How do you calculate CPR and CDR on a loan pool?
Monthly prepayments and defaults annualised by the SIFMA formulas, the CPR and default rates US consumer lenders file, Fitch's prepayment stresses for Latin America and what a CDR means over a pool's life.
CPR and CDR turn one month of a loan pool into an annual rate. The SMM is principal repaid early over the balance left after the scheduled payment, and CPR is 1 minus (1 minus SMM) to the 12th. CDR annualises defaults the same way. SoFi's 10-Q put its personal loans at a 25.8% CPR in June 2026.
SMM is the principal that came back early, over the balance that was not yet due
The standard text is chapter SF of the Uniform Practices of the Bond Market Association, now SIFMA. The single monthly mortality (SMM) is the share of a pool outstanding at the start of a month that is repaid during the month beyond its schedule. The US rule on uniform mortgage-backed securities, 12 CFR 1248.1, writes it from payments: SMM equals payments received minus scheduled interest minus scheduled principal, divided by the unpaid balance minus scheduled principal.
The conditional prepayment rate (CPR) compounds that month over a year: CPR = 1 − (1 − SMM)12. SIFMA is strict about the word: the term «CPR» for a monthly figure «is not recommended», and CPR means the annualised rate only. The conditional default rate (CDR) is built the same way from the monthly default rate (MDR), the balance that defaulted in the month over the balance still performing at the end of the month before.
Our computation, a modelled pool, per 100 of performing principal at the start of the month. SMM as in 12 CFR 1248.1; MDR on the prior month's performing balance as in SIFMA Uniform Practices, chapter SF; both annualised as 1 minus (1 minus the monthly rate) to the 12th.
| Line | Amount | Rate |
|---|---|---|
| Performing principal, start of month | 100.00 | Base of the default rate |
| Scheduled principal due | 2.40 | Taken out before the SMM |
| Repaid early, beyond the schedule | 1.80 | SMM 1.80 / 97.60 = 1.84%, CPR 20.0% |
| Stopped paying and defaulted | 0.55 | MDR 0.55 / 100 = 0.55%, CDR 6.4% |
| Performing principal, end of month | 95.25 | 100 minus 2.40, 1.80 and 0.55 |
Monthly rates look small and compound into large annual ones. A pool that loses half a percent of its balance to default in one month runs at a CDR above 6%.
A default in CDR is a loan that stopped paying, not a loan that is late
SIFMA's default standards are explicit on three points. Default analysis models «defaults only, not delinquencies»: a loan that falls behind and cures is not counted. It specifies «default rates, not loss rates»: the share of a default that is never recovered is a separate number, the loss severity. And the two rates sit on different bases: the default rate on the performing balance before the month's scheduled principal, the prepayment rate on the balance after it.
Filers do not all use the same words. SoFi's 10-Q defines its annual default rate as «the annualized rate of borrowers who do not make loan payments on time». Prosper describes its default rate as «an aggregate of conditional default rate curves for each credit grade», the share of principal expected to default per period by term and age. One counts borrowers, the other principal. A fund reading a lender's CDR asks which, and what event starts the clock.
US consumer lenders file their CPR and CDR every quarter
SoFi Technologies, Form 10-Q for the quarter to 30 June 2026, filed 6 August 2026: key unobservable assumptions in the fair value of loans, weighted by relative fair value. Prosper Marketplace, Form 10-Q for the quarter to 30 June 2026, filed 13 August 2026: key economic assumptions for servicing assets on personal loans, weighted averages and ranges.
| Book, 30 June 2026 | CPR | Default rate | Range of CPR |
|---|---|---|---|
| SoFi, personal loans | 25.8% | 4.8% | 15.4% to 32.1% |
| Prosper, personal loans serviced | 21.7% | 11.2% | 8.7% to 35.1% |
| SoFi, home loans | 14.9% | 0.5% | 8.2% to 14.9% |
| SoFi, student loans | 11.0% | 0.7% | 9.3% to 12.8% |
The same product carries a 4.8% default assumption at SoFi and 11.2% at Prosper, with a similar speed of prepayment. A CPR or CDR is a description of one lender's borrowers, not of a product, and a fund prices the lender's own.
A CDR does not tell you how much of the pool will default
Because each month's defaults are a share of what is still performing, a pool that prepays fast has less left to default. SIFMA draws the consequence itself: «a higher prepayment assumption at a given default rate will result in lower cumulative defaults. Therefore, a table must be produced that shows cumulative defaults in a matrix format». The term and the rate matter too, because they set how fast the schedule pays the balance down.
Our computation, a modelled pool: 36-month equal-payment loans at 30% a year, cash flows by the SIFMA chapter SF formulas (new defaults on the prior performing balance, voluntary prepayments on the amortised balance, scheduled principal on the balance that did not default). Cumulative defaults as a share of the original balance.
| Default rate | CPR 0% | CPR 10% | CPR 20% | CPR 30% |
|---|---|---|---|---|
| CDR 5% | 8.6% | 7.7% | 6.9% | 6.1% |
| CDR 10% | 16.6% | 15.0% | 13.5% | 12.0% |
| CDR 15% | 24.2% | 21.9% | 19.7% | 17.6% |
| CDR 20% | 31.3% | 28.4% | 25.6% | 23.0% |
Moving from no prepayment to a 30% CPR cuts lifetime defaults by 26% to 28% at every default rate. At 60% a year the same 10% CDR with no prepayment defaults 18.4% of the pool, because the schedule repays the balance more slowly.
Run on the filed assumptions, the same model puts SoFi's 25.8% CPR and 4.8% default rate at about 6.2% of a 36-month pool defaulting over its life, and Prosper's 21.7% and 11.2% at about 14.7%. Our computation, and only an illustration: real loans have different terms and their rates change with age.
A rating agency stresses prepayment in both directions, harder in Latin America
Fast prepayment lowers defaults and also takes away interest. In a pool that yields much more than it costs, that interest is what pays for losses: Fitch's consumer loan methodology of 26 November 2024 notes portfolio yields «de 40%-80% en algunas transacciones de Latinoamérica» and says the excess spread available to cover defaults depends on «el prepago, el rendimiento y la morosidad». So Fitch tests the base case up and down.
Fitch Ratings, Metodología de Calificación para Emisiones de Deuda Respaldadas por Créditos al Consumo, 26 November 2024: stressed prepayment rates by rating level, as a multiple of the base case. Example column ours, on a 20% base case, as in Fitch's own example.
| Rating level | Stress, up and down | On a 20% base case |
|---|---|---|
| AAAsf | plus or minus 50% | 30% and 10% |
| AAsf | plus or minus 40% | 28% and 12% |
| Asf | plus or minus 30% | 26% and 14% |
| BBBsf | plus or minus 20% | 24% and 16% |
| BBsf | plus or minus 10% | 22% and 18% |
| Bsf | base case | 20% |
The stress is relative, so a lender that states a low base case gets a small absolute stress. Fitch says it uses higher stresses where the base case is very low and where a deal relies heavily on excess spread.
the base case prepayment rate Fitch's top rating can be stressed to in Latin America
Fitch, consumer ABS methodology, 26 November 2024: in deals with a very high reliance on excess spread.
In Mexico a borrower may prepay by rule, and a partial prepayment shrinks the instalment
CONDUSEF's transparency rules for unregulated SOFOMs, published on 11 August 2015, set the right in article 21. A lender must accept early repayment of a loan below the equivalent of 900,000 UDIs, the inflation-indexed unit, or of a mortgage of any size, when the borrower asks, is current and pays at least the instalment due for the period. The money goes «en forma exclusiva al Saldo Insoluto del capital», and a partial prepayment reduces the remaining instalments unless the parties agree to reduce their number instead.
That rule decides how a Mexican pool is measured. After a partial prepayment the schedule changes, so the scheduled principal in the next month's SMM must come from the new schedule, not the original one. A loan tape, the file with one row per loan, that carries the scheduled and the paid principal for each month lets a fund recompute both rates; one that carries only balances does not.
Formulas are SIFMA's and the FHFA's, assumptions SoFi's, Prosper's and Fitch's, the prepayment rule CONDUSEF's; the worked month and the matrix of cumulative defaults are our computation from them.
Questions this raises
- What is the formula for CPR?
- CPR equals 1 minus (1 minus SMM) to the 12th power, where SMM, the single monthly mortality, is the principal repaid in a month beyond the schedule divided by the balance left after the scheduled principal. SIFMA's standard formulas use CPR for the annualised rate only.
- What is the difference between SMM and CPR?
- SMM is the share of a pool's balance prepaid in one month. CPR is the same speed expressed as an annual rate, compounding the monthly figure over twelve months. An SMM of 1.84% is a CPR of 20%.
- How do you calculate CDR?
- Divide the balance that defaulted in a month by the performing balance at the end of the previous month to get the monthly default rate, then annualise it: CDR equals 1 minus (1 minus MDR) to the 12th. A monthly default rate of 0.55% is a CDR of 6.4%.
- What is the difference between CDR and cumulative default rate?
- CDR is an annual rate on the balance still performing; cumulative default is the share of the original pool that defaults over its life. On 36-month loans at 30% a year, a 10% CDR defaults 16.6% of the pool with no prepayment and 12.0% at a 30% CPR, by our computation.
- What CPR do personal loans have?
- At 30 June 2026 SoFi valued its personal loans at a weighted 25.8% CPR, within a range of 15.4% to 32.1%, and Prosper used 21.7% for the personal loans it services, within 8.7% to 35.1%, according to their quarterly 10-Q filings.
- Can a borrower in Mexico prepay a loan?
- Yes. Under article 21 of CONDUSEF's transparency rules for unregulated SOFOMs, a lender must accept early repayment of loans below 900,000 UDIs and of mortgages of any size when the borrower is current and pays at least one instalment. The prepayment goes to principal and, if partial, reduces the instalments unless the parties agree to cut their number.
Where every figure on this page comes from6 sources
- 01The Bond Market Association (now SIFMA), Uniform Practices, chapter SF, Standard Formulas for the Analysis of Mortgage-Backed Securities and Other Related Securities, 1 February 1999: SMM and CPR (SF-5, SF-6), default standards and definitions (SF-17, SF-18), cash flows with defaults (SF-18) and the monthly default rate (SF-21).
- 02Code of Federal Regulations, 12 CFR 1248.1 (Federal Housing Finance Agency): definition of the single month mortality rate and the three-month conditional prepayment rate.
- 03SoFi Technologies, Form 10-Q for the quarter ended 30 June 2026, filed with the SEC on 6 August 2026: key unobservable assumptions in the fair value of loans and of servicing rights, and their definitions.
- 04Prosper Marketplace, Form 10-Q for the quarter ended 30 June 2026, filed with the SEC on 13 August 2026: significant unobservable input ranges, key economic assumptions for servicing assets and borrower loans, and the definitions of default and prepayment rates.
- 05Fitch Ratings, Metodología de Calificación para Emisiones de Deuda Respaldadas por Créditos al Consumo, 26 November 2024: stressed prepayment rates by rating level, prepayment stresses in Latin America, portfolio yields and excess spread.
- 06CONDUSEF, Disposiciones de carácter general en materia de transparencia aplicables a las Sociedades Financieras de Objeto Múltiple, Entidades No Reguladas, Diario Oficial de la Federación, 11 August 2015: article 2, fraction XVII, and article 21.