Prepayment Modeling

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Prepayment Modeling

• Michael Bykhovsky
• Chief Executive Officer
• Applied Financial Technology

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Applied Financial Technology Who We Are

• Since 1996, Applied Financial Technology
  has delivered high-quality risk analytics to the
  mortgage industry via the company's cutting edge
  quantitative methods.
• The AFT library offers prepayment models for
  fixed, adjustable, prime and sub-prime mortgages,
  home equity loans and home equity lines of
  credit.
• AFT counts leading broker/dealers, institutional
  investors and mortgage banks as clients,
  including the five largest U.S. banks.
• The AFT library also houses interest rate
  processes and option-adjusted valuation and risk
  management tools for MBS, ABS, and CMOs.
• The AFT library is integrated with all major
  analytics systems and every day hundreds of users
  depend on AFT prepayment analysis distributed on
  Bloomberg. 
• The company houses decades of Wall Street and
  mortgage banking experience in its offices in San
  Francisco, Boston and New York.  Learn more about
  the company at www.aftgo.com.

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AFT Philosophy

• In recent years, some new approaches have been
  developed in modeling the refinancing behavior of
  mortgage loans. What makes these new approaches
  work is the focus on modeling borrower behavior
  and the reasons for changes in that behavior,
  instead of focusing on the model's tenability
  within existing statistical machinery.
• Statistical analysis generates both "signals"
  (the effect you're measuring) and "noise" (random
  events that have nothing to do with what you're
  measuring but may affect your measurement
  results). The idea behind statistical
  significance is that the information you want is
  obscured by other information you do not care
  about. By finding confidence levels, you are
  hoping to determine what effects from your data
  are significant and what are not. The problem
  with using statistical analysis on a large pool
  of loans is that every effect is a signal. There
  is no noise in your measurements. Any effect
  large enough to register is significant. When you
  analyze a large pool of loans and get noise or
  errors, it is reflective of mistakes in the
  statistical model. Moreover, when you run r2
  minimizations on signals, you are attempting to
  minimize mistakes, not noise or errors.
• Prediction is a very difficult art, especially
  with respect to the future. --Mark Twain
• 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 participant in the mortgage market.
  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.

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AFT Philosophy

• Modeling Approaches
• OLD
• Parsimonious
• Statistically-fit
• Poor performance
• Unstable
• Requires frequent recalibration
• NEW
• Behavior-based
• Well-modeled relationship between projected
  mortgage rates and resulting prepayment behavior
• Proven performance in volatile markets
• Seldom requires recalibration

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AFT Philosophy

• Prepayment models do not PREDICT prepayments
• Predicting future rates is impossible
• AFT models the interest rate/borrower behavior
  relationship based on
• Loan characteristics
• Borrower characteristics
• Interest rate

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Modern Model Construction

• Two contributors to mortgage prepayments
• Housing turnover
• Refinancing
• Major contributor to the cost of the prepayment
  option

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Housing Turnover Component

• 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
• Peak in late summer
• Trough in January and February

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Projecting Existing Home Sales
The fit is based on pre 1977 data - note
seasonality.
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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

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Housing Turnover Component of Prepayments
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Borrower Refinance Activity

• Contributes the most to the prepayment option
• Most volatile
• Most challenging component to model
• Successful models
• Complete and accurate modeling of underlying
  phenomenon

Accurate models do not change frequently because
human behavior does not change frequently.
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Borrower Refinance Activity

• Refinancing Incentive
• Ratio of WAC to effective 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

Two Major Aspects of Refinancing Modeling
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Borrower Refinance Activity ? Modeling Burnout
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Borrower Refinance Activity ? 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

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Borrower Refinance Activity ? Historically Low
Rates Drive Publicity Effect
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Borrower Refinance Activity

• High premium-originated loans
• Generally slower than current-coupon originated
  loans
• Credit quality
• Loan size

Additional Drivers of Refinancing
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Accuracy and Stability
Accurate forecasts over time are critical.
Five Years
Your model should be accurate over long periods
of time and through rate changes.
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Accuracy and Stability
Stability Matters..a lot How can a model that
changes every few months based on recent model
inaccuracy be used to model prepayments over
several years?
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Accuracy and Stability

• Major parameters set in 1996
• Did not over project 1996-1997 refinancing
• Did not under project high levels of 1998-2001
  refinancing
• Excellent fit to history

Stability and Accuracy are the hallmarks of the
AFT model.
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Model accuracy One Example
How Would These Errors Effect YOU?
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AFT Model accuracy Comparison
Model users must understand the risk inherent in
model error.
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Model Risk ?Buying Mortgage Servicing Rights

• Assume
• You are given the task of pricing the acquisition
  of 1 billion of mortgage servicing rights.
• You rely on a prepayment model to tell you the
  prepayment vectors associated with various
  changes in interest rates and you use these to
  price the MSRs.
• Your are responsible for any write downs in the
  value of the MSRs that are caused by unexpected
  (improperly modeled) prepayments.
• You are not responsible for hedging expected
  changes in value caused by changes in interest
  rates.
• Your prepayment model has a 30 error (you trust
  it to be correct).
• How good or bad could life be a year from now?

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Prepayment Model Risk
How good or bad could life be a year from now?

• Goal? Buy mortgage servicing rights with a
  1 billion c.p.b. that will generate an OAS of 50
  basis points.
• Use model prepayments and IRP to calculate the
  value of 25 bps of IO to be 68.8bps.
• Use this price to calculate a servicing value of
  1 of 1 billion or 10 million.
• Actual prepayments are 30 greater than forecast
  for actual changes in rates.
• Correct value of the IO was 59.4 bps or 15.7
  less than you calculated using your prepayment
  model.
• The 15.7 overpayment resulted in a write down of
  1.57 million.

Loss of 1.5 million
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Model Risk ?Hedging Mortgage Servicing Rights

• Assume
• You are long a 10 billion c.p.b. servicing
  rights portfolio valued at 150 million.
• Your job is to hedge your MSR portfolio value
  exposure to a one year, one sigma change in
  interest rates which is or 60 basis points
  today.
• You rely on a prepayment model to tell you the
  effective duration of your servicing rights.
• Your prepayment model has a 30 error (you trust
  it to be correct).
• How good or bad could life be a year from now?

Accuracy has significant value. How accurate is
your current model?
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Prepayment Model Risk
How good or bad could life be a year from now?
Plan MSR Hedge Model
duration -43.3 43.3 Change in
rates -.60
-.60 Change in value - 25
25 change in value -37.5
million 37.5 million
Actual MSR Hedge Actual
duration -54.4 43.3 Change in
rates -.60
-.60 Change in value - 32.5
25 change in value -48
million 37.5 million
Loss of 10.5 million
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Opportunity Better understanding prepayments at
the loan level
These loans have 7.5 coupons and were originated
in August 1999 Todays prepayment analytics see
them as identical.
How likely is each loan to prepay in the next
three months? Do they all have the same servicing
value? Should you offer to refinance?
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Actual Prepayments for a portfolio of loans over
42 months? Same WAC/WAM
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AFTs prepayment model does a great job of
predicting average speeds
Inputs to the model ? WAC, WAM, Loan Type
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Some loans with the same WAC,WAM and Loan Type
always prepay faster than others..
How can we know this and why does it matter?
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AFT has used this insight to develop a score for
prepayment propensity
Adding more data provides more insight into each
loans prepayment behavior
All loans have the same coupon, age and loan
type.
.but different relative prepayment propensities.
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Loan Level Prepayments
How good is your intuition?
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Prepayment Scoring- Why it matters
Mortgage values are a function of prepayments,
which are a function of rates and other
variables..
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Prepayment Scoring- Why it matters
3.2 billion pool. Average value is 97 bps. 32
million investment that will evaporate over
time. Scoring allows a closer look at value.
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Prepayment Scoring- Why it matters
3.2 billion pool. Average value is 97 bps, but
modifying prepayments as a function of the score
uncovers significant economic value relative to
the market.
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Prepayment Scoring- Why it matters
The relative values in each of the 12 largest
pools.looks pretty consistent. The relative
value range in a pool can be significant32 basis
points in this example.