Mortgage Reinsurance Loss Forecasting

Presented by: Kyle Mrotek, FCAS, MAAA

Four Seasons Hotel, Las Vegas

September 26, 2008

2

Agenda

Defined

Purpose

Methodology

Hedging

Closing Thoughts

3

Defined

Loss forecasting – application of models, assumptions and judgment to estimate both the future magnitude and timing of claim payments and accruals related to a cohort of exposure.

Stage 1 Model

Choice

Stage 5 Model

Selection

Stage 2 Model

Calibration

Stage 3 Model

Validation

Experience and prior knowledge

Data

Stage 6 Modify for

Future

Stage 4 Other Models

Source: Loss Models: From Data to Decisions

4

Purpose

Financial planning– Management– Pro forma financial statements– Baseline estimate

Business feasibility study– Regulator– Pro forma financial statements– Scenarios

• Baseline• Optimistic• Pessimistic

Valuation– Management/investors– NPV cash flows– Range

5

Purpose

Risk transfer– Regulator / auditor / potential litigators

• PV paid loss ratio• Expected reinsurer deficit (ERD)

Rating agency support / ERM– Management / rating agency– Capital flows

• Capital ratios• VaR / TVaR

Loss reserving– Management / auditor / regulator– Best estimate

In force at evaluation date

In force AND delinquent at evaluation date

Loss forecasting

Loss reserving

6

Purpose Premium Deficiency

– Regulator / auditor– Future loss of in force– Best estimate

A PV Future Paid Loss $50 $100 $75 $25 $250B PV Future Admin Expense $10

C = A+B Uses $260D PV Future Written Premium $40 $70 $60 $20 $190E Loss Reserve $10F Unearned Premium Reserve $5G Contingency Reserve $75

H = Sum (D:G) Sources $280I = Max (0, C-H) Premium Deficiency $0

7

Methodology

Characteristic Advantages Disadvantages

Aggregate Stability

Easier

Mix changes

Performance Reflects experience to date

Experience may not be indicative of future

Deterministic Future situation only has one chance to play out

Future uncertain as of evaluation date

Aggregate vs Loan-level Performance vs residual only Deterministic vs stochastic

8

Methodology Loss Development Method

– Aggregate / performance / (mostly) deterministic– Development of loss, by cohort, is function of age since origination – Relies on the historical changes in losses from one evaluation point to another to

project the current valuation of a loss rate to an ultimate loss basis.Development patterns that have been exhibited by more mature (older) years and historical experience are used to estimate the projected development of the less mature (more recent) years. Four Seasons Mortgage Insurer

Evaluated As Of December 31, 2007

Paid LDF MethodCumulative Paid Loss / Original Coverage A B C=A*B

PaidCumulative IndicatedBook Yr Age 1 Age 2 Age 3 Age 4 Age 5 Age 6 Book Yr Loss Rate DF ULR2002 0.01% 0.08% 0.66% 1.60% 2.00% 2.20% 2002 2.20% 1.80 3.96%2003 0.02% 0.34% 2.47% 3.71% 4.10% 2003 4.10% 1.98 8.12%2004 0.01% 0.14% 1.34% 2.01% 2004 2.01% 2.33 4.70%2005 0.02% 0.23% 1.85% 2005 1.85% 4.21 7.77%2006 0.01% 0.05% 2006 0.05% 34.71 1.74%2007 0.02% 2007 0.02% 423.97 8.48%

Age-to-Age Development Factors

Book Yr 2:1 3:2 4:3 5:4 6:52002 13.24 8.35 2.41 1.25 1.102003 16.93 7.30 1.50 1.112004 14.40 9.32 1.502005 11.51 8.032006 5.00

Average 12.22 8.25 1.80 1.18 1.10Selected 12.22 8.25 1.80 1.18 1.10 6:UltCumulative 423.97 34.71 4.21 2.33 1.98 1.80

9

Methodology

Bornhuetter-Ferguson Method (B-F Method)

– Aggregate / residual / (mostly) deterministic

– Estimate ultimates by adding together actual loss with expected future loss

– Expected future loss relies on a priori loss and selected loss development factors

Four Seasons Mortgage InsurerEvaluated As Of December 31, 2007

Paid BF Method

A B C=1-1/B D E=C*D F=A+E

Paid Cumulative Indicated A Priori Indicated IndicatedBook Yr Loss Rate DF % UnPaid ULR Unpaid ULR ULR2002 2.20% 1.80 44.4% 2.82% 1.25% 3.45%2003 4.10% 1.98 49.5% 3.68% 1.82% 5.92%2004 2.01% 2.33 57.1% 4.31% 2.46% 4.48%2005 1.85% 4.21 76.2% 7.42% 5.66% 7.51%2006 0.05% 34.71 97.1% 12.52% 12.16% 12.21%2007 0.02% 423.97 99.8% 9.90% 9.87% 9.89%

Four Seasons Mortgage InsurerEvaluated As Of December 31, 2007

Derivation of A Priori ULR

A B C D=B/C E=A*D

Initital Actual Expected Ratio ofA Priori Cumulative Cumulative Actual to A Priori

Book Yr ULR Persistency Persistency Expected ULR2002 5.00% 22% 39% 56% 2.82%2003 5.00% 35% 48% 74% 3.68%2004 5.00% 50% 58% 86% 4.31%2005 7.00% 75% 71% 106% 7.42%2006 12.00% 90% 86% 104% 12.52%2007 10.00% 97% 98% 99% 9.90%

10

Methodology A priori ultimate

– Underwriting characteristics

• FICO

• LTV

• Amortization

• IO/option ARM

• Loan purpose

– Economic characteristics

• Home Price Appreciation (HPA)

• Interest rates

• Unemployment rates

• GDP

• Affordability

• Property type

• Occupancy type

• Documentation type

• Loan size

11

Methodology A priori ultimate

Field Value Relativity ULR FormulaFICO 660LTV 90%

Amortization ARM 5/1 or longer 1.10 BInterest Only Non-IO/OARM 1.00 CLoan Purpose Rate/Term Refinance 0.95 DProperty Type Condo 1.20 EOccupancy Type Owner Occupied 1.00 FDocumentation Type Reduced 1.25 GLoan Size Conforming 1.00 H

Combined 1.57 I=Product(B:H)

Combined Adjusted 1.25 J=Sqrt(I)

U/W Adjusted 8.3% K=A*J

HPA Adjusted 14.4% L

U/W & HPA Adjusted 18.0% M=J*L

Period HPAOrigination to evaluation -2.1% NEvaluation through resolution -7.3% OOrigination to resolution -9.2% P=(1+N)(1+O)-1

Scenario HPA ULRCCC 13.2% 3.6% Q/RAAA -34.5% 26.7% S/T

Expected -9.2% 14.4% P/L

Formula SourceA:H, Q:T Rating agency publications and Milliman researchN OFHEOO Economics forecasting firms (e.g., Global Insight, Moody's, S&P)L Linear interpolation of Q:T and P

6.6% A

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MethodologyComparison of Delinquency Rate and HPA

0.0%

1.0%

2.0%

3.0%

4.0%

5.0%

6.0%

7.0%

1979-1 1981-1 1983-1 1985-1 1987-1 1989-1 1991-1 1993-1 1995-1 1997-1 1999-1 2001-1 2003-1 2005-1 2007-1

Yr-Qtr

De

linq

ue

ncy

Ra

te

-4%

-2%

0%

2%

4%

6%

8%

10%

12%

14%

16%

HP

A Delq

HPA

Source: OFHEO, MBA

13

Methodology

Source: Milliman, Fitch

Illustration of Frequency of Foreclosure Versus Cumulative Home Price Appreciation

-35% -30% -25% -20% -15% -11% -6% -1% 4% 8% 13%

Cumulative Home Price Appreciation

Fre

qu

ency

of

Fo

recl

osu

re

FICO 620-LTV 95

FICO 660-LTV 90

FICO 700-LTV 85

14

Year Over Year HPA By CBSA

-20%

-10%

0%

10%

20%

30%

40%

19

85

-2

19

86

-2

19

87

-2

19

88

-2

19

89

-2

19

90

-2

19

91

-2

19

92

-2

19

93

-2

19

94

-2

19

95

-2

19

96

-2

19

97

-2

19

98

-2

19

99

-2

20

00

-2

20

01

-2

20

02

-2

20

03

-2

20

04

-2

20

05

-2

20

06

-2

20

07

-2

20

08

-2

20

09

-2 f

20

10

-2 f

20

11

-2 f

Yr-Qtr

Ye

ar

Ove

r Y

ea

r H

PA

%

Las Vegas

Milwaukee

Riverside, CA

Springfield, IL

Washington, DC

Source: Historical OFHEO, Forecast Moody's Economy.com

Methodology

15

Case Shiller Historical HPI and CME Futures @ Sept 13, 2008

0

50

100

150

200

250

300

Year-Month

HP

I

Wash DC

Miami

Las Vegas

Composite 10

Source: Standard & Poor's, CME Group

Methodology

16

0% - 10%

10% - 20%

20% - 40%

40% - 60%

60% - 100%

Geographic Distribution of Market Risk IndexSM @ Summer 2008Probability That House Prices will be Lower in Two Years

Source: PMI Group

Methodology

17

Distribution

Property Type Before After Risk Weight1

Single family 85% 100% 1.00

2-4 Family 5% 0% 1.10

Condo 10% 0% 1.50

Total 100% 100

Indicated risk relativity 1.06 1.00

Indicated change -5%1 Moody’s Approach to Rating Residential Mortgage Pass-Throughs

Revised underwriting guidelinesSimplified example of the effect of a change in underwriting

18

Restricted Markets– More stringent eligibility

• Varies by MI, evolving with time• Lower maximum LTV• Higher credit score

Methodology

19

Methodology Loan-level transition process

– Loan in one of several ‘states’ each month

• In force – current

• In force – delinquent

• Terminated – prepay

• Terminated - claim

12

1

4

3

2

1

4

3

2

1

4

3– Transition probabilities depend on U/W & economics

– Calculate timing of CF’s & accruals

0 321Months since evaluation

20

Methodology Loan-level transition process

– Transition probabilities depend on U/W & economics

– Allows for amounts and timing of both payments and accruals

– Example monthly transition probability matrix

1 2 3 4

1 0.80 0.05 0.12 0.03

2 0.04 0.85 0.05 0.06

3 0.00 0.00 1.00 0.00

4 0.00 0.00 0.00 1.00

Next Month

Now

21

Methodology Loan-level transition process

– In force – delinquent can be further decomposed by time since development

– Delinquency status predictive of ultimate disposition

– More precisely calculate loss reserve

• Amount

• Adverse/favorable development

22

Hedging Steps to hedge

– Forecast premium, CC & loss

– Calculate net dividends/capital to parent

Flow chart

23

Hedging

Hedging Tools

– Premium

• Mortgage rates decrease, prepays increase, premium decrease

• Mortgage rates increase, prepays decrease, premium increase

• Go variable in interest rate swap

• Position determined by elasticity between rates and premium (composition of reinsured portfolio)

– Loss

• HPA favorable, losses decrease

• HPA adverse, losses increase

• Go short CME Real Estate Futures/Options and/or ABX.HE credit default swaps

• Position determined by distribution of geography and vintage

24

Closing Thoughts

Many uses

Magnitude & timing

Payment and accruals

Function of performance, underwriting, economic, mitigation

Hedgeable