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Statistical Review of Rating Variables for Mortgage Credit Risk Tanya Havlicek Kyle Mrotek, FCAS Milliman
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Statistical Review of Rating
Variables for Mortgage Credit Risk
Tanya Havlicek
Kyle Mrotek, FCAS
Milliman
Agenda
• Introduction/Scope
• Background
• Approach
• Results
• Closing
Introduction/Scope
• Purpose of study: Determine which attributes are
most predictive of credit event frequency in
residential U.S. mortgages
– Credit event is missed monthly payment
• Study restricted to loan attributes at origination
– E.g. Product Type, Loan Term, FICO score
– Did not consider economic variables
• E.g. unemployment, home price appreciation
Background
• Two major risks to mortgagee (owner of mortgage)
– Prepay (not evaluated here)-risk borrower pays
principal in advance of scheduled principal
• Generally in US, borrower has option to paydown principal on
mortgage ahead of amortization schedule at no penalty
– Refinance-borrower gets new mortgage on same property,
generally for better terms (like lower rate)
– Sell house (US mortgages not mobile)
– Pay extra principal with payment (lowers outstanding balance)
– Credit (focus of analysis)
• risk borrower does not make timely payments of principal
and/or interest
Background
• Two major risks (cont): Credit Risk
– Delinquent: borrower falls behind on P&I payments
– Default: borrower ultimately fails on obligation to pay
– Financial institutions with credit risk typically reserve
for loss provisions associated with delinquent loans
• Delinquency is incurral trigger
– Delinquency strong predictor of ultimate default
(Danis and Pennington-Cross 2005)
• Relationship increases with delinquency seriousness
• Foreclosure (FCL): Legal process by which mortgagee seeks
to re-gain possession of property
Background
• Two major risks (cont): Credit risk
– Myths - Credit risk minimal
• Home prices always thought to rise, equity in property would
limit credit loss
– peak to trough home prices in US down 30%
• Underwriting ensured borrower could afford mortgage
– lack of income/asset documentation, teaser rates that jump
after initial period, negative amortization products
Background
For years 2000-2007, the average
# of failed banks/year was 4.5
(www.FDIC.gov). In 2008, there
were 25 failed banks. In 2009,
140. As of March 2, 2010, there
have been 22. Annualized that's
about 132 for 2010. (ie, 22*12/2)
"At year end 2009, the FDIC's list
of problem institutions included
702 banks with assets in excess of
$403 billion"
http://www.failedbankreporter.com/
International Monetary Fund GFSR Oct 2009
Background
Estimate of write-downs by US banks for
2007-10 for loans and securities is $1.025T;
for residential mortgages held as loans or in
securities it's $419B
International Monetary Fund GFSR Oct 2009
Approach
• Which loan attributes known at origination are
predictive of delinquency?
– Delinquency status defined at 60-day (2 payments),
90-day (3 payments), and FCL stages of seriousness
– Delinquency within time since origination
• 12, 18, 24, 36 months
• Does loan ever achieve defined status within time horizon?
– 0 = “No”; 1 = “Yes”
– 4 x 3 : time since origination x delinquency status
– Are attributes differently predictive for different time
horizons or delinquency stages?
Approach
• Data:
– Large securities database available for lease
• LoanPerformance ABS Dataset (Alt-A and Subprime)
• Loans securitized into private label RMBS
• Nonconforming to Fannie/Freddie guidelines
– Loan level information on ~ 20 million unique loans
• Static data: does not change over life of loan
– e.g. Property Type
• Dynamic data: could change with each monthly update
– e.g. Delinquency Status
– Over 1 billion monthly loan level records
Approach
• Data
– Performance information since April 1992
• Includes loans originated prior to April 1992
– Evaluation through August 2009
– Subset of the database used
• Need information on every month since origination
• Only use loans with contiguous performance history for first
12, 18, 24, 36 months since origination
– 36 month dataset subset of 24 month set, etc.
• Loans originated between April 1992 and July 2008
• ~ 2 million observations in each final data set
Approach
• Data
– Underwriting attributes
• Loan-to-Value (grouped)
• FICO score (grouped)
• Interest rate delta (vs. avg 30-year fixed rate at origination)
• Loan Product (Fixed, ARM, Balloon, Interest Only)
• Property Type (Single Family, Condo, Multi-Unit)
• Loan Purpose (Purchase, Refinance, Other)
• Foreclosure type in state (Judicial, Non-judicial, Both)
• Loan Term (grouped)
• Documentation Type (Low, Full, Other)
Approach
• Data
– Underwriting attributes
• Lien Position (First, Second)
• Negative Amortization
• Occupancy (Owner, Investor, Vacation)
• Prepay Penalty
• Size of Loan (Less than $100K, $100K-$500K, >$500K)
– Other fields available but not used
• Not well populated
• Defined for subset of loans already identified by other field
– All independent variables discrete (categorical)
Approach
• Analysis
– SAS: data processing, proc logistic and proc genmod
– “Kitchen sink” approach
– Logistic Regressions
• A type of Generalized Linear Model (GLM)
• Individual loan observations
• Binary response variable
– 0 or 1 corresponds to ever delinquent No or Yes
• link function is logit, error ~ binomial, variance fnc x(1-x)
– log (µ/(1-µ)) = g(µ) = βX
– Inverse of the sigmoid or logistic 1/(1+e-µ)
Approach
• Analysis – Variable Significance
– Fit logistic model with all variables
– Test of global null hypothesis: all coefficients are zero
– Type 3 analysis – option in proc genmod
• Like type III SSQ - significance of variable when fitted last
• Convenient
– o/w fit full and reduced model and construct likelihood ratio test
• 14 possible indep variables for 4 x 3 =12 target variables
– Wald Chi-Square statistics for individual coefficients
• (coefficient / estimated standard error)2
• Not a likelihood ratio
Approach
• Analysis – Other Diagnostics
– Generalized R-square
• 1-exp(-L2/n) where L2 is likelihood ratio chi-square from
testing global null and n is sample size
• Intuitive appeal, usually similar to R2 if fit linear to binary data
• Look at max rescaled since dependent variable discrete
– change in probability for 1-unit change from base cat
• ∂pi/∂xi = βpi(1-pi) : depends on logit coefficient and probability
• Recall, log (µ/(1-µ)) = g(µ) = βX
• Change relative to overall default rate
• Some find this more intuitive than adjusted odds ratios
Results
• All hypothesis tests of global null that all coefficients
are zero were rejected
– i.e. all the models were an improvement over null
• All Type 3 analyses were significant
– Tests significance of each variable when added last
– At each time frame and delinquency status
– For classification variables, proc genmod tests null
that all coefficients in the set are equal to 0
• significance says that at least one of the coefficients is not 0
Results
• Type 3 analysis for FCL within first 36 monthsLikelihood Ratio Test Statistics For Type 3 Analysis
Chi-
Source DF Square Pr > ChiSq
CombProd 5 16288.3 <.0001
PropType 4 300.78 <.0001
PurposeM 3 2262.05 <.0001
GrpLTV 7 4796.11 <.0001
StateGrp 2 519.94 <.0001
LoanTerm 2 3272.01 <.0001
DocType 1 3694.49 <.0001
IntRtSpGrp 6 15040.3 <.0001
LIENGrp 1 4599.05 <.0001
NegAMGrp 2 2880.93 <.0001
OccupancyGrp 2 92.76 <.0001
PrePayPenGrp 2 3675.67 <.0001
Close_Bal_K 2 1284.61 <.0001
Orig_FICO_Group 13 15851 <.0001
Results
• Sample of Parameter Estimates and Wald likelihoods
FCL in first 36 months
• Odds Ratio 3.3892 for Balloon: predicted odds of FCL for Balloon ~3.4 times that for
Fixed rate loan, all else constant
Analysis Of Maximum Likelihood Parameter Estimates
Standard Wald 95% Wald Odds Ratio
Parameter DF Estimate Error Confidence Limits Chi-Square Pr > ChiSq Estimate
Intercept 1 -2.5266 0.0206 -2.567 -2.4861 14986 <.0001
CombProd ARM 1 0.4366 0.0079 0.4211 0.4521 3055.87 <.0001 1.5474
CombProd Balloon 1 1.2206 0.0176 1.1861 1.2552 4788.12 <.0001 3.3892
CombProd IO_ARM_5_Yrs_or_more 1 1.1994 0.0109 1.1781 1.2207 12169.4 <.0001 3.3181
CombProd IO_Fixed_5_Yrs_or_more 1 0.8926 0.0154 0.8625 0.9227 3372.7 <.0001 2.4415
CombProd IO_LT_5_Yrs 1 0.7024 0.0147 0.6735 0.7313 2271.94 <.0001 2.0186
CombProd Fixed 0 0 0 0 0 . . 1.0000
GrpLTV 50 1 -0.4906 0.0175 -0.5249 -0.4562 782.35 <.0001 0.6123
GrpLTV 60 1 -0.8013 0.0223 -0.8449 -0.7576 1296.57 <.0001 0.4487
GrpLTV 70 1 -0.4106 0.0169 -0.4438 -0.3774 588.08 <.0001 0.6633
GrpLTV 80 1 0.0028 0.0143 -0.0252 0.0307 0.04 0.8455 1.0028
GrpLTV 85 1 -0.1413 0.0167 -0.174 -0.1085 71.6 <.0001 0.8682
GrpLTV 90 1 -0.0809 0.0151 -0.1105 -0.0512 28.61 <.0001 0.9223
GrpLTV 95 1 -0.0834 0.0172 -0.1171 -0.0496 23.4 <.0001 0.9200
GrpLTV 99 0 0 0 0 0 . . 1.0000
Results
• Summary of Generalized Max Rescaled R-square
and Delinquency Rates by status and time frame
– Similar R-sq across the board
– Overall delinquency rate increases with time horizon
– In next slides, compare ∂pi/∂xi = βpi(1-pi) ; pi is overall
delinquency rate
– Change in expected probability from group base
category for 1 unit change in variable; measure of
response of delinquency probability to attribute
60 Days or More Delinquent 90 Days or more Delinquent FCL
12 18 24 36 12 18 24 36 12 18 24 36
Max Rescaled Rsq 0.17 0.18 0.19 0.17 0.17 0.18 0.18 0.16 0.17 0.18 0.18 0.16
Overall Cumul Delq Rate 4.3% 7.7% 10.9% 13.6% 3.3% 6.4% 9.4% 12.0% 2.4% 4.8% 6.9% 9.4%
Results
• ∂pi/∂xi = βpi(1-pi)
60 Days or More Delinquent 90 Days or more Delinquent FCL
Parameter 12 18 24 36 12 18 24 36 12 18 24 36
CombProd ARM 1.5% 2.4% 3.1% 3.8% 1.3% 2.3% 3.1% 3.8% 1.2% 2.1% 2.9% 3.7%
CombProd Balloon 3.8% 6.9% 9.9% 13.6% 3.1% 6.2% 9.1% 12.9% 2.5% 5.2% 8.0% 10.4%
CombProd IO_ARM_5_Yrs_or_more 3.6% 6.9% 9.7% 12.2% 2.9% 5.9% 8.8% 11.4% 2.5% 5.0% 7.2% 10.3%
CombProd IO_Fixed_5_Yrs_or_more 2.4% 5.3% 8.3% 10.0% 1.9% 4.5% 7.5% 9.2% 1.6% 3.5% 5.3% 7.6%
CombProd IO_LT_5_Yrs 0.8% 1.3% 1.9% 6.8% 0.8% 1.3% 1.9% 6.6% 1.0% 1.9% 2.7% 6.0%
CombProd Fixed 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%
PropType 2 to 4 Units 0.6% 0.8% 0.8% 0.9% 0.6% 0.8% 0.8% 0.9% 0.4% 0.5% 0.5% 0.4%
PropType Condo -0.8% -1.3% -1.4% -1.3% -0.7% -1.0% -1.2% -1.2% -0.5% -0.8% -0.9% -1.3%
PropType Other 0.3% 0.6% 0.7% 2.0% 0.4% 0.6% 0.7% 1.8% 0.2% 0.4% 0.6% 1.3%
PropType Planned Urban Dev -0.5% -0.6% -0.4% -0.4% -0.5% -0.6% -0.3% -0.4% -0.4% -0.6% -0.5% -0.6%
PropType SingleFamily 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%
PurposeM Other -2.1% -3.0% -3.4% -1.5% -1.8% -2.7% -3.2% -2.0% -1.4% -2.2% -2.8% -2.0%
PurposeM Refi Cash Out -1.9% -2.5% -2.9% -3.0% -1.6% -2.2% -2.7% -2.9% -1.3% -2.0% -2.5% -2.7%
PurposeM Refi No Cash Out -0.6% -0.4% -0.3% -1.3% -0.5% -0.4% -0.3% -1.2% -0.6% -0.6% -0.6% -1.2%
PurposeM Purchase 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%
GrpLTV 50 -1.9% -4.5% -7.1% -8.9% -1.4% -3.7% -6.3% -8.0% -0.3% -1.6% -2.9% -4.2%
GrpLTV 60 -1.8% -4.7% -7.7% -10.9% -1.4% -4.0% -6.9% -10.2% -0.8% -2.5% -4.2% -6.8%
GrpLTV 70 -0.9% -2.7% -4.4% -6.6% -0.7% -2.4% -4.0% -6.1% -0.2% -1.2% -2.0% -3.5%
GrpLTV 80 0.0% -0.4% -0.5% -1.6% 0.0% -0.3% -0.5% -1.4% 0.3% 0.3% 0.6% 0.0%
GrpLTV 85 -0.6% -1.4% -1.9% -3.2% -0.5% -1.1% -1.7% -2.9% -0.1% -0.4% -0.5% -1.2%
GrpLTV 90 -0.4% -1.0% -1.2% -2.6% -0.3% -0.7% -1.1% -2.3% 0.0% -0.1% -0.1% -0.7%
GrpLTV 95 -0.6% -1.1% -1.4% -2.5% -0.4% -1.0% -1.3% -2.4% 0.0% -0.3% -0.4% -0.7%
GrpLTV 99 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%
Results
• ∂pi/∂xi = βpi(1-pi)
60 Days or More Delinquent 90 Days or more Delinquent FCL
Parameter 12 18 24 36 12 18 24 36 12 18 24 36
LoanTerm greater than 360 2.8% 5.8% 9.0% 12.4% 2.1% 4.8% 8.0% 11.1% 1.4% 3.0% 4.9% 8.3%
LoanTerm less than 360 -2.4% -4.9% -7.1% -8.2% -1.8% -4.3% -6.4% -7.8% -1.7% -3.8% -5.7% -6.5%
LoanTerm 360 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%
DocType LOW 1.4% 2.7% 4.1% 4.9% 1.2% 2.3% 3.7% 4.4% 0.9% 1.7% 2.6% 3.3%
DocType FULL 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%
IntRtSpGrp <=-4% -0.1% -1.3% -1.0% 0.0% 0.1% -1.1% -0.7% 0.3% 0.1% -0.7% -0.1% 0.2%
IntRtSpGrp >-4% to <=-2% 1.9% 1.8% 2.1% 1.2% 1.9% 1.8% 2.1% 1.7% 1.4% 1.6% 2.3% 1.9%
IntRtSpGrp >-2% to <=-0.5% -2.0% -4.1% -6.1% -7.7% -1.7% -3.7% -5.4% -7.1% -1.5% -3.0% -4.5% -5.7%
IntRtSpGrp >-0.5% to <0.5% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%
IntRtSpGrp >=0.5% to <=2% 4.1% 5.7% 6.0% 4.5% 3.6% 5.2% 5.8% 4.5% 2.8% 4.2% 4.8% 4.2%
IntRtSpGrp >2% to <=4% 7.0% 10.1% 11.5% 10.1% 6.1% 9.2% 10.8% 9.7% 4.7% 7.3% 8.7% 8.5%
IntRtSpGrp >4% 10.1% 15.3% 18.3% 17.7% 8.6% 13.6% 16.8% 16.6% 6.4% 10.4% 12.7% 13.6%
LIENGrp Second -2.8% -3.1% -1.8% -1.5% -2.7% -3.0% -1.9% -1.4% -4.8% -8.0% -10.6% -13.1%
LIENGrp First 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%
NegAMGrp Unk -1.5% -2.9% -4.4% -4.4% -1.2% -2.4% -3.8% -4.0% -0.7% -1.3% -2.1% -2.7%
NegAMGrp Yes -1.9% -0.7% 0.2% 2.6% -1.8% -1.0% -0.1% 2.1% -1.1% -0.3% 0.4% 1.7%
NegAMGrp No 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%
OccupancyGrp Investor -0.3% -0.2% 0.2% 0.3% -0.3% -0.2% 0.3% 0.4% -0.2% -0.1% 0.4% 0.6%
OccupancyGrp SecondHome -0.8% -1.0% -0.9% -1.3% -0.7% -1.0% -0.9% -1.1% -0.6% -0.8% -0.7% -0.8%
OccupancyGrp Owner 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%
Results
• ∂pi/∂xi = βpi(1-pi)
60 Days or More Delinquent 90 Days or more Delinquent FCL
Parameter 12 18 24 36 12 18 24 36 12 18 24 36
PrePayPenGrp Unk 1.0% 0.9% 0.7% 0.6% 1.0% 1.1% 0.9% 0.9% 0.4% 0.2% 0.0% 0.3%
PrePayPenGrp Yes 1.1% 2.4% 3.7% 4.9% 0.9% 2.0% 3.2% 4.4% 0.5% 1.2% 2.0% 3.2%
PrePayPenGrp No 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%
Close_Bal_K 100k_or_less -0.4% -0.5% -0.4% 1.6% -0.3% -0.4% -0.3% 1.4% -0.2% -0.2% 0.0% 1.3%
Close_Bal_K over_500k 2.5% 3.8% 4.4% 4.3% 2.2% 3.4% 4.1% 3.9% 1.8% 2.7% 3.2% 3.1%
Close_Bal_K 100k_500K 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%
Orig_FICO_Group 581 - 600 -1.0% -1.4% -1.6% -1.8% -0.7% -1.1% -1.3% -1.5% -0.5% -0.8% -1.0% -1.2%
Orig_FICO_Group 601 - 620 -1.4% -2.2% -2.7% -3.2% -1.1% -1.7% -2.1% -2.6% -0.7% -1.2% -1.5% -2.0%
Orig_FICO_Group 621 - 640 -2.0% -3.3% -4.1% -4.6% -1.5% -2.6% -3.3% -3.8% -1.1% -1.8% -2.2% -3.0%
Orig_FICO_Group 641 - 660 -2.6% -4.4% -5.7% -6.5% -1.9% -3.4% -4.6% -5.4% -1.4% -2.3% -3.0% -4.2%
Orig_FICO_Group 661 - 680 -3.5% -5.8% -7.6% -8.1% -2.5% -4.5% -6.1% -6.7% -1.9% -3.2% -4.2% -5.3%
Orig_FICO_Group 681 - 700 -4.3% -7.3% -9.8% -10.8% -3.1% -5.7% -7.9% -9.0% -2.2% -4.0% -5.4% -7.1%
Orig_FICO_Group 701 - 720 -4.9% -8.5% -11.6% -13.1% -3.6% -6.6% -9.4% -10.9% -2.6% -4.7% -6.7% -8.6%
Orig_FICO_Group 721 - 740 -5.8% -10.1% -13.7% -15.6% -4.2% -8.0% -11.3% -13.2% -3.1% -5.8% -8.0% -10.3%
Orig_FICO_Group 741 - 760 -6.4% -11.6% -15.9% -18.3% -4.7% -9.2% -13.3% -15.8% -3.4% -6.7% -9.6% -12.4%
Orig_FICO_Group 761 - 780 -7.4% -13.7% -18.8% -21.7% -5.5% -10.9% -15.7% -18.7% -4.2% -8.2% -11.7% -14.9%
Orig_FICO_Group 781 - 800 -8.3% -15.0% -21.0% -24.7% -6.2% -11.9% -17.7% -21.4% -4.7% -8.9% -12.9% -17.1%
Orig_FICO_Group 801_or_more -7.6% -14.8% -21.6% -25.5% -5.4% -11.9% -18.0% -22.2% -3.8% -8.6% -12.7% -17.6%
Orig_FICO_Group Unknown -2.3% -4.8% -7.5% -8.5% -1.4% -3.3% -5.7% -6.9% -0.4% -1.1% -2.0% -3.1%
Orig_FICO_Group 580_or_less 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%
Results
• Generalized Max Rescaled R-square for single
variable models
– Mixture of trends, or lack of, across time frame
• Product increases while Interest rate delta decreases
60 Days or More Delinquent 90 Days or more Delinquent FCL
12 18 24 36 12 18 24 36 12 18 24 36
CombProd 3.1% 3.5% 4.0% 4.8% 3.0% 3.4% 4.0% 4.8% 3.6% 4.0% 4.5% 4.8%
PropType 0.3% 0.3% 0.2% 0.2% 0.4% 0.3% 0.1% 0.1% 0.4% 0.3% 0.2% 0.2%
PurposeM 0.1% 0.1% 0.1% 0.1% 0.2% 0.1% 0.1% 0.1% 0.2% 0.2% 0.2% 0.1%
GrpLTV 1.0% 1.4% 1.7% 1.7% 0.9% 1.4% 1.7% 1.7% 0.7% 1.0% 1.2% 1.3%
StateGrp 0.3% 0.3% 0.3% 0.2% 0.3% 0.3% 0.3% 0.2% 0.2% 0.2% 0.3% 0.2%
LoanTerm 0.8% 1.0% 1.1% 0.4% 0.7% 0.9% 1.0% 0.4% 1.5% 1.9% 2.4% 1.2%
DocType 0.2% 0.1% 0.0% 0.0% 0.2% 0.1% 0.0% 0.0% 0.1% 0.1% 0.0% 0.0%
IntRtSpGrp 9.6% 9.1% 7.9% 6.5% 9.5% 8.9% 7.8% 6.4% 8.2% 7.3% 5.9% 5.1%
LIENGrp 0.4% 0.3% 0.2% 0.0% 0.4% 0.3% 0.1% 0.0% 1.6% 1.8% 2.1% 1.2%
NegAMGrp 1.1% 0.8% 0.6% 0.4% 1.1% 0.8% 0.6% 0.3% 0.8% 0.4% 0.2% 0.2%
OccupancyGrp 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.3% 0.3% 0.3% 0.3% 0.2% 0.2%
PrePayPenGrp 1.8% 2.5% 3.2% 3.8% 1.5% 2.3% 2.9% 3.5% 1.5% 2.2% 2.8% 3.4%
Close_Bal_K 0.1% 0.1% 0.1% 0.3% 0.1% 0.1% 0.1% 0.3% 0.0% 0.0% 0.1% 0.1%
Orig_FICO_Group 9.1% 9.4% 8.8% 7.8% 8.3% 8.5% 8.0% 7.1% 8.1% 8.1% 7.7% 6.9%
Closing
• All well populated fields significant
– Not surprising, that’s why those fields are tracked
• Type 3 provides convenient method to analyze large
number of variables in a kitchen sink approach
• In general, larger |∂pi/∂xi| for longer time frames and
smaller |∂pi/∂xi| for increased delinquency
seriousness
• FICO Score, Interest rate delta, Product Type, Loan
Term, Prepay Penalty, and LTV showed the largest
|∂pi/∂xi| and had the highest single variable
generalized R-sq
Closing
• Many opportunities to expand analysis
– Analyze contrasts of categories within each variable
• Are categories different from one another, not just to base
– Consideration of extrinsic variables, specifically economics
like home prices, prevailing interest rates, unemployment
• Banks, Insurers, Investors and Government have
financial interest in performance of loans. They may
originate/buy/hold/sell/insure loans or derivatives
whose value depends on underlying loans
• Credit analysis great opportunity for actuaries to
contribute
Closing
• References
– Allison, P.D. Logistic Regression Using the SAS System
Theory and Application. 1999. The SAS Institute.
– Anderson et al. A Practitioner’s Guide to Generalized Linear
Models, A CAS Study Note. Second Edition, May 2005.
– Danis, M. A. & Pennington-Cross, A. "A Dynamic Look at
Subprime Loan Performance." Federal Reserve Bank of St.
Louis, Working Paper Series. 2005.
http://research.stlouisfed.org/wp/2005/2005-029.pdf
– International Monetary Fund. Global Financial Stability
Report: Navigating the Financial Challenges Ahead. October
2009.
– SAS 9.1.2 Documentation. The SAS Institute
