Residential Mortgage Portfolio Risk Analytics
ROGER M. STEIN, ASHISH DAS
NOVEMBER 19, 2010
Agenda
¾Why are mortgages complicated to model?
9 Many (many) scenarios are required to capture the behavior of mortgages in different states of the world
9 Loan-level behaviors are not homogenous
9 Single period analysis cannot generally be used for path-dependent instruments like mortgages
¾How did we model residential mortgages?
9 Overview and economic modeling
¾Modeling it this way permits one to:
9 Generate full collateral loss distribution and losses for MEDC and user-defined scenarios
9 Use actual or simulated macro-factors directly (scenario analysis, historical validation)
9 Model seasoned pools and new issuance in one framework (using pool-level & loan-level data)
9 Explicitly model primary and pool-level mortgage insurance
9 Perform tranching, VaR, and capital allocation using tail risk contribution of loans
9 Generate full loss distributions for individual tranches of an RMBS or RMBS portfolios
¾Conclusion
Residential Mortgage Portfolio Risk Analytics - Nov 2010
2
¾Why are mortgages complicated to model?
9 Many (many) scenarios are required to capture the behavior of mortgages
in different states of the world
9 Loan-level behaviors are not homogenous
9 Single period analysis cannot generally be used for path-dependent instruments like mortgages
¾How did we model residential mortgages?
9 Overview and economic modeling
¾Modeling it this way permits one to:
9 Generate full collateral loss distribution and losses for MEDC and user-defined scenarios
9 Use actual or simulated macro-factors directly (scenario analysis, historical validation)
9 Model seasoned pools and new issuance in one framework (using pool-level & loan-level data)
9 Explicitly model primary and pool-level mortgage insurance
9 Perform tranching, VaR, and capital allocation using tail risk contribution of loans
9 Generate full loss distributions for individual tranches of an RMBS or RMBS portfolios
¾Conclusion
Residential Mortgage Portfolio Risk Analytics - Nov 2010
3
Loan level modeling in different economies
5
10
10
20
40
10
15
pers[filt]
20
25
0.02
0.04
0.02
0.0
10
5
10
15
pers[filt]
Residential
20
30
40
0.015
0.030
loan= 98 ; econ= 885
0
5
10
15
20
25
30
pers[filt]
loan= 98 ; econ= 889
Default Hazard Rates
0
40
pers[filt]
40
0.020
Default Hazard Rates
0.020
5
30
0
loan= 98 ; econ= 888
0.010
Default Hazard Rates
30
0.0
Default Hazard Rates
0.030
0.015
0.04
0.02
0.0
0
30
loan= 40 ; econ= 889
pers[filt]
0.0
Default Hazard Rates
0.04
20
pers[filt]
25
loan= 98 ; econ= 887
0.02
10
20
pers[filt]
loan= 98 ; econ= 886
0
15
20
20
25
0.06
25
10
0.0
Default Hazard Rates
0.020
0.010
Default Hazard Rates
20
pers[filt]
0
pers[filt]
Same loan in
different
20
30
40
0
10
20
30
40
economies
pers[filt]
pers[filt]
exhibits different
98 ; econ= 883
loan= 98 ; econ= 884
behavior and
correlations
0.0
0.020
0.010
0.0
Default Hazard Rates
loan=
40
0.02
10
30
LOAN # 98
15
20
loan= 40 ; econ= 888
Default Hazard Rates
0
loan= 98 ; econ= 882
10
10
pers[filt]
0.04
40
pers[filt]
5
0
0.0
30
0.02
Default Hazard Rates
20
0.0
0.010
10
40
loan= 40 ; econ= 887
0.0
Default Hazard Rates
loan= 40 ; econ= 886
0
30
0.03
20
pers[filt]
0.0
10
Default Hazard Rates
0
0.0
Default Hazard Rates
0.04
40
loan= 40 ; econ= 885
Default Hazard Rates
30
0.010
20
pers[filt]
0.0
10
0.02
Default Hazard Rates
0
loan= 40 ; econ= 884
0.0
0.02
0.0
Default Hazard Rates
loan= 40 ; econ= 883
0.0
LOAN # 40
loan= 40 ; econ= 882
0
Mortgage Portfolio Risk
10
20
30
pers[filt]
Analytics
- Nov
2010
40
4
Using Aggregate Pool Statistics I
Consider two pools drawn from this population: one homogeneous and one barbelled
(but both with approximately the same mean CLTV and FICO)
FICO SCORE
Combined LTV
Low
<70
Medium
[70,80)
High
[80,85)
Very High
>=85
Low < 710
2.4
4.9
5.5
9.7
Medium [710,750)
1.0
3.2
3.5
7.0
High [750,775)
0.5
1.5
1.7
4.0
Very High >= 775
0.1
0.7
0.9
1.8
FICO
CLTV
Def. rate
Homogeneous
746
77.5
2.5
Barbell
738
75.0
4.9
Residential Mortgage Portfolio Risk Analytics - Nov 2010
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¾Why are mortgages complicated to model?
9 Many (many) scenarios are required to capture the behavior of mortgages in different states of the world
9 Loan-level behaviors are not homogenous
9 Single period analysis cannot generally be used for path-dependent
instruments like mortgages
¾How did we model residential mortgages?
9 Overview and economic modeling
¾Modeling it this way permits one to:
9 Generate full collateral loss distribution and losses for MEDC and user-defined scenarios
9 Use actual or simulated macro-factors directly (scenario analysis, historical validation)
9 Model seasoned pools and new issuance in one framework (using pool-level & loan-level data)
9 Explicitly model primary and pool-level mortgage insurance
9 Perform tranching, VaR, and capital allocation using tail risk contribution of loans
9 Generate full loss distributions for individual tranches of an RMBS or RMBS portfolios
¾Conclusion
Residential Mortgage Portfolio Risk Analytics - Nov 2010
6
Multi-period Simulation and path dependence
¾Home prices start at 100 and end, 10 years later, at 134.
¾Scenario 1: home price appreciation of 3% per year for 10 years
¾Scenario 2: home price depreciation of 20% over 3 years followed by a gain
over the next 7 years
Pool
1
2
3
4
5
EL
(Scenario 1)
9.0
6.6
6.0
7.0
1.6
EL (Scenario 2)
15.8
10.3
9.0
11.5
2.1
Multi-period simulation is valuable due to strong path dependency.
Residential Mortgage Portfolio Risk Analytics - Nov 2010
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Why are Mortgages Complicated to Model?
¾If loan-level data is available, it may be preferred because
9A single loan can behave very differently in different economic scenarios.
9Different loan types behave very differently in the same economic scenario.
¾Drivers of mortgage performance, including prepayment and default, are
strongly path dependent.
¾Mortgages have many embedded options, including
9the option to prepay (call)
9the option to walk away from the loan (put).
¾The terms of these options do not generally average out analytically.
Residential Mortgage Portfolio Risk Analytics - Nov 2010
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¾Why are mortgages complicated to model?
9 Many (many) scenarios are required to capture the behavior of mortgages in different states of the world
9 Loan-level behaviors are not homogenous
9 Single period analysis cannot generally be used for path-dependent instruments like mortgages
¾How did we model residential mortgages?
9 Overview and economic modeling
¾Modeling it this way permits one to:
9 Generate full collateral loss distribution and losses for MEDC and user-defined scenarios
9 Use actual or simulated macro-factors directly (scenario analysis, historical validation)
9 Model seasoned pools and new issuance in one framework (using pool-level & loan-level data)
9 Explicitly model primary and pool-level mortgage insurance
9 Perform tranching, VaR, and capital allocation using tail risk contribution of loans
9 Generate full loss distributions for individual tranches of an RMBS or RMBS portfolios
¾Conclusion
Residential Mortgage Portfolio Risk Analytics - Nov 2010
9
It is helpful to distinguish between the different
dimensions of portfolio analysis
Level of analysis
Basis of analysis
Loan-level
Aggregate-level
Single path
MPA
Macro scenario
MPA
Rep-lines
Simulated
distribution of
paths
MPA full lossdistribution
analysis
N/A
Residential Mortgage Portfolio Risk Analytics - Nov 2010
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Overview I
¾Our model is an analytic tool for assessing the credit risk of a portfolio of
residential mortgages (RMBS & whole loans) .
¾The model comprises loan-level econometric models for default,
prepayment, and severity.
¾These models are integrated through common dependence on local macroeconomic factors, which are simulated at national and local (MSA) levels.
¾This integration produces correlation in loan behaviors across the portfolio.
¾Because we use a multi-step Monte Carlo approach, the model can be
combined with an external cash flow waterfall tool and used for simulation
of RMBS transactions.
¾The models also use pool-level performance to update the output in real-time.
Residential Mortgage Portfolio Risk Analytics - Nov 2010
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Mortgage Modeling: Overview II
Output
Default
scenario)
Loan Level
Pool Data
(User data)
Supplemental
user data
(loan level
override, pool
performance,
etc.)
Severity
Prepayment
Σ
Pool Level E(L)
Economic Data
(simulated or
MODELS
Loan Level E(L)
FACTORS
Residential Mortgage Portfolio Risk Analytics - Nov 2010
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¾Why are mortgages complicated to model?
9 Many (many) scenarios are required to capture the behavior of mortgages in different states of the world
9 Loan-level behaviors are not homogenous
9 Single period analysis cannot generally be used for path-dependent instruments like mortgages
¾How did we model residential mortgages?
9 Overview and economic modeling
¾Modeling it this way permits one to:
9 Generate full collateral loss distribution and losses for MEDC and user-
defined scenarios
9 Use actual or simulated macro-factors directly (scenario analysis, historical validation)
9 Model seasoned pools and new issuance in one framework (using pool-level & loan-level data)
9 Explicitly model primary and pool-level mortgage insurance
9 Perform tranching, VaR, and capital allocation using tail risk contribution of loans
9 Generate full loss distributions for individual tranches of an RMBS or RMBS portfolios
¾Conclusion
Residential Mortgage Portfolio Risk Analytics - Nov 2010
13
A Mortgage Portfolio Loss Distribution
In addition to generating the full loss distribution, it is possible
to estimate losses under MEDC or user-defined scenarios.
Residential Mortgage Portfolio Risk Analytics - Nov 2010
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¾Why are mortgages complicated to model?
9 Many (many) scenarios are required to capture the behavior of mortgages in different states of the world
9 Loan-level behaviors are not homogenous
9 Single period analysis cannot generally be used for path-dependent instruments like mortgages
¾How did we model residential mortgages?
9 Overview and economic modeling
¾Modeling it this way permits one to:
9 Generate full collateral loss distribution and losses for MEDC and user-defined scenarios
9 Use actual or simulated macro-factors directly (scenario analysis, historical
validation)
9 Model seasoned pools and new issuance in one framework (using pool-level & loan-level data)
9 Explicitly model primary and pool-level mortgage insurance
9 Perform tranching, VaR, and capital allocation using tail risk contribution of loans
9 Generate full loss distributions for individual tranches of an RMBS or RMBS portfolios
¾Conclusion
Residential Mortgage Portfolio Risk Analytics - Nov 2010
15
Scenario Analysis using Observable Macroeconomic Factors
Observable macro-economic factors facilitate insightful what-ifs.
Residential Mortgage Portfolio Risk Analytics - Nov 2010
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¾Why are mortgages complicated to model?
9 Many (many) scenarios are required to capture the behavior of mortgages in different states of the world
9 Loan-level behaviors are not homogenous
9 Single period analysis cannot generally be used for path-dependent instruments like mortgages
¾How did we model residential mortgages?
9 Overview and economic modeling
¾Modeling it this way permits one to:
9 Generate full collateral loss distribution and losses for MEDC and user-defined scenarios
9 Use actual or simulated macro-factors directly (scenario analysis, historical validation)
9 Model seasoned pools and new issuance in one framework (using pool-
level & loan-level data)
9 Explicitly model primary and pool-level mortgage insurance
9 Perform tranching, VaR, and capital allocation using tail risk contribution of loans
9 Generate full loss distributions for individual tranches of an RMBS or RMBS portfolios
¾Conclusion
Residential Mortgage Portfolio Risk Analytics - Nov 2010
17
US Jumbo RMBS Performance
Source: Moody’s Investors Service
Delinquent loan pipeline makes up a key part of future losses.
Residential Mortgage Portfolio Risk Analytics - Nov 2010
18
Modeling Seasoned Mortgage Pools: Delinquent
loans
¾We categorize delinquent loans into: 30, 60, and 90+ Days Past Due.
¾Default and prepayment hazard rates differ substantially between
delinquent loans and current loans.
¾Each delinquency status has different default and prepayment behavior.
¾Explicitly modeling delinquent loans permits much finer analysis than “rollrate” approaches for portfolio monitoring.
Delinquent loans behave very differently than current loans.
Residential Mortgage Portfolio Risk Analytics - Nov 2010
19
Modeling Seasoned Loans: Incorporating poolspecific Realized Performance To-date
¾Realized performance can, on occasion, be very different than predicted due to
unobservable differences in underwriting, servicing, borrower characteristics, etc.
¾It is important to incorporate individual components of the realized performance, namely
default, prepayments, and severity, separately.
¾In the majority of cases, the predicted and observed behaviors generally agree closely. In
some cases, however (e.g., table below), the pool-performance information can be valuable.
Portfolio
Without mid‐
course update
With mid‐course update
Comments
1
2
3
4
15.2
19.6
22.9
29.7
13.7
23.7
17.3
14.4
Good originator
Severity higher than expected
Conservative originator
Retail. Good underwriting
Pool-level idiosyncratic behavior can be useful in future projection.
Residential Mortgage Portfolio Risk Analytics - Nov 2010
20
¾Why are mortgages complicated to model?
9 Many (many) scenarios are required to capture the behavior of mortgages in different states of the world
9 Loan-level behaviors are not homogenous
9 Single period analysis cannot generally be used for path-dependent instruments like mortgages
¾How did we model residential mortgages?
9 Overview and economic modeling
¾Modeling it this way permits one to:
9 Generate full collateral loss distribution and losses for MEDC and user-defined scenarios
9 Use actual or simulated macro-factors directly (scenario analysis, historical validation)
9 Model seasoned pools and new issuance in one framework (using pool-level & loan-level data)
9 Explicitly model primary and pool-level mortgage insurance
9 Perform tranching, VaR, and capital allocation using tail risk contribution of loans
9 Generate full loss distributions for individual tranches of an RMBS or RMBS portfolios
¾Conclusion
Residential Mortgage Portfolio Risk Analytics - Nov 2010
21
Single-loan Loss Histogram with different Rescission
Assumptions on Primary Mortgage Insurance (PMI)
Original
Balance
$250,000
FICO
605
State
CA
Loan Type
IO ARM
Doc Type
Full
income –
No
assets
LTV
»
90
occurrences of no default not shown for either data set (14% each)
Residential Mortgage Portfolio Risk Analytics - Nov 2010
22
¾Why are mortgages complicated to model?
9 Many (many) scenarios are required to capture the behavior of mortgages in different states of the world
9 Loan-level behaviors are not homogenous
9 Single period analysis cannot generally be used for path-dependent instruments like mortgages
¾How did we model residential mortgages?
9 Overview and economic modeling
¾Modeling it this way permits one to:
9 Generate full collateral loss distribution and losses for MEDC and user-defined scenarios
9 Use actual or simulated macro-factors directly (scenario analysis, historical validation)
9 Model seasoned pools and new issuance in one framework (using pool-level & loan-level data)
9 Explicitly model primary and pool-level mortgage insurance
9 Perform tranching, VaR, and capital allocation using tail risk contribution of
loans
9 Generate full loss distributions for individual tranches of an RMBS or RMBS portfolios
¾Conclusion
Residential Mortgage Portfolio Risk Analytics - Nov 2010
23
PD based tranching approach (VaR)
¾ A tranche has adequate
capitalization for a predefined PD
value, PDR if:
Tranche PD = P ( L > A)
1
= ∫ f L ( L) ⋅ dL
A
≤ PDR
¾ Where,
A ≡ tranche attachment point
L ≡ loss rate on the portfolio
f L (⋅) ≡ pdf of the collateral loss rate
PD-based CE is equivalent to VaR with α = PDR (the target default rate).
Residential Mortgage Portfolio Risk Analytics - Nov 2010
24
Tail risk contribution
¾ Tail risk contribution (TRC) is a portfolio referent risk measure for an individual loan.
¾ It measures how much capital the loan uses up in the tail of the distribution.
TRCi = E[ Li | LP > VaRα ],
TRCi = tail risk contribution for the i th loan
Li = loss on the i th loan
LP = loss on the portfolio
VaRα = 1 − α VaR level for the portfolio,
i.e., the capital required to support the portfolio
¾ The TRC of a loan depends on its correlation with the other loans in a portfolio.
¾ TRC indicates which loans increase or decrease the capital (“attachment point”) for a
specific VaR, and is useful for:
9 Portfolio construction
9 Loan pricing
9 Hedging
Residential Mortgage Portfolio Risk Analytics - Nov 2010
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Tail Risk Contribution to VaR
¾TRC is the contribution a loan makes to the tail risk of a portfolio.
EL
99.5% VaR
Level
Original portfolio
4.0%
12.6%
With 100 highest EL loans
removed
2.9%
10.2%
With 100 highest
contributors to VaR
removed
3.1%
9.7%
Tail risk of a loan is often different than its stand-alone risk.
Residential Mortgage Portfolio Risk Analytics - Nov 2010
26
¾Why are mortgages complicated to model?
9 Many (many) scenarios are required to capture the behavior of mortgages in different states of the world
9 Loan-level behaviors are not homogenous
9 Single period analysis cannot generally be used for path-dependent instruments like mortgages
¾How did we model residential mortgages?
9 Overview and economic modeling
¾Modeling it this way permits one to:
9 Generate full collateral loss distribution and losses for MEDC and user-defined scenarios
9 Use actual or simulated macro-factors directly (scenario analysis, historical validation)
9 Model seasoned pools and new issuance in one framework (using pool-level & loan-level data)
9 Explicitly model primary and pool-level mortgage insurance
9 Perform tranching, VaR, and capital allocation using tail risk contribution of loans
9 Generate full loss distributions for individual tranches of an RMBS or RMBS
portfolios
¾Conclusion
Residential Mortgage Portfolio Risk Analytics - Nov 2010
27
A-1
A-2
A-3
A-4
A-5
X
R
B-1
B-2
B-3
B-4
B-5
Residential Mortgage Portfolio Risk Analytics - Nov 2010
28
0
20
40
60
80
100
0
20
40
60
80
100
0
20
40
60
80
100
0
20
40
60
80
100
0
20
40
60
80
100
4000
R
0
4000
X
0
4000
A-5
EL: 0
8000
8000
EL: 0
0
4000
A-4
0
4000
A-3
EL: 0
8000
8000
EL: 0
0
4000
A-2
0
0
4000
A-1
EL: 0
8000
EL: 0
8000
8000
EL: 0
0
20
40
60
80
100
0
20
40
60
80
100
8000
EL: 2.3
0
4000
B-1
0
20
40
60
80
100
60
80
100
60
80
100
60
80
100
60
80
100
5000
EL: 17.6
0
2000
B-2
0
20
40
4000
EL: 36.9
0
2000
B-3
0
20
40
1000 2000
EL: 53.4
0
B-4
0
20
40
2000
EL: 73.4
0
1000
B-5
0
20
40
Residential Mortgage Portfolio Risk Analytics - Nov 2010
29
Modeling This Way Permits One To…
¾Generate full loss distribution and losses for MEDC and/or user defined scenarios.
¾Conduct scenario analysis using observable macro-economic factors.
¾Conduct validations using realized economies to-date.
¾Use the same framework to evaluate seasoned portfolios and new originations:
9 Model delinquent loans differentially than current loans, and
9 Incorporate realized performance to-date into future projections of defaults, prepayments, and severity
(combine pool and loan-level approaches)
¾Calculate PD-based and EL-based VaR and tranche attachment points.
¾Calculate the tail risk contribution for each loan and thus help in managing the tail
risk of a portfolio of mortgage loans.
¾Provide collateral loss distribution and the cash flows that can be combined with a
waterfall engine to produce tranche-level loss distributions.
Residential Mortgage Portfolio Risk Analytics - Nov 2010
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Conclusion
¾ Modeling at the loan level significantly improves detail in estimating losses.
¾ Modeling each loan behavior (default, prepayment, and severity) separately
provides substantial flexibility in calibration and specification.
¾ Prepayment can have a dominant effect in determining the distribution of
losses during periods of home price appreciation and/or falling interest rates.
¾ The state of the local and national economy significantly impacts the
performance of pools.
¾ Default, prepayment, and severity appear to be correlated through their joint
dependence on common economic factors.
¾ The multi-step approach to simulation offers advantages when assets have
path dependent behavior, as in the case of mortgages.
Residential Mortgage Portfolio Risk Analytics - Nov 2010
31
Research contacts:
»
Roger M. Stein
[email protected]
»
Ashish Das
[email protected]
Product information:
»
David Little
[email protected]
Residential Mortgage Portfolio Risk Analytics - Nov 2010
32
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