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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 TracyUCLA Ziman Center/Economics ConferenceApril 29 & 30, 2011
.
• 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
IFE uses competing risk model to assess expected default rate on FHA portfolio
MortgageOrigination
Prepay:• house sold• mortgage refinanced to
non-FHA• mortgage refinanced to
new FHA
Default:
Mortgage Event Analysis:
IFE uses competing risk model to assess expected default rate on FHA portfolio
MortgageOrigination
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:
IFE uses competing risk model to assess expected default rate on FHA portfolio
MortgageOrigination
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
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
Contrasting FHA performance based on mortgage or insurance events
Active: 72%Prepaid: 20%Default: 8%
Defaulted
Figure 1a. Mortgage Event View
39,262 mortgages
29%
71%
140,011 mortgages
Prepaid
Active
Contrasting FHA performance based on mortgage or insurance events
Active: 72%Prepaid: 20%Default: 8%
Active: 83%Prepaid: 8%Default: 9%
Defaulted
Figure 1a. Mortgage Event View
39,262 mortgages
29%
71%
140,011 mortgages
Prepaid
Active
Defaulted
Figure 1b. InsuranceEvent View
18,746 mortgages
54%46%
Prepaid
Active
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
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
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 defaultTable 1. Time from 1st Missed Payment to “Default” Trigger for Loans Paid
Off with Claim
TriggerDefinition Mean Std
DevMinimu
m25th 50th 75th Maximu
m60+ 1.8 1.5 1 1 1 2 9
90+ 3.9 3.9 2 2 2 4 25Foreclosure start
8.4 7.1 3 4 6 10 38
Claim start 13.6 8.6 4 7 11 17 42Notes: Authors calculations based on a 10 percent random sample of FHA loans from CoreLogic.
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
TriggerDefinition
ReachedTrigger
Delin asLast obs
Current as
Last obs
ServicingTransferred Paid Off
PctPaid Off
Pct w.Claim
60+ 3,574 2,290 516 86 682 19.1 80.1
90+ 2,640 1,679 288 63 610 23.1 89.5
Foreclosure start
1,366 703 62 19 582 42.6 93.8
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
Determinants of Prepayment and Default:
• Loan-specific factors: • LTV (dynamic)• Credit score [FICO] • DTI • Loan purpose• Documentation level • ARM & term
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
• 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:
Hazard Estimates: LTV on prepayment
Prepayment Hazard
Variable(1)
Unlinked(2)
LinkedLoan-to-Value:
80 – 84 1.043**(0.049)
0.924(0.074)
85 – 890.916
(0.038)
0.694**(0.051)
90 – 94 0.856**(0.033)
0.651**(0.042)
95 – 990.963
(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)
Hazard Estimates: LTV on default
Default Hazard
Variable(3)
Unlinked(4)
LinkedLoan-to-Value:
80 – 841.172
(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)
Hazard Estimates: FICO
Prepayment Hazard
Default Hazard
Variable(1)
Unlinked
(2) Linke
d
(3) Unlinke
d
(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 – 6191.005
(0.020)0.995(0.038
)
8.638**(0.469)
9.347**(0.514)
620 – 6791.009
(0.017)0.970(0.030
)
4.690**(0.249)
4.814**(0.259)
680 – 7190.991
(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)
Hazard Estimates: Debt-to-income
Prepayment Hazard
Default Hazard
Variable(1)
Unlinked
(2) Linke
d
(3) Unlinke
d
(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)
Hazard Estimates: economic environment
Prepayment Hazard
Default Hazard
Variable(1)
Unlinked
(2) Linke
d
(3) Unlinke
d
(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)
Hazard Estimates: baseline prepayment hazard
4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 360.0000
0.0005
0.0010
0.0015
0.0020
0.0025
0.0030
0.0035
0.0040
0.0045
0.0050
Months Since Origination
Rel
ati
ve P
repaym
ent
Haza
rd
Linked
Unlinked
Hazard Estimates: baseline default hazard
4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 330.0000
0.0001
0.0002
0.0003
0.0004
0.0005
Months Since Origination
Rel
ati
ve D
efault
Haza
rd
Linked
Unlinked
Forecasted Performance for active FHA mortgages: 5-year horizon
Active: 19.6%Prepaid: 69.6%Default: 10.8%
Defaulted
Figure 2a. Mortgage Event View
81,002 mortgages
87%
13%
100,749 mortgages
Prepaid
Active
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%
Defaulted
Figure 2a. Mortgage Event View
81,002 mortgages
87%
13%
100,749 mortgages
Prepaid
Active
Defaulted
Figure 2b. InsuranceEvent View
29,021 mortgages
50%50%
94,224 mortgages
Prepaid
Active
Forecasted Performance: by vintage
Table 5. Default and Prepayment Probability Forecasts: 5-Year Horizon (%)
Baseline Scenario
Linked
Unlinked
2007 Vintages Default 25.1 4.5Prepayment 21.5 85.8Default/
Terminations 53.9 5.02008 Vintages
Default 19.5 9.9Prepayment 23.4 80.1Default/
Terminations 45.5 11.02009 Vintages
Default 15.0 11.3Prepayment 13.5 69.6Default/
Terminations 52.6 14.0