A New Loss Severity Model Framework for Residential Mortgages *

A New Loss Severity Model Framework for Residential Mortgages * Jian Chen IFE Group and Johns Hopkins University, USA Junrong Liu IFE Group, USA Tyler Yang IFE Group, USA Abstract This paper investigates loss given severity data from residential mortgages purchased by Freddie Mac. We propose a new loss severity model framework, consisting of a disposal selection model, and two loss given default (LGD) models. Compared with traditional simpler version of loss given default models, this new framework has several advantages. First, the disposition selection model is capable of adjusting the probability of the defaulted mortgage loans going into different termination events, e.g. Real Estate Owned (REO) vs. foreclosure alternatives. Second, the LGD models can capture different effects of credit loss drivers on those termination events. Overall, the new loss severity model framework provides a more flexible and accurate approach to estimate the GSE mortgage loss amounts. It will be useful in the risk assessing and pricing of the GSE s risk transfer and/or sharing deals. We also show that widely used determinants in previous studies in loss severity, like current loan-to-value ratios, relative loan sizes, default episode duration, and credit scores of borrowers, all prove to be very significant in those models, whereas with different effects. These findings provide insights into credit risk management for mortgage investors and policy makers. Key Words: loss given default, foreclosure, residential mortgage JEL Classification: G21, G32, H81, R51 Initial version: February 11, 2015 Current version: March 3, 2015 * Address correspondence to: Jian Chen, jian.chen@ifegroup.com or jian.chen@jhu.edu; Junrong Liu, junrong.liu@ifegroup.com; Tyler Yang, tyler.yang@ifegroup.com, IFE Group, 51 Monroe Street, Suite 1100, Rockville, MD 1

1. Introduction Three models are of vital importance in credit risk management: Exposure at Default (EAD) model, Probability of Default (PD) model and Loss Given Default (LGD) model. Among them, LGD model has not been widely investigated in residential mortgage market and has been lagging behind the PD models in the literature. There are two major reasons: one is the lack of reliable loss data from mortgage default; the other is the poor fitness when traditional credit risk models are applied to the historical data. Historical literatures have been mainly concentrated on the determinants of LGD ratio, i.e. the percentage loss from the defaulted outstanding balance. Studies on the drivers of different termination events, e.g. Real Estate Owned (REO) vs. Third Party Sale (TPS) vs. Pre-foreclosure Sale (PFS), have been rare. We would like to ask the following questions barely answered in the literature: 1) what are the determinants of termination event selection, and 2) do these determinants have the same or different effects on different disposition approaches? Answering these questions has important meaning for the credit risk managements to both the mortgage investors and policy makers, given the fact that the value of mortgage debt outstanding is close to $10 trillion. We provide answers to the above specific questions by using the loss severity data sets published by Freddie Mac. When a mortgage goes more than four months delinquent, the GSEs will typically pay off the MBS investor by buying out the loan from the MBS pool. They would try different loss mitigation techniques, including repayment plan, loan modification, and property disposition. Once a defaulted loan is deemed irrecoverable, the GSEs allow several foreclosure alternative approaches to dispose a defaulted loan, including pre-foreclosure sales (also known as short sales ), and third party sales. We find that current loan-to-value ratio (CLTV), loan size, default duration episode and borrower s credit scores tend to have significant effects on the likelihood of foreclosure alternative event, and the LGD ratios. The results are robust after we carry out several sensitivity analyses. These findings provide innovative insight into the credit risk management for the government insured mortgage portfolios. We contribute to the study of LGD in the following aspects. First, we are the first to propose a comprehensive loss severity model framework to combine the loss event selection model with multiple loss rate models. Second, multiple housing market cycles from 2000 to 2013 are covered, and this is byfar the most complete period in LGD study. Third, we find distinctive drivers for the foreclosure alternative events, which has not been explicitly studied before. Our findings have several policy implications for credit risk management for mortgage lenders both in the U.S. and emerging economy. First, government agencies should be aware of loss mitigation management by GSEs and other private mortgage servicers. It turns out that the most interested determinants (CLTV, loan size, borrower s credit score and default duration) have similar effects across the different mortgage markets. Second, junior mortgages (younger than 60 months) tend to have quite different effects on LGD of REO sales. Being junior mortgages tend to lower LGD of the conforming mortgages but increase that of the FHA-insured ones, which implies that government agencies should be cautious about loss management for the defaulted mortgages with governmental support. Finally, as the residential mortgage market has been booming in Asian countries, this paper provides meaningful knowledge to housing financial institutions like China Development Bank and Korea Housing Finance Corp. The rest of the paper is organized as follows. In section 2, we review the literatures that discuss the LGD of residential mortgages. In section 3, we describe the model structure. In section 4, we introduce the loss 2

severity data sets. In section 5, we investigate the empirical model results of the multiple LGD models. In section 6, we provide further analysis about the policy implication. In section 6, we conclude. 2. Literature Review Loan characteristics and market friction have been found to have significant effect on LGD of conforming loans. In the options-based mortgage default model, Lekkas et al. (1993), and Quigley and Van Order (1995) emphasize the importance of adding friction of transaction cost in validating the LGD of mortgages from GSEs. After introducing transaction costs into analyzing the thrift mortgages, Crawford and Rosenblatt (1995) finds that OLTV, bankruptcy status, foreclosure period length, mortgage note rate, prevailing market mortgage rate, and deficiency judgment are all significant in explaining LGD. In analyzing the defaulted mortgages of high LTV, Qi and Yang (2009) finds that CLTV ratio is more significant than the OLTV ratio in explaining the LGD. They also notice that recent home price growth, loan size, property type, loan purpose, occupancy, loan age are important drivers for LGD. Zhang, Ji and Liu (2010) finds that housing price cycles before the time of mortgage origination has an impact on LGD of sub-prime residential mortgage. More recent studies also use mortgage data from GSEs to provide supporting evidences to the LGD analysis (Pennington-Cross (2003), Calem and LaCour-Little (2004)). However, few papers contribute to understanding default of FHA-insured mortgages. Among them, majority of related studies have been conducted to understand the default probability of FHA-insured loans (Ambrose and Capone (1998)) while fewer proceed to further understand these loans LGD. Clauretie and Herzog (1990) investigates the effect of state foreclosure laws on the LGD of private and government (FHA-insured) mortgages 1. They find that even though the different measurements of LGD are used, the estimated coefficients of interest have the same signs among two datasets. Previous literatures mainly investigate the determinants of LGD (loan loss severity, or loss rate) for conforming loans. The identified loan characteristics often includes three families: the first is a vector of the loan borrowers, for example, origination loan-to-value ratio (OLTV), CLTV, loan age, loan size, default duration episode, borrow credit score. The second is a vector of property characteristics, like whether property experienced refinance, owner occupied status of property, and unit number. The third family is a vector of neighborhood characteristics, including judicial and deficiency foreclosure procedures, local economy conditions and neighborhood housing price appreciations. Impact of state foreclosure laws indicates the necessity of adding the judicial foreclosure dummy and deficiency judgment dummy in the analysis 2. Due to the legislative regulations to different extent, we also use the foreclosure law index constructed by Curtis (2014) in the robustness analysis. Chen, Dai, and Yang (2014) provides a comprehensive LGD model for FHA insured mortgage REO terminations, and it includes the above mentioned characteristics. Since the onset of the subprime meltdown and the subsequent financial crisis, REO termination is wide recognized as the worst outcome of a default mortgage disposition. Much loss mitigation efforts have been promoted by the federal, state, and local governments. The efforts are generally combined with techniques from different agencies (Fannie Mae, Freddie Mac, FHA) to guide the lenders/servicers to help 1 Note that Clauretie and Herzog (1990) used the original loan value rather than the unpaid balance at default (UPB) to calculate the LGD of FHA data due to lack of UPB. However, they use the risk-in-force in calculating the LGD of private defaulted mortgages. 2 See Clauretie and Herzog (1990), 3

the homeowners avoid foreclosure, and reduce the credit loss amounts borne by these agencies, ultimately borne by the taxpayers. Among these policy/procedures, mortgage modification has been the focus point for academic study and research. Posner (2009) proposes a loan modification approach allowing homeowners to reduce principal value while giving mortgage holders an equity interest. Haughwout, Okah and Tracy (2009) examines how the structure of a mortgage modification affects the modified mortgage re-default probability. Goodman, et al. (2011) has identified the key ingredients of modification success: principal reduction, substantial pay relief and modifying early in the delinquency cycle. Chen, Xiang, and Yang (2014) provides a comprehensive study on the re-default behavior of FHA insured mortgage modifications, which suggests although moderate payment reduction induced by loan modifications can reduce re-default rate initially, excessive payment reduction actually will increase the re-default risks. If loan modification doesn t work, or the modified loan re-defaults, the mortgage loan is generally deemed as non-recoverable, and enters the disposition process. There are several approaches the servicers can take to mitigate the credit loss. A pre-foreclosure sale (PFS) could be applied if the home is sold while the borrowers still reside in the property, but the house sale price is lower than the outstanding balance (thus this type of transaction is generally referred as short sale ). Under this scenario, the borrower doesn t need to go through the foreclosure process, and his/her credit profile would not be damaged as much as a foreclosure sale. If the PFS cannot be completed successfully, the foreclosure process will ensue. A foreclosed property will be put on sale at the auction, either at the local auction place (sheriff s sale), or online (auction.com). If a third-party outbids the lender s reserve price, the property will be acquired by the third party, and the sale is completed as a third-party sale (TPS). If the auction is not successful, the property becomes realestate owned (REO) by the lender, and will be put on the market as an REO sale property. Figure 2-1 shows the complete cycle of a non-performing loan goes through and the alternative outcomes. 4

Performing Loan Early Delinquency (<=D60) Non- Recoverable Loan Success Early Collection Fail Serious Delinquency (>=D90) Pre- Foreclosure Sale Fail Success Success Repayment Plan Foreclosure Foreclosure Alternatives Fail Serious Delinquency (>=D90) Third Party Sale Success Success Loan Modification Fail Fail REO Sale Figure 2-1. Loss Mitigation Road Map for a Non-Performing Loan Contrary to ample research on loan modifications, there has been very rare academic research performed on foreclosure alternative outcomes, although FHA and FHFA have put a lot of emphasis on the success of these alternative disposition schemes. HUD updated the Pre-Foreclosure Sale and Deed in Lieu of Foreclosure requirements to promote the foreclosure alternatives 3. FHFA has also been updating the Non- Performing Loan Sale Guidelines to make sure REO is the last option in the waterfall. Our paper is the first to study the determinants of different drivers for the foreclosure alternative choices, as well as the first to develop an econometric model to estimate the loss rates for these foreclosure alternative outcomes. 3. Model Setup Ideally we would formulate our LGD model realistically to mimic the series of dichotomous choices mentioned above, as illustrated by Figure 3-1. Thus the overall loss rate will be calculated as: 3 Mortgagee Letter 2013-23: http://portal.hud.gov/hudportal/documents/huddoc?id=13-23ml.pdf 5

Non- Recoverable Loan PFS? PFS Prob LGD for PFS Termination Foreclosure Prob Foreclosure TPS? TPS Prob LGD for TPS Termination REO Prob LGD for REO Termination Figure 3-1. Ideal LGD Model Framework for Residential Mortgages Unfortunately due to the data limits 4, we do not have the PFS and TPS indicator from the loan level mortgage termination data. The data we collected only contains the indicator of REO and foreclosure alternative (F/A)), and the raw loss severity percentage, along with other loan level attributes. As a result, the ideal LGD model framework is modified as the following: Non- Recoverable Loan Foreclosure Alternative F/A Prob LGD for F/A Termination REO Prob LGD for REO Termination Figure 3-2. LGD Model Framework for Residential Mortgages 4 Freddie Mac only provides the combined foreclosure alternative indicator, which includes PFS, TPS, Deed-in-Lieu, etc. 6

And the loss rate is calculated as the following: For the F/A and REO probability, we use a logistic model, due to the dichotomous nature of the binary choice, as the following: ( ) However, once we get more granular indicator of the true disposition type, e.g. PFS and TPS, we can easily extend the above model and use a nested binary logistic model to estimate the corresponding probabilities. For the two loss rate models, we use OLS approach as the following: For both REO and F/A, The loss rate is defined as a percentage of loss amount over the unpaid principal balance. The loss amount above equals to unpaid principal balance plus interest lost plus expenses occurred minus the net sale proceeds. In the next section, we are going to introduce the raw data we collected from Freddie Mac, and the model variables we constructed for our modeling purpose. 4. Data Recently, Freddie Mac released loss severity data for FRM30 mortgage loans originated during the last 13 years. This dataset include both the gross loss severity (before private mortgage insurance, or PMI coverage), and net severity (after PMI coverage), and net severity after pool insurance. Combining this dataset with the previously released loan origination and performance datasets, researchers can gain unprecedented insights into the default and loss experience borne by the GSE mortgages. This addition of loan performance information is a welcome move among both the academic and industry researchers, as it is viewed as one step forward to make the credit risk transfer deals more transparent. Some industry publications, have analyzed the data, and provided some useful insights into this dataset. E.g., Goodman and Zhu (2005) has found that the PMI companies are providing valuable relief for the loss coverage 5. However, no vigorous econometric model has been made public on the drivers for the credit loss events, as well as the credit loss rates. 5 http://blog.metrotrends.org/2015/02/private-mortgage-insurance-expected-protecting-taxpayers-losses/ 7

Freddie Mac Raw Data Origination Performance Loss Event & Loss Amount LGD Model Estimation Data Set Unemployment Rate by MSA Merge by Month & MSA Interest/Mortgage Rates FHFA Home Price Index by MSA Merge by Month Merge by Month & MSA After we download the loss severity dataset, we merge it back to the loan origination dataset, together with other MSA level macroeconomic variables, such as house price indices (HPI), unemployment rates, and state level policy variables, such as judicial foreclosure indicator, deficiency judgment indicator, etc. For the observations with missing MSA, the merge is implemented at State level. Next we define the model variables and give the detailed descriptions. Current Loan-to-Value Ratio (ltv_current): This variable is calculated as the origination Loan-to- Value (OLTV), divided by the appreciation factor since origination (i.e., inflating or deflating the denominator, the house price), adjusted for amortization. Empirical results show that the mortgage default rate is very sensitive to the CLTV ratio, when the property value moves into the negative equity range (at a CLTV near to or greater than 100%). This empirical result is consistent with option theory, when the put/default option is in-the-money when the property is underwater, and the borrower would have a financial incentive to exercise this option. The CLTV variable is a more direct way to capture the borrower s incentive to default than is the probability of negative equity variable (PNEQ) used in prior Reviews. However, PNEQ is still included in the ARM current-to-prepay equation. In general, ARM transitions are more difficult to predict than FRM s. CLTV was used as a continuous variable for transitions to prepayment and to cure (both self and modifications), but to capture nonlinearities and because of thin data at high CLTVs, we otherwise used splines, and constrained the CLTV function at a fixed level for transitions to default and to claim (all such transitions except for FRM15, FRM SR and ARM SR, where one of the transitions current to default and default to claim was not capped). For example, we applied a piece-wise linear spline function for the default-to-claim transition for FRM30 loans with knots (the k s) of 0.6 and 1.0 and constrained the CLTV function at its value at knot 1.0 for CLTVs above 1.0. The spline function with two knots k 1 and k 2 is specified as follows, where cltv is the continuous CLTV variable: 8

cltv cltv1 k1 if if cltv k cltv k 1 1 cltv2 0 cltv - k k 2 - k1 1 if if if cltv k k 1 cltv k cltv k 1 2 2 cltv3 0 cltv - k 2 if if cltv k cltv k 2 2 Coefficient estimates for each variable are the incremental slopes of the line segments between each knot point. They were estimated for each product and transition type combination, except for the exceptions noted above that use the linear form. The overall generic CLTV function for the 3-cltv segment example is given by: CLTV Function cltv1 2 cltv2 3 1 This function is estimated as a set of three variables in each binomial equation. For those cases where we capped the effect of CLTV at high levels (above the last knot point), we set the estimate of β 3 to zero. cltv3 Relative Loan Size (loansize): This variable is proxied by the mortgage origination amount divided by the average loan origination amount in the same state for the same fiscal year. It replaces the relative house price variable used in previous Reviews. Empirical results show this variable is very significant in prepayment-related termination. This is consistent with option theory, since loans with higher loan size could achieve higher monetary savings, given the same relative mortgage spread. House Price Appreciation (hpat2y): The home price enters the model via two variables, each of which has a different interpretation. Home price appreciation since origination (at the metro/non-metro area level) determines the CLTV ratio, which is used to measure the current equity in the property. Short-term house price appreciation, which proxies for people s expectation of future house price movements, is also used. The rationale for this variable is that borrowers make their decisions not only on the realized historical information, but also on their expectation about future house price appreciation. Short-term home price appreciation, HPA2y(t), is calculated as the projected house price index at the termination date, HPI(t), divided by historical house price index two year ago, HPI(t-24), measured at both the state level and at the Metropolitan Statistical Area (MSA) level, HPI(i): ( ) ( ) ( ) 9

When historical observations are used to estimate the transition equations, actual four-quarter-ahead observations are used to measure this variable. For simulations along future HPA/interest rate paths, the same measurement is made, using the projected HPAs four-quarters ahead. Loan Age (loan_age): This is the mortgage loan age measured in months. Duration of Default Episode (dur_def_episode): This is the length of the period the mortgage loan has stayed in delinquency, measured in months. Borrower Credit Score (fico): This the primary borrower s credit score. Mortgage Rate Spread (mr_sprd): This the spread between prevailing mortgage rate and the 10-year treasury rate. House Price Volatility (sigma_parm_a): Option theory predicts that the put (default) option value increases when the volatility of the collateral increases, everything else equal. Empirical results show the marginal effect of home price volatility on default behavior is generally positive, which is consistent with option theory. An easier way to interpret this phenomenon is that the home price volatility measures our uncertainty in calculating the updated property value; higher volatility would introduce more error on both positive and negative sides. However, the loss introduced on the negative side is not compensated by the gain on the positive side, due to the asymmetric nature of mortgage credit risk. The home price volatility is the same as the measurement of parameters a calculated in the Probability of Negative Equity, which indicates uncertainty with regard to the dispersion of individual house price appreciation rates around the market average, represented by the local-level HPI. The parameter a is estimated by FHFA when applying the three-stage weighted-repeat-sales methodology advanced by Case-Shiller (1987, 1989). Judicial Foreclosure State Indicator (judicial): Judicial state indicators are defined as the following: if the collateral property is in a judicial state, the indicator is equal to 1, otherwise it equals zero. Deficiency Judgment State Indicator (deficiency): Deficiency judgment state indicators are defined as the following: if the collateral property is in a deficiency judgment state where the lender has the right to go after the borrower s other assets and future income, even after the foreclosure, the indicator is equal to 1, otherwise it equals zero. Refinance Loan Indicator (refinance): This is the indicator whether the mortgage loan is originated as a refinance loan, instead of a purchase money mortgage. 2-4 Units Indicator (flag_24): This is the indicator that the underlying property is a 2-4 unit house. Non-Owner Occupancy Indicator (noowner_occ): This is the indicator that the underlying property is not an owner-occupied housing unit. Condo Property Indicator (condo): This is the indicator that the underlying property is a condo unit. Manufactured Housing Property Indicator (M_H): This is the indicator that the underlying property is a manufactured housing unit. 10

Planned Unit Development Property Indicator (PUD): This is the indicator that the underlying property is a PUD unit. The following table gives the summary statistics for Freddie Mac F/A dispositions: Variable N Mean Std Dev Median Minimum Maximum Lower Quartile Upper Quartile ltv_current 130,055 1.016 0.305 0.970 0.000 2.508 0.804 1.215 loansize 130,055 105.217 42.823 100.352 4.795 377.920 74.180 131.457 hpat2y 130,055-0.058 0.155-0.054-0.715 0.520-0.137 0.038 loan_age 130,055 60 24 59 8 171 43 75 dur_def_episode 130,055 5 3 4 1 34 3 6 fico 130,055 702 54 702 301 850 663 744 mr_sprd 130,055 1.711 0.254 1.672 1.264 2.658 1.540 1.918 sigma_parm_a 130,055 0.001 0.000 0.001 0.001 0.003 0.001 0.002 judicial 130,055 0.379 0.485 0 0 1 0 1 deficiency 130,055 0.716 0.451 1 0 1 0 1 refinance 130,055 0.593 0.491 1 0 1 0 1 flag_24 130,055 0.022 0.146 0 0 1 0 0 noowner_occ 130,055 0.118 0.323 0 0 1 0 0 Condo 130,055 0.113 0.316 0 0 1 0 0 M_H 130,055 0.009 0.094 0 0 1 0 0 PUD 130,055 0.189 0.392 0 0 1 0 0 The following table gives the summary statistics for Freddie Mac REO dispositions: Variable N Mean Std Dev Median Minimum Maximum Lower Quartile Upper Quartile ltv_current 242,091 0.915 0.258 0.864 0.022 2.736 0.742 1.033 loansize 242,091 88.941 41.731 81.020 6.888 451.191 58.606 111.055 11

hpat2y 242,091-0.047 0.142-0.040-0.715 0.519-0.115 0.050 loan_age 242,091 53 26 49 7 167 33 69 dur_def_episode 242,091 7 3 6 1 44 5 8 sigma_parm_a 242,091 0.001 0.000 0.001 0.001 0.003 0.001 0.002 rel_ue 242,091 1.073 0.250 1.063 0.329 3.939 0.878 1.233 fico 242,091 683 54 680 318 850 645 720 judicial 242,091 0.358 0.479 0 0 1 0 1 deficiency 242,091 0.833 0.373 1 0 1 1 1 refinance 242,091 0.603 0.489 1 0 1 0 1 flag_24 242,091 0.022 0.145 0 0 1 0 0 noowner_occ 242,091 0.121 0.326 0 0 1 0 0 Condo 242,091 0.074 0.261 0 0 1 0 0 M_H 242,091 0.023 0.150 0 0 1 0 0 PUD 242,091 0.106 0.307 0 0 1 0 0 5. Empirical Results In this section, we present the regression results for the three sub-models in this LGD model framework. 5.1 Foreclosure Alternative Selection Model Result The following table shows the logistic model results for the Foreclosure Alternative selection model. 12

Analysis of Maximum Likelihood Estimates Parameter DF Estimate Standard Error Wald Chi-Square Pr > ChiSq Intercept 1 10.3021 0.6559 246.6861 <.0001 ltv_current1 1-6.6617 0.1598 1737.5303 <.0001 ltv_current2 1 2.3841 0.0276 7467.1932 <.0001 ltv_current3 1-0.0553 0.0542 1.0421 0.3073 loansize1 1-0.00201 0.00192 1.0917 0.2961 loansize2 1 0.0133 0.000156 7298.2559 <.0001 loansize3 1 0.000660 0.000362 3.3267 0.0682 hpa_lag_2y1 1 6.7222 0.2287 864.2414 <.0001 hpa_lag_2y2 1 0.9618 0.0588 267.6012 <.0001 hpa_lag_2y3 1 1.6152 0.0708 521.0525 <.0001 loan_age1 1 0.0321 0.000266 14599.4351 <.0001 loan_age2 1 0.00431 0.000481 80.4080 <.0001 dur_def_episode1 1-0.3967 0.00154 66016.7911 <.0001 dur_def_episode2 1-0.0133 0.000695 365.1781 <.0001 prior_mod 1-0.2430 0.0167 213.0133 <.0001 fico1 1-0.00337 0.00111 9.2423 0.0024 fico2 1 0.00218 0.000212 105.6831 <.0001 fico3 1 0.00330 0.000142 540.5328 <.0001 fico000 1-0.7717 0.0928 69.1339 <.0001 judicial 1 1.5889 0.0116 18697.7366 <.0001 deficiency 1-1.4265 0.0129 12298.2073 <.0001 noowner_occ 1 0.1484 0.0138 115.4664 <.0001 Condo 1 0.2776 0.0153 328.3264 <.0001 13

Analysis of Maximum Likelihood Estimates Parameter DF Estimate Standard Error Wald Chi-Square Pr > ChiSq M_H 1-0.8784 0.0399 485.4880 <.0001 PUD 1 0.3468 0.0130 716.9268 <.0001 As the result suggests, increase in the following variables make the defaulted mortgage loans more likely to be terminated via foreclosure alternatives: TPS or PFS. Current LTV: Generally speaking, the higher the CLTV, the higher the loss rate. Thus spending time on high CLTV loans is likely to reward the lender/servicer more reduction in the loss severity. Also for deep underwater loans, the lender/servicer is more willing to accept a discounted price, compared to listing prices, which can effectively reduce the probability of REO. Loan Size: Given the same CLTV, larger loans size generally means potentially bigger amount of dollar loss. Thus it is not surprising that lender/servicer will put more effort into loans with higher balance and wish to reduce the loss amount via foreclosure alternatives. HPA: Because both TPS and PFS requires potential buyers to bid on these properties, it is not surprising that when the housing price is increasing, more interested buyers will bid on the property, and likely increase their bids during competition, which would effectively increase the success probability of foreclosure alternatives. Credit Score: PFS generally requires cooperation from the borrowers, since they would still live in the property, while it is listed as Short Sale. This type of transaction will not be reported as foreclosure in their credit records. For people with higher credit scores, they would value this foreclosure alternative more valuable, compared to borrowers with lower credit scores. Thus high FICO borrowers are more likely to end up with a foreclosure alternative transaction. Loan Age: As the GSE loans generally start with some amount of positive equity, new loans are unlikely to have very high CLTV, thus new loans are more likely to be selected for REO. For the following variables, increasing their value will make the defaulted mortgage loans less likely to be processed via foreclosure alternatives. Duration default episode: The longer a defaulted loan stays as delinquent, and doesn t cure implies that there could have been some loss mitigation already tested but have little effect. For example, probably a loan defaulted for 9 months might have been listed as Short Sale from month 3, but due to lack of buyer interest, the property is not sold under the foreclosure alternative. Thus these loans are more likely to end up in the lender/servicer s REO inventory. 5.2 REO Loss Rate Model Result The following table gives the LGD model coefficients for REO termination. 14

Variable DF Parameter Estimate Parameter Estimates Standard Error t Value Pr > t Intercept 1 0.45978 0.02783 16.52 <.0001 ltv_current1 1 0.83618 0.04816 17.36 <.0001 ltv_current2 1 0.72466 0.00425 170.66 <.0001 ltv_current3 1 0.25136 0.00507 49.62 <.0001 ltv_current4 1 0.24162 0.06413 3.77 0.0002 loansize1 1-0.00810 0.00011500-70.44 <.0001 loansize2 1-0.00462 0.00003696-124.94 <.0001 loansize3 1-0.00062125 0.00002887-21.52 <.0001 hpa_t2y1 1 0.14979 0.00994 15.07 <.0001 hpa_t2y2 1-0.25792 0.01109-23.26 <.0001 loan_age1 1-0.00107 0.00004214-25.49 <.0001 loan_age2 1 0.00221 0.00005395 41.04 <.0001 loan_age3 1 0.00520 0.00015071 34.54 <.0001 dur_def_episode1 1 0.04056 0.00065487 61.94 <.0001 dur_def_episode2 1 0.02820 0.00029961 94.11 <.0001 dur_def_episode3 1 0.02569 0.00151 17.02 <.0001 sigma_parm_a 1 6.60105 1.99696 3.31 0.0009 rel_ue 1 0.06210 0.00220 28.17 <.0001 fico1 1-0.00058777 0.00002043-28.77 <.0001 fico2 1-0.00024611 0.00001803-13.65 <.0001 fico000 1 0.10044 0.00849 11.83 <.0001 judicial 1 0.05302 0.00126 42.13 <.0001 deficiency 1 0.07847 0.00158 49.76 <.0001 refinance 1 0.07118 0.00112 63.80 <.0001 flag_24 1 0.16690 0.00363 46.04 <.0001 noowner_occ 1 0.09540 0.00167 57.07 <.0001 Condo 1-0.01643 0.00204-8.05 <.0001 M_H 1 0.07277 0.00347 20.94 <.0001 PUD 1-0.07874 0.00177-44.42 <.0001 15

As we can see in the table, increase in the following variables increase the loss severity rates: Current LTV: The higher the CLTV, the deeper a loan is underwater, the property will be mostly likely sold at a discounted price substantially lower than the loan value. The low net sale proceeds would lead to high loss amount, thus high loss rate. Loan Age: The larger the loan age, the lower the unpaid balance is. The impact is generally on the denominator of the loss rate calculation. Duration default episode: The longer a defaulted loan stays in delinquency, the higher the interest lost is. Additionally, the property will more likely to be damaged and sold at a lower price. Both would lead to higher loss amount. sigma_parm_a: The cross-section house price volatility is an indicator or the stability of a local housing market. Therefore, the higher the instability is, the higher the loss amount could be. rel_ue: the relative local unemployment rate is a macro economy indicator. The higher the unemployment rate is, the worse the economy is. Thus, the loss rate is more like to be higher with higher unemployment rate. Miscellaneous: there are also some categorical variable that would lead to higher loss rate, such as missing fico score, refinance, indicator for the number of units, etc. The loss rates change in the opposite direction with the following variables: Credit Score: Higher credit score borrowers typically have less severe delinquency status compared to the borrowers with lower score; thus the loss amount could be lower. Loan Size: The relative loan size variable used in the regression is defined as the relative size compared to the state-level average size originated in the same year. Typically, the servicer would allocate more effort in selling the larger-size properties to avoid higher amount of loss. HPA: When the housing appreciation rate is above zero, the higher the HPA, the lower the loss rate. Since the property will more likely to be sold at a higher price in a market with higher housing price appreciation rate. 5.3 Foreclosure Alternative LGD Model Result The following table gives the LGD model coefficients for terminations other than REO. 16

Variable DF Parameter Estimates Parameter Estimate Standard Error t Value Pr > t Intercept 1-0.24006 0.16091-1.49 0.1357 ltv_current1 1 0.83174 0.00811 102.57 <.0001 ltv_current2 1 0.31136 0.00597 52.13 <.0001 loansize1 1-0.00527 0.00007667-68.76 <.0001 loansize2 1-0.00101 0.00005753-17.60 <.0001 hpat2y 1-0.12610 0.00720-17.52 <.0001 loan_age1 1 0.00158 0.00009369 16.87 <.0001 loan_age2 1 0.00074249 0.00008323 8.92 <.0001 loan_age3 1 0.00356 0.00047374 7.52 <.0001 dur_def_episode1 1 0.03690 0.00072817 50.68 <.0001 dur_def_episode2 1 0.03169 0.00070655 44.85 <.0001 dur_def_episode3 1 0.03178 0.00385 8.26 <.0001 sigma_parm_a 1 32.05180 3.38893 9.46 <.0001 fico1 1 0.00003414 0.00027855 0.12 0.9025 fico2 1-0.00009989 0.00003910-2.55 0.0106 fico3 1 0.00002669 0.00003686 0.72 0.4689 mr_sprd 1-0.02531 0.00384-6.60 <.0001 fico000 1-0.05208 0.02420-2.15 0.0314 judicial 1 0.00651 0.00243 2.68 0.0073 deficiency 1 0.06246 0.00268 23.34 <.0001 refinance 1 0.06269 0.00208 30.21 <.0001 flag_24 1 0.16010 0.00677 23.66 <.0001 noowner_occ 1 0.08737 0.00315 27.76 <.0001 Condo 1 0.01664 0.00322 5.17 <.0001 M_H 1 0.03378 0.01039 3.25 0.0011 PUD 1-0.04929 0.00266-18.55 <.0001 Generally, the variables have similar impact on the loss rate of F/A to that on the loss rate of REO. In summary, higher CLTV, loan age, default episode will lead to higher loss rate while higher loan size, fico score and HPA will decrease the loss rate. The variable mortgage rate and 10-year Treasury rate spread has negative correlation with loss rate since higher spread suggests a growing economy. 17

6. Model Robustness In order to examine the model robustness, we list the model fit chart below for the three sub-models. The model fit charts examine the deviation of model prediction to actual observation along major model dimensions, and serve the purpose to identify model biases. 6.1 Model Fit of Foreclosure Alternative Selection Model The following six charts illustrate the model fit of the foreclosure alternative selection model. The blue line is the model prediction of foreclosure alternative probability, and the red line is the actual probability observation. The black line is the number of observations in the estimation sample along the variable of the interest. We list the model fit, with respect to six major continuous model variables: current LTV, relative loan size, 2-year HPA, loan age, duration default episode, and borrower credit score. Figure 6-1A. Model Fit: Foreclosure Alternative Probability against Current LTV 18

Figure 6-1B. Model Fit: Foreclosure Alternative Probability against Relative Loan Size Figure 6-1C. Model Fit: Foreclosure Alternative Probability against 2-Year HPA 19

Figure 6-1D. Model Fit: Foreclosure Alternative Probability against Loan Age Figure 6-1E. Model Fit: Foreclosure Alternative Probability against Duration Default Episode 20

Figure 6-1F. Model Fit: Foreclosure Alternative Probability against Borrower Credit Score 6.2 Model Fit of REO LGD Model The following six charts illustrate the model fit of the REO LGD model. The blue line is the model prediction of REO LGD as percentage, and the red line is the actual REO loss rate. The black line is the number of observations in the estimation sample along the variable of the interest. We list the model fit, with respect to six major continuous model variables: current LTV, relative loan size, 2-year HPA, loan age, duration default episode, and borrower credit score. 21

Figure 6-2A. Model Fit: REO LGD against Current LTV Figure 6-2B. Model Fit: REO LGD against Relative Loan Size 22

Figure 6-2C. Model Fit: REO LGD against 2-Year HPA Figure 6-2D. Model Fit: REO LGD against Loan Age 23

Figure 6-2E. Model Fit: REO LGD against Duration Default Episode Figure 6-2F. Model Fit: REO LGD against Borrower Credit Score 24

6.3 Model Fit of Foreclosure Alternative LGD Model The following six charts illustrate the model fit of the foreclosure alternative LGD model. The blue line is the model prediction of foreclosure alternative LGD as percentage, and the red line is the actual foreclosure alternative loss rate. The black line is the number of observations in the estimation sample along the variable of the interest. We list the model fit, with respect to six major continuous model variables: current LTV, relative loan size, 2-year HPA, loan age, duration default episode, and borrower credit score. Figure 6-3A. Model Fit: Foreclosure Alternative LGD against Current LTV 25

Figure 6-3B. Model Fit: Foreclosure Alternative LGD against Relative Loan Size Figure 6-3C. Model Fit: Foreclosure Alternative LGD against 2-Year HPA 26

Figure 6-3D. Model Fit: Foreclosure Alternative LGD against Loan Age Figure 6-3E. Model Fit: Foreclosure Alternative LGD against Duration Default Episode 27

Figure 6-3F. Model Fit: Foreclosure Alternative LGD against Borrower Credit Score 7. Policy Implication The policy implication of our research is at least three-fold: optimal loss mitigation strategy; accurate pricing of GSE risk transfer deals; and guidance on other government insurance programs. As we have illustrated in Figure 1, the loss mitigation procedure is generally a very lengthy and complicated process. A lot of the times, it is guided by business rules, instead of analytical models. Our research has shed light on the selection process of this process. Some of the loan attributes will help improve the chances a defaulted loan will end up in foreclosure alternatives, instead of REO, which is lengthy, costly, and detrimental to the borrower s credit profile. As a rule of thumb, PFS is always preferred than foreclosure. With foreclosure, TPS is generally preferred than REO. Our foreclosure alternative selection model has shown that the selection is mainly driven by dynamic variables, such as current LTV, duration default episode, loan age, and some macroeconomic variables, such as recent house price appreciation, local unemployment rate, etc. However, some of the variables are static loan attributes, such as relative loan size, and borrower credit score. Some of these impacts are likely driven by the lender/servicer, such as those loans with higher relative loan size, and/or current LTV would benefit more from foreclosure alternative; yet some of these impacts are likely driven by the borrowers, such as the 28

high FICO borrowers would try harder to avoid foreclosure. With this insight, the lender/servicer can actually target more accurately on the defaulted loans which are more likely to succeed with these loss mitigation strategies, and improve the bottom line. Also by applying the REO and Foreclosure Alternative LGD models, the lender/servicer can calculate the opportunity cost if a defaulted loan slip into REO from PFS, and back out the break-even PFS discount. Another important application for this new LGD model framework is the accurate pricing of GSE credit risk transfer deals. The federal government has repeatedly asked the two GSEs to shrink their portfolio size, and let the private sector take more exposure in the credit risk market of the housing finance sector. One approach is to issue new bonds (Structured Agency Credit Risk, or STACR by Freddie Mac; and Connecticut Avenue Securities, or CAS by Fannie Mae) that sells off some of the default risk of their residential mortgage holdings to private investors willing to gamble on its pool of loans. Although there are some appetites from the private investors, the demand for these bonds is far from enthusiastic. Part of the lukewarm reception is that the private sector lacks reliable loss severity data to accurately price these deals. With our comprehensive LGD model framework, the investors will be able to combine it with the PD model and accurately estimate the expected credit loss and its distribution under wide range of economic scenario. This will allow more transparent information sharing among different investors and promote a more liquid market for these new bonds. The federal government has other similar residential mortgage loan insurance programs, among which the most influential programs are the FHA Mutual Mortgage Insurance and VA loan guarantee programs. FHA has taken very similar steps as the GSEs to conduct loss mitigation procedures, such as loan modification, PFS, TPS, note sale, etc. The models derived from Freddie Mac loss data can be applied with relative ease on the FHA loss mitigation programs. Our preliminary research results have shown that Freddie Mac and FHA loans share very similar relationships, regarding the foreclosure alternative selection, as well as the REO, PFS, TPS loss rates. Given the fact that the loss mitigation strategies for defaulted loans are mainly driven by lender/servicers, and loan origination channel are of less importance once a loan becomes serious delinquent, our models can be extended to other government mortgage loan guarantee programs, such as VA loans, Farmer Mac loans, etc. 8. Conclusion We derived a set of equations linking the loss rate of Freddie Mac guaranteed defaulted loans that ended up in REO sales and other foreclosure alternatives (PFS and TPS) to various loan characteristics, durations, housing market conditions and borrower's characteristics as proxy for borrower behaviors. We use a large sample of property sales to test the hypotheses. We have made significant contributions to the study of LGD. First, we are the first to propose a comprehensive loss severity model framework to combine the loss event selection model with multiple loss rate models. Second, multiple housing market cycles from 2000 to 2013 are covered, and this is by-far the most complete period in LGD study. Third, we find distinctive drivers for the foreclosure alternative events, which has not been explicitly studied before. 29

For the loss event selection model, current LTV, relative loan size, 2-year HPA, loan age, and borrower credit score all seem to increase the likelihood of foreclosure alternatives, while duration default episode is the only major variable that reduces the foreclosure alternative probability. Regarding the LGD loss rate models, the evidence herein suggests that current LTV, relative loan size, loan age, recent 2-year HPA, duration default episode, and borrowers credit score are the major factors driving the loss behavior of defaulted loans insured by the GSEs. The coefficients on those predictors from the regression estimate are consistent with previous LGD studies. Current LTV, loan age, REO and default duration are positively correlated with loss rate. Higher current LTV at time of claim, older loan, and longer time in default episode will lead to more severe loss rate. On the other hand, relative loan size, HPA and borrower credit score demonstrate a negative relationship with loss rate. 30

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