Data Organization and Analysis in
Mortgage Insurance: The Implications of
Dynamic Risk Characteristics
Prepared for:
CAS 2008 Seminar on Ratemaking
March 17-18, 2008
Presented by:
Tanya Havlicek
Kyle Mrotek, FCAS
Background: What is Mortgage Insurance (MI)?
 The Mortgage Guaranty Model Act of the NAIC defines mortgage
insurance as insurance against financial loss by reason of
nonpayment of principal, interest, or other sums agreed to be paid
under the terms of any note or bond or other evidence of
indebtedness secured by a mortgage, deed of trust, or other
instrument constituting a lien or charge on real estate…(“Mortgage
Guaranty Insurance Model Act” Model #630-1, NAIC Section 2)
2
Background: What is Mortgage Insurance?
The
Applies for Loan
Borrower
The
Lender
Selects MI
The
MI
Makes the
Loan
Payment
including
MI fee
The
Servicer
Forwards
Interest Yield
and MI Claim Checks
Fannie /
Freddie
Investors
3
Reserving Considerations
 Generally accepted methodology of reserving for mortgage guaranty claim liabilities is
to reserve for loans currently delinquent, both known and IBNR: Occurrence is at
missed payment
 Mortgage guaranty insurance companies do not reserve for loans insured but not
delinquent (i.e. loans current on payments do not have associated reserves) –
(“Mortgage Guaranty Insurance Model Act” Model #630-1, NAIC Section 16)
 The cohort of insured loans currently delinquent changes monthly
 Many delinquent loans do not result in a claim
 Delinquency status (categorical classification of a mortgage’s overdue payment) is an
established strong predictor of future losses
 The relationship between delinquency status and future losses can be stable or change
over time
4
•
changes in economic conditions (unemployment, home price appreciation)
•
changes in mortgage products (dist’n of ARM’s or high Loan-To-Value loans)
•
changes in foreclosure or claims mitigation procedures
Reserving Considerations
 Commonly use a frequency-severity approach to estimate required reserves in mortgage
insurance
 In general, the further a loan is in default, the more likely the loan will not cure (become
current on payments) and potentially lead to a claim
 Delinquency status can be based on the number of monthly payments missed or how long
the loan has been consecutively delinquent
• One payment behind for 6 months (Delinquent 1 month vs 6 months since missed pmt)
 Other considerations for frequency factors include underwriting risk characteristics and
macroeconomic variables:
• Loan-To-Value
• Borrower credit rating
• Property geography
• Home price appreciation
• Market interest rates
 Severity component often conditioned on claim having occurred, thus the dynamic input
variable delinquency status has no effect
• this presentation focuses on the frequency component of losses
5
Reserving Considerations
 Goal: Develop frequency factors that predict the claim rate for the current cohort of
delinquent loans in order to estimate required reserves
•
Select factors along specified risk dimensions (including delinquency status)
 The dynamic nature of loan delinquency status manifests itself in MI reserving in
several aspects:
–
Determines the cohort of loans that currently need reserves
–
A loan’s active delinquency status is a strong predictor of future losses
–
Need to calculate historical conditional claim frequencies to derive selected
reserving factors
 Establishing loss reserves conditioned on delinquency status presents particular data
issues
 There is a need to collect, organize, warehouse, and analyze large data sets that
contain loan level detail over monthly evaluation dates to measure the probability of
claim conditioned on delinquency status
6
Delinquency Status
 Once a loan becomes delinquent, over time it can maintain the same status, become
progressively more delinquent, or move back and forth between delinquency stages
before eventually resolving into one of two fates: it may become current in payments
and be considered cured, or it may remain in default and result in a claim
•
To derive historical indications, need to track each delinquency over
consecutive monthly evaluations to its ultimate cure or claim
 Loans can cure but then become delinquent at a later date
•
Must be able to distinguish delinquency trips to calculate pure claim rates
 Ability to distinguish and quantify delinquency trips and subsequent fates for all
delinquent loans every month historically and then aggregate along risk-characteristic
dimensions to develop reserving factors requires data availability and storage over
consecutive monthly evaluation dates, otherwise tracking capability lost in data
uncertainties
7
Delinquency Status
 Consider the following example to better understand the data organization and analysis
issues created by delinquency status
Illustrative Example of One Loan's Status Over Time
Eval Month Status
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
8
Current
Delinquent-30
Delinquent-60
Current
Delinquent-30
Current
Current
Delinquent-30
Delinquent-60
Delinquent-90
Delinquent-60
Delinquent-90
Delinquent-60
Delinquent-30
Current
Delinquent-30
Delinquent-60
Delinquent-90
Delinquent-120
Current
Delinquent-30
Delinquent-60
Delinquent-90
Delinquent-120
Claim
Need Reserve? Delinquency Trip #
No
Yes
Yes
No
Yes
No
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
No
Yes
Yes
Yes
Yes
No
Yes
Yes
Yes
Yes
NA
NA
1
1
NA
2
NA
NA
3
3
3
3
3
3
3
NA
4
4
4
4
NA
5
5
5
5
5
 This loan’s delinquency status changes every
month
 As delinquency status changes, the expected
loss changes via frequency (or probability of
claim)
 The expected frequency of claim for a “30” may
be different in Eval Month 2 and Eval Month 16
•
e.g. change in economic conditions
 Only on Trip 5 does this loan result in a claim
(overall Claim Rate=1/5)
 To develop historical claim frequencies requires
tracking each loan at each month to its ultimate
resolution for that delinquency trip
Data Organization
 Two types of loan characteristics an actuary may want to use as dimensions in developing
reserving factors: dynamic and static
 Static characteristics: do not change over the lifetime of the loan
•
e.g. original loan-to-value, borrower original credit score
–
Static information can be stored in a database with one record for each policy
–
Updated and appended to as new policies originated
 Dynamic characteristics: can change monthly
•
e.g. delinquency status, current loan-to-value
–
Dynamic information should be stored in a database with a policy record for every
month of the loan’s lifetime
–
Updated and appended to each successive month
–
Allows for accurate reconstruction and analysis of historical delinquency cohorts and
their fates
 Size requirements and processing time considerations may make it infeasible or impractical
to store all attributes of all loans at every month
9
Data Organization
 Consider database size necessary to store monthly records of 100 fields for 100,000 loans for
156 months (a single book year of business over its lifetime), but only 5 fields change over
the life of the loan
 Repeat this to add 5 book years of business
 Single database will grow rapidly to an unmanageable size (PC environ)
 Suffices to have a unique primary key ID field in two databases (dynamic and static) so they
can be merged one-to-many correctly
 Field typically used for this is policy certificate number assigned by mortgage guaranty insurer
 Some challenges that can be addressed with a two database organization:
–
–
10
Data purging occurs in a single policy database with key dates
•
If a loan cures but becomes delinquent again at a later date, information on prior
delinquency trip lost as new information written for new delinquency trip
•
Dynamic database with every monthly evaluation date stores complete performance
history
Storage requirements potentially massive for single database with all characteristics of all
loans every month
Data Organization
 Time window of claims performance data
–
As much as is available
•
Data availability partly determines constraints of analysis
–
Minimum: enough consecutive months of complete data to observe credible amount of
delinquency resolutions
–
Ideally, enough to:
•
capture an entire economic cycle
•
observe claims development for many delinquency cohorts (each policy can be inforce upwards of 15 years)
•
observe claims performance of all currently insured loan types (business mix)
 Time periods need to be contiguous
11
–
Data “holes” where delinquency activity absent may make it impossible to determine
fate of any loan actively delinquent to and leading into missing evaluation date
–
Delinquency cohorts of missing months cannot be used for analysis
Data Organization
Claim Rate
60.0%
50.0%
40.0%
30.0%
Clm Rate
20.0%
10.0%
Ja
n99
Ju
l-9
Ja 9
n00
Ju
l-0
Ja 0
n01
Ju
l-0
Ja 1
n02
Ju
l-0
Ja 2
n03
Ju
l-0
Ja 3
n04
Ju
l-0
Ja 4
n05
Ju
l-0
Ja 5
n06
Ju
l-0
Ja 6
n07
0.0%
 Delinquency cohort April ‘03 is missing from the data
 Without adjusting the data, all outstanding delinquencies cure in April ‘03 by virtue of not
being delinquent in that month (failure in data continuity)
 Can adjust using assumptions, but will not know exact history
Note: Illustrative data for discussion purposes only
12
Data Organization
Claim Rate
60.0%
50.0%
40.0%
30.0%
Clm Rate
20.0%
10.0%
Ja
n99
Ju
l-9
Ja 9
n00
Ju
l-0
Ja 0
n01
Ju
l-0
Ja 1
n02
Ju
l-0
Ja 2
n03
Ju
l-0
Ja 3
n04
Ju
l-0
Ja 4
n05
Ju
l-0
Ja 5
n06
Ju
l-0
Ja 6
n07
0.0%

Delinquency cohort April ‘03 is missing in the data (Note: Illustrative data for discussion purposes
only)

Here, the data “hole” is plugged by repeating March ’03 for April ’03 in tracking fates (in effect,
bridging the data “hole”)

Much better, but still not exact – use with caution!

Decline in claim rate for recent time in part due to unresolved delinquencies
13
Data Organization
 Set of loans to warehouse in databases: All loans vs delinquent to date
 Delinquent to date requires considerably less storage space than all loans ever written to date
 Delinquent to date requires more assumptions, merging, and date logic to program and
process
 If all loans ever written are included in the databases, there is no ambiguity associated with
an omitted loan: it is a data error
•
either because of an accidental omission or because the loan did not belong to the
mortgage guaranty company and was removed
 By storing only delinquent loans at each evaluation date, a loan may not appear for at least
two reasons: the loan is no longer delinquent or there has been a data error
 Potential sources of ambiguity include delinquency status or in-force status at any given
evaluation date
 Design decision of all loans vs delinquent to date loans should be based on the analytical
requirements of the user and the hardware and software platforms that will support the data
14
Data Processing
A
B
C
Record # Evaluation Date Loan ID
1
Jan-06
1
2
Jan-06
2
3
Jan-06
3
4
Jan-06
4
5
Jan-06
5
6
Feb-06
1
7
Feb-06
2
8
Feb-06
3
9
Feb-06
4
10
Feb-06
5
11
Mar-06
1
12
Mar-06
2
13
Mar-06
3
14
Mar-06
4
15
Mar-06
5
16
Apr-06
1
17
Apr-06
2
18
Apr-06
3
19
Apr-06
4
20
Apr-06
5
21
May-06
1
22
May-06
2
23
May-06
3
24
May-06
4
25
May-06
5
26
Jun-06
1
27
Jun-06
2
28
Jun-06
3
29
Jun-06
4
30
Jun-06
5
D
Status*
E
Delq
F
Delq Trip
G
Cure
0
30
90
60
0
0
30
90
0
30
30
30
120
30
60
0
30
FCL
60
30
30
30
FCL
FCL
0
0
30
CLM
CLM
0
* 0 = Current; 30, 60, 90, 120 = payment days past due; FCL = foreclosure; CLM = claim
15
H
Claim
 Table1: Five loans over six
delinquency months
 Six delinquency cohorts
 Goal: determine fate of each loan
for every month it is delinquent
while keeping track of delinquency
trips, so claim ratios can be
calculated for each cohort
 DelqTrip: If a loan cures, it no
longer needs a reserve
 If a loan cures and later re-delq’s
and claims, first trip still gets credit
for cure
 MI’s do not reserve for ultimate
claims for all currently insured loans
Data Processing
 Delinquency fates are determined by looking forward in time from each evaluation month to
determine the resolution of each delinquency
 Once delinquency fates are determined, the empirical conditional probability of claim for each
monthly cohort and each delinquency status can be calculated via aggregation
 Tallies are summed by delinquency cohort and risk characteristics
 Consider Loan ID 3 from previous Table
A
B
Record # Evaluation Date
3
Jan-06
8
Feb-06
13
Mar-06
18
Apr-06
23
May-06
28
Jun-06
C
Loan ID
3
3
3
3
3
3
D
Status*
90
90
120
FCL
FCL
CLM
E
F
Delq Delq Trip
1
1
1
1
1
1
1
1
1
1
0
1
G
Cure
0
0
0
0
0
0
* 0 = Current; 30, 60, 90, 120 = payment days past due; FCL = foreclosure; CLM = claim
 Loan ID 3 claims in Jun-06 and backfills as a claim (col H) for all evaluation dates
16
H
Claim
1
1
1
1
1
1
Data Processing
 Alternatively, consider Loan ID 4
A
B
Record # Evaluation Date
4
Jan-06
9
Feb-06
14
Mar-06
19
Apr-06
24
May-06
29
Jun-06
C
Loan ID
4
4
4
4
4
4
D
Status*
60
0
30
60
FCL
CLM
E
F
Delq Delq Trip
1
1
0
NA
1
2
1
2
1
2
0
2
G
Cure
1
NA
0
0
0
0
H
Claim
0
NA
1
1
1
1
* 0 = Current; 30, 60, 90, 120 = payment days past due; FCL = foreclosure; CLM = claim
 There are two delinquency trips for Loan ID 4: one that began prior to Jan-06 and a second that
begins in Mar-06
 Loan ID 4 backfills as a cure for Jan-06 (col G) for its first delinquency trip and backfills as a
claim (col H) for its second delinquency trip
 Cannot just look at final ultimate status to determine tallies
 MI companies reserve only for losses related to current delinquencies that will not cure before
leading to the insurance loss
 Contiguous history key to determining resolutions and tallies
17
Data Processing
A
B
Record # Evaluation Date
1
Jan-06
2
Jan-06
3
Jan-06
4
Jan-06
5
Jan-06
6
Feb-06
7
Feb-06
8
Feb-06
9
Feb-06
10
Feb-06
11
Mar-06
12
Mar-06
13
Mar-06
14
Mar-06
15
Mar-06
16
Apr-06
17
Apr-06
18
Apr-06
19
Apr-06
20
Apr-06
21
May-06
22
May-06
23
May-06
24
May-06
25
May-06
26
Jun-06
27
Jun-06
28
Jun-06
29
Jun-06
30
Jun-06
C
Loan ID
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
D
Status*
0
30
90
60
0
0
30
90
0
30
30
30
120
30
60
0
30
FCL
60
30
30
30
FCL
FCL
0
0
30
CLM
CLM
0
E
F
Delq Delq Trip
0
NA
1
1
1
1
1
1
0
NA
0
NA
1
1
1
1
0
NA
1
1
1
1
1
1
1
1
1
2
1
1
0
NA
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
0
NA
0
NA
1
1
0
1
0
2
0
NA
G
Cure
NA
0
0
1
NA
NA
0
0
NA
1
1
0
0
0
1
NA
0
0
0
1
1
0
0
0
NA
NA
0
0
0
NA
* 0 = Current; 30, 60, 90, 120 = payment days past due; FCL = foreclosure; CLM = claim
18
H
Claim
NA
0
1
0
NA
NA
0
1
NA
0
0
0
1
1
0
NA
0
1
1
0
0
0
1
1
NA
NA
0
1
1
NA
 Table 1 with complete fate
tallies
 Observe Loan ID 2 is
unresolved as of Jun-06, so
contributes neither as cure
nor claim
 Loan ID 2 remains one
payment behind for the six
month time period
Data Processing
 In practice, there are not 30 records for five loans to analyze but potentially millions of records
for hundreds of thousands of loans
 At the end of 2006, the private mortgage industry had nearly $800 billion of primary insurance
in force
 Use a programming language that can handle do-loops and consecutive record comparison,
so that key ID fields, delinquency statuses, and evaluation dates can be compared and
processed
•
19
C++, Visual Basic
Delinquency Analysis
 Once fates are tallied at the loan level, they can be aggregated and analyzed for each
delinquency cohort and delinquency status
 Consider delinquency cohort Mar-06 from the previous example
 Use only resolved delinquencies to calculate ever-to-date empirical claim rate
 Can make assumptions about claim rate on unresolved delinquencies for projections
•
ultimate claim rate
•
maximum claim rate
A
B
C
D
E
Delinquency
Cohort
Status*
Delqs
Cures
Claims
Mar-06
30
3
1
1
Mar-06
60
1
1
0
Mar-06
90
0
0
0
Mar-06
120
1
0
1
Mar-06
FCL
0
0
0
30, 60, 90, 120 = payment days past due; FCL = foreclosure
20
F = D+E G = E/F
Resolved
Claim
Delqs
Rate
2
50%
1
0%
0
NA
1
100%
0
NA
Delinquency Analysis
 Once fates are tallied at the loan level, they can be aggregated and analyzed along various
risk dimensions after loan characteristics are merged on from the static database – can
assess risk interactions
 Risk dimensions selected depend on data availability and actuary’s judgment on predictive
value and credibility (homogeneity vs data thinning)
A
B
C
D
E
Status* Loan-To-Value
Delqs
Cures
Claims
30
90
1000
930
70
95
1200
1092
108
100
1400
1232
168
60
90
800
720
80
95
900
792
108
100
1000
860
140
90
90
600
528
72
95
700
595
105
100
800
664
136
120
90
300
240
60
95
350
266
84
100
400
288
112
FCL
90
100
65
35
95
120
72
48
100
140
77
63
*30, 60, 90, 120 = payment days past due; FCL = foreclosure
21
F = D+E
Resolved
Delqs
1000
1200
1400
800
900
1000
600
700
800
300
350
400
100
120
140
G = E/F
Claim
Rate
7%
9%
12%
10%
12%
14%
12%
15%
17%
20%
24%
28%
35%
40%
45%
Incorporating Economic Variables
 Economic variables can be incorporated into the data organization and analysis similar to
underwriting variables and delinquency status
 Economic variables found to be predictive include:
–
–
–
22
Home price appreciation
•
Historical data available from Office of Federal Housing Enterprise Oversight
(OFHEO)-quarterly home price indices by MSA since mid 1970s
•
Annual and quarterly forecasts available for purchase from Global Insight and
Moody’s Economy.com
Market interest rate
•
Historical data available from Freddie Mac-monthly interest rates by geographic
regions
•
Actuary can calibrate interest rate model for simulations, or interest rate forecasts
available from various sources including Mortgage Bankers Association
Unemployment rate
•
Historical data available from Bureau of Labor Statistics
•
Forecasts of unemployment available for purchase
Reserve Factor Analysis
 Claim rate frequency indications can be calculated using summary statistics of the actuary’s
choice by using different groupings of delinquency cohorts
 From these indications, along with other sources for consideration, the actuary can select
frequency factors to be applied to the current, and potentially future, cohort of delinquent
loans for loss reserving purposes
 Severity factors can be derived by delinquency cohort using the output from the tally
processing at the loan level in conjunction with exposure and claim loss dollar information
23
Conclusions
 Mortgage guaranty loss reserves are provisions for losses due to insured loans currently
delinquent, both reported and unreported
 Specifically, there need not be a provision for losses due to loans insured but not delinquent
 As a result, the status of whether a loan is delinquent or not is integral to the reserve estimate
 The degree of a loan’s delinquency is a significant predictor of loan default and insured loss
 A loan’s delinquency status can change monthly
 These issues combined create a need for the reserving actuary to have a contiguous
historical performance data warehouse that is usually best organized into two databases:
dynamic and static
 A two database organization addresses computer processing and storage considerations and
constraints
 The ability to reconstruct accurate historical claim rates requires monthly database updating,
relational database fields with integrity, and maintenance without purging data
24
Acknowledgments
 This presentation is based on “Data Organization and Analysis in Mortgage Insurance: The
Implications of Dynamic Risk Characteristics”
 Special thanks to Paul Keuler, whose advice and collaboration was critical in creating and
developing the analysis methods presented herein
 Special thanks to Dave Hudson and the Committee on Management of Data and Information
for the opportunity to submit our paper and their valuable feedback
 Special thanks to the Committee on The Ratemaking Seminar for inviting us to present and
offering a venue
25
References
 “Mortgage Guaranty Insurance Model Act” Model #630-1, National Association of Insurance
Commisioners, Section 16.
 DeFranco, Ralph, “Modeling Residential Mortgage Termination and Severity Using Loan
Level Data”, Spring 2002.
 “Mortgage Guaranty Insurance Model Act” Model #630-1, National Association of Insurance
Commisioners, Section 2.
 “Mortgage Guaranty Insurance Model Act” Model #630-1, National Association of Insurance
Commisioners, Section 9.
 Siegel, Jay, “Moody’s Mortgage Metrics: A Model Analysis of Residential Mortgage Pools”,
April 1, 2003.
 Inside Mortgage Finance, Feb 16, 2007.
26