Download - Mortgage Insurance Loss Forecasting
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
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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
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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
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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
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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
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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
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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
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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%
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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
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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
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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
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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
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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
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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
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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
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Restricted Markets– More stringent eligibility
• Varies by MI, evolving with time• Lower maximum LTV• Higher credit score
Methodology
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Methodology Loan-level transition process
– Loan in one of several ‘states’ each month
• In force – current
• In force – delinquent
• Terminated – prepay
• Terminated - claim
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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
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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
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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
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Hedging Steps to hedge
– Forecast premium, CC & loss
– Calculate net dividends/capital to parent
Flow chart
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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
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Closing Thoughts
Many uses
Magnitude & timing
Payment and accruals
Function of performance, underwriting, economic, mitigation
Hedgeable