Prepayment Models: PSA and CPR

Prepayment risk—the uncertainty of when borrowers will pay off their loans early—shows up in MBS portfolios as cash flows arriving sooner than modeled, duration estimates that swing with rate moves, and yield projections that miss reality by hundreds of basis points. In SIFMA's 2024 securitization data, the U.S. agency MBS market exceeded $9.5 trillion in outstanding balance, making prepayment modeling one of the highest-stakes analytical exercises in fixed income. What works instead isn't ignoring prepayment variability. It's mastering the PSA and CPR frameworks so you can stress-test your holdings before rate moves force the lesson on you.

What Prepayment Risk Actually Means (and Why You Can't Ignore It)

When a homeowner refinances, sells, or makes extra principal payments, the mortgage pool behind your MBS shrinks faster than scheduled. You get your principal back early—at par, not at the premium you paid. That sounds harmless until you realize you bought the bond at 103 expecting a certain yield over 15 years, and now you're getting repaid in 7.

The core problem: prepayments are voluntary. Unlike corporate bonds where the issuer controls call decisions, MBS prepayments emerge from millions of individual borrower decisions—each driven by personal finances, local housing markets, and prevailing mortgage rates. You can't predict any single borrower's behavior. But in aggregate, patterns emerge. That's where models come in.

Two frameworks dominate the industry:

• CPR (Conditional Prepayment Rate): the annualized percentage of a pool's outstanding balance that prepays in a given period
• PSA (Public Securities Association benchmark): a standardized prepayment curve that ramps CPR over a mortgage's early life, providing a baseline for comparison

Why this matters: every dollar of early prepayment changes your bond's yield, duration, and convexity. If you're not modeling prepayments explicitly, you're implicitly assuming they don't matter—and in MBS, that assumption will cost you.

CPR: Translating Borrower Behavior into a Single Number

CPR expresses the annual rate at which borrowers prepay their mortgages as a percentage of the remaining pool balance. It's the fundamental unit of prepayment speed.

The calculation: CPR = Annual Prepayments / Outstanding Pool Balance

Example:

• Pool outstanding balance: $1,000,000,000
• Annual prepayments observed: $80,000,000
• CPR = $80M / $1B = 8% CPR

Interpretation:

• 0–4% CPR: Slow prepayments (typical in rising-rate environments where refinancing incentive disappears)
• 4–8% CPR: Moderate (baseline conditions, some housing turnover)
• 8–15% CPR: Fast (falling rates, active refinancing wave)
• 15%+ CPR: Very fast (aggressive rate drops, often seen in the first 6–12 months after a major rate cut)

The point is: CPR gives you a single, comparable number to benchmark prepayment speeds across pools, vintages, and market conditions. A pool running at 12% CPR behaves fundamentally differently from one at 4%—in cash flow timing, average life, and reinvestment risk.

From CPR to Monthly: The SMM Conversion

Since mortgage payments happen monthly, you need the Single Monthly Mortality rate (SMM) to model actual cash flows.

The formula: SMM = 1 – (1 – CPR)^(1/12)

Example at 8% CPR:

• SMM = 1 – (1 – 0.08)^(1/12)
• SMM = 1 – (0.92)^(0.0833)
• SMM = 0.00693, or approximately 0.69%

That means in any given month, roughly 0.69% of the remaining balance prepays. On a $500 million pool, that's about $3.46 million per month in unscheduled principal—money you need to reinvest, potentially at lower yields.

The core principle: CPR is the language of prepayment analysis. Every other model (including PSA) ultimately expresses its assumptions in CPR terms. Learn to think in CPR first, and everything else becomes a translation exercise.

PSA: The Benchmark Curve (and How to Use It)

The Public Securities Association (now SIFMA) created the PSA benchmark to standardize prepayment assumptions across the industry. Without it, every trader and analyst would use different baseline assumptions, making relative value comparison nearly impossible.

How the 100% PSA Curve Works

The 100% PSA model assumes a specific ramp-up pattern for new mortgages:

• Month 1: CPR starts at 0.2% (annualized)
• Months 1–30: CPR increases by 0.2 percentage points per month
• Month 30 onward: CPR levels off at 6.0% and stays flat for the remaining life

This ramp reflects a real behavioral pattern: new borrowers rarely prepay immediately (they just closed on their home), but prepayment rates increase as borrowers settle in, build equity, and encounter life changes (job moves, divorces, rate-driven refinancing opportunities). By month 30 (2.5 years), the pool is considered "seasoned" and prepayment behavior stabilizes.

The key insight: 100% PSA isn't a prediction—it's a yardstick. Nobody expects actual prepayments to follow this curve exactly. Instead, analysts express their assumptions as multiples of PSA.

PSA Multiples: Stress-Testing Made Simple

How to read the table: at 150% PSA, every point on the standard curve is multiplied by 1.5. Month 30 CPR goes from 6% to 9%. At 300% PSA, it triples to 18%—meaning nearly one-fifth of the remaining pool balance prepays annually.

Why this matters: a single MBS tranche priced at 100% PSA can have radically different yields at 50% vs. 200% PSA. The spread between those scenarios is your prepayment risk exposure, and you need to quantify it before you buy.

Worked Example: Pricing a Pass-Through Under Different PSA Scenarios

Here's how PSA assumptions flow through to actual portfolio decisions.

Your situation: You're evaluating a $100 million par agency MBS pass-through, 30-year collateral, 5.5% coupon, currently priced at 102.50 (a 2.5-point premium). The pool is 12 months seasoned.

Step 1: Determine CPR at Each PSA Level

At month 12, the 100% PSA curve implies:

• CPR = 0.2% × 12 = 2.4%

Now scale by PSA multiple:

Step 2: Calculate Monthly Prepayment Dollars

Using the base case (100% PSA, SMM = 0.202%):

Monthly unscheduled principal = $100,000,000 × 0.00202 = $202,000

At 175% PSA:

Monthly unscheduled principal = $100,000,000 × 0.00357 = $357,000

That's 77% more unscheduled principal per month in the fast-prepay scenario—and the gap widens as the pool seasons toward month 30.

Step 3: Estimate Average Life Impact

The practical point: you paid a 2.5-point premium expecting roughly 11.8 years of above-market coupon income. If prepayments accelerate to 175% PSA, your average life compresses to 7.4 years—you amortize that premium over fewer years, and your yield drops by 37 basis points. That's the prepayment risk you're taking, expressed in dollars and basis points (not theory).

For deeper analysis of how average life shifts under stress, see Average Life and Weighted Average Maturity.

What Drives Prepayment Speeds (The Inputs Behind the Model)

PSA and CPR are frameworks, not forecasts. The quality of your analysis depends on calibrating those models to actual market conditions. Four factors dominate:

1. Mortgage rate differential (the refinancing incentive) This is the single biggest driver. When prevailing mortgage rates drop 50+ basis points below the pool's weighted average coupon, refinancing activity accelerates sharply. A 300 basis point spread (pool at 7%, market at 4%) can push CPR above 40% in some vintages.

2. Seasoning (borrower tenure) New loans prepay slowly. The PSA ramp captures this—but real-world seasoning curves vary by loan type, geography, and origination channel. FHA/VA loans often season faster than conventional loans (due to assumability features and borrower demographics).

3. Housing turnover and home prices Rising home prices increase equity, enabling borrowers to sell or refinance more easily. In markets where home price appreciation exceeds 10% annually, turnover-driven prepayments can push CPR 2–3 percentage points above baseline even without rate incentives.

4. Burnout (the saturation effect) After a prolonged low-rate period, the most rate-sensitive borrowers have already refinanced. The remaining pool is "burned out"—less responsive to further rate drops. This is why CPR often peaks and then declines during extended easing cycles, even as rates stay low.

The lesson worth internalizing: no single PSA multiple captures all of these dynamics simultaneously. Professional MBS analysts run multiple scenarios, adjusting PSA assumptions for each driver, and focus on the range of outcomes rather than a point estimate.

Risks, Limitations, and Common Pitfalls

Pitfall 1: Treating PSA as a Forecast

The PSA curve is a benchmark, not a prediction. Actual prepayment behavior rarely follows the smooth ramp the model assumes. Pools with heavy refinancing incentive can blow through 300% PSA in the first year, then slow dramatically as burnout sets in. Using a single PSA multiple for the life of a bond is the most common modeling error in MBS analysis.

Pitfall 2: Ignoring the Premium/Discount Asymmetry

Prepayment risk is asymmetric depending on whether you bought at a premium or discount:

• Premium bonds (price > 100): faster prepayments hurt you (you lose the premium faster)
• Discount bonds (price < 100): faster prepayments help you (you receive par on bonds bought below par)

If you're holding premium MBS, you need to stress-test against high-PSA scenarios specifically. Discount holders should worry more about extension risk (see Extension Risk in Rising Rate Environments).

Pitfall 3: Neglecting the CPR-to-Cash-Flow Translation

Analysts sometimes focus on CPR as an abstract metric without tracing it through to actual cash flow impact. An 8% CPR on a $50 million tranche means roughly $4 million in annual unscheduled principal. That's money you need to reinvest—potentially at lower yields if rates have fallen (which is likely the same reason prepayments accelerated in the first place). The reinvestment problem and the prepayment problem are two sides of the same coin.

Pitfall 4: Using Stale Assumptions

Prepayment models require continuous recalibration. A PSA assumption that fit last quarter's environment may be dangerously wrong today. The data shows that a 100 basis point rate decline can accelerate CPR by 300–500 basis points for 30-year conventional mortgages, while a 200 basis point increase might slow CPR by 200–300 basis points. If your model hasn't been updated for the current rate regime, your duration and yield estimates are unreliable.

Pitfall 5: Overlooking Structural Protections

Some MBS tranches (particularly in CMO structures) include lockout periods, prepayment penalties, or planned amortization classes (PACs) that redirect prepayment risk to companion tranches. Before applying raw PSA assumptions, check whether the tranche structure modifies how prepayments flow to your specific bond. A PAC tranche with a 75%–200% PSA band will behave very differently from a pass-through under the same prepayment scenario.

Summary Metrics Table

Prepayment Analysis Checklist (Tiered)

Essential (high ROI)

These four steps prevent the majority of prepayment-related pricing errors:

• Calculate CPR and SMM for your current pool using the latest available factor data
• Run at least three PSA scenarios (slow, base, fast) and compare yield and average life across each
• Check your purchase price relative to par—if you're at a premium, quantify the downside from accelerated prepayments
• Verify the current refinancing incentive by comparing the pool's weighted average coupon to prevailing mortgage rates

High-Impact (workflow and calibration)

For investors managing MBS portfolios systematically:

• Update PSA assumptions quarterly (at minimum) to reflect current rate environment and observed speeds
• Track actual vs. modeled CPR each month and adjust your forward assumptions when divergence exceeds 1 percentage point
• Map prepayment sensitivity across your entire portfolio—identify which holdings have the most exposure to speed changes
• Review tranche structure for PAC bands, lockout periods, or other features that modify prepayment flow

Optional (for active MBS traders)

If you're trading MBS or managing duration tactically:

• Build a rate-scenario matrix linking rate changes (±50, ±100, ±200 bps) to PSA multiples for each pool vintage
• Monitor burnout levels in your pools by comparing current CPR to historical peaks for similar rate incentives
• Incorporate housing turnover data from regional MLS statistics for geographically concentrated pools

The point is: prepayment modeling isn't something you set once and forget. The best MBS analysts treat PSA and CPR as living inputs—recalibrated monthly, stress-tested quarterly, and always interpreted in the context of current market conditions. Start with the essential checklist, run your three scenarios, and build from there.