A Variable-Rate Loan-Prepayment Model for Australian Mortgages (

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A Variable-Rate Loan-Prepayment Model for
Australian Mortgages(Daniel Model)

• Evan Rosenberg
• Hui Gang Wu

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I. Objective of This Paper

• To investigate Australian mortgage prepayment by
  developing and testing prepayment models for
  loans in Australian MBSs

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II. Method

• Daniel used U.S. MBS variable-rate loan
  prepayment models (notably McConnell and Singh
  1991 and the related Sanyal 1994 model) as
  foundations and then accounted for the
  differences between the U.S. and Australian
  markets

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III. Differences between U.S. and Australian
Markets

• Tax (in Australia occupying owners cannot deduct
  their mortgage payments ? more incentive to
  prepay than in U.S.)
• Fixed-Rate Loan Term Period (sub-periods in
  Australia)
• Variable-Rate Mortgage Rate (set by lender in
  competitive mkt in Australia ? acts more like a
  floating rate than in U.S. where rates are tied
  to indices)
• Ratio of FRM and VRM (VRM dominates in Australia
  FRM dominates in U.S.)
• Partial Prepayment (uniquely significant in
  Australia avg. approx. 1/3 of full prepayments
  often deemed insignificant in U.S.)
• Resource/Non-resource Mortgage Loans (lenders in
  Australia can access assets beyond the property
  if borrower defaults)
• Subprime/Low Documented Loans (far less in
  Australia est. 2 v. 15)
• Caps/Floors (Australian VRMs do not have caps or
  floors unlike U.S.)

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IV. Types of Prepayers And Variables

• Relocators sell their home and move to other
  places (maybe due to job change etc.)
• Refinancers refinance to take the advantage of
  lower market interest rates
• Switchers change the loan type from FRM to VRM
  or vice versa
• Partial Prepayers (ADDED FOR UNIQUE AUSTRALIAN
  MODEL) prepay less than the full amount Daniel
  considered potential causes of tax, partial
  prepayment by default (maintaining constant
  payments despite decrease in rate), and aversion
  to debt and/or future interest-rate volatility

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A. Relocator Variables

• AgePool ? expected to have positive correlation
  with Conditional Prepayment Rate (CPR)
• Weighted Average Seasoning (WAS) ? average age
  of the mortgages in the pool, weighted by the
  value of the mortgages
• MAXWAS ? maximum WAS over all pools

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• 2. Squareroot of AgePool (SQR(AGEPL)) ?
  expected to have negative correlation with CPR

3. Seasonal ? expected to have a positive
correlation with CPR (people tend to move during
summer)
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B. Refinancer Variables

• 1. Differential between pool origination
  coupon rate and current market rate (FXDdifl) ?
  expected to have a positive correlation with CPR
  (this is a commonly used variable to express
  refinancing incentive in U.S. FRM pools)

(where 3yrFXDthree year fixed mortgage rate)
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2. Burnout variables
Fixed-rate mortgagors are differentially
sensitive to declines in the rate on fixed-rate
mortgages when making refinancing decisions. The
first time that the market coupon rate on
fixed-rate mortgages falls below the coupon rate
of an existing mortgage, e.g., the most sensitive
mortgagors in a pool will refinance. That is, the
most rate-sensitive fixed-rate mortgage
refinancers will ?burnout? of the pool. The
second time that the pool is subject to a decline
in the current market rate to this same level,
prepayments will be lower than during the first
interest-rate cycle. Only if the current rate on
fixed-rate mortgages falls below its previous low
will the next level of rate-sensitive fixed-rate
refinancers be induced to refinance their loans.

• a. r new min (adopted from U.S. models) ?
  expected to have a positive correlation

b. BURNOUT ? expected to have a negative
correlation
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C. Switcher Variables

• 1. New Long Minimum (NLM)? each time the fixed
  mortgage rate declines to a new minimum,
  switchers will tend to prepay to switch to a FRM
  ? expected to have a positive correlation

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• 2. The change in the slope of the yield curve
  the relative change in spread over each month
  between long- and short-term interest rates ? the
  expected sign of the coefficient is left as
  indeterminate.

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D. Partial Prepayer Variables

• 1. Alternative Investment (ALTINV) ? due to
  non-deductibility of owner/occupier mortgage
  interest in Australia there is an incentive to
  prepay ? partial prepayment funds effectively
  earn the mortgage rate as an after-tax interest
  rate (alternative investments are only attractive
  if the after-tax return exceeds the mortgage
  rate) ? expected to have a positive correlation
• RAOA the average continuous compounded return
  on the All Ordinaries Accumulation Index (over
  the previous twelve months)
• SVR an acronym for standard variable rate,
  the standard variable-rate in Australia,
  calculated, (by the RBA), by averaging the
  variable-rates of Australian commercial lenders.

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• 2. Default Partial Prepayment (ParDFLT) ?
  prepayment by default where a borrower optionally
  maintains payment levels even as the rate and
  amount due declines (common in Australia where
  banks encourage borrowers to maintain payment
  levels and often directly debit borrowers
  accounts) ? expected to have a positive
  correlation

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• 3. Rate Volatility ? aversion to debt may lead
  borrowers to partially prepay in response to
  increasing rate volatility ? expected to have a
  positive correlation

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V. Empirical Evaluation of the Australian
Variable-Rate Model
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• After using statistical methods to examine the
  aforementioned variables, some variables are
  eliminated. Finally, the following formulas can
  be defined for CPR Partial, CPR Full, and CPR
  total.

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VI. Findings

• a) most noteworthy result of empirical tests is
  how well the restricted model performed compared
  to the unrestricted model

unrestricted model CPR f(AGEPOOL,SQR(AGEPL),ParD
FLT,ALTINV,FXDdifl, BURNOUT,VOLy,
SLYC,NLM,SEASONAL,rNewMin)
restricted model CPR f(AGEPOOL,SQR(AGEPL),ParDFL
T)
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VI. Findings (cont.)

• b) the ParDFLT1 variable is highly significant
  as a predictor for full prepayments and partial
  prepayments, whereas it was intended as a
  predictor for partial prepayments only ? ParDFLT
  is a measure of the differential rate between
  rates of a (variable-rate) borrower repaying by
  direct debit and the current market
  variable-rate. Daniel had assumed that there was
  not a significant enough difference between
  competing lenders variable-rates to induce
  VRM-to-VRM refinancing ? In review the
  possibility that some variable-rate borrowers
  find refinancing to another more competitive
  variable-rate loan clearly cannot be excluded
  (same for switch to FRM) ? thus, the way the
  ParDFLT variable is calculated results in the
  capture of partial prepayers, refinancers, and
  perhaps switchers

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VI. Findings (cont.)

• c) the age of the pool is a strong influence on
  full prepayment. (Age means the average number of
  months since origination of the mortgages in the
  pool).
• d) FXDdifl, VOLy1, and SLYC were univariately
  significant and correct sign interest-rate
  variables for full prepayments of VRM holders
  (though not significant as variables for the best
  model multivariate tests)
• e) the prepayment data revealed that in
  Australia partial prepayment is on average
  approximately one third of full prepayments for
  variable-rate loans.
• f) the independent variables explain full
  prepayment much more effectively than partial
  prepayment.
• g) the new Australian prepayment model proved
  successful when tested on (Reuters) Australian
  MBS data parsimonious forms of the model were
  able to successfully explain both total
  prepayment and the components of total
  prepayment full and partial prepayment.