Agency MBS Prepayment Mechanics & Negative Convexity: PSA Models, CPR-to-SMM & Option-Adjusted Spreads

The $12 trillion U.S. Agency Mortgage-Backed Securities (MBS) market—issued by Fannie Mae, Freddie Mac, and Ginnie Mae—constitutes the second largest and most liquid fixed income sector in the world after U.S. Treasuries. While Agency MBS carry essentially zero credit default risk due to explicit or implicit federal guarantees, their price behavior is radically different from sovereign debt due to a single structural feature: the homeowner's prepayment option.

When an investor purchases an Agency MBS pass-through, they effectively purchase a portfolio of home loans and simultaneously sell an embedded American-style call option to millions of individual homeowners. This structural short-call position induces negative convexity, causing MBS price performance to systematically lag Treasuries during bull rallies and suffer severe duration extension during bear sell-offs.

01. The Embedded Call Option & Agency Backing

In the United States, conforming residential mortgages typically allow borrowers to prepay any portion of their outstanding loan balance at par without prepayment penalties. Borrowers exercise this option when:

Refinancing for Lower Rates: Current mortgage rates fall below the borrower's existing loan rate, allowing them to refinance into a cheaper loan.
Housing Turnover / Relocation: The borrower sells the home due to employment relocation, divorce, or life changes, paying off the remaining mortgage principal.
Curtailments: Incremental monthly principal prepayments to amortize debt faster.

02. Prepayment Metrics: CPR, SMM & PSA Benchmark

MBS cash flows are modeled using three standardized prepayment rates:

1. Conditional Prepayment Rate (CPR) $$\text{CPR} = \text{Annualized percentage of pool balance expected to prepay}$$

2. Single Monthly Mortality (SMM) $$\text{SMM} = 1 - (1 - \text{CPR})^{1/12}$$ $$\text{Prepayment Principal Cash Flow} = (\text{Beginning Balance} - \text{Scheduled Principal}) \times \text{SMM}$$

The Public Securities Association (PSA) benchmark standardizes prepayment speeds across a loan pool's 30-year lifecycle:

PSA Prepayment Benchmark Standard (100% PSA) $$\text{CPR}(t) = \min\left(6.0\%, 6.0\% \times \frac{t}{30}\right) \times \frac{\text{PSA}}{100}$$

Under $100\%$ PSA, prepayments start at $0.2\%$ CPR in month 1, ramp up by $0.2\%$ each month until reaching $6.0\%$ CPR at month 30, and remain constant at $6.0\%$ CPR thereafter. A pool prepaying at $200\%$ PSA ramps to $12.0\%$ CPR at month 30.

03. The S-Curve Refinancing Function & Burnout

Prepayment speeds do not respond linearly to mortgage rates; they follow an S-Curve characterized by three distinct behavioral regimes:

The Turnover Floor: When mortgage rates are higher than existing pool coupons (loans are out-of-the-money to refinance), prepayments do not fall to zero. A baseline turnover floor of $4\%$ to $6\%$ CPR persists from home sales and corporate relocations.
The Media Refinance Wave: As rates drop $50$ to $150\text{ bps}$ below the pool coupon, prepayments accelerate exponentially as mortgage brokers advertise rate savings and homeowners apply for refinancings.
The Burnout Plateau: When rates drop further, prepayments hit a saturation ceiling ($40\%$ to $50\%$ CPR). Borrowers who remain in the pool after multiple refinance waves exhibit credit constraints, small loan balances, or financial inertia ("prepayment burnout").

04. Negative Convexity & Duration Extension Risk

The consequence of the embedded borrower call option is negative convexity:

Effective Duration & Extension $$D_{eff} = \frac{P(\Delta y-) - P(\Delta y+)}{2 \cdot P_0 \cdot \Delta y}$$

When Interest Rates Fall: Homeowners refinance, returning principal to investors at par ($100$). The investor is forced to reinvest cash at newly lowered interest rates, truncating price upside above par (duration contracts from 5.0 years down to 2.0 years).
When Interest Rates Rise: Homeowners keep their low-rate mortgages, and refinance activity freezes. Expected mortgage maturity extends from 5 years out to 8-10 years just as bond yields surge, magnifying capital losses (duration extends from 5.0 years up to 8.5 years).

05. Option-Adjusted Spread (OAS) vs. Z-Spread

Because nominal spreads and static Zero-Volatility Spreads (Z-spreads) fail to price the asymmetric cost of the homeowner's option, institutional mortgage investors evaluate pools via Option-Adjusted Spread (OAS):

OAS Decomposition $$\text{Nominal Spread} = \text{Z-Spread} = \text{OAS} + \text{Option Cost}$$ $$\text{OAS} = \text{Nominal Spread} - \text{Option Cost}$$

The Option Cost is extracted using Monte Carlo simulations generating hundreds of stochastic interest rate paths. High-coupon pools with severe refinance risk carry option costs of $50$ to $90\text{ bps}$, whereas locked-in discount pools carry option costs of under $20\text{ bps}$.

06. Hedging MBS Duration & Convexity Swaps

Because MBS duration constantly shifts with interest rates, portfolio managers dynamic-hedge mortgage books using 10-year Treasury futures and interest rate swaps. When rates drop, hedgers must buy Treasuries to match shortening duration; when rates rise, hedgers must sell Treasuries to match extending duration. This systematic feedback loop exacerbates Treasury yield volatility during major rate cycles.