Introduction
The mortgage crisis and steep decline in home values presents challenges to both lenders and defaulted borrowers that are in homes that are “underwater” in terms of equity. What was once a simple decision to foreclose on a property has since become much more difficult and in some circumstances can be near impossible to complete within a reasonable timeline. As a result, new methods of turning a non-performing asset into performing again have become more prevalently used in the market. The most common of which is a modification.
Loan modifications are contract negotiations between a lender and a borrower that occur when there is a desire from both parties to resolve delinquency and allow the borrower to remain in the home. The United State government has begun to guide and offer assistance for modifications through the Home Affordable Modification Program (HAMP). These guidelines set forth the requirements that a lender must meet as well as certain milestones a borrower must complete on their way to a modification.
A typical modification is often just a re-extension of the term of the loan, whereas it may have been maturing in 2011 a modified loan could set a new maturity date of 2025 to allow the borrower to get back on track making payments consistently. There are inherent benefits and detractions in the modification process; a loan that is brought to some semblance of current after a modification can re-default. A re-default will remove the new terms brought about by the modification and thus the borrower will be in the same position they were before. This is made even more complex by the fact that since it was difficult for the lender to receive payments before and there is still no appreciable change in equity there is little that they can do unless they choose to foreclose and then sell the home themselves as an REO which is an even more costly process.
The purpose of this research paper is to look into that factors that go into the decision making process behind modifying a loan and then to create a model to predict the likelihood of re-default of a modification candidate. It is in our opinion that certain factors are directly linked to the propensity to default and that those characteristics may be accounted for during a modification qualification check and those that don’t meet the standard can be sent for a different resolution plan.
Literature Review
There is a long history of studies published on the subject of first default. According to Roberto Quercia and Michael Stegman, “An important stream of literature, beginning in the 1960s and extending through the present, addresses default principally from the perspective of the individual mortgage lender” (1992, 344). These models use a variety of techniques and variables, with the oldest using linear probability models and ordinary least squares regression to later papers featuring logit and various hazard models to try to diagnose the time, probability and causes of mortgage default (Quercia and Stegman 1992). These methods would be required for any analysis on subsequent default.
Unfortunately there is little published on second default after a loan modification; this is because modification is a rare and difficult process. Joseph Badal explains, “Traditionally, when homeowners wished to reduce their mortgage interest rate or alter the terms of their loan, the only available option was to refinance” (2005, 15). Even with the post mortgage crisis popularity of modification with policy makers, “the Home Affordable Modification Program has been very selective in providing relief to homeowners” (Collins 2010, 1). This selectivity means that those who are in the most unaffordable loans have a difficult path to modification:
In today’s market, a large fraction of struggling homeowners may have mortgage obligations that are not affordable. Bankruptcy law does not permit debtors to modify the terms of mortgages secured by a principal residence. This limitation on restructuring home mortgage loans may pose an insurmountable barrier to families who are trapped in unaffordable loans. (Eggum, Katherine and Twomey 2008, 1125)
Eggum et al conclude by stating that, “Repealing the prohibition on modifying home mortgage loans in bankruptcy would improve the effectiveness of chapter 13 bankruptcy as a home-saving device and reduce the economic and policy consequences of the foreclosure crisis by giving millions of families a chance to save their homes” (1167-1168). Fortunately there seems to be a push in the right direction.
Despite the early limited availability of loan modifications, there is evidence that these numbers are swelling. George Fitzgerald writing for Mortgage Banking reports, “One thing is certain: With HMP requiring all modifications to be completed by the end of 2012, servicers need to be prepared for a marked and continued increase in HMP related activity, along with all of the associated new data that will be required” (2009, 50). While the Home Affordability Modification Program was initially discerning, it is indicated that given its early success, there will be a loosening of standards, particularly as the program draws to a close. Government programs are not the only driver of modification; lenders are turning toward restructuring loan terms to try to recoup some of the lost equity.
Consider the precipitous drop in home prices since 2008. According to the latest Case-Shiller home price press release, “Measured from their peaks in June/July 2006 through February 2011, the peak-to current decline for the 10-City Composite and 20-City Composite are -32.5% and -32.6%, respectively”(2011, 1). This reduced home value comes into play when lenders try to salvage the value of their loan through foreclosure, “Costs to lenders and institutions are incurred when the net cash recouped from foreclosure proceedings is less than the value of the financial asset” (Quercia and Stegman 1992, 342). Foreclosing on homes that are worth little results in losses for the lender; therefore, there is an incentive for modification to avoid foreclosure losses. With increases in modification driven by government program, as well as a lack of equity, new data is now available on modified loans, including those who default on their modified loans.
Data Source
Our analysis employs a database comprised of performance and historical data of individual loans that have been aggregated from a mortgage servicing firm. The loans are distributed across the United States and are a collective of the efforts of many prior lenders and servicers. The final selection of observations was based on the completeness of the entries, as is common in the current mortgage climate there was a severe lack of complete data relating to the loan itself, the borrower, and the asset (home). Our data was compiled for the specific purpose of this research as is still in flux as all accounts being observed are still currently being serviced.
As mentioned above, data relating to a troubled asset falls into one of three main categories: loan data, asset data, and borrower data. Loan data points are the mechanics of how the loan is carried out such as the original balance and the interest rate. These data points indicate the viability of the paper in a default and will serve as the basis for modification proceedings should that become an option. Asset data is anything relating specifically to the home itself. The value, condition and any information about subsequent liens will indicate to a servicer whether modification proceedings are more viable than foreclosing. Data on the borrower is any information that describes the borrower’s demographic characteristics or ability to pay their debts. Often in the case of defaulted borrowers, there are many existing issues that may have led to a default including being unemployed or having a reduction in their income. Depending on the financial security of a borrower, a servicer will make the effort to pursue a modification that will bring the monthly cost of keeping the home and paying down the debt in line with their current outlook.
Selection of the data for this paper began with an understanding of some of the basic metrics that directly dictate the performance of a mortgage. The observations included in the study were selected for being the most complete as whole data relating to troubled assets is very difficult to gather in the current climate given the ebb and flow of firms responsible for carrying out the servicing of such assets. As previously mentioned, the loans included in our study are still active and being serviced and may be monitored on an ongoing basis to gain more insight into the overall process that leads up to and comes out of a loan modification. Each observation exists in one of three possible states: modified without re-default, modified with re-default and currently in the modification process. Thus, we are able to take the three states of a modification and research the probability that one outcome, in our case a re-default, is likely to occur.
Table 1: Description of Variables and Summary Statistics
| Variable | Description | Obs. | Mean | Std. Dev. | Min | Max |
| REDEF | coded variable: 0 - modified with no re-default, 1 - modified with a re-default, 2 - currently being modified | 568 | 1.610915 | 0.5681312 | 0 | 2 |
| INTRATE | the current interest rate of the loan in percent | 568 | 0.0946195 | 0.0317495 | 0 | 0.179 |
| ORIGAMT | the original amount of the loan in dollars at time of lending | 568 | 49321.94 | 38365.35 | 10000 | 400000 |
| PRICBAL | the current amount of the loan based on any payments or modification terms in dollars | 568 | 13859.46 | 27252.1 | 0 | 209936.9 |
| EQUITY | the equity of the property to the lender as a function of the value of the asset minus the amount left on any outstanding liens in dollars | 568 | 33874.94 | 175087.9 | -1020336 | 1030000 |
| UNEMP | dummy variable indicating unemployment | 568 | 0.5757042 | 0.4946713 | 0 | 1 |
Variable Explanation
A total of five exogenous variables and one endogenous variable were selected based on the availability of data and the information provided by prior research included in our literature base. The observed variables selected to determine the probability of re-default on a modification are the endogenous variable of the position of a modification in the process (REDEF), the current interest rate of a loan at the time of observation (INTRATE), the original amount that a loan was made for (ORIGAMT), the current principal balance remaining on a loan (PRICBAL), the amount of equity at the time of observation on a given asset (EQUITY), and an indication of the borrower’s employment status (UNEMP). Table 1 contains a brief description of each variable used in addition to the summary statistics for each observed variable. Our method of analysis for the purposes of this paper is a multinomial logit that will indicate the probability of a certain outcome, re-default in our case, in a group of potential outcomes given the exogenous variables acting on the model. The model will be discussed in detail in the methodology description below.
The endogenous variable selected for this research is REDEF. It is a coded indication of what position a loan finds itself in the modification process. A code of 0 indicates that the loan has been modified and has not exhibited a default since modification, codes of 1 are loans that had been modified and have subsequently become defaulted once more and a code of 2 indicates that a loan is currently in the process of being modified by the lending institution. A total of 30% of all loans that had been through the modification process had re-defaulted at the time of data collection.
The first exogenous variable that was considered for our model is INTRATE, the interest rate of a loan. An interest rate change should have no effect on the likelihood of re-default as it is often unchanged when a modification takes place and more often the term of the loan is just extended to meet the ability of the borrower. A higher interest rate will increase the amount of the monthly payment and thus increase the financial burden of maintaining ownership of the home. Having a lower interest rate is helpful but can be counteracted by the term of the loan and the original and existing balance of the loan.
The second exogenous variable considered in our model is the original amount of the loan ORIGAMT. Original loan amounts can be used as both an indication of equity at the time of the loan being made and later as an indication in loss of value of an asset. (Elul et al. 2010) Original loan amount is also a baseline for costs that are faced by the borrower at the inception of the lending process.
PRICBAL is the remaining balance on a loan at the time of data collection. This indicates both how much is still owed and can be used in the equity formula. The higher the remaining balance the more cumbersome that a monthly obligation of a loan is both pre and post modification.
Another of our exogenous variables is EQUITY, or the amount of remaining value left in a home when subtracting the total amounts owed on liens from the appraised value of a home. Due to the current vast reduction in home prices, equity position is important to gauge the likelihood that a loan will be modified. By indicating that there is or is not enough equity to cover the costs of foreclosure and the potential costs of selling a property post foreclosure, the likelihood that a loan will re-default can be predicted. Additionally, the loss of value in a home decreases the liquidity of the asset and can both tie the hands of a borrower and lender. (Elul 2010) When a loan is modified the equity position is not necessarily influenced as the term of the loan is likely to be increased to such a point that the loan is once again viable based on the general terms.
The final exogenous variable being considered in our model is the current employment status of the borrower as represented by the dummy variable UNEMP. The employment status of a borrower is obviously directly related to their ability to pay and there is a very high correlation with unemployment and re-defaults as observed in the data. (Kau, Keenan, and Li 2009) The employment status is represented by 0 – employed and 1 – unemployed.
During data collection a few other variables worth mentioning were considered. A coded variable indicating the reason for default was originally considered as it would have provided more information relating to the specific reason an individual account defaulted in the first place and could have served as a cautionary piece to monitor during a modification. It was determined that for the purposes of this model and will be discussed later in the paper, the default reason was not useful due to the inherent bias in that it was self-reported and there was no validation that occurred. Also, many of the default reasons were reflected in other variables such as employment status. Additionally, whether a loan was an adjustable rate or fixed rate was considered but there was a 100% occurrence of re-defaults in our observations among loans that were adjustable rates.
Methodology
Due to the categorical nature of the dependent variable, REDEF, multinomial logit was the best model to use for this data set. A multinomial logit model measures the probability of moving from a base state of the world to a different state of the world; in this case it measures the probability of candidates for loan modification to either enter a default state after modification or continue to keep up with their payments. A functional form for this type of equation has been taken from Using Stata for Principles of Econometrics and modified for our purposes here (Atkins and Hill 2008, 370).
Where,
These results would require additional transformations to obtain the marginal effects, assuming all else constant, given by,
This indicates a change in probability that one will move from the base outcome to the new outcome given a one unit shift in the given variable at the mean of each other variable.
Results
| Obs. | 568.0000 |
| LR chi2(10) | 420.8200 |
| Prob > chi2 | 0.0000 |
| Pseudo R2 | 0.4786 |
| Log Likelihood | -229.2119 |
Table 2. Results of Multinomial Logit
| REDEF | Coef. | Std. Error | Z |
| 0 | | | |
| INTRATE | -98.820710 | 14.4156000 | -6.86 |
| ORIGAMT | -0.0000952 | 0.0000245 | -3.89 |
| PRICBAL | 0.0000668 | 0.0000208 | 3.21 |
| EQUITY | -0.0000001 | 0.0000017 | -0.04 |
| UNEMP | -1.9465820 | 0.6531887 | -2.98 |
| CONS | 8.1942790 | 1.2375090 | 6.62 |
| 1 | | | |
| INTRATE | -60.347070 | 6.0464570 | -9.98 |
| ORIGAMT | -0.0000149 | 0.0000044 | -3.43 |
| PRICBAL | -0.0000370 | 0.0000084 | -4.44 |
| EQUITY | -0.0000027 | 0.0000011 | -2.45 |
| UNEMP | -2.2153170 | 0.2848157 | -7.78 |
| CONS | 6.8744110 | 0.6515896 | 10.55 |
| 2 | Base outcome | | |
Tests of fit:
· Pseudo R2 – for our primary model, we see a pseudo R2 of 0.4786 which exhibits a moderately good fit of the overall model.
Tabe 3. Marginal Effects Outcome 1
| variable | dy/dx | Std. Err. | z | P>z | [ 95% | C.I. ] | X |
| INTRATE | -9.234115 | 0.98251 | -9.4 | 0 | -11.1598 | -7.30843 | 0.094619 |
| ORIGRAMT | -2.25E-06 | 0 | -3.36 | 0.001 | -3.60E-06 | -9.40E-07 | 49321.9 |
| PRICBAL | -5.73E-06 | 0 | -4.56 | 0 | -8.20E-06 | -3.30E-06 | 13859.5 |
| EQUITY | -4.09E-07 | 0 | -2.44 | 0.015 | -7.40E-07 | -8.10E-08 | 33874.9 |
| UNEMP | -0.3706805 | 0.04935 | -7.51 | 0 | -0.467398 | -0.273963 | 0.575704 |
Tabe 4. Marginal Effects Outcome 0
| variable | dy/dx | Std. Err. | z | P>z | [ 95% | C.I. ] | X |
| INTRATE | -.1665046 | 0.13066 | -1.27 | 0.203 | -.422602 | .089593 | 0.094619 |
| ORIGRAMT | -1.76E-07 | 0 | -1.41 | 0.158 | -6.8E-07 | 6.8E-08 | 49321.9 |
| PRICBAL | 1.41E-07 | 0 | 1.42 | 0.156 | -5.4E-08 | 3.4E-07 | 13859.5 |
| EQUITY | 8.18E-10 | 0 | 0.26 | 0.795 | -5.3E-09 | 7.0E-09 | 33874.9 |
| UNEMP | -0.0029764 | 0.00277 | -1.07 | 0.283 | -0.008411 | 0.002458 | 0.575704 |
At first INTRATE does not seem to make sense; however, the marginal effect must be multiplied by .01 to be in the proper scale, since interest rates are in decimal form. Furthermore, a negative sign does not seem to make sense; why would a higher interest rate induce better mortgage performance? Perhaps it is an artifact of the data; at the interest rate ranges experienced here, re-default is rather unlikely due to interest rate issues. Another possibility is that a higher interest rate comes with more favorable terms, thus actually decreasing the likelihood of default. In any case, a low interest rate implies continuing payments, which is perfectly in line with theory.
A higher original amount of the loan also seems to have a small, negative effect on re-default; bigger original loans default less. This is another result that seems counter intuitive; however, since someone borrowing more money is more likely to have a higher ability to pay, perhaps this should be less surprising. On the other hand, low original amount also implies that the borrower will keep up with his payments, again with a small marginal effect. Similarly, big principal balances ought to be part of what induces a default, but in absolute terms, may only represent someone with a bigger loan and more ability to pay. This one is even stranger since big principal balances are also correlated with repayment; this supports the ability to pay theory.
The real key here seems to be equity. Having more equity causes fewer defaults; this makes sense, because few people are willing to walk away from a house they have money in. This is also supported by high equity being linked to better payment. Unemployment, on the other hand, is another weird variable; being unemployed should not imply that one will not default, as seems the case here. Once again, being employed implies paying the modified loan. However, being unemployed generally disqualifies one from the modification process. It is likely that the unemployed will not re-default because they will never be given the opportunity.
This seems to be a running theme to this study; the small effects matter more than the large ones. If one was in perfect condition then one would not need a modification; remember the data set consists of people who have all defaulted at least once. Likewise, if one is in such dire straits as to be certain to default, no lender in the world would take on their portfolio. Hence, unemployment and principal balance returning such odd results; if one has no job or a high loan to value ratio, one will never re-default since one would not receive a modification in the first place.
One way to try to parse out who will or will not default on the modification is to find out why applicants defaulted in the first place; however, the reason for default was not included in the base model discussed earlier. Also discussed earlier are the reasons for not including it in that model, but that data could prove to be an interesting supplement. Therefore, a copy of the results, summary statistics and marginal effects will be included in Appendix 1 and discussed here. Although there are problems with the reporting mechanisms for default reason, it can still yield useful insights into further study.
One such result is that there are quite a few more statistically significant factors influencing the risk of default as opposed to predicting mortgage success, especially at 90% significance. It seems that it is much easier to predict failure than success. For example, excessive obligations results in a significant 22% increase in re-default likelihood; however, it is not a significant factor for predicting if one is up to date in their modified loan payments. This also seems to agree with the narrative that excessive obligations were significant factors in the crisis; if one had excessive obligations before modification that caused a default, it is unlikely that those obligations have disappeared.
In fact another variable may have influenced those burdens. Business failure is the third most reported reason for default in this sample; it significantly increases the probability of after modification default by 25%. Strangely, it is also positive and significant for a lack of post modification default. The marginal effects are small, however, and it is possible that those with failing businesses can pay their bills after the modification. Business failure can also result in reduced income, the number one reason reported in this sample for default. While it is insignificant at the 95% level, with a p=.058 it is not far off, and well significant at the 90% level, and contributes nearly 15% to re-default probability.
Another hot topic is worth mentioning. Adjustable rate mortgages were heavily panned during the subprime crisis as products sold to, “underqualified borrowers lured by years of low fixed-interest fell behind when interest rates rose” (Tedeschi 2010). The idea is that when the rate adjusts upward, the poor borrower is unable to pay the higher interest rate and must default on his loan. While representing a small number in the sample, rate adjustment is a significant factor for re-default, but not for continued payment. Given that the modification fixes the rate, if the adjusted rate were the culprit in a default, in all likelihood, the modification fixes the problem, and the customer should have no problems repaying. However, since this is not the case, perhaps the storyline of adjustable rate mortgages being sold to people who perhaps should have no mortgage at all seems fitting.
Interestingly disputed payments are significant at the 90% level for both re-defaulters and payers alike. Often times the subject of the dispute is linked to an adjustable rate; the borrower, unaware of the adjusting rate, refuses to pay what is considered an incorrect balance. Given the already established results surrounding those in adjustable rate mortgages, it makes sense that payment disputes give a nearly 60% probability of re-default; however, it also gives a 3% probability of remaining current. Perhaps there are a large number of people with less than credible disputes who continue to default, while there are some who default based on logical disputes, have their mortgage modified and leave happy with their problem solved and payment forthcoming.
More study with better data could potentially answer these questions. A study that collects data keeping in mind the balance between those in good enough financial shape to not need a modification and those in such poor shape that a modification would never be considered. It also seems like there is a potential study in every reason for loan default; many of the signs of the variables had ambiguous meanings. Perhaps with even more loan modifications in the works, a larger, more detailed data set could be obtained to better analyze these early results.
Appendix 1: Regression, Marginal Effects, and Summary Statistics of Reason Model
Works Cited
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Adkins, Lee C., and R. Carter Hill. 2008. Using Stata for Principles of Econometrics. New Jersey: John Wiley & Sons.
Badal, Joseph. 2005. “Loan Modification Programs: A Great Alternative to Refinancing a Mortgage.” Real Estate Financing, October: 15-17.
Collins, Brian. 2010. “HAMP Mod Selectivity Means Lower Redefaults.” Mortgage Servicing News 14(9).
Eggum, John, Katherine Porter, and Tara Twomey. 2008. “Saving Homes in Bankruptcy: Housing Affordability and Loan Modification.” Utah Law Review (3): 1123-1168.
Elul, Ronel. 2010. “What Have We Learned About Mortgage Default?” Business Review Q4: 12-19. www.philidelphiafed.org/research-and-data/publications/.
Elul, Ronel, Nicholas S. Souleles, Souphala Chomsisengphet, Dennis Glennon, and Robert Hunt. 2010. “What ‘Triggers’ Mortgage default?” AEA Papers and Proceedings 100(2): 490-494. doi: 10.1257/aer.100.2.490.
Fitzgerald, George. 2009. “Sustainable Loan Modifications.” Mortgage Banking, June: 46-50.
Kau, James B., Donald C. Keenan, and Xiaowei Li. 2009. “An Analysis of Mortgage Termination Risks: A Shared Frailty Approach with MSA-Level Random Effects.” J Real Estate Finance Econ 42: 51-67. doi:10.1007/s11146-009-9179-x.
Quercia, Roberto G., and Michael A. Stegman. 1992. “Residential Mortgage Default: A Review of the Literature.” Journal of Housing Research 3(2): 341-379.
Tedeschi, Bob. 2010. “Rethinking Adjustable Rate Mortgages.” The New York, Times August 27. http://www.nytimes.com/2010/08/29/realestate/29mort.html.
Equations and tables are missing since I more or less copy/pasted from the Word document. Hopefully it doesn't end up getting lost...
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