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CFA Level I Exam · Mortgage-Backed Security (MBS) Instrument and Market Features

Prepayment Risk and Measurement: SMM, CPR and PSA

Updated 7 October 2026 · Fact-checked

Prepayment risk is the risk that borrowers repay mortgage principal earlier or later than scheduled, changing an MBS's cash flows. Falling rates speed prepayments (contraction risk); rising rates slow them (extension risk). You measure speed with SMM (monthly), CPR (annualized) and the PSA benchmark, where 100 PSA means a CPR that ramps to 6%.

Understand Prepayment Risk and Measurement

A mortgage pass-through security passes borrowers' payments to investors: interest, scheduled principal and any prepayments. A prepayment is any principal paid beyond the scheduled amount. Borrowers can pay extra, refinance or sell the house. The investor therefore does not know when the principal will come back.

Prepayment risk is the uncertainty about the timing of principal. The borrower effectively holds a call option on the loan. When market mortgage rates fall below the loan's rate, borrowers refinance. Investors get principal back early and must reinvest at lower rates. This is contraction risk. The MBS price rises less than a comparable option-free bond, which is negative convexity.

When rates rise, refinancing slows and borrowers stay put. The MBS lasts longer than expected and the investor is stuck with a below-market coupon. This is extension risk. Duration lengthens just when you would like it to be short.

Other factors also affect prepayments. Refinancing incentive (the gap between the loan rate and current rates) is the main one. Others are seasoning (new loans prepay slowly at first), seasonality (home sales are higher in spring and summer), burnout (borrowers who did not refinance when rates fell are less likely to later), housing turnover and the economy, and loan features such as prepayment penalties.

To measure speed, you use three tools. SMM is the fraction of the outstanding balance, after scheduled principal, that prepays in one month. CPR is the same idea annualized. The PSA benchmark is a standard path of CPRs by loan age: 0.2% in month 1, rising by 0.2% a month to 6% at month 30, then flat at 6%. Faster or slower speeds are expressed as a percentage of this path.

Key formulas to remember

SMM
SMM = Prepayment in the month ÷ (Beginning balance − Scheduled principal payment)
Prepayment is measured against the balance left after scheduled principal, not the beginning balance.
CPR from SMM
CPR = 1 − (1 − SMM)^12
Annualizes by compounding survival, not by multiplying by 12.
SMM from CPR
SMM = 1 − (1 − CPR)^(1/12)
On a calculator use the 1/12 power (y^x with 0.083333...).
100 PSA CPR path
CPR = 6% × (month ÷ 30) for months 1 to 30; CPR = 6% after month 30
Equivalent to 0.2% per month of loan age up to month 30.
Scaled PSA
CPR at x PSA = (x ÷ 100) × CPR at 100 PSA
150 PSA is 1.5 times the benchmark CPR at each age. The 6% plateau is also scaled: 150 PSA plateaus at 9%.
Risk direction
Rates fall → prepayments rise → contraction risk; rates rise → prepayments fall → extension risk
Both are adverse for the investor relative to expectations; the MBS shows negative convexity.

How to solve Prepayment Risk and Measurement questions

Use this method for any prepayment question, whether it is conceptual or numerical.

  1. 1Identify what is asked: risk concept, SMM, CPR, or PSA speed.
  2. 2For concept questions, check the direction of interest rates versus the loan rate. Lower rates mean faster prepayment and contraction risk; higher rates mean slower prepayment and extension risk.
  3. 3For SMM, first subtract scheduled principal from the beginning balance, then divide the prepayment by that figure.
  4. 4To convert between SMM and CPR, use the compounding formulas. Never multiply or divide by 12 unless the question asks for an approximation.
  5. 5For PSA, find the loan age. If age is 30 months or more, 100 PSA CPR is 6%; otherwise it is 0.2% × age. Then scale by the PSA multiple.
  6. 6Convert the final CPR to SMM if the question asks for monthly prepayment, then multiply SMM by the balance after scheduled principal.
  7. 7Sanity check: SMM should be much smaller than CPR, and a higher PSA means faster prepayments.

Quickest way: Fast CPR and PSA shortcut

When to use it: Use when the exam gives a PSA speed and loan age and asks for CPR or a prepayment amount.

  1. CPR = (PSA ÷ 100) × 6% × min(age, 30) ÷ 30.
  2. CPR ÷ 12 is only a rough approximation of SMM and can understate it. Use it only to eliminate far-off options.
  3. Always confirm with SMM = 1 − (1 − CPR)^(1/12) when options are close.
  4. Prepayment = SMM × (Beginning balance − Scheduled principal).
  5. On the BA II Plus: enter 1 − CPR, press y^x, enter 0.083333 (or 1 ÷ 12), then = and subtract the result from 1.

Common mistakes in Prepayment Risk and Measurement

  • Calculating CPR as SMM × 12.

    Annual figures from monthly ones feel like simple multiplication.

    Fix: Use CPR = 1 − (1 − SMM)^12. The multiply-by-12 result overstates CPR.

  • Dividing prepayment by the beginning balance to get SMM.

    Students forget scheduled principal is paid first.

    Fix: Subtract scheduled principal from beginning balance, then divide.

  • Mixing up contraction and extension risk.

    Both words sound like changes in size rather than in life.

    Fix: Contraction: rates fall, the MBS life shortens. Extension: rates rise, the life lengthens.

  • Treating 100 PSA as a 100% prepayment rate or as a constant 6% CPR.

    The number 100 looks like a percentage of the balance.

    Fix: 100 PSA is a benchmark path: CPR ramps up 0.2% a month to 6% at month 30, then stays at 6%.

  • Applying the 6% cap to faster PSA speeds.

    Students remember 6% as the limit.

    Fix: Scale the whole path. At 200 PSA the plateau is 12%, reached at month 30.

  • Saying prepayment risk only hurts when rates fall.

    Students focus on reinvestment loss.

    Fix: Both directions are adverse relative to expectations: falling rates cause contraction risk and rising rates cause extension risk.

Worked examples

Example 1

A mortgage pool has a beginning balance of $200,000,000 for the month. Scheduled principal is $2,000,000 and prepayments are $9,900,000. What is the SMM? A. 4.95%, B. 5.0%, C. 5.5%

Show the solution
  1. Balance after scheduled principal = 200,000,000 − 2,000,000 = 198,000,000.
  2. SMM = 9,900,000 ÷ 198,000,000 = 0.05.
  3. SMM = 5.0% for the month.

Answer: SMM = 5.0%, so B is correct. Option A, 4.95%, wrongly divides by the full beginning balance (9,900,000 ÷ 200,000,000).

Example 2

A pool of seasoned loans prepays at 150 PSA and is 40 months old. What is the SMM? A. 0.75%, B. 0.78%, C. 0.90%

Show the solution
  1. Age is above 30 months, so 100 PSA CPR = 6%.
  2. CPR at 150 PSA = 1.5 × 6% = 9%.
  3. SMM = 1 − (1 − 0.09)^(1/12).
  4. (0.91)^(1/12): ln 0.91 = −0.09431; ÷ 12 = −0.007859; e^(−0.007859) = 0.992172.
  5. SMM = 1 − 0.992172 = 0.007828, about 0.78%.

Answer: SMM ≈ 0.78% per month (the implied CPR is 9%), so B is correct. Option A, 0.75%, is the CPR ÷ 12 approximation (9% ÷ 12), which understates the compounded SMM. Option C, 0.90%, is not close.

Exam tips

  • Questions are three-option, so use direction logic first: falling rates mean contraction risk, rising rates mean extension risk.
  • Expect SMM, CPR and PSA conversions. Keep the formula for the SMM denominator fixed in memory.
  • Remember that the MBS shows negative convexity because the borrower holds a call option.
  • When a question asks about factors, think refinancing incentive, seasoning, burnout, seasonality and housing turnover.
  • There is no penalty for wrong answers, so always answer; eliminate options with the sanity check that SMM is far smaller than CPR.

Practice questions from Mortgage-Backed Security (MBS) Instrument and Market Features

Prepayment Risk and Measurement: frequently asked questions

What is the difference between SMM and CPR?

SMM is the share of the outstanding balance that prepays in one month, after scheduled principal. CPR is the annualized version. They are linked by CPR = 1 − (1 − SMM)^12.

What does 100 PSA mean?

It is a benchmark prepayment path. CPR starts at 0.2% in month 1 and rises by 0.2% each month until it reaches 6% at month 30. After that it stays at 6%. Other speeds are multiples of this path.

What is the difference between contraction and extension risk?

Contraction risk occurs when rates fall and prepayments speed up, shortening the MBS's life. Extension risk occurs when rates rise and prepayments slow, lengthening it. Both are forms of prepayment risk.

What factors affect mortgage prepayments?

Main factors are the gap between the loan rate and current mortgage rates, loan age (seasoning), burnout, seasonality, housing turnover, the economy, and prepayment penalties.