AFTSeattleBreakfastSeminarApr06

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					MBS Analytics - New
Approaches and Techniques




AFT Breakfast Seminar
          April 2006
                              Agenda
•   AFT Basic Modeling Approaches
    AFT Model Structure and Philosophy
    AFT Model Types

•   Prepayment Scores
    Short Term Scores
    Long Term Scores
    AFT Prepayment score, its performance
    Geographic analysis
    Scoring of loans, agency pools, CMO, non-Agency CMO
    Burnout calculations, observations
    Economic value of the score

•   Default Modeling
    Default Modeling Issues
    Default Model Structure
    Examples of Fitting Process
    AFT non-agency database
                           Agenda
•   Prepayment Model Performance
    AFT Model version 5.42 release
    Recent Prepayments Observations
    Deal vs. Loan level Model
    Short term vs. Long Term Modeling Accuracy
    Short term and Long term dynamic adjustments
    Analyzing Model Performance

•   Other Topics
    Prepayment Drivers – Primary to Secondary Spreads Modeling
    AFT non-agency loan database
    Custom Model fitting
    Third party integration levels
AFT Prepayment Modeling Philosophy
 In recent years, new approaches have come to dominate modeling of the
 prepayment behavior of mortgage loans. What makes these new approaches
 work is the focus on modeling the borrower behavior and the reasons for
 changes in that behavior, instead of focusing on the model's tenability within
 the existing statistical machinery.

 The purpose of constructing a prepayment model is not to project
 prepayments. It is impossible to project prepayments, since future mortgage
 rates are not known. The purpose of a model is to define a relationship between
 projected mortgage rates and the resulting rates of prepayment activity, given
 all available information regarding the mortgage, the mortgage holder, the
 current state of the economy, etc. If this relationship is well modeled, it will in
 turn allow one to answer all of the questions that one may ask as a holder of a
 mortgage-backed security. Questions like: the value of the option to refinance,
 the average advantage of owning a mortgage vs. owning other instruments,
 how one can compare a mortgage to a collection of bonds and short positions in
 interest rate derivatives, etc. Therefore, a well-constructed model should
 incorporate all known factors that effect a mortgage holder's inclination to move
 or to refinance, as well as the overall state of the US housing market.

       “Prediction is a very difficult art, especially with respect to the
 future.”

  --Mark Twain
               AFT Model Structure
• OLD
  –   Parsimonious
  –   Statistically-fit
  –   Poor performance
  –   Unstable
  –   Required frequent recalibration



• NEW
  – Behavior-based
  – Well-modeled relationship between projected mortgage rates and
    resulting prepayment behavior
  – Proven performance in volatile markets
  – Seldom recalibration
              AFT Model Structure

Two contributors to mortgage prepayments:

• Housing Turnover
   – Proper connection of housing turnover to the projection of
     the index of existing home sales

• Refinancing
   – Incentive includes the shape of the curve
   – Proper modeling of burnout
   – Proper modeling of publicity effects
             AFT Model Structure
• Step 1 – Projecting existing home sales index

• Change in interest rates
   – Rates increase/home sales slow down
   – Rates decrease/home sales speed up
   – Mean-revert over time to a “normal” level

• Seasonality

• Before 1998 EHS rate has been 3.5-4.3 million
  units/year. After 1998-2005 it has been 5.5-6.8(latest)

• What is it long term? We assume 6.7 million units,
  Solomon assumes about 5.0 million units. Who is right?
AFT Model - Existing Home Sales
    AFT Model - Housing Turnover Component

•    Mortgage age
      – A borrower with a newly purchased home is less likely to move.

•    Lock in effect
      – If prevailing rates are higher than current rate being paid, the
        incentive to move decreases.

•    Self-selection
      – Excess points paid – discount origination
      – No points/no fees - premium origination.

• Historically, AFT translation of EHS rate into actual HT
  prepayments projections has been near perfect.
AFT Model - Housing Turnover Component
    AFT Model - Refinancing Component

• Refinancing Incentive
   – Ratio of WAC to effective mortgage rates
   – Two drivers – 30-year and 15-year mortgage rates

• Burnout
   – Pool is not homogeneous
      • There are sub-pools of fast, medium and slow
        refinancers
      • As the ratio of sub-pools changes the response to
        refinancing incentive changes
AFT Model - Refinancing Component
             Burnout
     AFT Model - Refinancing Component
                  Publicity


• Publicity
   – Overlooked by many models
   – Historic lows cause dramatic change in refinance
     pattern
      • Pools considered “burned out” start to refinance
      • Loans begin to refinance for a lower incentive
      • Overall sensitivity increases
AFT Model - Refinancing Component
             Publicity
AFT Model - Refinancing Component Other
                 Effects

• High premium-originated loans
   – Generally slower than current-coupon originated
     loans

• If Available: Loan Size, LTV, Documentation Level,
  Geography, Single Family, Primary Residence, Cash-out
   – Some of these variables can be inputted directly to
     the model, others through the scoring mechanism.
        AFT Model - Other Model Types

Five Basic Model Types (different types of algorithms):

• Fixed Rate – Agency, WL, AA, RL, MH

• ARM - Agency, WL, AA, RL

• Hybrid - Agency, WL, AA, RL

• BC/BA

• HEL - Fixed, ARM, HELOC, Prepay Penalty
                   AFT Model - FRM



• The driver is the ratio of effective mortgage rate to
  effective WAC. The structure has been discussed in a
  variety of presentations and publications by AFT.
  Highlights
   – First step- project EHS as function of mortgage rates
   – Based on EHS project HT component of the model
   – Using a multi-population algorithm project the refinancing
     component
                  AFT Model - ARM



• The overall structure is similar to FRM, the incentive
  structure is different.
   – Primary driver: The difference between projected ARM
     WAC and projected 30-year conforming rate.
   – Secondary driver: The difference between projected 30-
     year conforming rate and 30-year conforming rate at the
     time of ARM origination.
   – Overall multiplier based on the difference between
     projected ARM WAC and ARM life cap.
                 AFT Model - Hybrid

• Uses an FRM like structure for the fixed period.

• Uses ARM like structure for the ARM period.

• The library accepts input of an ARM structure and uses
  the initial reset period to determine if it‟s a hybrid.

• Currently have models for 3,5,7,10-year hybrids.
                   AFT Model - BC

• Uses an FRM like structure.

• The same structure is used for both BC fixed and BC
  ARMs.

• The refinancing drive is the difference between
  projected 30-year conforming rate and 30-year
  conforming rate at the time of BC origination – that
  sensitivity is parameterized – can be changed to be a
  function of incentive. The refinancing aging ramp is a 2-
  D function of age and SATO (spread at origination)
             AFT Model - HEL, HELOC

• Uses an BC like structure for economically driven
  prepayments (defined in fr20herf.def and fr20heht.def).

• Uses a separate structure for credit driven refinancings
  (loan consolidation, term extension, credit
  improvements, etc.) defined in hegereri.def and
  hespecif.def.

• The same structure is used for both fixed and ARMs.

• Accepts as an input a vector of WAC projections.
               AFT Model - HEL, HELOC
               Credit Driven Refinancing

• Measure of credit is SATO (Spread At Origination).
    – Lower credits experience faster credit driven refinancings and
      slower economic driven refinancings.
    – Publicity accelerates credit driven refinancings.
    – Credit driven refinancings decrease as mortgage rates increase
      vs. the rates at origin.
    – Shorter term loans experience faster credit driven refinancings.

• Generic credit refinancing function is defined in hegereri.def.

• For each HEL type – FRM, ARM, Prepay Penalty, High LTV,
  HELOC there is a separate refinancing aging ramp and
  separate economic refinancing sensitivity (defined in
  hespecif.def).
          AFT Model - HEL, HELOC
  Credit Driven Refinancing – Type Specific

• The model names start with HE followed by
   –   _GN   for   HEL generic
   –   _AR   for   regular HEL ARM
   –   _GR   for   HEL without prepay penalty
   –   _GP   for   HEL with prepay penalty,
   –   _LC   for   HELOC
   –   _LP   for   HELOC with prepay penalty
   –   _HP   for   high LTV HEL with prepay penalty
   –   _HI   for   high LTV HEL with no prepay penalty
   –   _HL   for   HELOC with prepay penalty
   –   _HA   for   ARM HEL.

• If only HE name is used, then the the generic function is
  applied, otherwise, for example, a name HE_HI would invoke
  a high LTV HEL model.
Projected vs. Historical Prepayments
        Very Few Surprises
Standard modeling vs. scoring
 •   There is a large number of indicatives which a model may not be able
     to accept as inputs.

 •   Different data sets may have varying contents. It is difficult to use the
     same model on different data sets.

 •   It is difficult to compare one loan vs. another.

 •   The process for interpreting/translating loan indicatives into value is
     complex and expensive and requires difficult to find expertise.

 •   Loan information gets lost when transferred.

 •   Recalculating the burnout function from the changing distributions of
     factors is impossible
AFT Prepayment Score
• AFT has created a prepayment score that can be attached to
  each loan.

• The score reflects all additional data that is available at the
  loan level (other than WAC and age).

• The score modifies the results of the AFT prepayment model
  and therefore the value of the assets.

• AFT has created two scores – refinancing score and housing
  turnover score

• The score described above is a “Long term Score”

• “Short Term Score” is just a short term projection of
  prepayments for each loan.
These loans have 7.5% coupons and were originated in August, 1999.




         How likely are they to prepay in the next three months?
      Should you offer to refinance? Which one should you call first?
Adding more data allows the                         So, we have developed a score
model to differentiate each loan’s                  for prepayment propensity that
Forecasted prepayment behavior                      modifies the prepayment forecast
                                                    at the loan level

           Loan Size LTV     Loan Purpose   State    Score
           $203,150.00 94%   PURCH          AZ         1.33
           $201,850.00 95%   PURCH          CO         1.29
           $201,500.00 90%   RREFI          CA         1.17
           $158,000.00 80%   PURCH          DE         1.06
           $167,000.00 65%   PURCH          DC         1.05
           $168,000.00 67%   PURCH          MD         1.02
           $161,150.00 85%   SREFI          CA         1.01
           $171,500.00 70%   RREFI          CO         1.00
           $184,571.00 72%   RREFI          GA         0.92
            $90,000.00 61%   PURCH          AZ         0.92
            $60,000.00 74%   PURCH          IN         0.91
           $200,000.00 59%   CREFI          IL         0.88
           $115,450.00 80%   PURCH          AZ         0.87
           $131,000.00 95%   PURCH          CA         0.87
           $128,250.00 95%   PURCH          CO         0.85
           $105,000.00 60%   PURCH          MD         0.84
           $166,600.00 85%   RREFI          GA         0.83
           $320,000.00 64%   CREFI          FL         0.81
           $155,000.00 84%   RREFI          VA         0.78
           $105,000.00 71%   WREFI          NV         0.77
           $119,910.94 80%   RREFI          CA         0.77
           $100,000.00 54%   CREFI          CO         0.75
How good was your intuition?


                                  1&2


                                                 18




    Will you make money if you solicit a refinance from
             The loans most likely to prepay?
Historical Loan Prepayment Speeds by Score
                                  EXAMPLE
     Conforming loans originated in 1997 with WAC of 7.5 (+-25 basis points)
                   Bucketed into deciles by Refinancing Score.
Geography Contribution to the Prepayment Score



• Housing turnover related prepayments make up a
  relatively small portion of total prepayments over the
  last 5 years

• Refinancing related prepayments generally present a
  good statistical sample

• Statistics for smaller states are fairly limited

• Used Bayesian statistical analysis to come up with best
  estimates

• AFT tracked coefficient‟s stability as a function of
  observation period
                Geography Contribution to the Prepayment Score - Refi
                                       Refinance Modifiers

                900



                800




                700
                                                                                                 WI
7/2002-6/2005




                600

                                                                                      IL

                500                                                              MI

                                                                      CA   CO


                400




                300
                             TX   NY


                200
                      200   300        400        500           600        700             800        900
                                                    1/2000-6/2002
Geography Contribution to the Prepayment Score - HT
Scoring of Agency Pools

• Additional data is being released by the agencies: Loan
  Size, FICO, LTV, Geographic Distribution

• Using an algorithm similar the the loan scoring, we
  score all of the agency pools in the same manner as we
  score individual loans

• The scores for loans, pools, and CMOs are available
  from AFT
Scoring of Agency Pools
                                   Example

                               Agency Pool Prepayment Speed,
                                Origination = 2001, WAC = 7.5%


           16



           14



           12


                                                                            Score = 150
           10
                                                                            Score = 250
 SMM (%)




                                                                            Score = 350
            8                                                               Score = 450
                                                                            Score = 550
                                                                            Score = 650
            6
                                                                            Score = 750


            4



            2



            0
                40   50   60        70                 80        90   100
                                  Month (Since 2000)
Scoring of Agency CMOs

• Loan Size, FICO, LTV, Geographic Distribution is
  generally NOT available for Agency CMOs

• Knowing the pools backing CMOs and all individual pool
  scores, AFT calculates CMO scores

• User knows up-front which CMO will be a more
  responsive and which less

• The differences in economic value can be several %

• Traders can immediately profit from the economic
  value, since the market does not yet recognize it
               Scoring of Agency CMOs
                                  Example
                           CMO Deal Prepayment Speeds


          16



          14



          12

                                                               FNM02025 373
                                                               FNM01041 432
          10
                                                               FNM02019 455
SMM (%)




                                                               FNM02027 462
           8                                                   FNM02008 529
                                                               FNM01033 536
                                                               FNM02037 579
           6
                                                               FNM01052 589
                                                               FNM01058 606
           4



           2



           0
           2001     2002   2003                 2004    2005
                                  Date
Scoring of Agency CMOs - Analysis

 CMO projected vs. observed historic average SMM
 using AFT standard model (not adjusted by the scores)

 9.000
 8.000
 7.000
 6.000
 5.000
 4.000
 3.000
 2.000
 1.000
 0.000
     0.000   1.000   2.000   3.000   4.000   5.000   6.000   7.000   8.000
Scoring of Agency CMOs - Analysis

 Scored CMO projected vs. observed historic average
 SMMs using AFT model modified by the scores

  9.000
  8.000
  7.000
  6.000
  5.000
  4.000
  3.000
  2.000
  1.000
  0.000
      0.000   1.000   2.000   3.000   4.000   5.000   6.000   7.000   8.000
Scoring of Agency CMOs - Analysis
CMO observed historic average SMMs as a ratio to standard
   AFT model projections as function of CMO score

                                              Response To Score

                              1.6

                              1.4
    CMO Speed / Model Speed




                              1.2

                               1

                              0.8

                              0.6

                              0.4

                              0.2

                               0
                                    0   100   200     300      400      500   600   700
                                                    Refinancing Score
Scoring of Non-Agency CMOs - Analysis
• Adequate loan-level information is not available for non-
  Agency CMOs from CMO cash-flow generators.

• AFT has put together a non-Agency CMO loan database or a
  customer‟s database may be used in conjunction with AFT
  extraction software or AFT web site.

• For all non-Agency CMOs, AFT uses an extract from the
  database, where loans are bucketed by Loan Type, WAC,
  WAM, as well as OLTV and MSA if default calculations are
  required. For each bucket an HT score, Refi score, as well as
  Default score if needed are calculated

• AFT Software tells CMO cash-flow generator how to bucket the
  collateral.

• For each bucket, the software looks up the score, and invokes
  the model using the appropriate score.
Burnout – what happens, how do we
measure

• The prepayment response function of a pool of loans exposed
  to refinancing opportunity is different from the response
  function of “fresh” loans. The effect is called burn-out

• Burnout happens due to changes in population composition

• Using the scoring algorithm, we can measure it directly

• Burnout rate of a relatively homogeneous pool of loans will be
  different from the rate of a heterogeneous pool – it is a
  function of the standard deviation of scores within pool.
Burnout
                             Example
 Average score over time of 8% conforming loans originated in 1997

                             1997 Originations, 8.0% WAC

                    500

                    475
    Average Score




                    450
                                                           Average Score
                    425
                                                           Predicted Score
                    400

                    375

                    350
                      1998   2000          2002    2004
                                    Date
 Burnout

                                  Example
Difference between historical prepayment projections by AFT model applied to
 a pool with an average score of 500 and “standard” score distribution (Pool
       Model) and the model applied only to loans with the score of 500
                  8% conforming loans originated in 1997

                           1997 Originations, 8.0% WAC

                   12
                   10
         SMM (%)




                   8
                                                         Pool Model
                   6
                                                         Score 500 Model
                   4
                   2
                   0
                   1997   1999     2001    2003
                                 Date
 The AFT Prepayment Score improves
 knowledge of the true value of mortgage
 assets




 The score has been used to modify the prepayment vector used in
calculating the price associated with the market OAS of 50 bps for the
                  securities and 200 bps for the strip.
         The AFT Prepayment Score is
         available at the point of sale
•   MBS market has not priced in the economic value of the score. Even
    low loan balance pools pay-ups bear little relationship to their
    economic vale

•   Some hedge funds and broker-dealers now bid aggressively for MBS
    with desirable scores and avoid the ones with less desirable

•   Some Originators are beginning to change pricing to customers
    based on the score

•   Several of the largest banks are using it to price and hedge their
    loans.

•   Both Long term and Short term score are available to subscribers to
    the McDash data base.

•   AFT can accept your loans on its FTP site and score them (as well as
    perform a complete OAS analysis on them).
Default Modeling Issues
 • Issuer Related
    • 1996 to 1999 data involved a lot of appraisal fraud (e.g.Conti)
    • Issuers have an incentive to understate the LTV
    • Issuers have a lot of latitude in dealing with delinquencies
    • Many actually have departments that “manage triggers” –
      manipulate the process of handing delinquencies and defaults for
      the purpose of triggering desired outcomes for their securities
      holdings
    • Reported delinquencies and defaults for individual CMOs often
      have little to do with the underlying borrower behavior.
    • Over the long term – the data on which the models are based – all
      of these games average out
Default Modeling Issues
 • Data Related
    • Due to appraisal fraud, data from 1996 to 1999 is not necessarily
      representative of newer deals
    • Most of the data came from the last 8 years which experienced an
      unprecedented HPI. A lot of underwriting “liberties” consequences
      have been masked by the high HPI
    • Losses due to defaults have often been zero
 • HPI and Economy
    • HPI historically has had a very low correlation to interest rates.
    • Wide distribution of HPI across US. “Tails” are critical
    • Attempts to connect unemployment simulation to defaults is
      superfluous. There is a one-to-one connection between
      unemployment and HPI
Default Modeling
 • Drivers
    • Primary driver is a function of OLTV and CLTV
    • Historical CLTV is calculated based on MSA HPI indexes
    • There has been a wide enough distribution of HPI for different
      MSAs that we can observe the effects of negative HPI, but the data
      set is somewhat limited
    • The model uses all loan and borrower level information available
 • Structure
    • There are a large number of variables that affect default propensity
      – which makes it impossible to perform aggregations. AFT
      generates a default score based on time-independent
      characteristics thus cutting the dimensionality of the problem
    • Transition matrix based
Default Modeling Input/Output

 • Inputs To Scoring Algorithm
    • Originator, MSA, FICO, ΔFICO, IO, DocLevel, ResidencyType,
      SingleFamily, LoanPurpose, LoanSize
 • Inputs to The Model
    • CLTV, OLTV, Default Score, Prepayment Score, Age, Current
      WAC, Projected WAC, Initial Payment, Projected Payment,
      Projected HPI, Projected Mortgage rates (30, 15, 5, 7)
 • The prepay/default model may, as an option, include the
   scoring algorithms internally.
 • Output
    • Del30(360), Del60(360), Del90(360), Foreclosure(360),
      Liquidation(360), Severity(360), Prepay (360)
Default and Prepayment Model deployment
     for Non-Agency CMOs - Analysis
• Adequate loan-level information is not available for non-
  Agency CMOs from CMO cash-flow generators.

• AFT has put together a non-Agency CMO loan database or a
  customer‟s database may be used in conjunction with AFT
  extraction software or AFT web site.

• For all non-Agency CMOs, AFT uses an extract from the
  database, where loans are bucketed by Loan Type, WAC,
  WAM, OLTV, MSA. For each bucket an HT score, Refi score, a
  Default score are calculated

• AFT Software tells CMO cash-flow generator how to bucket the
  collateral (only WAM-WAC buckets).

• For each WAM-WAC bucket, There may be 100‟s of OLTV, MSA
  buckets. For each of them the software looks up the scores,
  calculates CLTV based on MSA specific historic HPI and
  invokes the model using the appropriate score and an input
  HPI projection for each MSA.
Default Modeling Structure
 • Model Structure
    • Calculate principal transition function (from any state into the
      subsequent state) D(t).
    • Calculate modifier transition function M(T) (that modifies other
      allowed transitions,) keeping D(t) unchanged
    • D(t), M(t) are functions of default Score, CLTV, OLTV, Accumulated
      Prepayments, Change in Pay Level, age, seasonality
    • Follow the transition matrix over time to calculate all delinquency
      transitions.
    • Loss severity is calculated based on Coupon, Average Time to
      Liquidate, Loan balance, Fraction of value recovered, Fixed costs
      per loan
Current Default Score:

S0 =   F(Originator)*F(MSA)* F(FICO, ΔFICO)* F(IO)*F(DocLevel)*F(ResidencyType)*
       F(SingleFamily)*F(LoanPurpose)*F(LoanSize)

D(t), M(t) = S0*Fi (CLTV(ALTV, Π(HPI)),OLTV)*
Fi(AccumulatedPrepayments0-t)*Fi(ΔPayLevel)* Fi(age)*seasi(t)

Transition Matrix Tij(t)

               TO
               0       30   60     90+    Foreclosure   Default
       0       #       #    0      0      0             0
       30      #       #    #      0      0             0
From 60        #       #    #      #      #             #
       90+     #       #    #      #      #             #
Foreclosure    #       #    #      #      #             #

Constraints:
Σj Tj,6(t)=PP(t)
Σi Tj,i (t)=1
Σj Tj,5 (t)=D(t) j<7
To calculate the total projected default, curing, and liquidation rates, follow the transitions.

Loss severity

Loss=min(LB*(Frac-CLTV-IR(T))- FC, 0)

IR(T)               - Interest rate owed
T                   - Average number of months that interest is owed on a repossessed loan.
LB                  – Loan Balance
Frac                – Fraction of value recovered – constant
FC                  – Fixed costs per loan
Default Modeling Structure

                                                           Los Angeles
                                                       Metropolitan Division

                              45.00
                              40.00
  Transition Rate (%/month)




                              35.00
                              30.00                                                      Historic 0->30
                              25.00                                                      model 0->30
                              20.00                                                      Historic 30->60
                              15.00                                                      model 30->60
                              10.00
                               5.00
                               0.00
                                 1/2/2002   1/2/2003    1/2/2004   1/1/2005   1/1/2006
                                                          Date
Default Modeling Structure

                                                          New York
                                                     Metropolitan Division

                                70.00
    Transition Rate (%/month)




                                60.00

                                50.00
                                                                                          Historic 0->30
                                40.00                                                     model 0->30
                                30.00                                                     Historic 30->60
                                                                                          model 30->60
                                20.00

                                10.00

                                 0.00
                                   1/2/2002   1/2/2003   1/2/2004   1/1/2005   1/1/2006
                                                          Date
Default Modeling Structure

                                                  Non-delinquent Loans
                                                Becoming 30-day delinquent
                                                    (Age = 12 months)

                                   10
     Transition Rate (% / month)




                                    9
                                    8                                            OrigLTV = 0.5
                                    7                                            OrigLTV = 0.6
                                    6
                                                                                 OrigLTV = 0.7
                                    5
                                                                                 OrigLTV = 0.8
                                    4
                                    3                                            OrigLTV = 0.9
                                    2                                            OrigLTV = 1.0
                                    1
                                    0
                                        0.4     0.6           0.8            1
                                              Current (adjusted) LTV
Default Modeling Structure

                                                     90-day delinquent Loans
                                                      Entering Foreclosure
                                                        (Age = 12 months)


                                  60
    Transition Rate (% / month)




                                  50
                                                                                   OrigLTV = 0.5
                                  40                                               OrigLTV = 0.6
                                                                                   OrigLTV = 0.7
                                  30
                                                                                   OrigLTV = 0.8
                                  20                                               OrigLTV = 0.9
                                                                                   OrigLTV = .10
                                  10

                                   0
                                       0.4     0.6              0.8            1
                                             Current (adjusted) LTV
Default Modeling Structure
 •   Total access to parameters. All functions are defined as
     piecewise linear and saved in parameter files. Easy to edit,
     easy to create new models and model types.

 F(age)
 0 0
 12 .3
 24 .8
 60 1.1
 90 0.7

 •   Fully integrated with AFT libraries (including full integration
     with INTEX)
                HPI Simulatoin

•   There are four ways to simulate HPI.
    A) User supplies a single HPI scenario for all MSA
    B) User supplies an HPI scenario for every MSA
    C) User does an OAS simulation using an MSA level HPI simulation in
       conjunction with interest rates based on MSA level HPI variance-
       covariance matrix provided by AFT.
AFT Model New Release: Version 5.42
           New Structures I
• Changed historical rates file from monthly FNCR3010 to weekly
  MBA survey rates
• Changed the connection from between the last mortgage rate in
  Mort30.dat file and the last existing home sales projection in
  htecnmy.dat file to a file that contains both of the numbers in the
  same place – avoids consistency issues
• Allows to keep a history of the mort30 and htecnmy pairs – for
  back-testing
• Allowed dynamic creation of the 5 model types discussed above
• Allows weighting of the intra-month lows to be heavier than
  other rates
• Added the ability to have origination year dependent RF
  multiplier
• Created the capability to either treat the incentive as a ratio of
  WAC to effective mortgage rates or their difference
AFT Model New Release: Version 5.42
           New Structures II

 • Lags can now be a function of age for the housing
   turnover component (in addition to the being a function
   of age for the refinancing component)
 • Elbow can shift as a function of publicity
 • Refinancing aging ramp can be a function of SATO (the
   spread at origination)
 • Accumulator-like function to deal with capacity
   constraint situations
 • Hybrid-specific ARM parameter files capability added
   which can have sensitivity to when first reset took place
 • Additional spreads as a function of program e.g WL, AA,
   HE
AFT Model New Release: Version 5.42
           New Structures III

 • Prepay penalty function can now be used as a multiplier
   to overall refinancing response or a modifier to the
   effective mortgage rate as before
 • The DLL can accept prepayment scores
 • The DLL now reads the “normal” and actual standard
   deviations of the scores and modifies the burnout rate
   based on that
 • Ability to handle “real” loan sizes and “normalized”
 • Ability to have an elbow be a function of “normalized”
   loan sizes
 • FICO sensitivity
 • Three ways to interpret age-dependent refinancing lags
AFT Model New Release: Version 5.42
     Major Parameters Modifications

• Changed weights for calculating effective mortgage rate from
  month 2 at 25% and month 3 at 75% to month 2 at 100%
• Lowered burnout by about 20%
• Lowered sensitivity to publicity
• Hybrids are driven by rates difference rather than their ratio as
  an incentive
• Prepay penalty function now multiplies the refinancing
  component for HEL/HELOC
• Modified lags sensitivity as a function of age, rates direction
• Made elbow be a function of publicity
• Slightly modified the refinancing curves
• Slightly lowered refinancing elbow
• Variety of modifications for credit collateral
         Prepayments Observations

• Unprecedented increases in existing home sales rate, have
  been stubbornly high for the last 7 years.

• Every existing home sale is a housing turnover related
  prepayment

• What is the long term expected existing home sales rate?

• The drop off in refinancings of the marginally refinancible
  collateral was greater than implied by last 5 years of data. Is
  the original (version 5.4) burnout function a better way to
  model? Is amelioration of burnout rate a transient
  phenomenon?
• HT aging ramp has stayed short
• Refinancing aging ramp is now present in all models
Changes in jumbo hybrid responses, near-zero
incentive refinancings and WAC dispersion

  • Jumbo hybrids have exhibited significant changes in
    refinancing response
     – Refinancing response increased for near-zero incentive
     – Refinancing responses for larger incentives are inconsistent
       between different deals
     – Substantial differences by originator

  • Some changes may be explained by the borrower‟s
    expectations that interest rates would rise – term extension
    behaviors

  • Jumbo deals tend to have a very wide WAC distribution
     – Near zero incentive refinancings may actually be refinancings for a
       substantial incentive
        Deal vs. Loan Level Models


•   CMO deals tend to have a wide distribution of WACs, origination dates,
    prepay penalty structures, and even of collateral types. It is especially
    true for non-agency deals
•   AFT models have been generally fit against deal-level data since they
    usually have to perform against CMO deals, or other relatively wide
    aggregates
•   Users may need to analyze individual loans or loans bucketed tightly by
    WAC or other characteristics.
•   AFT has come up with a closed form solution to translate deal-level
    model into a loan-level model based on the expected and realized
    standard deviation of WACs and other factors
•   Will demonstrate the corrections based on WAC dispersion, corrections
    based on other factors will be discussed in the scoring part of the
    presentation
                    Deal vs. Loan Level Models
                         WAC Distribution
                            Distribution of Coupons in Jumbos

                   40
                   35                                           WFMBS 2005-002 as of
                                                                6/1/2005
Percent of Loans




                   30                                           WFMBS 2004-001 as of
                   25                                           6/1/2005
                                                                WFMBS 2003-016 as of
                   20                                           1/1/2004
                   15                                           WFMBS 2000-013

                   10
                                                                NASCOR 2000-002
                    5
                    0
                        4       6           8         10
                               Gross Coupon (%)
 Deal vs. Loan Level Models
Refinancing Curve Correction

                                   Coupon Dispersion, Sigma = 0.35%

                          12

                          10
 Refinancing Multiplier




                          8

                                                                               Single Loan Model
                          6                                                    5.42 Incentive Curve


                          4

                          2

                          0
                               1    1.1            1.2             1.3   1.4
                                          Relative Current Rates
AFT Additional Naming Conventions
•   Third party systems allow for differing sets of inputs

•   AFT attempts to allow users bypass these systems‟ constraints by
    using the agency name field to pass information to the model that
    these systems won‟t allow. Result: complex naming conventions

•   Example: FNMA_7BLN|152.3|0.71$1@25.B1

•   Decoding:
     – FNMA model type
     – _7BLN means use 7-year balloon model. Used for systems that would not
       indicate to our model that a balloon collateral is being run
     – |151.3|0.71 means 151.3 loan size, 0.71 LTV. Used for systems that would
       not send to our model the loan size and LTV
     – $1 means use the scoring algorithm if available and $0 means don‟t use
       scoring algorithm
     – @25 means that the WAC distribution of the collateral that you are running
       is 25 basis points.
     – .B1 means use fnma.b1 file for the definition of the prepayment penalty
       structure.
Short term vs. long term modeling
accuracy
• Valuations of MBSs are largely functions of the model‟s long-
  term projections, e.g. over more than a year. These
  valuations will be accurate if given an interest rate scenario,
  the model‟s projections are quite close to the actual on that
  scenario
• Retention efforts, dollar roll values, and quarterly income
  projections depend on a model‟s short-term projections.
• Model evaluations should be clear on whether one evaluates
  the short term accuracy or the long term one
• There is certain information that is available for making short-
  term projections that is not available for making long-term
  projections.
• Along with monthly data releases, AFT also releases a set of
  short term adjustment coefficients for Agency collateral.
  These files just need to be placed in the parameters folder to
  be utilized.
Projections Without ST adjustment
Projections With ST adjustment
Deal-Specific Long Term Adjustments

• Individual deals or cohorts may behave differently from the
  expected for a variety of not easily identifiable reasons.

• AFT has created a solver for HT multiplier, Refi multiplier, and
  elbow shift to minimize the r-squared errors. The first few
  months of data a ignored (since they tend to be least reliable
  and most volatile)

• The solver is integrated within several analytical systems and
  within Regressor

• One can use the solver against CMO deals or against any
  cohort

• One needs to be careful that the modifications are predictive
Deal-Specific Long Term Adjustments




 Historical fit without long term adjustments
Deal-Specific Long Term Adjustments




 Historical fit with long term adjustments
   Analyzing a model’s performance

• The primary consideration in evaluating a model‟s
  performance is its stability. Frequent releases indicate
  an attempt to predict the last few months of
  prepayment speeds, which are well known, leaving no
  room for prolonged out-of-sample observations.

• When comparing historical model performance, ALWAYS
  compare models of the same “vintage”, e.g. if you are
  looking at 2004 performance, you cannot compare a
  2001 vintage model to 2004 vintage.
   Analyzing a model’s performance

• Given two models of similar vintage, one can compare
  their OUT-OF-SAMPLE performances using a variety of
  statistical tools.

• Comparisons of “in sample” model performances are of
  less value. They can serve as indicators (and indicators
  only) of the extent of the model flexibility in reflecting
  accurately and completely the underlying phenomenon.

• Fit to history “in sample”, if analyzed blindly, may give
  no information as to the model potential for future
  performance.
   Analyzing a model’s performance

• The analysis still has to involve a deep understanding of
  model structure in order to attain a degree of
  confidence that it reflects the phenomenon. The “in
  sample” performance has to be a result of that
  structure, rather than of a blind collection of parameters
  that happen to fit well but have no predictive power.
          What rates should drive
              prepayments?


• Mortgage prepayments can only be driven by rates that
  a borrower sees – what happens in the secondary
  markets is of no consequence to the borrower.

• A prepayment model may only connect primary, not
  secondary, rates to prepayments - otherwise you need
  a new model each time primary/secondary spreads
  change.
Primary/secondary spreads modeling
• Most analysis is based on rates available in the secondary
  market. These rates change minute by minute

• Primary rates are available on a weekly basis at best

• One needs to make an assumption about the effect on the
  primary rates from the secondary market

• The common assumption is to assume a constant spread

• The assumption breaks down when the production volume hits
  capacity constraints
Primary/secondary spreads modeling
• AFT prepayment model can accept projected primary
  mortgage rates, or current coupon rates, or treasury rates, or
  LIBOR rates as inputs. Flags in espparamconfig.def tell the
  model which it is.

• Normally, unless a primary mortgage rate is sent, the model
  adds a constant spread to the rate. The spreads are specified
  in either mrprimccsprds.dat, or mrprimcomsprds.dat, or
  mrtrsprds.dat depending on the control flags

• Another method of calculating primary mortgage rates is to
  use a spread model based on these rates.

• The spread model may be applied externally by the system
  vendor, or internally through our prepayment library directly
  by using the above flags.
Primary/secondary spreads modeling

• There are three spread models. A separate algorithm
  and a separate parameter set is used to calculate
  primary mortgage rates based on each of the following:
  Current Coupon rates, LIBOR, FNMA 10-day
  commitment rates.

• In addition to the above, one can define „manual‟ spread
  adjustments. The files that control that are described in
  “AFT Model Technical Structure III, Spreads Control Files”
New AFT Non-Agency Database

•   AFT has been collecting data for loans backing all non-agency CMOs
    from a variety of sources

•   Currently have collected loan-level data for about 80% of non-agency
    universe CMOs.

•   The data is processed into Dynamic Aggregator, or will be soon
    available through McDash or in “raw” format

•   AFT uses McDash agency database to complete its data. AFT has data
    for about 70% of the loans in existence
Model fitted to customer data set
           uncorrected
Model fitted to customer data set
            corrected
AFT Vendor Integration

				
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