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

1. A Variable-Rate Loan-Prepayment Model for Australian Mortgages(“Daniel” Model) Evan Rosenberg Hui Gang Wu

2. I. Objective of This Paper • To investigate Australian mortgage prepayment by developing and testing prepayment models for loans in Australian MBSs

3. 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

4. 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.)

5. 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

7. 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 MAX{WAS}  maximum WAS over all pools

8. 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)

9. 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 3yrFXD=three year fixed mortgage rate)

10. 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. rnew min (adopted from U.S. models) expected to have a positive correlation b. BURNOUT  expected to have a negative correlation

11. 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

12. 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.

13. 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.

15. 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

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

17. V. Empirical Evaluation of the Australian Variable-Rate Model

25. 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.

27. 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),ParDFLT,ALTINV,FXDdifl, BURNOUT,VOLy, SLYC,NLM,SEASONAL,rNewMin) restricted model CPR = f(AGEPOOL,SQR(AGEPL),ParDFLT)

28. 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

29. 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.