Decomposing Mortgage Portfolio Risk: Default, Prepayment, and Severity YUFENG DING

Transcription

1 Decomposing Mortgage Portfolio Risk: Default, Prepayment, and Severity YUFENG DING NOVEMBER 19, 2010

2 Overview» The loss on a mortgage portfolio is an aggregate of the losses of the loans in the portfolio» The loan behaviors that have direct impacts on loan losses: A loss may occur if a loan defaults. The magnitude is determined by severity, or loss-givendefault of the loan. If a loan prepays, there will be no loss on this loan. Statistically, higher prepayment probability reduces the chance for a loan to default.» Default, prepayment and severity are all affected by loan and borrower characteristics and macro economic factors. A factor may have an intuitive relationship with the individual behaviors, but not necessarily so with loan loss.» MPA integrates the individual models through their dependence on common (especially economic) factors in a quasi-structural way to generate the loan level losses in a natural way. This correlates the loans in a natural way.» Loan level losses are then aggregated to get the pool level losses. Decomposition simplifies complicated processes. Re-integration gets it back to the complex real world. 2

3 Mortgage Modeling: Overview II Output FACTORS MODELS Economic Data (simulated or scenario) Loan Level Pool Data (User data) Supplemental user data (loan level override, pool performance, etc.) Default Severity Prepayment Loan Level E(L) Σ Pool Level E(L) 3

4 Agenda 1. Building the component models» Default / Prepayment models» Severity model 2. Simulating macro economic factors 3. Putting it altogether: Mortgage Portfolio Analyzer 4. Conclusion 4

5 1. Building the component models» Default / Prepayment models 1» Severity model 2. Simulating macro economic factors 3. Putting it altogether: Mortgage Portfolio Analyzer 4. Conclusion 5

6 Default/Prepayment models: Cox regression» Default/Prepayment: Cox Proportional Hazard Model is a natural choice. Both default and prepayment are discrete events. Both are affected by many factors (macro economic factors, loan characteristics and etc.). Both are affected by seasoning (age) of the loan in a highly non-linear way.» Cox Proportional Hazard Model h i (t) = h 0 (t) e β x In the equation, i indicates i th loan. t indicates loan age. h i (t) is the hazard rate we want to estimate. More specifically, it is the probability of i th loan to default or prepay conditional on that it has survived till time t. h 0 (t) is the baseline hazard of all loans (of the same type) on average. It is a non-parametric function of t and captures differences in loan behavior throughout a loan s life. The β x i in the exponential term is the regression component. It, as in any other regression, estimates the β coefficients for the factors. Cox model offers both flexibility and interpretability. 6

7 Default/Prepayment models: Example of baselines Prepayment Baseline ARM 2/28 Prepayment Baseline ARM 3/ Loan Age (months) Loan Age (months) 7

8 Default/Prepayment models: Variable selection» Common sense/economic theory» Statistical robustness The coefficient of a factor should reflect economic reasoning, with correct direction (sign) and magnitude. A factor should not be highly correlated with other factors in the model.» Practical implementation A factor should be readily available. A factor should be defined relatively unambiguously.» Uni-variate / multi-variate analysis This provides a direct view of the relationship between the factors and the hazard rate 8

9 Default/Prepayment models: Uni-variate analysis 9

10 Default/Prepayment models: Multi-variate interactions Model factors are carefully selected and tested. 10

11 Default model: Key factors (see Whitepaper for the complete list and more detailed discussions) FICO: The higher the FICO, the better the borrower quality and the lower the default rate Mortgage Premium at Origination: The higher the mortgage premium at origination, the lower the borrower quality and the higher the default rate Change in Mortgage Premium: As mortgage premium gets higher, a borrower becomes worse off and thus the default rate gets higher. Updated Loan-to-Value: Higher values of the updated LTV imply lower equity in the home and thus reduced aversion to defaulting, i.e. higher default rate. Loan Type: ARM loans may be exposed to rate/payment shock and thus suffer a higher default rate. Many factors are explicitly related to macro economic factors. 11

12 Default model: Validation with real economy I Observable economic factors facilitate detailed validation. 12

13 Default model: Validation with real economy II Caveat: Not all extreme events are captured in the model. 13

14 Prepayment model: Key factors (see Whitepaper for the complete list and more detailed discussions) FICO: Higher FICO borrowers are more likely to find a more attractive refinancing terms and thus are more likely to prepay. Loan-to-Value: The higher the LTV, the less equity a borrower has in the house and the less flexibility he has in refinancing or selling the property. Home Price Change: Home price is positively related to the borrower s equity and thus positively related to the prepayment rate. Mortgage Premium at Origination: Higher mortgage premium means high incentive for the borrower to prepay. Credit curing may be another reason. Change in Mortgage Premium: A positive change means either a drop in the market rate or an increase in the loan rate, both lead to higher propensity to prepay. Prepayment Penalty Clauses: This increases the cost to refinance and thus reduces the prepayment rate. Burnout Effect: A borrower who missed past opportunities is more likely to miss future opportunities as well. Many factors are macro economy related and common to the ones in default model. 14

16 Severity model: Beta distribution» Distribution of loan severity: Beta distribution by observation Bounded Skewed 16

17 Severity model: Methodology and key factors» Two step approach Beta distributed severities are first transformed into a standard normal distribution A regression model is built in the Gaussian space Predicted values in the Gaussian space are then transformed back into the severity space» Some key factors (see Whitepaper for a more detailed discussions Judicial Regulation: Many states have regulations that make it harder to liquidate a property and thus severity tend to be higher in these states. Forward Loan-to-Value: The recovery is only made when a property is liquidated. As liquidation takes time, recovery usually happens months after default. Loan Amount: Smaller loans tend to suffer higher percentage losses as fixed costs constitute a bigger percentage of total cost and thus less incentive for the lender to pursue recover. Mortgage Premium: Higher mortgage premium leads to lower principle payment and also indicates a lower borrower quality. Both lead to higher severity. Again, many factors are macro economy related and common to the ones in default and prepayment models. 17

19 Simulating macro economic factors The key economic processes that are simulated in the model are: Interest rates (10-year CMT & 6-month LIBOR) Home Price Change (national, state, and MSA level) Unemployment rates (national, state, and MSA level) Loan market rates (Freddie Mac (FHLMC) mortgage rate or subprime market rate) Explanation of modeling process - Auto Regressive processes are used to model changes in the unemployment rate and the log of the home price index at the national level. Subsequently the unemployment rate and home price index at the state and MSA level are modeled using the results at the national level, plus their own lags. These macro factors are correlated through common dependence on interest rates and, in the case of the local economic factors, on the national levels of unemployment and home prices, respectively. 19

21 Putting it altogether: Mortgage Portfolio Analyzer Integrating the component models along each simulated economic path 21

22 The result: Loss distribution an example In addition to generating the full loss distribution, it is possible to estimate losses under MEDC or user-defined scenarios. 22

23 The result: Losses economic sensitivities Observable macro-economic factors facilitate insightful what-ifs. 23

24 LOAN # 40 LOAN # loan= 40 ; econ= 882 loan= 40 ; econ= 883 loan= 40 ; econ= 884 loan= 40 ; econ= Decomposing Mortgage Portfolio Risk: Default, Prepayment, and Severity - Nov loan= 40 ; econ= 886 loan= 40 ; econ= 887 loan= 40 ; econ= 888 loan= 40 ; econ= loan= 98 ; econ= loan= 98 ; econ= 883 Same loans in different economies exhibits different behavior and may be correlated differently loan= 98 ; econ= loan= 98 ; econ= loan= 98 ; econ= 886 loan= 98 ; econ= 887 loan= 98 ; econ= 888 loan= 98 ; econ= The result: Impact of economies on individual loans

26 Conclusion» Decomposing the mortgage portfolio risk into separate models helps to break down complicated processes into more tractable pieces.» The component models offer both flexibility and interpretability.» The explicit use of the macro factors facilitates validation, calibration, scenario analysis and sensitivity analysis.» The integration of the component models, through their dependence on common factors, reproduces the complexity in real world. 26

27 2010 Moody s Research Labs, Inc. and/or its licensors and affiliates (collectively, MOODY S ). All rights reserved. ALL INFORMATION CONTAINED HEREIN IS PROTECTED BY COPYRIGHT LAW AND NONE OF SUCH INFORMATION MAY BE COPIED OR OTHERWISE REPRODUCED, REPACKAGED, FURTHER TRANSMITTED, TRANSFERRED, DISSEMINATED, REDISTRIBUTED OR RESOLD, OR STORED FOR SUBSEQUENT USE FOR ANY SUCH PURPOSE, IN WHOLE OR IN PART, IN ANY FORM OR MANNER OR BY ANY MEANS WHATSOEVER, BY ANY PERSON WITHOUT MOODY S PRIOR WRITTEN CONSENT. All information contained herein is obtained by MOODY S from sources believed by it to be accurate and reliable. Because of the possibility of human or mechanical error as well as other factors, however, all information contained herein is provided AS IS without warranty of any kind. Under no circumstances shall MOODY S have any liability to any person or entity for (a) any loss or damage in whole or in part caused by, resulting from, or relating to, any error (negligent or otherwise) or other circumstance or contingency within or outside the control of MOODY S or any of its directors, officers, employees or agents in connection with the procurement, collection, compilation, analysis, interpretation, communication, publication or delivery of any such information, or (b) any direct, indirect, special, consequential, compensatory or incidental damages whatsoever (including without limitation, lost profits), even if MOODY S is advised in advance of the possibility of such damages, resulting from the use of or inability to use, any such information. The ratings, financial reporting analysis, projections, and other observations, if any, constituting part of the information contained herein are, and must be construed solely as, statements of opinion and not statements of fact or recommendations to purchase, sell or hold any securities. NO WARRANTY, EXPRESS OR IMPLIED, AS TO THE ACCURACY, TIMELINESS, COMPLETENESS, MERCHANTABILITY OR FITNESS FOR ANY PARTICULAR PURPOSE OF ANY SUCH RATING OR OTHER OPINION OR INFORMATION IS GIVEN OR MADE BY MOODY S IN ANY FORM OR MANNER WHATSOEVER. Each rating or other opinion must be weighed solely as one factor in any investment decision made by or on behalf of any user of the information contained herein, and each such user must accordingly make its own study and evaluation of each security and of each issuer and guarantor of, and each provider of credit support for, each security that it may consider purchasing, holding, or selling. 27