Prepayment Models: PSA and CPR

Prepayment modeling is the backbone of structured credit analysis. For mortgage-backed securities (MBS), cash flow uncertainty from borrower behavior directly impacts yield, duration, and risk profiles. Institutional investors must balance the tension between overestimating prepayments (which undervalues faster payoffs) and underestimating them (which exposes portfolios to extension risk). The Public Securities Association (PSA) and Conditional Prepayment Rate (CPR) frameworks provide standardized tools to navigate this complexity.

The PSA model establishes a benchmark prepayment curve. It assumes 6% annual CPR in the first year, with the rate increasing by 0.5% monthly until reaching 12% at 30 months. This "100% PSA" curve serves as a baseline for stress-testing scenarios. For example, a 150% PSA assumption would imply 9% CPR in month one, scaling up 0.75% monthly—a common proxy for low-rate environments. Conversely, 50% PSA reflects slower prepayment conditions, such as when rate hikes reduce refinancing incentives.

PSA: The Benchmark Curve PSA assumptions directly translate to Single Monthly Mortality (SMM) rates via the formula: SMM = 1 – (1 – CPR)^(1/12). A 100% PSA scenario generates ~0.5% SMM in month one. Originators and traders use PSA multiples to price MBS tranches; a $500 million pool with 10% CPR would see $50 million in annual prepayments, altering cash flow timing for all stakeholders.

CPR: Translating Behavior into Speeds CPR quantifies annual prepayment rates as a percentage of outstanding balances. If a $1 billion MBS pool experiences $80 million in prepayments over a year, the CPR is 8%. CPR metrics are derived from historical borrower behavior, seasoning curves, and macroeconomic signals like mortgage rate differentials. For instance, a 300 basis point drop in rates might push CPR from 4% to 12% within six months.

• Key PSA-to-CPR conversion steps: 1) Select PSA multiple, 2) Calculate monthly CPR using the benchmark curve, 3) Apply to the security’s outstanding balance.

Modeling prepayment risk requires continuous calibration. A 2023 scenario analysis by Moody’s showed that a 100 basis point rate decline could accelerate CPR by 400 bps for 30-year mortgages, while a 200 bps increase might slow it by 250 bps. By mastering PSA/CPR dynamics, investors gain actionable leverage in pricing complexity. Begin by stress-testing your MBS holdings against 150% and 50% PSA scenarios to quantify sensitivity to rate shifts.