented in the tables below summaries the findings. In the

tables, the number that really need to be paid attention to is the pool number on the top left hand

corner. This is the pool number that can be used to identify a specific mortgage pool and it can

also be used as a reference on Bloomberg to identify the source data. The dependent variable,

foreclosure percent is for reference only. The variable gives us the average foreclosure rate for

the pool for the year. For example, if there were 10,000 mortgages in the pool and 10 of them

went into foreclosure, then the foreclosure rate for the year will be 1%. The primary reason why

foreclosure rate was used as a variable is because it acts as a reference, so that we can observe

the degree to which the rates have changed over the seven year study period. Such an analysis

helps to ground the R2 results and gives us a reference point. The literature below in this section

suggested that any value less than 25% for R2 would not be significant, and that is the parameter

used in the entire body of research. That being said, Table 1 gives us a good reference with

respect to R2 and its explanatory power. Table 5-1 is a representation of what percentage of R2

40

represents its explanatory power in predicting or explaining one standard deviation. Based on the

data in table 5-1, in this thesis we benchmarked R2 value above 25% as being statistically

significant.

Table 5-1. R2 Explanatory Power

41

Based on the results of the regression analysis, presented in the discussion below, it was

observed that that there is a trend where foreclosure rate, the dependent variable; and the four

independent variables have a relationship. As the R2 is the main measure, it has been used to

determine the model fit in percentage terms, as well as whether the independent variables have

an influence on the dependent variables or not. The results showed that there was no constant

relationship between the dependent variable and the independent variable, but more of a dynamic

relationship between the foreclosure rate and the four independent variables. Additionally, the

input variables had a significant explanatory power over the foreclosure rate.

If we evaluate the data in Table 5-2, we look at mortgage backed security pool BCAP

2007-AA2 22A1, in the year 2008. The results show that for this MBS pool, credit score could

explain only 2.6 % of the total variance for the dependent variable. However, in 2012 credit

score accounted for 53.96% and 59.70% of variance in 2014 respectively. This is significant and

above our threshold. Table 5-2. Statistical Analysis for pool BCAP 2007-AA2 22A1

Pool: BCAP 2007-AA2 22A12008 2009 2010 2011 2012 2013 2014

Dependent variable: Foreclosure %Foreclosure % average for the year for reference 0.52% 4.29% 4.30% 13.36% 9.41% 6.29% 6.52%

R² valuesIndependent variable : 1 Credit score 2.60% 3.52% 20.73% 28.00% 53.96% 0.60% 59.70%Independent variable : 2 Perfect Payer % 32.10% 3.87% 6.90% 23.85% 9.20% 0.97% 59.09%Independent variable : 3 Balance < 417 k 6.54% 3.58% 6.90% 23.85% 9.20% 0.97% 59.09%Independent variable : 4 Geo < 50% of the pool 30.94% 1.05% 30.37% 35.38% 54.42% 11.61% 50.99%

Regression analysis using 95% confidence interval

42

BCAP here mean the name of the bank that produced the pool, BCAP is the code for

Barclay’s Capital, BOAA is the code for Bank of America. The next row of foreclosure % , this

row tells us of the total mortgages in the pool how many are in foreclosure, this is not a R2, but a

simple percentage. For example if there are 10,000 loans and 1,000 are in foreclosure then the

foreclosure % is 10%. This is included here to give the reader a sense how the pool is behaving,

higher foreclosure rate means pool is not performing and mortgages are failing. Since this is a

master thesis and not a PHD study, we are limited in the scope and breathe of the research and

presentation we can perform and display. Thus displaying all the variables is not feasible or

prudent. The next row gives us the R2 by year between the four independent variables and the

dependent variable.

What a 53.96% R2 implies is that, credit score accounted for at least 29% of the standard

deviation, and hence credit score can account for 29% of the 9.41% of foreclosure rate.

If we look at the average foreclosure rate, in 2008 it was 0.52% of the pool and by 2014

the foreclosure rate increased to 6.52%. There is an argument that over time, the good mortgages

leave the pool and only bad mortgages are left in the pool, so that the foreclosure rate

automatically increases. We agree with the statement in theory, but this cannot explain the

sudden spikes in foreclosure rate. An analysis of the year 2009 and 2008 shows that, the

foreclosure rate jumped to 4.29% in 2009 from 0.52% in 2008. Post this, in the year 2013, the

foreclosure rate dropped to 9.41% from 13.36% in 2012. As R2 is a measure of the explained

variance, it can be argued that good borrowers exited the pool as they found better rates, or

moved and sold their houses, and hence the resulting changes in the foreclosure rate.

Pool BCAP 2007-AA2 22A1; gives us a good example of how there is a linear

relationship between an increase in foreclosure rates, and credit scores. The pool highlights how

43

as the foreclosure rate increases, the explanatory power of credit score also increases. In the year

2013, all four independent variables fail to have any explanatory power, this tells us that there

was some factor outside the four we tested that had an impact on the foreclosure rate. The

foreclosure rate declined dramatically, from 9.41% to 6.29%, and all four independent variable

were below the 25% threshold. Based on the analysis of pool BCAP 2007-AA2 22A1, it can be

concluded that relationship between the independent variables and the dependent variables is

dynamic, and the input variables have an explanatory power over the dependent variable

majority of the time.

If we were to interpret the results for its significance in a business decision environment,

based on the regression analysis, we can argue that in the case of pool BCAP 2007-AA2 22A1;

for the year 2008, perfect payer and geography of the loans were the main factor in the

foreclosure rate. During this time period the average foreclosure rate was 0.52% of the total pool.

The results show that perfect payer and geography of the loans taken together highlight that fact

that, as the borrower’s current income situation in a particular region took a negative turn, there

was a negative impact on the cash flow of the borrower, giving rise to the increased foreclosure

rates. However, in 2013, geography was the most relevant but not the main factor, suggesting

that one particular state was having a macroeconomic issue that was causing the foreclosure rate

to spike. Alternatively, in 2014, all four factors were equally at play. Although the models

discussed above are used to come up with a probability of default and not for pinpointing the

exact macro environment behind the cause. However, it is important to see if the input variables

R2 results are telling a story that has a logical backing and are not just mathematically related.

An evaluation of Table 5-3 (pool: BOAA 2005-1 2A1), showed that in 2008, perfect

payer accounted for 49.94% of the variance in the dependent variable, and 84.05% in 2010. This

44

influence on the variance in the dependent variable decreased to 30.24% in 2011, and maintained

a downward trajectory reaching 7.77% in 2013 and 6.56% in 2014 respectively. In this pool,

perfect payer has the best explanatory power from 2008 to 2011. However, after 2012 even

though the foreclosure rate was high, the perfect pay variables’ ability to explain the variation

diminished significantly. The perfect payer is a variable that measures the borrower’s current

cash flow situation. Thus, if the borrower has sufficient income or saving, he or she can meet the

monthly mortgage payment. However, recent research has shown that paying mortgages first is

no longer a priority. “If we've learned one thing from the housing downturn, it's that making the

monthly mortgage payment is no longer a sacred concept in many American households. In

recent years, when facing financial pressure, homeowners have been more likely to let the

mortgage slide before they would fall behind on their credit card bills, researchers have found.

But it turns out that the mortgage is even less sacred than we thought: When times are tight,

consumers put paying for their cars first. Then the credit cards will be paid. The once-mighty

mortgage has slipped to No. 3” (Umberger, 2012page?).

Table 5-3. Statistical Analysis for pool BOAA 2005-1 2A1

45

Pool: BOAA 2005-1 2A12008 2009 2010 2011 2012 2013 2014

Dependent variable: Foreclosure %Foreclosure % average for the year for reference 0.07% 0.69% 3.87% 4.14% 4.95% 2.54% 5.49%

R² valuesIndependent variable : 1 Credit score 22.96% 63.12% 0.03% 1.13% 1.77% 0.95% 10.38%Independent variable : 2 Perfect Payer % 49.94% 39.88% 84.05% 30.24% 1.70% 7.77% 6.56%Independent variable : 3 Balance < 417 k 16.71% 16.05% 7.31% 5.54% 5.71% 13.12% 9.90%Independent variable : 4 Geo < 50% of the pool 0.53% 61.01% 17.86% 17.37% 10.45% 0.11% 10.05%

Regression analysis using 95% confidence interval

Taking a look at the data for the pool on a monthly basis we observed that in 2008 the

prefect payer percentage was 98.65%. This implies that 98.65% of the loans in the pool were

being paid on time, and the borrower had not missed a single payment. The total loans in the

pool for February 2008 were 29,654. By February 2012, the year, when perfect payer starting to

lose it significance in explaining the foreclosure rate, the perfect payer percentage dropped to

69.46%, and the number of loans in the pool also decreased to 15,940. Subsequently, by

February 2014, the perfect payer percentage of the pool had gradually decreased to 59.34%, and

the number of loans in the pool had also decreased to 7,834. Given the fact that the pool shrunk

in size from 29,654 to 7,834 between 2008 and 2014, and the foreclosure rate was below 5%

during this time period, it can be argued that foreclosure was not the main reason for the decrease

in the pool. It could be one of the other factor that cause a tremendous runoff in the number of

loans that have disappeared from the pool, and not via the foreclosure route.

A mortgage backed security is a closed-ended security, which means that once a pool is

formed, then as the mortgages retire from it the pool, this change is not refilled with new loans.

46

There are only two ways for the loan to exit out of the pool. The first one is voluntary runoff or

full payment by the borrower, either through cash from his saving or other sources, or by selling

the house. The second route is through foreclosure, where the borrower defaults on the loan by

not paying on his monthly payments.

An analysis of the pool, BOAA 2005-1 2A1, showed that the relationship between the

independent variable and the dependent variable is dynamic and constantly changing due to the

changing macroeconomic picture, and the unpredictable behavior of the consumer based on his

income and the overall economy. These variances were captured by each of the four independent

variables in their own way. In the case of pool BOAA 2005-1 2 A1, we observed that in 2008 the

foreclosure rate was only 0.07% of the total pool, but by 2012 it reached 4.95%; geography had

the maximum explanatory power at 10.45%, however perfect payer went from 49.94% to 1.70%.

An analysis of the data in Figure 5-3, shows that from 2008 to 2011, the four factors to some

degree had significant relationship with foreclosure rate and after 2011, other factors came into

play that had an impact on the foreclosure rate.

The data in Table 5-4 (pool BOAA 2005 10 5A1) showed that the average foreclosure in

the pool between 2008 and 2013 was less than 1%, and only 3.96% in 2014. With such a low

foreclosure rate, we can see that all four independent variables have a significant explanatory

power during different times. For example, credit score had a significant R2 of 47.62% in 2008,

46.43% in 2011 and 65.26% in 2012. Perfect payer had significant R2 of 40.07% in 2008,

46.09% in 2010, 52.35% in 2011 and 57.41% in 2014. The balance had a significant R2 of

67.94% in 2009 and 44.26% in 2011. Geography had 65.68% R2 in 2010 and 66.91% in 2012.

2013 have zero foreclosure rate this could be due to the fact that some pools were subject to

Robo-signing scrutiny were it was alleged that Bank of America did not follow proper procedure

47

to foreclosure , thus Bank of America stopped all foreclosure activity, thus leading to a different

result.

Table 5-4. Statistical Analysis for Pool B0AA 2005 10 5A1

Pool: BOAA 2005 10 5A12008 2009 2010 2011 2012 2013 2014

Dependent variableForeclosure % average for the year for reference 0.43% 0.32% 0.50% 0.99% 0.89% 0.00% 3.96%

R² valuesIndependent variable : 1 Credit score 47.62% 3.69% 21.28% 46.43% 65.26% 9.33% 3.94%Independent variable : 2 Perfect Payer % 40.07% 15.82% 46.09% 52.35% 0.08% 100.00% 57.41%Independent variable : 3 Balance < 417 0.03% 67.94% 23.96% 44.26% 0.11% 100.00% 3.94%Independent variable : 4 Geo < 50% 1.02% 15.74% 65.68% 13.11% 66.91% 100.00% 22.39%

Regression analysis using 95% confidence interval

Table 5-5. Statistical Analysis for pool BCAP 2007-AA2 33A1

Pool: BCAP 2007-AA2 33A12008 2009 2010 2011 2012 2013 2014

Dependent variable: Foreclosure %Foreclosure % average for the year for reference 0.00% 2.14% 3.03% 5.58% 7.55% 11.76% 12.25%

R² valuesIndependent variable : 1 Credit score 100.0% 64.3% 0.2% 0.0% 9.5% 77.1% 1.0%Independent variable : 2 Perfect Payer % 100.0% 78.8% 24.1% 14.1% 6.8% 62.8% 6.6%Independent variable : 3 Balance < 417 k 100.0% 66.7% 0.6% 14.5% 57.7% 99.0% 19.7%Independent variable : 4 Geo < 50% of the pool 100.00% 70.19% 30.78% 25.28% 0.82% 93.26% 10.52%

Regression analysis using 95% confidence interval

48

The data in Table 5-5 (pool BCAP 2007-AA2 33A1), is a good example of geography

being the most dominant of all the factors in explaining the dependent variable. In pool BCAP

2007-AA2 33A1 the foreclosure rate increased significantly from 2008 (0.0%) to 12.25% in

2014. This shows progressive deterioration of the mortgage pool, and the timeline is consistent

with the financial crisis which started in 2008, and whose impact were felt within the economy

till 2012. Of the seven years of the analysis, geography was significant in five out of the seven

years. It is important to point out at this stage that since we did not conduct a regression analysis,

the total factors combined together at times comes over 100%. The R2 is not an absolute

percentage term, but an indicator of the influence that the independent variables have over

dependent variable. The combined analysis of the four variables however, does provide a

complete picture which can assist us in our analysis. For example, in pool BCAP 2007-AA2

33A1 (year 2013) the foreclosure rate jumped from 7.55% to 11.76%. If we are analyzing purely

from a mathematical point of view, then balances and geography are the most relevant. But from

an analytical point of view, we observe that in 2012 geography was not a significant factor at all

(0.82%). However, in 2013 the R2 value for geography jumped to 93.26%. Similarly, perfect

payer percentage went from 6.8% in 2012, to 62.8% in 2013An analysis of these two variables in

entirety showed that, the sudden rise in 2013 can be attributed to geography and to loan balances

that were below $ 417,000. Thus it was a localized event in one particular state that is causing

the spike. One aspect that we had to be careful about was the lag in the foreclosure process.

There was a possibility that the triggering event, such as lay-offs or economic shocks, could had

also impacted the results. The cascading effect of such economic events on the local economy

causes a localized event where the foreclosure rises. But the process is not instantaneous, the

event might occur in January 2013 and the effect may be felt in say September. The defaults may

49

occur by December of 2013, and the loan may come into foreclosure may 2014. Thus, it was

difficult to pin point the exact source that was causing the spike in the foreclosure rate in the

current rate. But that still doesn’t take away from the explanatory power of the R2. Based on the

analysis of pool BCAP 2007-AA2 33A1, we observed that the relationship between the

dependent variable and the independent variable was dynamic and changes over time as different

economic factors take priority at different times.

As the pools were selected randomly, and not pre-screened, we had a cross section of

data where one factor dominated in its explanatory power over the other three, or a combination

of two could explain the cause in the rise of foreclosure rate. In pool BOAA 2005-6 7A1, credit

score and perfect payer variables, have significant R2 from 2008 to 2011, as the foreclosure rate

rises from 014% in 2008 to 3.78% in 2011. However, the foreclosure rates drops in the years

2012 and 2013, and suddenly spikes in 2014. Between 2012 and 2014, the R2 for the dependent

variables was not significant and could not be used to meaningfully explain the drop in

foreclosure rate in 2012(2.42%) and 2013 (2.20%); nor could it explain the sudden spike in 2014

to 6.11%.

Further analysis of the above data showed that the break in pattern was a consequence of

the pool primarily being from Bank of America; and some of the loans in the pool were under

scrutiny for the Robo signing scandal. “The banking industry has been roiled by revelations of

widespread flaws in the way it forecloses on homeowners who have stopped making their

mortgage payments—a lot of people. The foreclosures were being processed by "robo-signers," a

neologism that has quickly become part of the lexicon of housing-market infamy. In the face of

legal constraints and investigations by state and federal officials, lenders—led by behemoths

Bank of America and JPMorgan Chase and others—announced a temporary moratorium, which

50

they then lifted. Years of litigation loom. With a wave of foreclosures that could top 1 million

homes with $1 trillion in mortgages this year, banks have hired staff to process the tsunami of

paperwork. But a fair number of these hires had no experience or knowledge of the industry and

may not have reviewed the documents—hence the term robo-signers. One employee of GMAC

testified that he signed as many as 10,000 foreclosure affidavits a month—nearly 500 per

business day. Unless he was a robo-reader, he could not have read what he was signing. This

practice alone may be illegal. Then there is the additional issue of how the massive amount of

securitization of these loans—selling them off to investors in the form of bonds—may affect

litigation and regulation. Only the holder of a loan can legally foreclose, but with securitization,

these loans were sliced, diced and repackaged. The banks say they possess adequate

documentation of titles and ownership, but the suspension signaled serious concerns” (Karabell,

2010). Thus in the case of pool BOAA 2005-6 7A1, the relationship between the dependent

variable and independent variable was dynamic and not static.

Table 5-6. Statistical Analysis for pool BOAA 2005-6 7A1

Pool: BOAA 2005-6 7A12008 2009 2010 2011 2012 2013 2014

Dependent variable: Foreclosure %Foreclosure % average for the year for reference 0.14% 0.89% 3.21% 3.78% 2.42% 2.20% 6.11%

R² valuesIndependent variable : 1 Credit score 67.72% 18.16% 73.47% 59.79% 32.62% 13.82% 3.81%Independent variable : 2 Perfect Payer % 45.75% 75.10% 88.14% 52.21% 1.86% 8.11% 0.06%Independent variable : 3 Balance < 417 k 4.27% 18.27% 26.95% 70.57% 11.18% 4.32% 5.42%Independent variable : 4 Geo < 50% of the pool 0.22% 0.32% 22.66% 66.76% 2.76% 25.43% 8.79%

Regression analysis using 95% confidence interval

51

Table 5-7. Statistical Analysis for pool BOAA 2005-1 2A1

Pool: BOAA 2005-1 2A12008 2009 2010 2011 2012 2013 2014

Dependent variable: Foreclosure %Foreclosure % average for the year for reference 0.07% 0.69% 3.87% 4.14% 4.95% 2.54% 5.49%

R² valuesIndependent variable : 1 Credit score 22.96% 63.12% 0.03% 1.13% 1.77% 0.95% 10.38%Independent variable : 2 Perfect Payer % 49.94% 39.88% 84.05% 30.24% 1.70% 7.77% 6.56%Independent variable : 3 Balance < 417 k 16.71% 16.05% 7.31% 5.54% 5.71% 13.12% 9.90%Independent variable : 4 Geo < 50% of the pool 0.53% 61.01% 17.86% 17.37% 10.45% 0.11% 10.05%

Regression analysis using 95% confidence interval

Further analysis of the data in Table 5-6 and 5-7 (pool BOAA 2005-1 2A1), showed that

the foreclosure rate rose steadily between 2008 (0.07%) and 2014 (5.49%). The perfect payer

independent variable was the most significant from 2008 to 2011. However, starting 2012, none

of the four variables were significant. This again shows that the relationship between the

dependent variable and independent variable was dynamic and not static.

The data in Table 5-8 (pool AMAC 2003-12 2A) further helps throw light on our

research question, and deepens our understating of MBS. In 2008, the foreclosure rate was

0.00%, and most significantly all the independent variables had a value of 100% R2. This goes

on to support our argument, as well as show the robustness of model developed in this thesis.

Had any variable been less than 100%, it would have highlighted a potential issue. The

independent variable, credit score, was also significant in all the years as it was over 25%

benchmark that we adopted as the standard in this thesis. The variable, Perfect payer was

significant in four out of the seven years and the variable balance was also significant in four of

52

the seven years. The variable geography was also significant in five out of the seven years. These

values go on to highlight that the relationship between the independent variables and dependent

variables was dynamic and not static. The pool had 95,036 individual loans in March 2008,

which is a statistically significant number, as one loan or a cluster located in a small area or with

a particular characteristic can unduly influence the pool or the results of our analysis. The

original average credit score of the loan pool was 740, which puts it firmly in the area of prime

mortgages. The mortgage was issued in 2003, and before the lending standards were loosened by

banks. Thus the pool was quality diversified mortgages, and was a good sample for the study.

Table 5-8 further shoes that in 2009 the foreclosure rate was 0.49%, up from 0.0% the

previous year. Both credit score and perfect payer also had significant R2 values of over 70%.

This is logical and keeping with the argument developed in the thesis; as credit score is a

reflection of payment of the borrower in the past, and perfect payer is the reflection of the

payment of the borrower with the present mortgage. Thus the small rise in foreclosure can be

explained by both the variables. In 2012, as the foreclosure rate reached 5.02%, the R2 for both

credit score and perfect payer both was above 70%. Although these variables had a very high

explanatory potential, but their value was mitigated by the fact that the R2 of geography was only

15.51%. This implies that geography was not an important variable, as the loans were not from a

particular region causing the rise in foreclosure, but more general seasoning of the loans.

However, in 2013 and 2014 the foreclosure rate spiked to 6.80% and 8.94%, respectively, while

Geography also had a very high R2 value. Taking a look at the make-up of the geography from

2012 to 2014, the top four states as a percentage were California (39.0%), Florida (13.8%), New

York (12.7%) and Virginia (7.3%), as of January 2012. By January 2013, California was 38.2%,

New York was 15.5%, Florida dropped to 12.5% and Virginia rose to 8.4%. By January 2014,

53

the pool make-up had changed again with California at 26.5%, New York at 21.2%, Florida at

12.2% and Virginia at 11.1%. Thus we observed that California and Florida were the main states

where geography was the main culprit in causing the foreclosure rate to shoot-up. Thus, logically

the rise of R2 of geography explained the rise of the explanatory power of geography from 2012

to 2014. Based on the analysis, we concluded that the relationship between the dependent

variable and independent variable was dynamic not static.

In the case of Table 5-9 (pool AHM 2005-2 3A), it was observed that initially the pool

has a high foreclosure rate that steadily increased to 10%, and then started to decrease post 2012.

The two most important factors responsible for this decrease in the foreclosure rates were the

variable perfect payer and balances. The summary in Table 5-9 further supported our assertion

that the relationship between the dependent variable and the independent variable was dynamic.

Table 5-8. Statistical Analysis for pool AMAC 2003-12 2A

Pool: AMAC 2003-12 2A2008 2009 2010 2011 2012 2013 2014

Dependent variable: Foreclosure %Foreclosure % average for the year for reference 0.00% 0.49% 1.23% 4.05% 5.02% 6.80% 8.94%

R² valuesIndependent variable : 1 Credit score 100.00% 70.77% 26.61% 27.57% 71.93% 25.72% 29.88%Independent variable : 2 Perfect Payer % 100.00% 73.28% 47.39% 0.00% 76.62% 4.61% 43.48%Independent variable : 3 Balance < 417 k 100.00% 67.75% 5.77% 64.29% 69.58% 25.36% 16.98%Independent variable : 4 Geo < 50% of the pool 100.00% 28.18% 42.32% 50.32% 15.51% 58.98% 51.64%

Regression analysis using 95% confidence interval

54

Table 5-9. Statistical Analysis for pool AHM 2005-2 3A

Pool: AHM 2005-2 3A2008 2009 2010 2011 2012 2013 2014

Dependent variable: Foreclosure %Foreclosure % average for the year for reference 4.88% 7.68% 10.39% 10.31% 8.83% 7.81% 5.93%

R² valuesIndependent variable : 1 Credit score 4.44% 1.86% 16.12% 4.44% 11.47% 2.66% 0.67%Independent variable : 2 Perfect Payer % 67.65% 85.25% 17.73% 72.83% 74.59% 76.63% 10.56%Independent variable : 3 Balance < 417 k 53.14% 48.06% 1.12% 49.37% 40.01% 34.27% 16.98%Independent variable : 4 Geo < 50% of the pool 21.20% 74.17% 0.10% 70.94% 0.09% 27.94% 53.21%

Regression analysis using 95% confidence interval

As the study was a longitudinal study of the relationship between foreclosure rates and

the variables credit score, perfect payer, balance and geography, between the years 2008 and

2014; one of the patterns observed till now was that foreclosure rates increased from 2009 to

2012 and then started to decrease post 2013. One possible factor responsible for the decrease in

foreclosure, i.e court ordered stop to foreclosure, has been analyzed comprehensively. However,

another important factor influencing the foreclosure rate that has not been addressed till now is

the macroeconomic situation in the U.S. economy.

“The Federal Reserve Board’s Survey of Consumer Finances (SCF) for 2010 provides

insights into changes in family income and net worth since the 2007 survey.1 The survey shows

that, over the 2007–10 period, the median value of real (inflation-adjusted) family income before

taxes fell 7.7 percent; median income had also fallen slightly in the preceding three-year period

(Figure 5-1). The decline in median income was widespread across demographic groups, with

only a few groups experiencing stable or rising incomes. Most noticeably, median incomes

55

moved higher for retirees and other nonworking families. The decline in median income was

most pronounced among more highly educated families, families headed by persons aged less

than 55, and families living in the South and West regions. Real mean income fell even more

than median income in the recent period, by 11.1 percent across all families. The decline in mean

income was even more widespread than the decline in median income, with virtually all

demographic groups experiencing a decline between 2007 and 2010; the decline in the mean was

most pronounced in the top 10 percent of the income distribution and for higher education or

wealth groups. Over the preceding three years, mean income had risen, especially for high-net-

worth families and families headed by a person who was self-employed. The decreases in family

income over the 2007−10 period were substantially smaller than the declines in both median and

mean net worth; overall, median net worth fell 38.8 percent, and the mean fell 14.7 percent

(Figure 5-2). Median net worth fell for most groups between 2007 and 2010, and the decline in

the median was almost always larger than the decline in the mean. The exceptions to this pattern

in the medians and means are seen in the highest 10 percent of the distributions of income and

net worth, where changes in the median were relatively muted” (Bricker & Kennickell,2012)

An analysis of the macroeconomic charts of the US economy from 2008 to 2014 (Figure

5-3) suggested that the GDP growth rates were negative for the years 2007 and 2008, and even in

2009, the GDP growth rates improved marginally. There was negative unemployment growth

between 2007 and 2010 (Figure 5-4), and the employment growth rates picked up only

marginally in the year 2011.The unemployment rate peaked in the end of 2010, and gradually

decreased 2011 onwards. An analysis of the long term unemployment rate (Figure 5-5), showed

that it had decreased very gradually, and consequently had a negative impact on household

56

financial position of the average borrower. The recession between the years 2007 and 2011 was

not a localized event but a national one, and consequently, all aspect of life was affected in every

Figure 5-1. Change in Median and Mean Incomes 2001-2010. Source: (Bricker & Kennickell, 2012)

Figure 5-2. Change in Median and Mean Net worth 2001-2010. Source: (Bricker & Kennickell, 2012)

57

Figure 5-3. Change in real GDP. (Source: Bureau of Economic Analysis)

Figure 5-4. Monthly Change in Nonfarm Employment. (Source: Bureau of Labor Statistics)

58

Figure 5-5. Unemployment Rate. (Source: Bureau of Labor Statistics and National Bureau of Economic Research)

Figure 5-6. Long Term Unemployment. (Source: Bureau of Labor Statistics and National Bureau of Economic Research)

59

Family characteristic

2001 2004

Income

Percentage of families that saved

Percentage of families

Income

Percentage of families that saved

Percentage of families

Median Mean Median Mean

All families 48.9 83.3 59.2 100.0 49.8 81.4 56.1 100.0

(1.0) (2.4) (1.0) (1.4) Percentile of income Less than 20 12.6 12.3 30.0 20.0 12.8 12.4 34.0 20.0 20–39.9 29.9 29.6 53.4 20.0 29.5 30.0 43.3 20.0 40–59.9 48.9 49.4 61.3 20.0 49.8 50.0 54.5 20.0 60–79.9 79.4 79.9 72.0 20.0 78.5 79.6 69.3 20.0 80–89.9 120.9 120.2 74.9 10.0 120.5 122.6 77.8 10.0 90–100 207.8 371.0 84.3 10.0 212.7 347.7 80.6 10.0 Age of head (years) Less than 35 40.9 54.2 52.9 22.7 37.8 51.9 55.0 22.2 35–44 63.0 94.5 62.3 22.3 57.5 85.0 58.0 20.6 45–54 66.8 114.2 61.7 20.6 70.3 108.6 58.5 20.8 55–64 55.4 106.5 62.0 13.2 62.6 115.5 58.5 15.2 65–74 34.0 71.3 61.8 10.7 38.4 68.7 57.1 10.5 75 or more 27.4 45.0 55.5 10.4 27.3 47.1 45.7 10.7 Family structure Single with child(ren) 27.7 36.0 45.2 11.4 29.5 37.7 39.8 12.1 Single, no child, age less than 55 35.3 49.4 55.8 15.1 33.3 45.2 52.8 15.3 Single, no child, age 55 or more 20.8 39.9 49.5 13.2 24.5 39.2 45.9 14.6 Couple with child(ren) 76.5 115.0 61.9 31.1 75.6 113.9 61.7 31.7 Couple, no child 63.0 105.3 68.1 29.2 67.4 107.0 64.4 26.3 Education of head No high school diploma 20.8 30.8 38.7 16.0 22.3 29.8 35.9 14.4 High school diploma 41.6 54.9 56.7 31.7 41.1 51.5 54.0 30.6 Some college 50.1 68.0 61.7 18.3 47.3 64.5 51.0 18.4 College degree 83.1 142.9 70.0 34.0 84.4 135.3 68.3 36.6

Note: For questions on income, respondents were asked to base their answers on the calendar year preceding the interview. For questions on saving, respondents were asked to base their answers on the 12 months preceding the interview.

Percentage distributions may not sum to 100 because of rounding. Dollars have been converted to 2010 values with the current-methods consumer price index for all urban consumers (see the box "The Data Used in This Article"). See the appendix for details on standard errors (shown in parentheses below the first row of data for the means and medians here and in table 4) and for definitions of family and family head.

Figure 5-7. Before Tax Family Income 2001-2004 (Source: Bricker & Kennickell, 2012)

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Family characteristic

2007 2010

Income

Percentage of families that saved

Percentage of families

Income

Percentage of families that saved

Percentage of families

Median Mean Median Mean

All families 49.6 88.3 56.4 100.0 45.8 78.5 52.0 100.0

(.8) (1.4) (.6) (1.2) Percentile of income Less than 20 12.9 12.9 33.7 20.0 13.4 12.9 32.3 20.0 20–39.9 30.1 29.7 45.0 20.0 28.1 27.9 43.4 20.0 40–59.9 49.6 49.5 57.8 20.0 45.8 46.3 49.8 20.0 60–79.9 78.7 80.2 66.8 20.0 71.7 73.6 60.1 20.0 80–89.9 119.5 121.6 72.9 10.0 112.8 114.6 67.7 10.0 90–100 216.8 416.6 84.8 10.0 205.3 349.0 80.9 10.0 Age of head (years) Less than 35 39.2 54.2 58.9 21.6 35.1 47.7 54.6 21.0 35–44 59.3 87.7 56.4 19.6 53.9 81.0 47.6 18.2 45–54 67.2 117.8 55.8 20.8 61.0 102.2 51.8 21.1 55–64 57.2 116.5 58.4 16.8 55.1 105.8 51.4 17.5 65–74 40.8 96.8 56.7 10.5 42.7 75.8 53.6 11.5 75 or more 23.9 47.9 49.4 10.6 29.1 46.1 54.1 10.7 Family structure Single with child(ren) 30.2 44.1 41.6 12.2 29.5 39.4 38.2 12.0 Single, no child, age less than 55 35.5 49.4 54.9 14.0 30.5 42.4 49.8 14.7 Single, no child, age 55 or more 25.8 38.4 48.5 14.9 24.2 39.6 45.4 15.2 Couple with child(ren) 74.6 118.4 60.1 31.8 67.7 109.4 52.8 31.6 Couple, no child 64.6 120.5 64.0 27.1 61.8 101.7 62.2 26.5 Education of head No high school diploma 23.2 32.8 41.6 13.5 23.0 33.7 36.9 12.0 High school diploma 38.5 53.6 51.1 32.9 36.6 48.1 47.4 32.2 Some college 47.8 71.3 53.6 18.4 42.9 58.7 49.5 18.6 College degree 81.9 150.7 68.6 35.3 73.8 128.9 62.0 37.3

Figure 5-8. Before Tax Family Income 2007 - 2010 (Source: Bricker & Kennickell, 2012)

61

Family characteristic

2007 2010

Income

Percentage of families that saved

Percentage of families

Income

Percentage of families that saved

Percentage of families

Median Mean Median Mean

Race or ethnicity of respondent White non-Hispanic 54.3 101.6 58.8 70.7 52.9 90.1 55.8 67.5 Nonwhite or Hispanic 38.6 56.2 50.8 29.3 34.6 54.4 44.0 32.5 Current work status of head Working for someone else 59.3 87.1 60.3 59.9 55.9 84.2 55.2 56.9 Self-employed 79.3 201.0 62.8 10.5 64.5 149.9 55.1 11.4 Retired 25.9 53.5 46.6 25.0 29.1 44.4 47.3 24.9 Other not working 21.3 37.1 45.3 4.6 23.9 36.3 37.0 6.8 Current occupation of head Managerial or professional 89.4 163.6 70.2 27.5 81.3 148.7 62.9 27.7 Technical, sales, or services 46.3 70.8 55.6 21.8 42.0 59.5 49.0 21.7 Other occupation 51.7 60.7 53.6 21.1 50.0 57.3 51.1 18.8 Retired or other not working 24.9 51.0 46.4 29.6 27.4 42.7 45.1 31.7 Region Northeast 53.9 105.2 53.5 18.3 53.7 99.2 50.8 18.3 Midwest 46.3 78.5 58.2 22.9 46.5 70.9 57.2 22.4 South 45.0 83.1 56.9 36.7 40.7 71.5 49.8 37.1 West 54.4 92.9 56.3 22.1 48.8 80.8 51.4 22.2 Urbanicity Metropolitan statistical area (MSA) 52.8 95.6 57.0 82.9 48.8 84.8 51.7 82.7 Non-MSA 37.8 52.6 54.0 17.1 36.7 48.2 53.3 17.3 Housing status Owner 64.6 110.7 60.9 68.6 59.6 98.3 56.5 67.3 Renter or other 29.1 39.3 46.7 31.4 26.1 37.9 42.7 32.7 Percentile of net worth Less than 25 24.6 30.5 40.5 25.0 23.7 32.6 32.2 25.0 25–49.9 43.1 48.7 52.8 25.0 37.9 45.5 48.4 25.0 50–74.9 59.5 69.8 59.1 25.0 54.9 63.3 56.8 25.0 75–89.9 86.2 97.4 68.9 15.0 74.5 89.0 66.9 15.0 90–100 165.5 364.2 80.4 10.0 163.2 297.9 76.1 10.0

Figure 5-9. Before Tax Family Income 2007 – 2010 Continued (Source: Bricker, & Kennickell, 2012)

62

Figure 5-10. Amount Before Tax Family Income (Source: Bricker, & Kennickell, 2012)

Figure 5-11. U.S. Wages (Source: Thomson Reuters Datastream)

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An analysis of the macroeconomic charts of the US economy from 2008 to 2014 (Figure

5-3) showed that the GDP growth rates were negative for the years 2007 and 2008, and even in

2009, the GDP growth rates improved marginally. There was negative unemployment growth

between 2007 and 2010 (Figure 5-4), and the employment growth rates picked up only

marginally in the year 2011.The unemployment rate peaked in the end of 2010, and gradually

decreased 2011 onwards. An analysis of the long term unemployment rate (Figure 5-5), showed

that it has decreased very gradually, and consequently had a negative impact on household

financial position of the average borrower. The recession between the years 2007 and 2011 was

not a localized event but a national one, and consequently, all aspect of life was affected in every

part of the country. One of the main effects was the wage and income of people (Figure 5-1 and

Figure 5-2). Analysis of data in Figure 5-9 showed that that household incomes fell across all

areas and across all age groups. This phenomenon had a negative impact on the household’s

ability to pay its bills. When having to make a choice between basic necessity such as food and

fuel, and mortgage payments; the mortgage payments took a back seat, giving rise to

foreclosures. An analysis of the data in Figure 5-10, further showed that in the United States,

wages are the main source of income for households, thus if jobs were being lost or wage growth

was lagging (Figure 5-11), household finances had to suffer.

Therefore, when we look at the average foreclosure in our tables, we can see a similar

pattern where foreclosures started to rise in 2008 and by 2012 they either leveled off or were

starting to decline. Pools 10, 11, 12 and 13 (Table 5-10, 5-11, 5-12 and 5-13), showed a similar

result, where the relationship between the dependent variable and independent variable was not

static but dynamic, mirroring the 10 pools discussed above.

64

Table 5-10. Statistical Analysis for pool AMAC 2003-12 2A-2

Pool: AMAC 2003-12 2A2008 2009 2010 2011 2012 2013 2014

Dependent variable: Foreclosure %Foreclosure % average for the year for reference 4.86% 7.26% 8.70% 8.69% 9.43% 7.21% 6.70%

R² valuesIndependent variable : 1 Credit score 16.26% 0.79% 15.34% 4.37% 0.29% 1.84% 16.31%Independent variable : 2 Perfect Payer % 60.99% 89.17% 56.77% 28.40% 35.68% 1.79% 29.80%Independent variable : 3 Balance < 417 k 0.36% 36.85% 0.80% 1.33% 0.10% 36.91% 12.53%Independent variable : 4 Geo < 50% of the pool 25.68% 53.26% 12.29% 1.97% 2.18% 1.17% 41.67%

Regression analysis using 95% confidence interval

Table 5-11. Statistical Analysis for pool AHM 2005-1 8A1

Pool: AHM 2005-1 18A12008 2009 2010 2011 2012 2013 2014

Dependent variable: Foreclosure %Foreclosure % average for the year for reference 5.78% 7.24% 11.23% 11.89% 9.45% 8.22% 7.68%

R² valuesIndependent variable : 1 Credit score 4.69% 1.09% 17.12% 5.66% 9.35% 5.79% 1.69%Independent variable : 2 Perfect Payer % 62.35% 77.21% 18.36% 80.37% 77.99% 74.25% 11.91%Independent variable : 3 Balance < 417 k 58.36% 42.38% 2.98% 45.67% 48.69% 38.47% 19.37%Independent variable : 4 Geo < 50% of the pool 27.33% 79.34% 1.89% 78.36% 0.89% 22.64% 59.78%

Regression analysis using 95% confidence interval

65

Table 5-12. Statistical Analysis for pool AHM 2005-1 6A

Pool: AHM 2005-1 6A2008 2009 2010 2011 2012 2013 2014

Dependent variable: Foreclosure %Foreclosure % average for the year for reference 4.08% 5.83% 9.02% 9.04% 7.31% 6.73% 4.73%

R² valuesIndependent variable : 1 Credit score 9.88% 21.22% 0.02% 8.03% 15.91% 37.94% 37.94%Independent variable : 2 Perfect Payer % 56.12% 70.75% 26.45% 38.33% 23.61% 11.08% 59.88%Independent variable : 3 Balance < 417 k 21.32% 1.23% 33.85% 95.70% 73.78% 0.00% 0.00%Independent variable : 4 Geo < 50% of the pool 49.64% 65.66% 12.28% 82.23% 11.07% 3.06% 0.94%

Regression analysis using 95% confidence interval

Table 5-13. Statistical Analysis for pool AHM 2004-1 1A

Pool: AHM 2004-1 1A2008 2009 2010 2011 2012 2013 2014

Dependent variable: Foreclosure %Foreclosure % average for the year for reference 3.28% 0.77% 6.47% 6.57% 6.53% 4.53% 2.56%

R² valuesIndependent variable : 1 Credit score 3.89% 2.59% 0.81% 4.65% 14.43% 2.87% 29.25%Independent variable : 2 Perfect Payer % 0.75% 2.69% 65.17% 36.86% 8.27% 0.05% 2.66%Independent variable : 3 Balance < 417 k 0.15% 4.67% 0.00% 64.55% 18.85% 13.16% 4.82%Independent variable : 4 Geo < 50% of the pool 0.15% 4.67% 0.81% 4.65% 14.43% 11.43% 54.72%

Regression analysis using 95% confidence interval

66

5.3 Conclusion

The primary objective of this paper was to subject the data collected to statistical tests,

and observe whether they support our hypothesis or not. A compressive analysis of the data

using both statistical tools on primary data, and the use of secondary data sources, enabled us to

comprehensively test the hypothesis. The results suggested that there exists a correlation between

the dependent variable (foreclosure rates), and independent variables (credit score, perfect payer,

balance and geography) . Therefore it can be concluded that subsequent to the statistical analysis,

our hypothesis holds true, as we reject the null hypothesis, and fail to reject the alternate

hypothesis. Thus we have answered the research question, that, there exists a correlation between

the foreclosure rate of the pool, and variables such as Credit Score, Perfect Payer, Balance and

Geography; which are used to predict foreclosure rates.

67

Chapter 6 – Conclusions and Recommendations

6.1 Introduction

The objective of this thesis was to understand the input variables that go into a

Mortgage Backed Security, and most significantly, evaluate the explanatory potential of the

various variables used to develop an understanding of how these securities are valued. In this

section, we brought our discussion to close, highlighted the major learning from this study, and

identified the scope for future research and action. We also identified some of the limitations of

this study, and suggested steps that should be taken to further improve upon the thesis.

6.2 Conclusion: Hypothesis Holds True

The research question posed at the inception of this thesis was, what is the nature of

correlation between the factors used by the most common risk models (e.g. FICO score,

geography, loan balance, etc.) used to predict foreclosure rates and the foreclosure rate of the

pool? In order to answer the research question, we conducted an extensive literature review and

developed our hypothesis. Using primary and secondary data, we further tested our hypothesis.

The conclusion reached by us suggested that the alternate hypothesis argued by us holds true,

and that there exists a correlation between the foreclosure rate of the pool, and variables such as

Credit Score, Perfect Payer, Balance and Geography; which are used to predict foreclosure rates.

Another major findings of this thesis suggested that the input variables which comprise a MBS

had an explanatory power over the foreclosure rates.

6.3 Recommendations

Based on the analysis, banks and financial companies in the business of servicing and

buying of mortgage backed securities should use a multi factor valuation model that incorporates

more than one input factor (such as FICO score). Their model should be a multi factor model of

the four input factors in the least. Additionally, they should back test their model that goes over

68

one time period or event, as we showed that one input factor at one time which had a significant

explanatory power over time, eventually lost its explanatory power to another factor.

6.4 Summary

The mechanics of mortgage backed security is based on payments by the individual

borrowers. The borrower makes monthly payments and the servicing firm, the bank collects the

payments and amortizes the loan with part payment to interest and remaining to principal till the

balance becomes zero. The most common types of mortgages are 30 year fixed rate and 15 year

fixed rate mortgages. The problem with such complex instruments and cash flow issues is that it

is comprised of several moving pieces such as interest rates, income growth etc. Thus the way to

predict the effect is to use proxies. In the case of mortgage backed security, they are FICO score,

geography of the loan, payment history etc. It is essential that such proxies are relevant measures

and research is needed to establish this.

The main objective of this thesis was to investigate the various methodologies and

models that are used to calculate the value or price of a distressed MBS security, and conduct a

correlation analysis between the main inputs into the models (FICO score, geography, loan

balances) with the foreclosure rates. Such an analysis enabled us to understand whether the input

variables into the models have a high explanatory potential or not, and whether the models are

using the correct factors or not. The thesis answered the research question, what is the nature of

correlation between the factors used by the most common risk models (e.g. FICO score,

geography, loan balance, etc.) used to predict foreclosure rates and the foreclosure rate of the

pool?

A study done by Dunn and McConnell (1981), on the various methods used by banks to

value the portfolio of mortgage-backed securities on their balance sheet came to the conclusion

69

that there is no one model used at that time that is superior to the others, and therefore there can

be no one model that can be considered as the industry standard. During the 1980s MBS were

simple in their structure, unlike today, where computational power and complexity of the MBS

structure have greatly increased and with many counter parties involved, tracing the loans deal

and exposures to off-balance-sheet entities.

The data collection plan for the longitudinal study was a time series method. Most of the data

covered a 7-year period of mortgage-backed securities that were issued before 2004 and were

active with payments being made by the underlying cash flow. To add diversity to the data, the

study also included some mortgage-backed securities that either collapsed or were paid out. The

main data source used was the Bloomberg terminal that was accessed through the NYU library.

Specifically, using the Bloomberg fixed-income section and sorting for active pools of mortgage-

backed securities issued before 2004.

The data analysis plan had two steps. The first step was sorting the securities in Excel based

on the year of maturity, FICO score average, loan balance average, and average payment history.

Since these were our independent variables they would weed out securities that were too similar.

The part two of the analysis involved conducting a regression analysis using each independent

variables, with the dependent variable being the foreclosure rate.

The focus of the study was to find the R2 between the independent variables and the

dependent variable. For example, low FICO score pool has high default or high FICO score pool

has high foreclosure rate too or lower foreclosure rate. Thus using regression analysis was a

perfect tool to establish the relationship.

70

Based on our analysis, we were able to answer our research question and came to the

conclusion that, there existed a dynamic relationship between input factors and foreclosure rate

and not a static one.

6.5 Contribution of This Study

This study was an original piece of work as it builds upon existing literature. In the past

scholars used to analyze the effectiveness of only one specific model. However, in this study we

have taken the four input variables (FICO score, perfect payer, balance and geography) that are

common to the major models, and summarized their fit. This was achieved by using a

longitudinal study methodology by collecting actual pool data and performance of active MBS

pools. In this study, we showed that the four variables identified by us were major input variables

that primarily derived all of the various models identified by us in the literature review. The

study further showed that these variables had a significant relationship with foreclosure rates. In

essence, the models used in the industry are practical and relevant. Prior studies have not focused

on more than one factor.

6.5.1 Contribution to the Body Of Knowledge In The Field. This study is aimed to

benefit professionals in the mortgage backed security industry, as well as scholars engaged in

this field of research. Professionals now have empirical evidence to suggest that that not all

factors are weighted equally in their explanatory power, and the relationship changes over time.

For example, credit score was the dominant factor in 2008 that helped explain foreclosure rates,

but in 2014 geography was the main factor. For researchers, it sets the stage for further course of

study as we now need to understand how each independent variable contributes to the

explanation, and also we need to identify factors that accounted for unexplained variances. One

very interesting research idea would be to do a multiple regression analysis using the data used in

this study, and evaluate how all four variables taken together explain the total variance. In our

71

study all variables have the potential to be over 100%, but in the multiple regression study the

total of all four will be 100%, and so the analysis will be more robust. Such an analysis will help

us understand if these four variables are the main variables that can explain the foreclosure rate,

or is there is some other variable that itself can significantly explain the variance.

6.6 Limitations of the Study

This study is very focused in its scope and it primarily attempts to prove that there is a

relationship between the dependent variable and independent variable. The study did not aim to

establish what the nature of the relationship is, what the direction of the relationship is, or why

the relationship changes over time. Nor does the study establish what is the R2 value that we

should use as threshold for it to be dominant. The study was primarily a longitudinal study and

made comparisons between different pools over time. We suggest that the limitations presented

here be taken up as scope of future research by other scholars.

6.7 Scope for Future Research

This study was taken to answer a fundamental question is there a relationship between the

input factor and the foreclosure rates of the pool. Based on our findings, we suggested that future

studies look into the question of multiple regression of input factors and foreclosure rate, this

would shed light on how the individual factors interact with each other. Another suggestion for

future research would be to include more than the four factors that are used in the models

identified in the study. We suggest that an increased number of input factors should be used to

calculate the degree of correlation which is significant, and to include an input factor in an

analysis.

6.8 Conclusion

The thesis was initiated with the aim of highlighting the various input factors that are a

part of a Mortgage Backed Security, as well as the various independent variables that are used in

72

an MBS to understand the foreclosure rate. To develop my research question, and ground it in

the existing body of scholarly work, a comprehensive literature review was conducted. The

literature review helped identify numerous models that were used to evaluate MBS within the

industry. These models were then deconstructed, and variables used in all of these models to

identify foreclosure rates was identified. The literature review also helped further develop the

research question, and enabled us to identify the null and the alternate hypothesis. Once the

hypothesis was identified, the research design and research methodology was identified. The

hypothesis was subjected to statistical analysis using the methodology identified and results were

analyzed. The results suggested that the relationship between the dependent variable (foreclosure

rates) and independent variables (credit score, perfect payer, balance and geography) was not a

static one, but a dynamic once. Another major findings of this thesis was to suggest that the input

variables which compose a MBS have an explanatory power over the foreclosure rates.

73

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Appendix A – FEFUO Letter

From: Tom <tsc1@nyu.edu> Date: Monday, March 30, 2015 Subject: FEFUO Letter approval attached ... To: Simon Jean Ergas <sje2026@nyu.edu> Cc: Bhawani Singh <bs2644@nyu.edu>, scps.masythesis@nyu.edu Professor Ergas, Your student, Bhawani Singh, has been approved for a Formal Exclusion From UCAIHS Oversight (FEFUO). Please see the attached document which must be filed with their final completed electronic softbound Master’s thesis. Even though it is not classified as "Research" under the Federal and IRB guidelines, it is still subject to the same rigorous standards of research as defined by the course requirements. The approval is for using existing data. Therefore, any changes to the research protocol from those that were originally stipulated on the documents submitted would require a resubmission of all the documents that were reviewed before any data is collected for this research. Investigators are “strongly discouraged” by UCAIHS, and the SCPS - MASY department from “proposing any kind of recruitment of” other students including “fellow classmates” at NYU, “patients or similar groups” of individuals, “in order to avoid any potential for coercion or conflict of interest” (www.nyu.edu/ucaihs). Thank you, for your understanding, and cooperation in this matter. Professor Christo Research Coordinator NYU – SPS - Management and Systems

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Appendix B – Glossary

1. DEFINITION of 'Conditional Prepayment Rate - CPR' A loan prepayment rate that is

equal to the proportion of the principal of a pool of loans that is assumed to be paid off prematurely in each period. The calculation of this estimate is based on a number of factors such as historical prepayment rates for previous loans that are similar to ones in the pool and on future economic outlooks.

2. ALM model emanate from its ability to quantify existing balance sheet holdings and forecast future earnings and value in a timely fashion. This translates into enhanced earnings performance — directly from better financial decision-making, and indirectly from enhanced regulatory compliance.ALM models provide the equivalent of a speedometer in an automobile: a quantitative gauge of performance. With an ALM model, the balance sheet can be accurately pushed to its “speed limit” (i.e., maximum performance) while controlling risk. Having an ALM model also reduces the chances of going too slow, thus missing earnings opportunities or encountering unexpected risks. These models can be found on the Bloomberg terminal.

3. PSA: One of the most notable prepayment models is the PSA Prepayment Model by the Securities Industry and Financial Markets Association. The PSA model assumes increasing prepayment rates for the first 30 months and then constant prepayment rates afterward.”

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