A Note on Hybrid Mortgages

Transcription

1 A Note on Hybrid Mortgages Brent W. Ambrose*, Michael LaCour-Little**, and Zsuzsa R. Huszar*** * Gatton College of Business and Economics, University of Kentucky, Lexington, KY or ambrose@uky.edu. **Wells Fargo Home Mortgage and Washington University in St. Louis, Clayton, MO or michael.lacourlittle@wellsfargo.com. *** Gatton College of Business and Economics, University of Kentucky, Lexington, KY or zsuzsa.huszar@uky.edu. Abstract We extend previous research on traditional 1-year adustable-rate mortgages by analyzing the performance of 3/27 hybrid instruments. Under this contract innovation, which first appeared in the mid-1990s, note rates are fixed for three years after which they convert to a traditional 1-year adustment schedule with periodic and lifetime caps. We find high rates of prepayment, particularly at time of initial rate adustment, and relatively high rates of default, as would be consistent with the payment shock that often affects adustable-rate loans. The U.S. mortgage market continues to evolve, with contract innovations to adapt to economic and business conditions. Adustable-rate mortgages (ARMs) first appeared after the financial de-regulation of 1980, prompted by the inflationary environment of the late 1970s. Today, ARMs are a popular mortgage alternative for many households, especially those requiring larger loan amounts to finance higher priced housing. 1 The ARM share is much higher in the umbo market compared to the conforming loan segment, reaching as high as 72% of total originations during 1994 and 2000, which are both years with relatively higher rate levels (Nothaft 2003). The relative share of adustable-rate mortgages appears to rise in periods of rising interest rates, as consumers are attracted to the lower initial interest rates relative to fixed-rate mortgages (FRMs). For example, in 1994 during a period of rising market interest rates, adustable-rate mortgages accounted for 39% of all mortgage originations (Mortgage Bankers Association 2004). Another stylized fact about the ARM product is that it appears to be the preferred instrument for portfolio lenders, since it avoids much of the interest rate risks associated with long-term FRMs. As a result, a much smaller fraction of ARM volume is securitized. Ambrose and LaCour-Little (2001) report that, as of 1999, only about $138 billion in ARM-backed MBS were outstanding, as compared to about $1,776 billion in FRM-backed MBS. Since ARM loans are mainly held in the portfolios of depository institutions, they can be funded with relatively low cost liabilities, eliminating asset-liability mismatch during their initial fixed rate period. This cost advantage allows lenders to offer lower rates to borrowers who accept a limited horizon for payment stability, either because they do not expect to live in the house for an extended period or because they are 1

2 comfortable with future interest rate risk. As an example of the rate differential, as of July 30, 2004, the spread between the 30-year FRM rate and a 3/27 ARM rate was 132 basis points (HSH Associates 2004). As an example of balance sheet patterns, as of year-end 2002, Washington Mutual (the nation's largest thrift) reported $111 billion in single-family residential mortgages at a weighted average coupon of 5.97% (a rate suggestive of a high percentage ARMs, though not specifically broken out by financial reporting). Concurrently, their balance sheet showed $106 billion in interest-bearing deposits at an average rate of 2.50%, implying a net interest margin of 347 basis points on that mortgage portfolio. While adustable-rate mortgages have received significant theoretical and empirical research interest, 2 relatively little attention has focused on one of the latest product innovations: the hybrid mortgage contract that contains features of both traditional fixed- and adustable-rate instruments. 3 This study addresses that research gap by examining the performance on a set of 3/27 adustable-rate mortgages originated during the mid-1990s across the United States for a maor lender's portfolio. To briefly summarize the loan features, the 3/27 adustable-rate mortgage is a common hybrid mortgage that provides borrowers with a fixed-rate mortgage for three years following origination, after which it converts to a traditional 1-year adustable-rate mortgage, indexed to the 1-year Treasury note, for the remaining 27 years of amortization. Interest rate adustments are capped at 2% at first and subsequent adustments, and there is a lifetime cap of 5% over the initial rate. Other hybrid ARM structures include fixed periods of 5, 7, or 10 years, effectively allowing the borrower a menu of terms over which she may fix initial loan payments. In contrast, under a traditional 1-year adustable-rate mortgage, the borrower faces a potential payment shock after only 12 months as the contract rate is adusted to market. 4 Of course, the 3/27 design also exposes the borrower to interest-rate risk, though at a later date. After its introduction in the mid-1990s, the hybrid mortgages gained increasing acceptance, first in the non-conforming, then the conforming and then, most recently, the government segment of the market. 5 Interest rate adustments are capped at 2% at first and subsequent adustments, and there is a lifetime cap of 5% over the initial rate. As with traditional FRM and ARM, hybrid ARMs contain the usual explicit and implicit options for the borrower to terminate the mortgage through either prepayment or default. The theoretical and empirical literature on mortgage prepayment and default (both for fixed-rate as well as adustable-rate instruments) is now well developed so we do not belabor it here. Rather, we simply extend the empirical literature by addressing hybrid ARM performance in general and the effect of the adustment period in particular. Data Our data consists of 2,192 hybrid mortgages originated during 1995 and 1996 by a large national financial institution for portfolio, with performance observed through June Hence, the data contains loans that are seasoned between 3.5 and 5.5 years, a time period sufficient to observe the first re-set event for all loans but ust 2

3 barely sufficient to encompass peak default and prepayment periods (generally thought to occur in years 3-5 of loan life). A longer observation period would be desirable, of course, so our results should be viewed as an early assessment of termination risk for the hybrid mortgage category. Since these are all 3/27 in contract design, we observe the 3-year adustment period for all loans in the sample, assuming they survive up to that point. After adustment, note rates are indexed to the 1-year Treasury rate with a 250 basis point margin. Of these mortgages, 1,685 (76.8%) had prepaid by June 2000, 181 (8.2%) had defaulted (defined as the first instance of a 90-day delinquency, regardless of ultimate outcome) 6 and the remaining 326 (14.9%) were still active (censored) as of the end of the observation period. Conventional wisdom holds that since ARMs are subect to payment shock on adustment, they will tend to have higher default rates compared to FRMs. In support of this view, for example, the Mortgage Bankers Association National Delinquency survey reports that as of Q1-2004, 0.44% of prime FRMs were in foreclosure and 0.73% of prime ARMs were in foreclosure. As a result, lenders tend to more conservatively underwrite ARMs compared to FRMs, typically by imposing lower maximum loan-to-value ratios and/or higher minimum credit scores. Underwriting for hybrid ARMs, however, appears to be relatively less conservative, at least when compared to the traditional 1-year ARMs we previously studied. In this data, the average loan-to-value ratio is 74.9% compared to 73.4% as reported by Ambrose and LaCour-Little (2001) for traditional 1-year adustable-rate mortgages. Moreover, approximately 9% of the hybrid mortgages in this data set had LTV ratios greater than or equal to 95%; in contrast, fewer than 1% of the 1-year adustable-rate mortgages analyzed by Ambrose and LaCour-Little (2001) had LTV ratios that high (see Table 1). These difference may simply reflect a secular trend toward higher LTV lending over the decade of the 1990s. Another difference between the 3/27 mortgages studied here and the traditional 1-year adustable mortgages studied by Ambrose and LaCour-Little is the significant difference in defaults. The dataset used by Ambrose and LaCour-Little (2001) contained very few defaults; as a result, their default model had very little explanatory power. In contrast, we find that ust over 8% of our sample defaulted during the observation period providing a much richer dataset for studying this phenomenon. Moreover, the data represents a geographically diverse cross-section of hybrid mortgages. We note significant concentrations in the West (23%), consistent with the higher house prices and loan balances in that region. The average (median) loan amount is $259,878 ($224,350), and the amount ranges from $22,700 to $2,050,000. Since the conforming loan limit was $203,150 in 1995 and $207,000 in 1996, the maority of these loans were nonconforming at origination. The average initial fixed rate is 7.09%, with 0.30 origination points. Mean borrower credit score (FICO) at origination is 730 and ranges between 536 and Over the course of the study period, the general level of interest rates declined during 1997 and 1998, reaching a new low in October 1998 and then moving consistently higher during 1999 and As a result, we have a good cross section of rate environments at which adustments occurred. Figure 1 shows the average contract rate at origination (by monthly cohort), the 30-year FRM rate and the adustment rate (the 1-year Treasury rate plus the 250 basis point margin) over the period from 1995 through The figure indicates that a loan originated in midyear 3

4 1995 would have reset into a very low environment in 1998; in contrast, a loan originated in late 1996 would have encountered a rate structure roughly 200 basis points higher in To put these rates into perspective, consider three hypothetical mortgages originated in January 1995, January 1996 and December At the first adustment date (month 36), the January 1995 mortgage would have experienced a 5.6% payment reduction as the contract rate fell from 8.4% to 7.7%, while the January 1996 mortgage would have experienced a payment reduction of only 0.9% since the contract rates for this cohort only declined from 7.1% at origination to 7% in month 36. In contrast, the December 1996 mortgage would have experienced a payment increase of 14.4% at the first adustment as the contract rate increased from 6.9% at origination to 8.3% in month 36. Then, at the second adustment date (month 48), the January 1995 mortgage would have experienced another payment reduction of 6.4% as the contract rate declined from 7.7% in month 36 to 7% in month 48, while the January 1996 mortgage would have experienced a payment increase of 15.4% as the contract rate increased from 7% to 8.6%. The December 1996 mortgage would have experienced a 4% payment drop as the contract rate declined from 8.3% to 8.1%. As this simple exercise demonstrates, depending on when the hybrid mortgage was originated, the borrower faced significantly different payment shocks at the 36-month adustment date. Empirical Approach Following standard practice, we model prepayment and default as competing risks. This approach recognizes the mutually exclusive nature of the prepayment and default options. Recent studies such as Deng, Quigley and Van Order (2000), Ambrose and LaCour-Little (2001), Ambrose and Sanders (2003) and Calhoun and Deng (2002) use this framework. We first recognize that during our observation period, a borrower either prepays, defaults, or remains current through the end of the time-period of study (censored). We define T ( = 1, 2, 3) as the latent duration for each loan to end by prepaying, defaulting or being censored, and the observed duration, τ, is the minimum of the T. Conditional on a set of explanatory variables, x, that include personal risk characteristics and market conditions, the probability density function (pdf) and cumulative density function (cdf) for T are ( T x ) h ( T x ) exp( I ( r x ) f = (1.) ( T x ) 1 exp( I ( r x ) F = (2.) where I is the integrated hazard for outcome : I T ( ) T x = h ( s x ) ds (3.) 0 4

5 and h is the hazard function. The oint distribution of the duration and outcome is f ( τ x) h ( τ x ) exp I (, = ( 0 τ x)) (4.) where x=(x 1, x 2, x 3 ) and I 0 =Σ I is the aggregated integrated hazard. Thus, the conditional probability of an outcome is Pr (, x) h = 3 = 1 ( τ x ) h τ. (5.) ( τ x) In order to simplify estimation, we specify a separate exponential hazard function for each mortgage outcome h ( τ x ) = exp( x β ). (6.) and estimate (5) in a multinomial logit framework. Following Gross and Souleles (2002), we separate x into components representing borrower risk characteristics and economic conditions having the following linear form: adust (7.) x β = β0τ t + β1ageit + β2riskit + β3econit + β4 i where τ t represents a series of dummy variables corresponding to calendar quarter of origination, age it is a fourth order polynomial of time since origination, risk it represents a set of characteristics that reflect the lender s underwriting criteria (including borrower credit score (FICO), loan-to-value ratio (LTV) and payment-to-income (INCOME)), econ it is a set of variables capturing changes in economic conditions (including current yield curve, mortgage interest rates and property values) and adust i is a dummy variable denoting the 3-month window surrounding the anniversary marking the conversion of the loan from a fixed-rate to an adustable-rate mortgage. The calendar quarter dummy variables allow the propensity to default or prepay to shift over time. The age function allows for nonparametric variation in the prepayment and default hazard. 5

6 Following Ambrose and LaCour-Little (2001), we capture the dynamics of the prepayment option value by calculating the relative position of the market interest rate to the contract rate. Thus, we include the variable spread over fixed rates (SPD_FRM) defined as rc ( t) rf ( t) SPD _ FRM ( t) =, (8.) r ( t) f where r c is the current contract interest rate at t and r f is the current 30-year conventional fixed-term mortgage interest rate at t, as measured by the FreddieMac 30-year primary mortgage market survey (PMMS) rate. The spread over fixed rates represents the relative interest rate savings associated with switching from the current hybrid 3/27 to a fixed-rate mortgage. 8 Positive values of this variable indicate that the contract interest rate is greater than the market rate and, accordingly, the prepayment option is in-the-money; negative values indicate that the prepayment option is out-of-the-money. The current period t yield curve (TERMSTRU) is estimated as the difference between the 10-year and 1-year Treasury bond rates. This variable provides an indication of market expectations about future interest rates. Recognizing that the 3/27 hybrid converts to a 1-year adustable-rate mortgage in month 36, we include a variable that captures the payment shock (PMT_SHOCK) encountered by the borrower at each interest-rate adustment date. Specifically, we calculate the payment shock as follows: new _ pmt PMT _ SHOCK( t) = 1 old _ pmt (9.) where new_pmt is the new payment based on the remaining balance and the 1-year Treasury rate in period t plus the 250 basis point margin, and old_pmt is the prior year s payment. For example, for a mortgage still current between months 48 and 60, new_pmt is the new payment based on the 1-year Treasury rate at month 48 (plus the margin) and the old_pmt is the payment during months 36 to 47. Thus, payment shock is the percentage increase (or decrease) in the monthly payment relative to the payment in the previous year. We expect that the prepayment hazard should increase during periods of positive payment shock as borrowers attempt to control future interest rate shocks by converting to fixed-rate mortgages. We also anticipate that positive payment shocks should correspond to an increase in the default hazard, the conventional wisdom about adustable-rate mortgages. We capture the interaction of borrower equity and default-option value with prepayment probabilities by including the probability that an individual borrower has negative equity in the property. The probability of negative equity is calculated for each borrower based on the state-level house price growth and the variance of these growth rates 6

7 around the state-level mean appreciation rate. 9 Since house prices over the sample period were generally increasing, the probability of negative equity is small. As a result, we create a one-zero indicator variable (HIGHPROB) to capture months where the probability of negative equity exceeded 5%. In order to assess the variation in the probability of negative equity over time, Figure 2 shows the average probability of negative equity for each month since loan origination, segmented by quarterly origination cohort. For example, the line marked 95Q1 represents the average probability of negative equity experienced by mortgages originated during the first quarter of Figure 2 clearly indicates that loans originated during 1995 experienced higher probabilities of negative equity. In addition, we also incorporate the current period t loan-to-value ratio (LTV). LTV captures both the scheduled principal amortization as well as changes in the underlying property as reflected in the state level OFEHO repeat sales index. The adustment period dummy variable is one of the key variables of interest. Our hypothesis is that the hazards of prepayment and default should shift during the rate adustment window. We also interact the current interest rate spread with the adustment window indicator variable in order to isolate the impact of interest rates at adustment. Results Figures 3 and 4 report the baseline hazard rates and cumulative prepayment and default probabilities, respectively. We estimate the baseline hazards using the following specification: age. (10.) x β = β0τ t + β1 it This specification allows us to estimate the baseline hazard function without controlling for borrower characteristics, time-varying economic conditions or specific features of the 3/27 hybrid. As evident in Figure 3, the prepayment hazard displays the typical non-linear pattern of mortgage seasoning. Furthermore, the cumulative probabilities of prepayment and default (Figure 4) indicate that the probability of a mortgage surviving beyond 5 years is less than 1%. Table 2 reports results of the full competing risk model specification. In the prepayment function, we find statistically significant effects for loan age (positive), spread over fixed rates (positive), credit score (positive), loanto-value ratio (positive), loan balance at origination (positive), adustment date (positive), the ratio of the new payment relative to the old payment at each adustment date (positive) and the interest rate spread interacted with the adustment date period (negative). The estimates for the interest rate term structure and high probability of negative equity are not statistically significant. For the default function, we find statistically significant coefficients for the spread over fixed rates (positive) and credit score (negative). These results are consistent with prior expectations. For example, borrowers with higher credit quality scores at origination have a higher probability of prepayment and a lower probability of default. 7

8 Also, consistent with the findings of Ambrose and LaCour-Little (2001), we find strong evidence that financial factors drive prepayment. Following Ambrose and LaCour-Little, the spread over fixed rates is a proxy for the value of the call option. The positive coefficient indicates that the probability of prepayment is significantly higher when market interest rates (in this case, the 30-year fixed-rate mortgage) are below the contract rate (i.e., the prepayment option is in-the-money ). To put this result into perspective, a 1-basis-point increase in the spread over fixed rates variable (from 0.0 to 0.01) corresponds to approximately a 7-basis-point difference between the fixed-rate mortgage market rate and the contract rate when the contract rate is 7%. The significance of a change in this spread on prepayment is apparent through simulations. For example, if by month 12, the FRM interest rate falls 100 basis points below the hybrid contract rate at origination (from a 7% hybrid to a 6% FRM), then the probability of prepayment increases by 130 basis points (from 1.71% to 3.02%). 10 As discussed earlier, the variables of most importance for this study are those that characterize the period surrounding the switch from initial fixed-rate to fully adustable-rate (ADJUST, AFTER_ADJUST, PMT_SHOCK and SPDFRM_ADJUST). Since the adustment period imposes significant interest rate risk on the borrower, we anticipate that the prepayment and default hazards should increase during this period. Overall results are consistent with this expectation. Figure 5 shows that the prepayment and default hazard rates increase significantly following the first adustment. Figure 6 shows cumulative default and prepayment rates, with a clear inflection point around month 36. We note that with termination hazard rates this high, the probability of a hybrid mortgage surviving past month 60 is less than 1%. We include two dummy variables to estimate the impact of the initial adustment shock and the subsequent ARM period. The significant coefficient for the adustment window dummy variable (ADJUST) indicates that the hazard of prepayment increases significantly during the three-month window surrounding the origination anniversary when the hybrid converts from a fixed-rate to an adustable-rate mortgage. The marginal effect indicates that the probability of prepayment during this 3-month window is 78% higher than the corresponding prepayment hazard in other months. 11 This significant spike is clearly evident in Figure 5, which shows the monthly prepayment and default hazards. With the exception of this spike at the anniversary date, the prepayment hazard displays a characteristic non-linear pattern of rising slowly to month 36 and then declining, mirroring the seasoning observed in pool-level prepayment statistics. We also include a dummy variable controlling for the period following adustment (AFTER_ADJUST). This specification provides an estimate of the shift in the hazard rate from being a FRM to an ARM. The insignificant coefficients for this variable indicate that the ARM portion of the mortgage does not have greater default or prepayment risk, on average, than the FRM portion of the mortgage. However, the highly significant coefficient for PMT_SHOCK in the prepayment model (and marginally significant in the default model) indicates that termination risk is clearly associated with adustments to the mortgage payment. Recall, we include the PMT_SHOCK variable to control for the relative change in mortgage payment at each interest rate adustment. The significant positive 8

9 coefficient in the prepayment model indicates that borrowers are more like to prepay their mortgage after experiencing a positive shock to their payment. This result confirms that borrowers are sensitive to changes in interest rates suggesting that a positive increase in the mortgage payment provides borrowers with the necessary incentive to seek out refinancing alternatives. This pattern supports the results reported by Ambrose and LaCour- Little (2001) for teased ARMs. The results for teased ARMs indicated that the hazard of prepayment increased significantly during the window surrounding the adustment anniversary; this effect was particularly strong during the first anniversary when the teaser expired. Our results here indicate that the 3/27 hybrid mortgage displays a similar pattern. That is, after the initial teased period wears off or in this case, when the fixed-rate period expires the prepayment and default hazards increase substantially. Given this performance similarity, one might characterize 3/27 ARMs as simply standard 1-year ARMs with a 3-year teaser period. To isolate the impact of interest rates during the conversion window (months 35 to 37), we interact the adustment window dummy variable with the interest rate spread variable (SPDFRM_ADJUST). The coefficient for SPDFRM_ADJUST is significantly negative for the prepayment model. Recall, this variable measures the marginal impact of a change in interest rates at the time of adustment from the original contract interest rate. Thus, the negative coefficient suggests that during the adustment period window the impact of a decline in interest rates (relative to the origination contract rate) is lower than during other periods. In contrast, if interest rates are higher (SPD_FRM is negative), then the prepayment hazard increases, implying that borrowers recognize the risks associated with ARMs during periods of rising interest rates. Conclusions In this brief paper, we extended the research on the performance of adustable-rate mortgages to the hybrid ARM category. This product innovation is increasingly popular, especially in high-cost markets and higher-rate environments; however, we have shown that there seem to be some unique risk characteristics. Both prepayment and default risk are high, with particular concentrations around the time period of rate adustment, though the exact magnitude of the spikes in termination probability will depend on the rate environment at adustment date. Of course, since our data comes from the servicing records of a single lender and covers at most 5.5 years of history, it may be premature to generalize results. But as this product innovation enters the public securities arena through additional hybrid ARM pool securitization, additional empirical research is warranted to corroborate these initial findings on loan performance. We thank Michael Fratantoni, Jim Follain, Andrea Heuson, Susan Wachter, Nancy Wallace and an anonymous referee for helpful comments and suggestions on earlier versions of this paper. The views expressed are the authors' alone and not necessarily those of Wells Fargo and Company or any of its affiliates. 9

10 References Ambrose, B.W. and A. Sanders Commercial Mortgage Backed Securities: Prepayment and Default, Journal of Real Estate Finance and Economics 26 (2/3): Ambrose, B.W. and M. LaCour-Little Prepayment Risk in Adustable Rate Mortgages Subect to Initial Year Discounts: Some New Evidence. Real Estate Economics 29(2): Brueckner, J.K. and J.R. Follain The Rise and Fall of the ARM: An Econometric Analysis of Mortgage Choice. Review of Economics and Statistics 70: Calhoun, C.A. and Y. Deng A Dynamic Analysis of Fixed- and Adustable-Rate Mortgage Terminations. Journal of Real Estate Finance and Economics 24(1/2): Capone, C. and D.F. Cunningham Estimating the Marginal Contribution of Adustable-Rate Mortgage Selection to Termination Probabilities in a Nested Model. Journal of Real Estate Finance and Economics 5: Cunningham, D.F. and C. Capone The Relative Termination Experience of Adustable to Fixed-Rate Mortgages. Journal of Finance 45(5): Deng, Y Mortgage Termination: An Empirical Hazard Model with Stochastic Term Structure. Journal of Real Estate Finance and Economics 14: Deng, Y., J.M. Quigley and R. Van Order Mortgage Terminations, Heterogeneity and the Exercise of Mortgage Options. Econometrica 68(2): Dhillon, U., J.D. Shilling and C.F. Sirmans Choosing Between Fixed and Adustable Rate Mortgages. Journal of Money, Credit, and Banking 19: Gross, D.B. and N.S. Souleles An Empirical Analysis of Personal Bankruptcy and Delinquency. Review of Financial Studies 15(1): Houston, J.F., J. Sa-Aadu and J.D. Shilling Teaser Rates in Conventional Adustable-Rate Mortgage (ARM) Markets. Journal of Real Estate Finance and Economics 4(1): HSH Associates Hybrid ARM Mortgage Statistics. Lea, M.J. and P.M. Zorn Adustable-Rate Mortgages, Economic Fluctuations, and Lender Portfolio Change. AREUEA Journal 14(3): Linneman, P. and S. Wachter The Impacts of Borrower Constraints on Homeownership. AREUEA Journal 17(4): Mortgage Bankers Association to-4 Family Mortgage Originations. Nothaft, Frank Will Interest Change Lead to Higher ARM Share? Special Commentary from the Office of the Chief Economist. Stanton, R. and N. Wallace Arm Wrestling: Index Behavior and Prepayment of Adustable Rate Mortgages. Real Estate Economics 23: Stanton, R. and N. Wallace The Anatomy of an ARM: Index Dynamics and Adustable Rate Mortgage Valuation. Journal of Real Estate Finance and Economics 19(1):

11 Table 1: Descriptive statistics. The spread over fixed rates is the percentage by which the current note rate exceeds the current 30-year fixed mortgage rate. The term structure is defined as the difference between the 10-year and the 1-year Treasury rates. Payment-to-income is the monthly loan payment divided by borrower monthly income. Credit score is the primary borrower s FICO score. Loan-to-value ratio is estimated current LTV based on loan amortization and estimate house price changes. Loan amount is the original loan amount at origination. Points (in percentage of loan amount) are prepaid finance charges paid at origination. Region 1 through Region 10 are regional dummy variables for U.S. census regions. At Origination At Termination Variable Spread Over rc ( t) rf ( t) Fixed Rates rf ( t) Definition Mean Std. Dev Min Max Mean Std. Dev Min Max Term Structure 10 yr Treasury 1yr Treasury Payment-to- Ratio of loan payment to Income monthly income Credit Score Primary borrower FICO Loan to Value LTV Ratio (time-varying) Loan Amount Loan Amount at Origination $259,878 $184,585 $22,700 $2,050,000 Points Points paid at Origination Region 1 Region 2 Region 3 Region 4 Region 5 Region 6 Region 7 Region 8 Region 9 Region 10 New England 6.9% Northwest 2.1% Upper-West 5.6% Mid-West 17.8% NY/NJ 8.1% West 22.8% Southwest 6.5% Plains 3.5% South 14.0% Mid-Atlantic 12.6% 11

12 Table 2: Competing risks model of prepayment and default. Parameter estimates for the following competing risks model estimated via maximum likelihood in a multinomial logit framework Pr ( τ, x) h = 3 = 1 ( τ x ) h ( τ x) where we specify a separate exponential hazard function for each mortgage outcome h ( τ x ) = exp( x β ) and separate x into components representing borrower risk characteristics and economic conditions having the following linear form: = + age + risk + econ adust. x β β0τ t β1 it β2 it β3 it + β4 AGE is the number of month since origination. AGE2, AGE3 and AGE4 are AGE squared, raised to the third and raised to the fourth power, respectively. ϑ represents quarter dummies (Q through Q4 1996) that control for mortgage origination, where Q1 is the reference group. RISK represents the following variables designed to control for borrower risk characteristics: PAYMENT-TO-INCOME is loan payment relative to borrower monthly income; credit score (FICO) is the primary borrower s FICO score; LTV is a loan to-value ratio, monthly adusted for the mortgage payments and housing price movements; ORIBAL is the loan amount at origination; HIGPROB is a dummy variable, equal to 1 when the probability of negative equity exceeds 5%. ECON represents the following variables designed to control for economic risk factors: TERMSTRU is the difference between the ten-year and the 1-year Treasury bond rates; SPD_FRM variable is the loan interest rate spread over the fixed-mortgage rate. ADJUST represents the set of variables that control for risks associated with the switch from fixed- to adustable-rate mortgage: ADJUST is a dummy variable denoting the 3-month window surrounding the anniversary date of the conversion of the loan from a fixed-rate to an adustable-rate mortgage; AFTER_ADJUST is a dummy, equal to 1, for months after the adustment; SPDFRM_ADJUST is an interaction variable, which is the adustment window dummy (ADJUST) multiplied with SPD_FRM; PMT_SHOCK is the spread of new mortgage payment over the old mortgage payment at the adustment date. i 12

13 Prepayment Model Default Model Parameter Coefficient Chi-Sq p-value Parameter Coefficient Chi-Sq p-value INTERCEPT < AGE < AGE AGE3 9.6E E AGE4-6.5E E QUARTER QUARTER QUARTER QUARTER QUARTER QUARTER QUARTER SPD_FRM < TERMSTRU PAYMENT-TO- INCOME FICO <.0001 LTV ORIBAL 8.8E < E HIGHPROB ADJUST < AFTER_ADJUST PMT_SHOCK < SPDFRM_ADJUST

14 Figure 1: Monthly interest rates. Origination rate is the average mortgage rate at origination for the specific month during the period of January 1995 through December FRM rate is 30- year fixed-rate mortgage from the Primary Mortgage Market Survey (PMMS). Adustment rate is the 1-year Treasury rate plus 250 basis points measured each month, 36 month after origination. 14

15 Interest Rates Over Study Period: Origination Rate ; Adustment Rate ; FRM Rate % Origination Rate Adustment Rate FRM Rate Jan-95 Jul-95 Jan-96 Jul-96 Jan-97 Jul-97 Jan-98 Jul-98 Jan-99 Jul-99 Jan-00 Jul-00 Date 15

16 Figure 2: Average probability of negative equity by month from mortgage origination, segmented by quarterly origination cohort. 16

17 Figure 3: Baseline prepayment and default hazard rates. Baseline hazard function shows the estimated probability of default and prepayment as a function of time since origination. Baseline Hazards % 0.03 prepay default Month 17

18 Figure 4: Cumulative prepayment and default probabilities for the baseline model % prepay default Month 18

19 Figure 5: Prepayment and default hazard rates for the competing risk model (Table 2). Estimated prepayment and default rates, conditional on flat term structure, as function of time since loan origination. Prepayment and Default Hazards (flat term structure) prepay default Months 19

20 Figure 6: Cumulative prepayment and default hazards for the competing risk model (Table 2) prepay default

21 1 Linneman and Wachter (1989) note that adustable-rate mortgages reduce the constraints on homeownership. 2 For important early research on adustable-rate mortgages, see, for example, Lea and Zorn (1986), Dhillon, Shilling and Sirmans (1987), Brueckner and Follain (1988), Cunningham and Capone (1990), Houston, Sa-Aadu and Shilling (1991), Capone and Cunningham (1992) or Stanton and Wallace (1995, 1999). 3 See Ambrose and LaCour-Little (2001) for a more comprehensive literature review. 4 Ambrose and LaCour-Little (2001) address adustment shock on traditional 1-year adustable-rate mortgages with initial "teaser" rates. 5 For example, on July 29, 2004, Ginnie Mae announced that it would begin to guarantee hybrid ARM loans in pools backed by FHA 3/27, 5/25, 7/23 and 10/20 hybrid ARMs effective September 1, Some fraction of the loans that reached 90-day delinquency (that, using our terminology, "defaulted") ultimately paid off in full, so the lender realized no net credit loss from the default. After a 90-day delinquency, however, loans were transferred to a special servicing department for foreclosure, workout or other resolution, and we do not have records from that period of time to examine ultimate outcome. 7 Fair Isaac and Company (FICO) is the industry leader in credit scores, with scores ranging from A higher score indicates better credit. Scores above 700 are generally considered prime credits. 8 Obviously, borrowers could also refinance into a new 3/27 hybrid mortgage or a number of alternative mortgages (e.g., fullyadusting ARMs or other hybrid products). 9 Using the variance of the OFHEO repeat transaction index (ε 2 ), the probability of negative equity is calculated as PROBNEQ=Φ log ( pvbal) log( mktval) 2 ε 21

22 where pvbal is the present value of the remaining mortgage payments, mktval is the current market value of the property estimated using the repeat transaction index and Φ is the cumulative normal density function (see Deng 1997 and Deng, Quigley and Van Order 2000). 10 To isolate the effect of the spread over fixed-rate variable, the simulations were performed assuming a 75% LTV mortgage, a term structure value of 0.011, a FICO score of 730 and a payment-to-income ratio of The marginal effect is calculated as eβ