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

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:


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:


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



Defaulted


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


• 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]


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


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


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

Documents

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