The PSA Prepayment Benchmark and SMM

Mortgage prepayment speed changes with the age of a loan — a brand-new mortgage rarely prepays in its first month, but by year three or four, prepayment (from moving, refinancing, or selling the home) settles into a steadier rate. Quoting "this pool prepays at 6% a year" is ambiguous if you don't say how old the loans are. The PSA benchmark (named for the Public Securities Association, now SIFMA) solves this by defining a standard age-based ramp that the whole market uses as a common reference point.

From CPR down to a monthly cash flow

CPR is an annualized rate — the percentage of the remaining pool balance expected to prepay over a year. To actually run a monthly cash-flow model, that annual rate has to be converted into a single monthly mortality (SMM), the percentage of the current month's beginning balance expected to prepay that month:

$$SMM = 1 - (1 - CPR)^{1/12}$$

In words: take one minus the annual prepayment rate, find its twelfth root, and subtract that from one — this correctly compounds a monthly rate up to the stated annual rate, the same way a monthly interest rate compounds up to an annual one.

Worked example

A pool is quoted at 150% PSA and is 10 months seasoned. At 100% PSA, month 10's CPR would be $0.2\% \times 10 = 2.0\%$ (still on the ramp, since month 10 is before month 30). At 150% PSA, scale that by 1.5: $2.0\% \times 1.5 = 3.0\%$ CPR for that month. Converting to SMM: $SMM = 1 - (1 - 0.03)^{1/12} = 1 - 0.97^{0.0833} \approx 0.00254$, or about 0.254% of the current balance expected to prepay this month. Multiply that by the pool's current outstanding balance to get the dollar amount of unscheduled principal expected that month.

What this means in practice

Quoting a pool's speed as a single PSA number lets traders compare pools of very different ages on equal footing — a 5-year-old pool running at 180% PSA and a brand-new pool running at 180% PSA are both described by the same ramp, scaled the same way, even though their month-by-month CPR numbers look completely different in raw terms.