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DESK 11 // STRUCTURED CREDIT & RELATIVE VALUE PAR VALUATION // BALANCED CONVEXITY

Agency MBS Prepayment & Negative Convexity Underwriter

Underwrite Fannie Mae and Freddie Mac residential mortgage pools. Model PSA prepayment speeds, convert CPR to Single Monthly Mortality (SMM), quantify negative convexity duration extension across interest rate cycles, and isolate true Option-Adjusted Spread (OAS).

Authoritative Reference METHODOLOGY • COVENANTS • PROOF

Institutional Methodology & Underwriting Dossier

Deconstructs Agency Mortgage-Backed Securities (MBS) cash flows, calculates Conditional Prepayment Rate (CPR) and Single Monthly Mortality (SMM), quantifies negative convexity duration extension in sell-offs, and underwrites Option-Adjusted Spread (OAS).

1. Target Audience & Practical Application

How different financial market participants apply this quantitative model to real-world capital allocation:

Mortgage Portfolio Managers

Evaluate negative convexity drag and prepayment burnout across conforming Fannie Mae and Freddie Mac pools.

Fixed Income Risk Officers

Quantify duration extension risk when mortgage rates rise and refinance activity freezes.

TBA & Structured Product Desks

Model specified pool pay-ups, loan balance call protection, and roll-to-cheapest delivery.

Bank Treasury ALM Desks

Stress-test mortgage asset duration extension against sticky retail deposits during monetary tightening cycles.

2. Mortgage Prepayment & Duration Extension Formulas

1. Single Monthly Mortality (SMM) from CPR:
SMM = 1 - (1 - CPR)^(1/12)

2. Monthly Prepayment Cash Flow ($):
Prepay_Principal = (Beginning_Balance - Scheduled_Principal) × SMM

3. PSA Benchmark Speed (t months of seasoning):
CPR(t) = min(6%, 6% × t / 30) × (PSA / 100)

4. Effective Duration & Negative Convexity:
D_eff = [P(Δy-) - P(Δy+)] / [2 × P_0 × Δy]
Negative Convexity: D_eff extends as rates rise and shortens as rates drop.

3. Agency MBS Prepayment Invariants & Structural Guardrails

Negative Convexity Asymmetry: Unlike sovereign Treasuries, MBS bondholders sell homeowners an embedded call option (the right to refinance). When mortgage rates drop, homeowners refinance, capping price upside. When rates surge, refinancings collapse to turnover-only speeds, causing MBS duration to dramatically lengthen.
Prepayment Burnout Phenomenon: Even if mortgage rates drop significantly, borrowers who failed to refinance during previous rate declines exhibit diminishing responsiveness ('burnout'), stabilizing high-coupon pool cash flows.
Agency Guarantee vs. Interest Rate Risk: Agency MBS (Fannie Mae, Freddie Mac, Ginnie Mae) carry zero or negligible credit default risk due to explicit or implicit government backing; their entire risk premium consists of prepayment and extension volatility.

4. Frequently Asked Questions (FAQ)

What is the Public Securities Association (PSA) prepayment benchmark?

The PSA benchmark models mortgage prepayments assuming a CPR that starts at 0.2% in month 1, increases by 0.2% per month up to 6.0% at month 30, and remains flat at 6.0% thereafter. A speed of 150% PSA means prepayments occur at 1.5 times the standard baseline.

Why do Agency Mortgage-Backed Securities exhibit negative convexity?

Homeowners hold a free prepayment option. In a bond rally, prepayments accelerate as borrowers refinance, returning principal at par and capping price appreciation. In a sell-off, prepayments halt, extending the mortgage duration precisely when investors want low duration, resulting in a concave, negatively convex price-yield relationship.

What is Option-Adjusted Spread (OAS) in MBS valuation?

OAS is the constant spread that, when added to the Treasury spot curve across hundreds of Monte Carlo interest rate paths, equates the average present value of mortgage cash flows to the observed market price. It strips out the cost of the borrower's embedded prepayment option to reveal the true unhedged credit/liquidity spread.

What is mortgage duration extension risk?

When benchmark mortgage rates climb (such as from 3% to 7%), existing homeowners have zero economic incentive to refinance. Expected maturities lengthen from 4-5 years out to 8-12 years, causing existing fixed-rate MBS holdings to suffer severe mark-to-market capital losses.

MBS Pool Characteristics Pass-Through Specs

Pass-Through Coupon Rate % p.a.

Current Primary Mortgage Rate (30Y Fixed) % Freddie PMMS

PSA Benchmark Prepayment Speed % PSA

Current MBS Market Price % of Par

Original Amortization Term Months

Portfolio Pool Notional ($M Par) $ Millions

                        Modeled Prepayment (CPR)
                        11.4%
                        Annual Conditional Prepayment Rate
                    

Single Monthly Mortality (SMM) 1.01% Monthly principal prepay share

Weighted Average Life (WAL) 6.8 Years Expected principal return horizon

Effective Duration (Base) 4.90 yrs Interest rate price sensitivity

Duration Extension (+100 bps) 6.76 yrs Negative convexity in sell-off

Option-Adjusted Spread (OAS) +118 bps Net spread stripped of option cost

Prepayment Response Function (S-Curve Dynamics) Refinance Spread vs. CPR Speed

• Left Flat Zone: Housing turnover floor (4-6% CPR) • Steep Mid-Slope: Mass refinance wave • Right High Plateau: Burnout saturation ceiling

2D Negative Convexity Stress-Testing Matrix Simulated MBS Price (% of Par)

Benchmark Rate Shock	75% PSA	100% PSA	150% PSA	200% PSA	300% PSA

Exhibits negative convexity: price gains in rallies are truncated by par prepayments, while price losses in rate sell-offs extend due to frozen refinance activity.