Work out the single monthly mortality rate (SMM), conditional prepayment rate (CPR), weighted average maturity and weighted average coupon for a mortgage pool.
The idea
The single monthly mortality rate, SMM, is the share of the pool's balance that prepays in a month, measured after scheduled principal: SMM = prepayment in the month ÷ (beginning balance − scheduled principal). The conditional prepayment rate, CPR, annualises it with monthly compounding: CPR = 1 − (1 − SMM)^12. Multiplying SMM by 12 is the usual shortcut error and overstates CPR. Going the other way, from an annual rate to a monthly one: SMM = 1 − (1 − CPR)^(1/12). The weighted average coupon, WAC, is the average of the loans' coupons, weighted by current balance. The weighted average maturity, WAM, weights their remaining terms, in months, the same way. Simple averages are wrong when loans differ in size. The PSA benchmark at 100% raises CPR by 0.2 percentage points per month of age, up to 6% at month 30, and holds it there. Other speeds are multiples of that path. The exam point is to convert with the compounding formulas and weight by balance.
Formulas
Single monthly mortality rate
SMM = prepayment ÷ (beginning balance − scheduled principal)
- prepayment
- unscheduled principal paid in the month
- beginning balance
- the pool balance at the start of the month
- scheduled principal
- the amortisation due in the month
Measure prepayment against the balance left after scheduled principal, not against the beginning or original balance.
Conditional prepayment rate from SMM
CPR = 1 − (1 − SMM)¹²
- SMM
- the single monthly mortality rate, as a decimal
Monthly compounding. SMM × 12 overstates CPR; the reverse is SMM = 1 − (1 − CPR)^(1 ÷ 12).
Weighted average coupon of a pool
WAC = Σ(Bᵢ × cᵢ) ÷ ΣBᵢ
- Bᵢ
- the current balance of loan or group i
- cᵢ
- its coupon
Weight by current balance, never a simple average. WAM is the same calculation with each remaining term, in months, in place of the coupon.
A practice question
The single monthly mortality rate (SMM) of a mortgage pool in a given month is:
- Unscheduled principal prepaid in the month divided by beginning balance less scheduled principal. - correct
- Total principal paid in the month, scheduled plus unscheduled, divided by the beginning balance.Why not: Includes scheduled principal, which SMM excludes.
- Prepayments in the month divided by the original balance at issuance.Why not: Uses the original balance; SMM is conditional on the balance still outstanding.
- The annualized fraction of the pool's balance that prepays over a twelve-month period.Why not: Describes the CPR, not the monthly rate.
SMM measures prepayments only, as a fraction of the balance that remained after scheduled principal was paid. Its annualized form is the CPR.
A harder one
A mortgage pool has a beginning balance of USD 200 million, scheduled principal of USD 4.0 million and an ending balance of USD 186.2 million for the month. The SMM is closest to:
- 4.90%Why not: Divides by the beginning balance without deducting scheduled principal.
- 6.90%Why not: Counts all 13.8 of principal paid as prepayment.
- 5.00% - correct
- 45.9%Why not: Annualizes the SMM into a CPR when the monthly rate was asked.
Prepayment = 200 - 4.0 - 186.2 = 9.8. SMM = 9.8 / (200 - 4.0) = 5.00%.
The hardest tier
Under the PSA benchmark, 100% PSA has CPR rising by 0.2 percentage points per month of age up to 6% at month 30 and constant at 6% thereafter. A pool is 40 months old and prepays at 150% PSA. The SMM for the month is closest to:
- 0.750%Why not: Divides the 9% CPR by 12 instead of using the compounding conversion.
- 1.062%Why not: Applies the 0.2% ramp beyond month 30 (CPR 12%) and then converts correctly.
- 0.783% - correct
- 1.000%Why not: Applies the uncapped ramp (12% CPR) and divides by 12.
Past month 30 the ramp is capped: CPR = 6% x 1.5 = 9%. SMM = 1 - (1 - 0.09)^(1/12) = 0.783%.
In the app: 6 practice questions on this outcome, spaced review that brings it back before you forget it.
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