# LO 35.8: Explain the prepayment forecasting methodologies and calculate the

LO 35.8: Explain the prepayment forecasting methodologies and calculate the constant prepayment rate (CPR) and the Public Securities Association (PSA) rate.
Common methodologies used to estimate prepayments for an MBS or ABS collateralized by mortgages or student loans are the constant prepayment rate (CPR) and the Public Securities Association (PSA) method. Assumptions regarding the rate of prepayment are required to estimate the cash flows for an MBS. Prepayments will reduce the yield of an MBS, assuming principal payments remain unchanged.
The CPR is calculated as: CPR = 1 (1SM M )12. The single monthly mortality (SMM) is the single-month proportional prepayment. Factors that influence the CPR are market environment, characteristics of the underlying mortgage pool, and the outstanding balance of the pool.
2018 Kaplan, Inc.
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Topic 35 Cross Reference to GARP Assigned Reading – Choudhry, Chapter 12
Example: Constant prepayment rate
Suppose an ABS has an SMM of 1.5%. This implies that the approximate prepayment for the month is equal to 1.5% of the remaining mortgage balance for the month less the scheduled principal repayment. Calculate the CPR for this MBS.
The CPR for this MBS equals 16.59%, calculated as: CPR = 1 (1 0.015)12 = 0.1659.
The PSA typically assumes that prepayments will increase as a pool approaches maturity. The MBS pool of mortgages has a 100% PSA if its CPR begins at 0 and increases 0.2% each month for the first 30 months. A graph of the CPR for an ABS as it approaches maturity is illustrated in Figure 5.
Note that the middle line in Figure 5 represents 100% PSA where the prepayments are assumed to start at 0 and increase 0.2% each month up until month 30. After 30 months, the 100% PSA is assumed to be at a constant 6% (calculated as 0.2 times 30 months) until maturity. Other prepayment scenarios are then calculated as a percentage of this 100% base case. Thus, a 50% PSA assumes 50% of the initial increase for the first 30 months. In Figure 5, the bottom line represents the 50% PSA scenario where prepayments are assumed to increase 0.1% each month for the first 30 months, before reaching a constant prepayment rate of 3%. Similarly, the top line represents the 150% PSA scenario where prepayments are assumed to increase 0.3% each month for the first 30 months, before reaching a constant prepayment rate of 9%.
0
30
60
Months
90
120
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2018 Kaplan, Inc.
Topic 35 Cross Reference to GARP Assigned Reading – Choudhry, Chapter 12
Figure 6 summarizes performance tools discussed in this topic based on the type of ABS or MBS.
Figure 6: ABS and MBS Performance Tools
Performance Analysis Tools
loss curves
absolute prepayment speed (APS)
delinquency ratio
default ratio
monthly payment rate (MPR)
debt service coverage ratio
(DSCR)
Asset Type auto loans auto loans credit cards
credit cards credit cards
Calculation
expected cumulative losses prepayments / pool balance past due receivables / pool
balance
defaults / pool balance
receivables collected / pool
balance
commercial mortgages
NOI / debt payments
weighted average coupon (WAC)
mortgages
weighted average maturity
(WAM)
weighted average life (WAL)
mortgages
mortgages
single monthly mortality (SMM) mortgages, home-equity,
student loans
constant prepayment rate (CPR)
Public Securities Association
(PSA)
mortgages, home-equity,
student loans
mortgages, home-equity,
student loans
weighted pool coupon
payments
weighted pool maturity
^ (a / 365) x PF(t)
prepayment / pool balance – (1-SMM)12 1 – (1-SMM)12
[CPR / (0.2)(months)] x 100
S e c u r i t i z a t i o n a f t e r t h e C r e d i t C r u n c h