Prepayment S-Curves and Refinancing Incentive
Prepayment speed does not scale smoothly with how much a refinancing would save a borrower — it barely moves at first, then rises steeply, then flattens out again as almost everyone who was going to refinance already has.
Prerequisites: The PSA Prepayment Benchmark and SMM
If refinancing incentive drove prepayment in a straight line, a small drop in mortgage rates would nudge prepayment speed up a little, and a big drop would nudge it up a lot, proportionally. Real prepayment data doesn't behave that way. Plot prepayment speed (CPR) against how far a borrower's current loan rate sits above the prevailing refinance rate, and the result is an S-curve: flat near zero incentive, a steep climb through the middle, and flattening again once the incentive is large.
The S-shape exists because refinancing has a fixed cost — closing costs, paperwork, time. A tiny rate saving doesn't clear that cost for most borrowers, so speed stays low; once the saving clearly exceeds the cost, most people who can refinance do, and speed shoots up; beyond that, speed can't rise much further because only a shrinking pool of borrowers (poor credit, low equity, disinterest) hasn't already refinanced.
Reading the curve
The x-axis is typically the gap between the loan's note rate and the current market refinance rate. Near zero or negative gap (the borrower's rate is already at or below market), CPR sits at a "base case" level driven only by ordinary turnover — people moving, selling, or paying off loans for reasons unrelated to rates. As the gap widens past roughly 0.5–0.75 percentage points, CPR accelerates sharply. Past about 2 percentage points of incentive, the curve bends over and flattens at a ceiling, because the borrowers left in the pool at that point are disproportionately the ones who, for whatever reason, aren't going to refinance regardless of how attractive the math looks.
Worked example
A pool of 6.5% mortgages sits against a current refinance rate of 6.3% — only 0.2 points of incentive. The S-curve says this is still near the flat base of the curve, so expected speed stays close to base turnover, around 6% CPR. Rates then fall and the refinance rate drops to 5.2%, a full 1.3-point gap — squarely in the steep part of the curve — and the model now projects speed jumping to roughly 35% CPR. If rates fell further still, to a 2.5-point gap, the model would project speed leveling off around 45% CPR rather than continuing to climb proportionally, because most of the borrowers able and willing to refinance have already been absorbed by the move from 0.2 to 1.3 points of incentive.
What this means in practice
The S-curve is exactly why premium mortgage bonds have negative convexity: as rates fall, prepayment speed rises fastest right in the range that matters most to a bondholder, returning principal at par just as the bond's high coupon becomes most valuable to keep — the opposite of what a fixed-income holder wants.
Extrapolating prepayment speed linearly from a small move in rates badly misprices a mortgage bond, because the real relationship is anything but linear. A model built only on data from a low-incentive environment will systematically underpredict how violently speed accelerates once incentive crosses into the steep part of the curve.
Related concepts
Practice in interviews
Further reading
- Fabozzi, The Handbook of Mortgage-Backed Securities