1. These views are my own and do not necessarily represent the views of the Federal Reserve Bank of New York or the Federal Reserve System Underestimating Insurance Risk: The FHA Case Andrew Caplin, Anna Cororaton, Joseph Tracy UCLA Ziman Center/Economics Conference April 29 & 30, 2011.

2. FHA is intended to be self-financing Each FHA mortgage carries a credit guarantee FHA’s Mutual Mortgage Insurance Fund (MMIF) covers any credit losses minimum capital of 2% of insurance-in-force FHA charges borrowers guarantee fees which fund the MMIF up-front fee which is typically financed in the balance annual fee Annual external audit of MMIF to assess funding level Conducted by Integrated Financial Engineering (IFE) 2010 audit - $2.72b, which is below the 2% level

3. IFE uses competing risk model to assess expected default rate on FHA portfolio Mortgage Origination Prepay: house sold mortgage refinanced to non-FHA mortgage refinanced to new FHA Default: Mortgage Event Analysis:

4. IFE uses competing risk model to assess expected default rate on FHA portfolio Mortgage Origination Prepay: house sold (credit risk ends) mortgage refinanced to non-FHA (credit risk ends) mortgage refinanced to new FHA (credit risk continues) Default: (credit risk realized) Mortgage Event Analysis:

5. IFE uses competing risk model to assess expected default rate on FHA portfolio Mortgage Origination Prepay: house sold (credit risk ends) mortgage refinanced to non-FHA (credit risk ends) Default: (credit risk realized) Insurance Event Analysis: Internal FHA refinance Insurance events can span multiple FHA mortgages – covers the span of time that credit risk exists between the borrower and the FHA

6. CoreLogic Linked FHA Data: FHA originations from 2007 to 2010 Q3 For each FHA origination that was a refinance, CoreLogic searched its deeds records to see if there was a preceding FHA mortgage. Currently, our linked FHA data are only 2 mortgages long CoreLogic is working on extending the chains CoreLogic also provided a random sample of purchase mortgages and refinances from non-FHA mortgages Built a random sample by working backwards in time For 2010, randomly select a k% sample based on FHA published data on each origination type If we select in a linked FHA refinance, we bring in its prior FHA mortgage as well Repeat for 2009, 2008 and 2007 – adjust the count of each type of origination that we need based on FHA linked loans that have been pulled in for that year Selected the largest value of k where we did not run short of any type or origination in any year – 4.5% sample

7. Contrasting FHA performance based on mortgage or insurance events Active: 72% Prepaid: 20% Default: 8%

8. Contrasting FHA performance based on mortgage or insurance events Active: 72% Prepaid: 20% Default: 8% Active: 83% Prepaid: 8% Default: 9%

9. What are implications of switching from a mortgage event to an insurance event analysis for expected default rate of active FHA mortgages? Estimate a competing risk model with common data, specifications and switch between mortgage event and insurance event data structure

10. What are implications of switching from a mortgage event to an insurance event analysis for expected default rate of active FHA mortgages? Use the hazard estimates to calculate expected prepayment and default probabilities over a 5-year horizon – S(t) is estimated joint survivor

11. How should we define the “default” event? Claim on FHA takes place long after the initial delinquency Variability of these time lags will make it difficult to estimate effect of time-varying determinants of default Table 1. Time from 1 st Missed Payment to “Default” Trigger for Loans Paid Off with Claim Trigger DefinitionMeanStd DevMinimum25 th 50 th 75 th Maximum 60+ 1.81.511 1 2 9 90+ 3.9 22 2 425 Foreclosure start 8.47.134 61038 Claim start13.68.647111742 Notes: Authors calculations based on a 10 percent random sample of FHA loans from CoreLogic.

12. How should we define the “default” event? Reducing the variance by selecting earlier delinquency triggers also reduces the conditional probability of a claim given that a mortgage hits that delinquency trigger Table 2. Definition of “Default” and Likelihood of a Claim Trigger Definition Reached Trigger Delin as Last obs Current as Last obs Servicing TransferredPaid Off Pct Paid Off Pct w. Claim 60+3,5742,2905168668219.180.1 90+2,6401,6792886361023.189.5 Foreclosure start1,366 703 621958242.693.8 Notes: Authors calculations based on a 10 percent random sample of FHA loans from CoreLogic. Percent with claim is conditional on a loan being paid off. 90-days delinquent provides a reasonable tradeoff

13. Determinants of Prepayment and Default: Loan-specific factors: LTV (dynamic) Credit score [FICO] DTI Loan purpose Documentation level ARM & term

14. Determinants of Prepayment and Default: Loan-specific factors: LTV (dynamic) Credit score [FICO] DTI Loan purpose Documentation level ARM & term State-specific factors: Judicial foreclosure Recourse

15. Loan-specific facors: LTV (dynamic) Credit score [FICO] DTI Loan purpose Documentation level ARM & term State-specific factors: Judicial foreclosure Recourse Economic: MSA unemployment (dynamic) House price change – 12 months (dynamic) Distress sales (dynamic) Interest rate differential [prepayment only] (dynamic) Percent change in monthly payment [internal FHA refi] Determinants of Prepayment and Default:

16. Hazard Estimates: LTV on prepayment Prepayment Hazard Variable (1) Unlinked (2) Linked Loan-to-Value: 80 – 84 1.043** (0.049) 0.924 (0.074) 85 – 89 0.916 (0.038) 0.694** (0.051) 90 – 94 0.856** (0.033) 0.651** (0.042) 95 – 99 0.963 (0.035) 0.667** (0.040) 100 – 104 1.045** (0.038) 0.714** (0.044) 105 – 109 0.993** (0.038) 0.672** (0.045) 110 – 114 0.845** (0.037) 0.552** (0.044) 115 – 119 0.776** (0.041) 0.558** (0.056) 120 or higher 0.737** (0.037) 0.421** (0.044)

17. Hazard Estimates: LTV on default Default Hazard Variable (3) Unlinked (4) Linked Loan-to-Value: 80 – 84 1.172 (0.104) 1.156 (0.104) 85 – 89 1.257** (0.097) 1.204** (0.095) 90 – 94 1.404** (0.098) 1.383** (0.099) 95 – 99 1.765** (0.118) 1.653** (0.113) 100 – 104 2.199** (0.149) 2.216** (0.153) 105 – 109 2.460** (0.176) 2.769** (0.202) 110 – 114 2.795** (0.220) 3.184** (0.256) 115 – 119 2.953** (0.271) 3.513** (0.326) 120 or higher 3.170** (0.275) 3.784** (0.332)

18. Hazard Estimates: FICO Prepayment Hazard Default Hazard Variable (1) Unlinked (2) Linked (3) Unlinked (4) Linked Credit Score (FICO): Less than 580 1.008 (0.025) 0.978 (0.046) 12.980** (0.720) 13.910** (0.783) 580 – 619 1.005 (0.020) 0.995 (0.038) 8.638** (0.469) 9.347** (0.514) 620 – 679 1.009 (0.017) 0.970 (0.030) 4.690** (0.249) 4.814** (0.259) 680 – 719 0.991 (0.019) 0.988 (0.036) 2.257** (0.138) 2.268** (0.141) Missing 0.635** (0.028) 1.207** (0.076) 5.978** (0.405) 7.289** (0.500)

19. Hazard Estimates: Debt-to-income Prepayment Hazard Default Hazard Variable (1) Unlinked (2) Linked (3) Unlinked (4) Linked Debt-to-Income (DTI): 28 – 35 1.131** (0.032) 1.091 (0.060) 1.205** (0.063) 1.215** (0.065) 36 – 43 1.248** (0.034) 1.132** (0.059) 1.430** (0.070) 1.430** (0.072) 44 or higher 1.252** (0.033) 1.222** (0.062) 1.700** (0.082) 1.712** (0.085) Missing 1.226** (0.035) 1.308** (0.070) 1.659** (0.084) 1.823** (0.094)

20. Hazard Estimates: economic environment Prepayment Hazard Default Hazard Variable (1) Unlinked (2) Linked (3) Unlinked (4) Linked Economic determinants: Lag unemp rate change 1.072** (0.004) 0.985 (0.008) 1.104** (0.007) 1.103** (0.007) House price change (12 m) 0.730** (0.010) 0.723** (0.019) 0.913** (0.021) 0.952** (0.022) Distress sales share (1%) 0.989** (0.001).977** (0.002) 0.995 (0.002) 0.993** (0.002) Interest rate diff (1%) 3.043** (0.041).864** (0.091) % change in monthly pmt.382** (0.058) 1.251** (0.043)

21. Hazard Estimates: baseline prepayment hazard

22. Hazard Estimates: baseline default hazard

23. Forecasted Performance for active FHA mortgages: 5-year horizon Active: 19.6% Prepaid: 69.6% Default: 10.8%

24. Forecasted Performance for active FHA mortgages: 5-year horizon Active: 19.6% Prepaid: 69.6% Default: 10.8% Active: 69.2% Prepaid:15.3% Default: 15.5%

25. Forecasted Performance: by vintage Table 5. Default and Prepayment Probability Forecasts: 5-Year Horizon (%) Baseline Scenario LinkedUnlinked 2007 Vintages Default25.14.5 Prepayment21.585.8 Default/Terminations53.95.0 2008 Vintages Default19.59.9 Prepayment23.480.1 Default/Terminations45.511.0 2009 Vintages Default15.011.3 Prepayment13.569.6 Default/Terminations52.614.0