MORTGAGE LENDING The Competing Risks Framework for Mortgages: Modeling the Interaction of Prepayment and Default by Arden Hall and Kyle G. Lundstedt his article discusses how prepayment and default constitute competing risks in mortgage lending, provides Texamples of the importance of using a combined approach when evaluating the risk of whole loans and MBS, and concludes with practical implications of using the competing risks framework. hough it may seem apt, Inside Mortgage Finance (IMF, June tions. The IMF estimated that the phrase “competing 10, 2005) noted the following fact: the 50 largest financial services Trisks” in the title of this “During the first three months of holding companies held a com- article does not refer to the annual the year, non-prime lenders bined $1.01 trillion in whole loans budget battle between various churned out an estimated $184 bil- during that same first quarter of risk management functions within lion in new loans. Putting that into 2005. Moreover, according to large financial institutions. Rather, perspective, more than one out of Inside MBS & ABS (July 17, 2005), it is a framework for modeling the every four loans—or 28.5%—of all a weekly newsletter published by impact of separate causes for attri- new mortgages made during the the IMF, Fannie Mae and Freddie tion. In the mortgage world, these first quarter of the year went to Mac bought $212 billion in non- are the separate, but interdepen- borrowers in the subprime and Alt conforming MBS during 2004, dent, risks of prepayment and A categories.” Moreover, SMR assuming much of the credit risk default. For prime mortgages Research Corporation estimates for the underlying mortgages.1 (whole loans) and for mortgage- over $700 billion in junior liens Thus, the increasing credit risk in backed securities (MBS), prepay- outstanding at the end of 2004 the system is held by a large num- ment risk has long dominated the (Home Equity Loans: 2005 Outlook). ber of institutions, and even the issue of credit risk. Historically, in Therefore, loans with greater credit GSEs now must learn to assess the secondary market, the three risk represent a significant and the greater credit risk from non- government-sponsored enterprises increasing portion of the primary conforming products. (GSEs) guaranteed the credit risk mortgage market. These recent developments of most conforming mortgage A large number of these increase the importance of default loans, which represented the bulk loans, and the associated credit risk vis-à-vis prepayment risk for of the primary market. risk, are held on the balance mortgage lenders, whether they However, a recent issue of sheets of large financial institu- are portfolio lenders or buyers of © 2005 by RMA. Arden Hall is senior vice president in Wells Fargo’s Consumer Credit Group. He leads the Modeling and Analytics Group within Strategic Risk Management. He has worked for Bank of America and the Federal Home Loan Bank of San Francisco and has an economics Ph.D. from U.C. Berkeley. Kyle Lundstedt directs the credit risk modeling effort at Andrew Davidson & Co, Inc. (ADCo). He has worked for LoanPerformance and KMV and has a finance Ph.D. from U.C. Berkeley. This article represents the views of the authors and does not necessarily reflect the views of Wells Fargo or ADCo. 54 The RMA Journal September 2005 The Competing Risks Framework for Mortgages: Modeling the Interaction of Prepayment and Default MBS. However, the presence of hazard model is simply a model tive variables, such as the current prepayment risk limits the appli- designed to predict the probabili- loan-to-value (LTV) ratio or the cability of traditional approaches ty of attrition given that the sub- FICO score, affect both prepay- to default modeling. The compet- ject has not yet left. For prepay- ment and default. For example, ing risks framework for modeling ment, this means predicting the increased current LTVs or prepayment and default confers probability of prepayment in a decreased FICOs likely increase important advantages relative to given month for all borrowers who default for mortgages; however, these traditional approaches, par- have not yet prepaid. This these same variables may ticularly in the context of valua- methodology sees heavy use in decrease prepayment likelihood. tion, risk management, and capital prepayment modeling.3 Hazard Significant academic and reg- allocation. models for prepayment commonly ulatory literature applies the com- include age and current rate levels peting risks framework to the haz- The Need for Hazard Models as explanatory variables. ards of prepayment and default.5 As with other types of con- While the hazard modeling is However, industry use of compet- sumer assets, it is important to well understood by investors and ing risks models for mortgage pre- address the timing of the default by Wall Street, technique has less payment and default is still in its event, and to account for static commonly been applied to mort- infancy. predictive variables. But mort- gage default. Hazard models, how- gages are unique in offering the ever, are frequently used in assess- Understanding How Prepayment borrower an important and valu- ing the risk of default or bankrupt- and Default Affect One Another able option to prepay the loan cy for corporate bonds.4 In the case When there is more than one early. Other consumer loans are of mortgages, a hazard model risk (hazard) affecting survival, prepayable, but only mortgages would predict the probability that they compete. Mortgages face the offer a significant financial reward the mortgage defaults in a particu- risk of attrition either from pre- for careful use of the option. This lar month, given that it has not yet payment or from default. poses a particular challenge for defaulted or prepaid. Such a model Simultaneous estimation of these default modelers.2 Consumers fre- typically would include age, cur- hazards produces a competing quently use the prepayment rent house-price levels, and bor- risks model.6 competing risks haz- option when it is to their advan- rower FICO scores as explanatory ard models, like traditional pre- tage. When interest rates reached variables. payment models, have different 30-year lows in 2003, the monthly One might expect that a implications, depending on the prepayment rate for prime mort- default hazard model for mort- projected economic scenario. gages reached nearly 7%. The gages could simply be estimated Thus, looking at results in differ- average lives of mortgages vary and then used with an existing ent scenarios is the easiest way to enormously due to differing pre- prepayment model. As it turns understand the interaction of the payment rates and lead to signifi- out, however, the two hazards of prepayment and default hazards cantly different cumulative losses prepayment and default compete in a competing risks framework. for mortgages with similar credit with each other in a way that Consider Figures 1 through 6, characteristics. As a result, build- requires simultaneous develop- which depict a representative ing an accurate life-of-loan loss ment and estimation of the com- competing risks model applied to model for mortgages is very diffi- peting risks. The underlying logic a hypothetical pool of loans.7 The cult. is straightforward: Loans that have results are illustrative only; how- Prepayment modelers take a prepaid cannot default, and vice ever, the relative prepayment and different approach (as illustrated versa. As a result, any forecast of default behavior is reasonable for by the fact that the life-of-loan cumulative defaults must be built credit-sensitive mortgages. In prepayment rate is a concept up from monthly predictions of each graph, the age of the loan is unheard of in the industry), using both prepayment and default. varied along the x-axis, while the what are called hazard models. A Moreover, some observed predic- other variables, such as the LTV 55 The Competing Risks Framework for Mortgages: Modeling the Interaction of Prepayment and Default Figure 1 is low. In the rising-rate scenario, Conditional Prepay and Default Incidence 4% however, the increased duration of the pool leaves more opportunity Prepay 3% for default; hence, the cumulative default rate is much higher for the 2% same collateral. The key point of Figure 2 is 1% the inverse relationship between Default prepayment and default. When 0% rates fall, more loans prepay but 0 24 48 72 96 120 fewer default, so overall attrition Age in Months is less than it would have been had the number of defaults been ratio and FICO scores, are held conditional prepayment rate falls. unchanged. Similarly, when rates constant. Similarly, several credit-related rise, attrition slows because of Figure 1 gives hypothetical variables, such as FICO and LTV, slower prepayment, but the conditional prepayment and affect the conditional probability impact is reduced by additional default rates by age. These condi- of default. defaults. The effects of prepay- tional rates correspond to an The first graph of Figure 2 ment and default on overall attri- “intensity” rate or “flow” of pre- shows the cumulative prepay- tion are negatively correlated. payment and default. Thus, a ments and default rates in a sce- Changes in prepayments driv- mortgage still on the books after nario where interest rates increase en by interest rates not only affect 23 months has roughly a 3% 100 basis points over one year. the magnitude (cumulative chance of prepaying in month 24 The survival curve shows the pro- defaults), but also timing (default and a 0.5% chance of defaulting. portion of the original pool incidence), as shown in Figure 3. Let’s now consider default remaining, revealing the level of The two cumulative default and prepayment estimates from attrition. The second graph shows curves in the left graph are taken our competing risks model in a the same pool subjected to an from the earlier pair of graphs in variety of future scenarios.