Negative Convexity and Mortgage Securities
title: "Negative Convexity and Mortgage Securities" description: "Why MBS prices cap gains when rates fall and extend losses when rates rise. Master the mechanics of prepayment risk and negative convexity for smarter fixed income allocation." slug: "negative-convexity-and-mortgage-securities" category: "Fixed Income" subcategory: "Yield Duration and Convexity" difficulty: "advanced" readingTime: "8 min" author: "Equicurious" lastUpdated: "2025-12-29"
Mortgage-backed securities violate the rules. Regular bonds have positive convexity: when rates fall, prices rise more than duration predicts. MBS do the opposite. The point is: negative convexity means your upside is capped while your downside extends—and if you don't understand why, you'll consistently overpay for MBS yield or miss their true risk profile.
The Prepayment Option You Didn't Know You Sold
When you buy an MBS, you're buying a pool of mortgages where each homeowner holds a free refinancing option. That option belongs to the borrower (and costs you money). Here's the asymmetry:
Rates fall → Homeowners refinance → Your high-coupon mortgages get repaid at par
You receive principal back exactly when you don't want it (when reinvestment rates are lower). The price appreciation you expected from falling rates gets cut short because cash flows accelerate.
Rates rise → Nobody refinances → Your low-rate mortgages extend in duration
Now you're stuck holding below-market paper for longer than anticipated. Duration extends precisely when you need it to shorten for protection.
This asymmetric behavior is negative convexity in action. You own the downside and the homeowner owns the upside (Hayre & Rajan, 2024).
Why This Matters: The 2020-2021 Prepayment Wave
The 2020-2021 period created a textbook case. Average mortgage rates dropped to 2.5%-4.0%, triggering a massive refinancing wave. Investors holding agency MBS watched:
- Price gains capped as prepayments accelerated
- Duration shortened exactly when portfolios wanted more rate sensitivity
- Reinvestment at lower rates forced when principal returned early
Then rates reversed. By 2024, mortgage rates exceeded 6%, and those 2020-2021 vintage mortgages remain unrefinanced. Result: portfolios now face extension risk because nobody with a 3% mortgage is refinancing at 6%+ (DWS Research Institute, 2024).
The durable lesson: Falling rates → contraction risk. Rising rates → extension risk. You lose on both sides of the trade compared to option-free bonds.
Quantifying Negative Convexity (How the Math Works)
For an option-free bond, price change approximation uses:
%ΔP = -ModDur × Δy + 0.5 × Convexity × (Δy)^2
The convexity term is always positive for bullet bonds (adding to gains when rates fall, cushioning losses when rates rise).
For MBS, effective convexity turns negative. A simplified illustration:
Setup: Agency MBS, effective duration 5.2 years, effective convexity -1.2
Rates fall 100 bps:
- Duration-only estimate: +5.2%
- Convexity adjustment: 0.5 × (-1.2) × (0.01)^2 = -0.006%
- Adjusted estimate: approximately +5.19%
But that understates the problem. As rates fall further, prepayments accelerate non-linearly, and effective duration itself drops (from 5.2 to perhaps 3.5 years). Your sensitivity to further rate declines shrinks.
Rates rise 100 bps:
- Duration-only estimate: -5.2%
- But now effective duration extends (from 5.2 to perhaps 6.5 years) as prepayments slow
- Actual loss exceeds the initial duration estimate
Why this matters: MBS may underperform equivalent-duration Treasuries by 2-3% in rate rallies (CFA Institute, 2025). The negative convexity penalty is real and material.
The Option-Adjusted Spread Trap
MBS offer higher yields than Treasuries (the spread), but part of that spread compensates for negative convexity and prepayment uncertainty. The option-adjusted spread (OAS) strips out the embedded option cost to show "pure" credit/liquidity spread.
Nominal spread: 80 bps over Treasuries OAS: 45 bps over Treasuries
The 35 bps difference represents compensation for the prepayment option you've sold to homeowners. The point is: if you compare MBS to corporates on nominal spread alone, you overestimate relative value. Always compare OAS to OAS.
Duration Comparison: MBS vs. Other Fixed Income
Bloomberg US MBS Index duration: 5.18 years (March 2022) Bloomberg US Aggregate Index duration: 6.58 years (March 2022)
Agency MBS run approximately 1.4 years shorter than the Agg and roughly 3 years shorter than investment-grade corporates (DoubleLine, 2022). Why this matters: shorter stated duration doesn't mean less risk. The negative convexity can make MBS more volatile than their duration suggests during large rate moves.
The test: Compare an MBS fund's behavior in a 50 bps rate rally versus a Treasury fund of similar stated duration. The Treasury fund will outperform because its convexity works for you rather than against you.
Loan Size and Prepayment Sensitivity
Prepayment behavior isn't uniform. Larger loans refinance faster because:
- Higher dollar savings from rate reduction
- Borrowers with large loans tend to be more financially sophisticated
- Fixed transaction costs represent smaller percentage of loan value
The weighted average loan size in generic MBS pools increased by over $200,000 in five years through 2024 (DWS Research Institute, 2024). This structural shift increases refinancing sensitivity at the pool level—amplifying negative convexity during rate declines.
Detection Signals: You're Likely Mispricing MBS If...
- You compare MBS yield to Treasury yield without adjusting for negative convexity
- You assume stated duration accurately predicts MBS price moves during large rate shifts
- You hold MBS for "income" without modeling prepayment scenarios
- You're surprised when your MBS fund underperforms Treasuries during a rate rally
- You evaluate MBS spreads without calculating OAS
Three Prepayment Scenarios (Setup → Calculation → Interpretation)
Scenario 1: Rates Fall 150 bps, Prepayments Surge
Setup: You hold $100,000 in 30-year FNMA 4.5% MBS at 102 (2% premium to par), effective duration 5.0 years.
Calculation: Rates fall from 5% to 3.5%. Prepayment speeds jump from 8% CPR to 25% CPR. Effective duration compresses to 3.2 years. Price rises to 104 instead of the 109 you'd expect from a 5-year duration bond.
Interpretation: You captured roughly 40% of the gain an option-free bond would have delivered. Principal returns at par (100), erasing the premium you paid. Reinvestment now happens at 3.5% instead of 4.5%.
Scenario 2: Rates Rise 200 bps, Extension Hits
Setup: Same position, rates rise from 5% to 7%.
Calculation: Prepayment speeds collapse to 3% CPR. Effective duration extends to 7.5 years. Price drops to approximately 85 (a 17% loss) rather than the 10% loss you'd expect from stated duration.
Interpretation: Duration extension magnified your losses by 70%. You're now locked into below-market coupons for an extended period.
Scenario 3: Rates Unchanged, Carry Matters
Setup: Rates stay flat at 5% for 12 months.
Calculation: You collect the coupon spread over Treasuries. Prepayments remain stable at 8% CPR. Principal returns gradually at par, causing slight negative price drift on premium-priced pools.
Interpretation: In stable rate environments, MBS carry advantage can be captured. But you earn less than the nominal spread suggests due to premium amortization.
Checklist: Managing Negative Convexity Exposure
Essential (do these first)
- Use effective duration and effective convexity (never modified duration) for MBS
- Model prepayment scenarios at +/-100 bps and +/-200 bps rate shocks
- Compare OAS rather than nominal spreads when evaluating relative value
- Understand vintage composition (2020-2021 pools behave differently than 2024 pools)
High-impact refinements
- Monitor prepayment model assumptions (PSA speed, CPR, SMM) in fund reports
- Consider specified pools with prepayment-dampening characteristics (lower loan balances, geographic concentration)
- Pair MBS with positive convexity assets (Treasuries, option-free corporates) to balance portfolio-level convexity
Why Institutional Investors Still Hold MBS
Despite negative convexity, agency MBS offer:
- Government guarantee (Fannie, Freddie, Ginnie) eliminating credit risk
- Yield premium over Treasuries (typically 50-100 bps OAS)
- Liquidity in the world's second-largest fixed income market
- Diversification from corporate credit cycles
The durable lesson: Negative convexity is a cost, not a disqualifier. Sophisticated investors price that cost explicitly through OAS analysis and position sizing. Unsophisticated investors get surprised when their "safe" MBS funds lag Treasuries in rate rallies.
The Convexity Hedge: Barbell Construction
One response to negative convexity: pair MBS with positive-convexity instruments. A portfolio holding:
- 50% agency MBS (negative convexity, yield advantage)
- 50% long Treasuries (positive convexity, rate sensitivity)
...can achieve higher total convexity than an all-MBS portfolio while retaining some yield pickup. The Treasury allocation gains more than duration predicts when rates fall, partially offsetting MBS underperformance.
Your Next Step
Pull up your fixed income holdings. For any MBS or MBS fund position, answer: (1) What is the current effective duration? (2) What prepayment speed assumption drives that number? (3) How does effective duration change if rates fall 100 bps versus rise 100 bps? If you can't answer these questions from fund documentation, you don't fully understand your convexity exposure. This matters because the next 100 bps rate move—in either direction—will reveal whether negative convexity is friend or foe in your portfolio.
Related: Convexity Concept and Calculation | Effective Duration for Callable Bonds | Yield to Call and Yield to Worst