## Incorporating the Possibility of Prepayments

Mortgage prepayments are the central concern for MBS. With the exception of some smaller programs backed by loans with prepayment penalties (noted earlier), the loans backing agency pass-throughs may be paid off at any time prior to maturity, typically because the borrower sells the property or refinances. The possibility of prepayments means that cash flows cannot be predicted with certainty.

Assumptions must be made concerning the likely prepayment pattern in order to estimate the cash flows. The simplest way of expressing a prepayment assumption is as a constant fraction of principal at the beginning of the period. Expressed as an annual rate of prepayment, this is called a CPR.10

Exhibit 3-3 depicts the cash-flow patterns for the 5%, 30-year pass-through with a 5.4589% WAC and a 357-month WAM when a constant fraction of the remaining principal is prepaid each month, in this case 10CPR. That is, we are assuming that 10% of the principal would prepay over 12 months (i.e., annual-ized, assuming monthly compounding, or that 0.8742% of the principal prepays

- The alternative to a current WALA would be to impute the current weighted-average age of loans from the original weighted-average term and the current WAM.
- For constant or conditional (on the balance at the beginning of the period) prepayment rate.

EXHIBIT 3-3

Cash Flows on Sample Pool at 10 CPR 16,000 14,000 12,000 10,000 8,000 6,000 4,000 2,000 0

### 1 60 119 178 237 296 355

- Scheduled Principal a Interest a Prepayments ■ Servicing |
- 1 mm pool of 5.4589%, 30-year mortgages, and a 5% pass-through certificate. Assumes no prepays.

per month).11 The cash flow is no longer level in each month over the period. Instead, cash flows decline continuously from the first month as both prepayments and remaining scheduled principal payments reduce the remaining principal balance of the pool. In particular, assuming a constant rate of prepayment means that the largest prepayment in dollar terms would occur in the first month. Notice also that prepayments lower the total amount of interest paid over the life of the pass-through.

At 10CPR, half the principal balance is paid down within six years, but some cash flow is received up to the expected maturity of the pool (a WAM is properly an expectation; some mortgages still would be outstanding). As a matter of fact, 10CPR is a reasonable prepayment rate for 5% conventional securities in the current (circa January 2005) interest-rate environment. However, in a sharp rally there is a likelihood that much higher prepayment rates could be observed. Exhibit 3-4 illustrates the cash-flow pattern at 60CPR. In this figure, prepayments swamp all other cash flows, and interest payments are sharply reduced. The life of the investment is significantly shortened; over half the principal returns in three quarters, and 90% is paid down in less than 2.5 years.

A constant prepayment assumption is not realistic. At best, prepayment assumptions or projections one, two, or three months forward may be realistically based on current interest rates or current prepayment speeds. Beyond that window, assuming constant prepayments is comparable to assuming that interest rates will remain at current levels.

11. The monthly rate is called a single monthly mortality (SMM).

EXHIBIT 3-4

Cash Flows on Sample Pool at 60 CPR

90,000 80,000 70,000 60,000 50,000 40,000 30,000 20,000 10,000 0

1 12 24 36 48 60 72 84 96 108 120 132 144 □ Scheduled Principal ■ Interest H Prepayments ■ Servicing

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