Constant Conditional Prepayment Rate (CPR) Calculator

The Constant Conditional Prepayment Rate (CPR) Calculator calculates annualised prepayment rates from monthly loan pool data and projects cash flow implications.

What Is a Constant Conditional Prepayment Rate (CPR) Calculator?

A CPR calculator converts observed or assumed monthly prepayments into a standardized annualized rate. Constant Conditional Prepayment Rate, or CPR, expresses the probability that the remaining principal in a loan pool prepays over the next year, assuming the same monthly pattern persists. Analysts use CPR to compare prepayment speeds across different collateral, coupons, and seasoning.

The calculator works with Single Monthly Mortality (SMM), which is the monthly prepayment rate. It estimates SMM from the month’s prepayment cash flow and then annualizes it into CPR. CPR is central in pricing mortgage-backed securities (MBS) and asset-backed securities (ABS), projecting cash flows, and measuring prepayment risk.

Because CPR is conditional, it is applied to the balance that survives scheduled amortization. The calculator helps you isolate that conditional effect, reduce manual mistakes, and maintain consistent assumptions across portfolios.

How to Use Constant Conditional Prepayment Rate (CPR) (Step by Step)

Start with a single period, usually a month. You need the pool’s beginning balance, the scheduled principal for that month, and the actual unscheduled principal paid (prepayments). The calculator estimates SMM and then converts it to CPR for apples-to-apples comparisons.

• Collect monthly data: beginning balance, scheduled principal, and prepayments.
• Compute the surviving balance after scheduled principal but before prepayment.
• Divide the month’s prepayments by that surviving balance to get SMM.
• Convert SMM to CPR using the 12-month compounding relationship.
• Review the breakdown, test ranges, and adjust assumptions if needed.

Use the result to compare against dealer quotes, historical norms, or internal targets. For risk work, repeat across months and examine trends rather than a single point.

Constant Conditional Prepayment Rate (CPR) Formulas & Derivations

CPR converts monthly prepayment intensity into an annualized measure that assumes a constant monthly pattern. The link between SMM and CPR is a compounding relationship. Below are the key formulas the calculator uses and the logic behind them.

• Surviving balance before prepayment: Survive = Beginning balance − Scheduled principal.
• Single Monthly Mortality (SMM): SMM = Prepayments / Survive.
• CPR from SMM: CPR = 1 − (1 − SMM)^12. This assumes the same monthly SMM repeats for 12 months.
• SMM from CPR (inverse): SMM = 1 − (1 − CPR)^(1/12).
• Projected prepayment for a month using CPR: Prepay_t = SMM × (Balance after scheduled principal in month t).

Derivation intuition: If the probability of surviving prepayment in one month is (1 − SMM), then surviving 12 independent months is (1 − SMM)^12. Annual prepayment is one minus that survival probability. This links the monthly and annual measures in a clean way.

Inputs, Assumptions & Parameters

The CPR calculator needs a few core inputs. These represent the cash flow mechanics of an amortizing pool. Keep each input consistent across months to avoid mixing definitions.

• Beginning balance (for the month): The principal outstanding at the start of the period.
• Scheduled principal: Contractual principal due that month, excluding prepayments.
• Prepayments: Unscheduled principal paid during the month (includes full and partial payoffs).
• Period length: Typically one month; the CPR conversion assumes 12 periods per year.
• Rounding/precision assumption: Decimal places for rates and currency; affects small pools.

Reasonable ranges: SMM and CPR both run from 0% to 100%, though real-world CPR often sits between 2% and 35% outside surge events. Edge cases include months with very small surviving balances, where tiny prepayments produce very high SMM, or months with zero scheduled principal on interest-only structures. Always review outliers and confirm whether they reflect true borrower behavior or data noise.

Using the Constant Conditional Prepayment Rate (CPR) Calculator: A Walkthrough

Here’s a concise overview before we dive into the key points:

1. Open the Calculator and select the CPR tool.
2. Enter the beginning balance, scheduled principal, and prepayments for the month.
3. Confirm the period is “monthly” so the tool uses 12-month annualization.
4. Click Compute to see the SMM and CPR results with a clear breakdown.
5. Toggle precision settings if you need more decimal places for small pools.
6. Export or copy the results to share with your team or to audit your assumptions.

These points provide quick orientation—use them alongside the full explanations in this page.

Example Scenarios

Refi wave month: A prime 30-year mortgage pool starts at $250,000. Scheduled principal is $400. Prepayments are $5,000 as borrowers refinance. Survive = 250,000 − 400 = 249,600. SMM = 5,000 / 249,600 ≈ 0.0200 (2.00%). CPR = 1 − (1 − 0.0200)^12 ≈ 21.6%. Interpretation: high rates of full and partial payoffs are accelerating cash flows and shortening weighted average life. What this means: The pool is prepaying fast; price premium coupons cautiously and revisit spread assumptions.

Stable month: The same pool has $300 in prepayments. Survive = 249,600 as above. SMM = 300 / 249,600 ≈ 0.00120 (0.12%). CPR = 1 − (1 − 0.00120)^12 ≈ 1.44%. Interpretation: these speeds align with a quiet market and limited rate incentive. What this means: Extension risk dominates; the collateral is likely to run longer unless conditions change.

Accuracy & Limitations

CPR is a clean metric, but it simplifies behavior. It assumes constant monthly conditions and ignores borrower heterogeneity unless you layer in more detail. Use it with care, especially in turning points for rates and credit.

• Seasonality and turnover can shift SMM month to month, breaking the “constant” assumption.
• Rate incentive, burnout, and credit constraints impact speeds beyond the simple formula.
• Data quality issues (late postings, curtailments vs. payoffs) can distort prepayment amounts.
• Very small surviving balances can inflate SMM, producing unstable CPR readings.
• EX- or IN-criteria differences across servicers affect comparability without adjustments.

For better realism, analyze a history of monthly SMM and compute a rolling CPR. Segment by coupon, loan size, and seasoning. Validate your assumptions with multiple data sources, not just one report.

Units and Symbols

Prepayment math mixes cash amounts and rates. Clear units prevent misinterpretation, especially when comparing across desks or systems. The table below shows common symbols, meanings, and typical units or ranges.

Read CPR and SMM as percentages. When entering into the Calculator, use amounts for B, SP, and PP in the same currency. Ensure consistency across months to keep rates comparable.

Troubleshooting

If results look unreasonable, start with the denominator. The surviving balance (B − SP) must be positive and correct. Next check that prepayments exclude scheduled principal. Finally, confirm the period is monthly; otherwise the CPR conversion will be off.

• Unexpectedly high CPR: Verify PP did not include scheduled principal or charge-offs.
• Zero or negative SMM: Check that PP is not missing or that SP does not exceed B.
• Inconsistent month-over-month: Look for data lags, buyouts, or servicer reversals.

When in doubt, compare against a known month from disclosures or a dealer model. Use the breakdown in the Calculator to trace each step and confirm assumptions.

FAQ about Constant Conditional Prepayment Rate (CPR) Calculator

Is CPR a forecast or a measurement?

CPR can be both. From actual cash flows, it is a measurement. From a model, it is a forward assumption used to project future prepayments.

How does CPR relate to PSA speeds?

PSA is a benchmark curve that ramps prepayments over time. CPR is a direct annualized rate. You can convert between PSA and CPR using published mappings or model formulas.

Can I compute CPR for non-mortgage ABS?

Yes. Any amortizing pool with unscheduled principal payments can use SMM and CPR. Just ensure scheduled principal is clearly separated from prepayments.

Why does CPR spike near pool cleanup?

As balances shrink, small absolute prepayments represent a larger fraction of the surviving balance. That inflates SMM and, by compounding, the CPR.

Constant Conditional Prepayment Rate (CPR) Terms & Definitions

Constant Conditional Prepayment Rate (CPR)

An annualized measure of prepayment intensity, assuming the same monthly prepayment pattern continues for 12 months.

Single Monthly Mortality (SMM)

The fraction of principal that prepays in a month, conditional on surviving scheduled amortization.

Scheduled Principal

The contractual principal due in a period under the loan’s amortization schedule, excluding any unscheduled prepayment.

Prepayment

Any unscheduled principal reduction, including curtailments and full payoffs, made before the loan’s maturity.

Seasoning

The age of the loan or pool in months, often affecting prepayment behavior due to turnover, burnout, and ramp effects.

Burnout

The tendency for prepayment response to rate incentives to weaken over time as eager refinancers exit the pool.

Weighted Average Life (WAL)

The average time to principal repayment, weighted by principal amounts; sensitive to CPR assumptions.

Public Securities Association (PSA) Model

A standard prepayment benchmark that ramps assumed prepayments over the first 30 months, then holds steady.

Disclaimer: This tool is for educational estimates. Consider professional advice for decisions.

References

Here’s a concise overview before we dive into the key points:

• Investopedia: Constant Prepayment Rate (CPR) definition and examples
• The Yield Book Technical Note: Prepayment Speeds (CPR, SMM, PSA)
• Fannie Mae Single-Family MBS Disclosure: Pool-level prepayment and performance data
• FINRA Investor Insights: Mortgage-Backed Securities and prepayment risk
• Wikipedia: Public Securities Association (PSA) Standard Prepayment Model

These points provide quick orientation—use them alongside the full explanations in this page.