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FRM Exam Part I · Mortgages and Mortgage-Backed Securities

Prepayment Risk and Prepayment Models: CPR, SMM and PSA

Updated 11 October 2026 · Fact-checked

Prepayment risk is the risk that borrowers repay mortgage principal earlier than scheduled, changing the cash flows and value of a mortgage-backed security. You measure speed with SMM (monthly) and CPR (annualized), converted by SMM = 1 − (1 − CPR)^(1/12). The PSA benchmark ramps CPR to 6% over 30 months.

Understand Prepayment Risk and Prepayment Models

A mortgage lets the borrower repay early without penalty in most markets. The investor in a mortgage pass-through therefore does not know when principal will come back. That uncertainty is prepayment risk.

Borrowers prepay for several reasons. The main one is refinancing: when market mortgage rates fall below the borrower's rate, refinancing saves money. Others are housing turnover (selling the home triggers repayment), default (in a guaranteed pool, a default is paid out as principal), and curtailment (extra partial payments). Seasoning, season of the year and the loan's age also matter.

Prepayment hurts investors in both directions. When rates fall, prepayments speed up and you get principal back that must be reinvested at lower yields. This is contraction risk. When rates rise, prepayments slow and the security lasts longer than expected, which is extension risk. This is why a pass-through shows negative convexity: its price rises less than a normal bond when rates fall.

Two measures describe speed. SMM (single monthly mortality) is the fraction of the remaining balance, after scheduled principal, that prepays in a month. CPR (conditional prepayment rate) is the same idea annualized. CPR is the share of the pool balance that would prepay over a year if the monthly rate stayed constant.

The PSA benchmark (Public Securities Association) gives a standard path. At 100% PSA, CPR starts at 0% and rises by 0.2% per month of loan age until month 30, where it reaches 6% and stays flat. Faster or slower speeds are quoted as multiples: 200% PSA doubles every CPR on the path, 50% PSA halves it. Refinancing burnout is the pattern where a pool that has already been through a rate-drop episode prepays more slowly later, because the borrowers most able and likely to refinance have already left.

Key formulas to remember

CPR to SMM
SMM = 1 − (1 − CPR)^(1/12)
CPR and SMM as decimals. Compounding survival, not dividing by 12.
SMM to CPR
CPR = 1 − (1 − SMM)^12
Inverse of the above.
SMM definition
SMM = Prepayment in month t ÷ (Beginning balance − Scheduled principal payment)
The denominator is the balance after scheduled principal, not the beginning balance.
100% PSA CPR
CPR = 6% × (t ÷ 30) for t ≤ 30; CPR = 6% for t > 30
t is the age of the loan in months. Equals 0.2% per month for the first 30 months.
PSA at speed x%
CPR = (x ÷ 100) × 100% PSA CPR
For example 150% PSA at month 20 gives 1.5 × 4% = 6%.
Prepayment amount
Prepayment = SMM × (Beginning balance − Scheduled principal)
Total principal received = scheduled principal + prepayment.

How to solve Prepayment Risk and Prepayment Models questions

Use this order for any question on prepayment speeds or PSA.

  1. 1Identify what is given: CPR, SMM, a PSA multiple, or a loan age, and what is asked.
  2. 2If a PSA speed is given, find the loan age t and compute 100% PSA CPR: 0.2% × t up to month 30, then 6%.
  3. 3Multiply by the PSA multiple (x ÷ 100) to get the CPR for that month.
  4. 4Convert CPR to SMM using SMM = 1 − (1 − CPR)^(1/12). Use decimals.
  5. 5Find the balance after scheduled principal: beginning balance minus scheduled principal.
  6. 6Prepayment = SMM × that balance. Add scheduled principal if total principal is asked.
  7. 7For conceptual questions, link the rate move to refinancing, then to contraction or extension risk, then to negative convexity.
  8. 8Sanity check: SMM should be a little above CPR ÷ 12 for small CPR, and CPR should be below 100%.

Quickest way: Quick SMM estimate and PSA lookup

When to use it: When options are well separated and you need speed, or when no calculator power function is handy.

  1. For small CPR, SMM is roughly CPR ÷ 12, slightly higher. Use it to eliminate options.
  2. Calculate PSA CPR mentally: months × 0.2% until month 30, 6% after.
  3. Scale by the PSA multiple.
  4. On the calculator, enter (1 − CPR), take the y^x with 1 ÷ 12 (0.083333), then subtract from 1.
  5. Confirm with the exact formula only if two options are close.

Common mistakes in Prepayment Risk and Prepayment Models

  • Computing SMM as CPR ÷ 12.

    Dividing an annual rate by 12 is the habit from simple interest.

    Fix: Use SMM = 1 − (1 − CPR)^(1/12). CPR ÷ 12 is only an approximation and is slightly too low.

  • Applying SMM to the beginning balance.

    The definition is easy to misremember.

    Fix: Subtract scheduled principal first, then multiply by SMM.

  • Using the wrong loan age for PSA.

    Students use months since the pool was bought instead of the age of the loans.

    Fix: Use the seasoning of the loans, from the question's wording. A 10-month-old pool at 100% PSA has CPR 2%.

  • Thinking 200% PSA reaches 6% CPR at month 30.

    Confusing the multiple with a change in the ramp length.

    Fix: The multiple scales every CPR. At 200% PSA, CPR is 12% from month 30 onward and ramps at 0.4% per month.

  • Saying falling rates cause extension risk.

    Mixing up the direction of prepayment response.

    Fix: Falling rates: faster prepayments, contraction risk. Rising rates: slower prepayments, extension risk.

  • Treating refinancing burnout as a rise in prepayment.

    The word burnout is read loosely.

    Fix: Burnout means prepayments slow, even when rates stay low, because rate-sensitive borrowers have already refinanced.

Worked examples

Example 1

A mortgage pool has a CPR of 6%. Compute the SMM.

Show the solution
  1. Formula: SMM = 1 − (1 − CPR)^(1/12).
  2. 1 − 0.06 = 0.94.
  3. 0.94^(1/12) = exp(ln(0.94) ÷ 12) = exp(−0.061875 ÷ 12) = exp(−0.0051563) ≈ 0.994857.
  4. SMM = 1 − 0.994857 = 0.005143.

Answer: SMM ≈ 0.514% per month. Note that CPR ÷ 12 would give 0.5%, which is a poor approximation here and slightly too low, so use the exact formula.

Example 2

A pool is 20 months old and prepays at 150% PSA. The balance at the start of the month is ₹40,00,00,000 and scheduled principal is ₹40,00,000. Compute the CPR, the SMM and the prepayment for the month.

Show the solution
  1. 100% PSA CPR at month 20 = 0.2% × 20 = 4%.
  2. At 150% PSA: CPR = 1.5 × 4% = 6%.
  3. SMM = 1 − (0.94)^(1/12) ≈ 0.005143.
  4. Balance after scheduled principal = ₹40,00,00,000 − ₹40,00,000 = ₹39,60,00,000.
  5. Prepayment = 0.005143 × ₹39,60,00,000 ≈ ₹20,36,600.

Answer: CPR = 6%, SMM ≈ 0.5143%, prepayment ≈ ₹20,36,600 (about ₹20.4 lakh).

Exam tips

  • Memorise the 100% PSA path: 0.2% per month to 6% at month 30, then flat. Most numeric questions start here.
  • Always do the CPR to SMM conversion exactly; options often differ by the CPR ÷ 12 trap.
  • For conceptual questions, name the direction: falling rates lead to faster prepayment, contraction risk and negative convexity.
  • Check whether the question gives SMM on the beginning balance or after scheduled principal.
  • Know that PSA is a benchmark for speed, not a forecast; a model such as a refinancing-incentive model forecasts actual speeds.

Practice questions from Mortgages and Mortgage-Backed Securities

Prepayment Risk and Prepayment Models: frequently asked questions

How do I convert CPR to SMM in FRM Part I?

Use SMM = 1 − (1 − CPR)^(1/12), with CPR as a decimal. To go back, use CPR = 1 − (1 − SMM)^12. Do not divide by 12 or multiply by 12, as that is only an approximation.

What does 100% PSA mean?

It is the standard benchmark path where CPR rises by 0.2% each month from 0% to 6% at month 30, then stays at 6%. Other speeds are multiples of this path, so 300% PSA is three times each month's CPR.

What is prepayment risk in mortgage-backed securities?

It is the uncertainty over when borrowers repay principal. Fast prepayments force reinvestment at lower rates (contraction risk), and slow prepayments extend the security's life (extension risk). Both make cash flows hard to predict.

What is refinancing burnout?

Burnout is the slowing of prepayments in a pool after a period of strong refinancing. Borrowers who benefit most from refinancing have already left, so the remaining ones respond less to further falls in rates.