An agency pass-through is a claim on a pool of residential mortgages. Every borrower holds an American call on their own loan, struck at par, exercisable any month, at little cost beyond refinancing friction, the most generous option in fixed income, and the pass-through holder is short all of it.
The vocabulary of speed. Prepayment is measured three ways, and converting between them must be a reflex:
- SMM (single monthly mortality), the fraction of the outstanding balance net of scheduled principal that prepays in a month.
- CPR (conditional prepayment rate), the annualised equivalent:
CPR = 1 − (1 − SMM)¹², and inverting,SMM = 1 − (1 − CPR)^(1/12). - PSA: a benchmark ramp, not a rate. 100 PSA means CPR ramps linearly from 0.2% in month 1 by 0.2% per month to 6.0% at month 30, then stays flat at 6.0%. A speed of n PSA is that ramp scaled by n/100. So 165 PSA in month 12 is
6% × (12/30) × 1.65 = 3.96%CPR, which is an SMM of 0.336146%.
The relationship is convex, so conversions cannot be eyeballed: CPR 6% is SMM 0.514301%, but CPR 30% is SMM 2.928553%.
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Why does prepayment speed matter so much?
Why speed is the whole story. Take a $500m pool, 6.00% weighted-average coupon, 5.50% net pass-through rate (the 50 bp difference is the servicing and guarantee strip), 360 months. Weighted-average life (the average time in years at which a dollar of principal returns) depends violently on speed:
| Speed | WAL |
|---|---|
| 50 PSA | 14.53 yrs |
| 100 PSA | 11.36 yrs |
| 165 PSA | 8.68 yrs |
| 250 PSA | 6.56 yrs |
| 400 PSA | 4.60 yrs |
| 600 PSA | 3.36 yrs |
Same pool, same borrowers, same contract, and the security you own is a 14-year asset or a 3-year asset depending on a behavioural assumption. That is extension risk (rates rise, prepayments stop, your short asset lengthens just as you wanted it short) and contraction risk (rates fall, everyone refinances, your long asset shortens just as you wanted it long). Both always arrive at the worst possible time, because the same rate move drives both the speed change and the discount-rate change.
How do you isolate the prepayment option?
Isolating the option. The cleanest proof that prepayment, not cash flow timing, makes MBS negatively convex: price the pool at a 5.75% base discount rate twice, first letting the speed respond to rates as borrowers actually behave, then freezing it at 165 PSA and changing only the discount rate.
| Regime | Effective duration (±50 bp) | Effective convexity |
|---|---|---|
| Speed responds (400/260/165/120/90 PSA at −100/−50/0/+50/+100 bp) | 6.461 | −318.0 |
| Speed frozen at 165 PSA | 6.175 | +64.8 |
The identical pool at identical discount rates is positively convex with the borrowers' option off and violently negatively convex with it on. Nothing else changed.
The practical consequence: the model is the risk. Two houses running the same pool at the same price report different durations because they have different prepayment models, different assumptions about refinancing incentive, burnout (a pool already through a refi wave has slower survivors), seasoning, seasonality and turnover. No arbitrage forces them to agree, because the option is not exercised optimally. The number you report is a claim about human behaviour; say so out loud.