What is the difference between CPR and SMM in MBS prepayment modeling, and how do you convert between them?

CPR (Conditional Prepayment Rate) and SMM (Single Monthly Mortality) both measure the rate at which mortgage borrowers prepay their loans, but at different time frequencies.

Definitions:

• CPR: The annualized percentage of the remaining mortgage pool balance that is expected to prepay within one year
• SMM: The percentage of the remaining balance (after scheduled payments) that is expected to prepay in a single month

Conversion Formula:

SMM = 1 - (1 - CPR)^(1/12)

CPR = 1 - (1 - SMM)^12

Think of it like converting annual interest rates to monthly: you use compound, not simple, conversion.

Example: If CPR = 8%:

SMM = 1 - (1 - 0.08)^(1/12) = 1 - (0.92)^(0.0833) = 1 - 0.99306 = 0.00694 or 0.694%

Verification: CPR = 1 - (1 - 0.00694)^12 = 1 - (0.99306)^12 = 1 - 0.9200 = 8.00% (confirmed)

Monthly Cash Flow Projection — Greystone Mortgage Pool (fictional):

Month	Beginning Balance	Scheduled Principal	Prepayment (SMM x remaining)	Total Principal	Ending Balance
1	$10,000,000	$25,000	$69,228	$94,228	$9,905,772
2	$9,905,772	$25,100	$68,523	$93,623	$9,812,149
3	$9,812,149	$25,200	$67,874	$93,074	$9,719,075

Prepayment in month 1 = SMM x (Beginning Balance - Scheduled Principal) = 0.00694 x ($10,000,000 -$25,000) = $69,228

PSA Benchmark: The Public Securities Association (PSA) standard prepayment model starts at 0.2% CPR in month 1 and increases by 0.2% per month until reaching 6% CPR in month 30, then remains at 6% CPR.

• 100% PSA = this standard ramp
• 200% PSA = double the CPR at each month (ramp to 12% CPR by month 30)
• 50% PSA = half the CPR at each month

Exam Tip: The CFA exam will test the CPR-to-SMM conversion and may ask you to compute prepayment amounts for a given month. Remember: SMM is applied to the balance after scheduled payments, not the beginning balance.

Practice MBS cash flow projections in our CFA Level II bank.