Negative Convexity

What Is Negative Convexity?

Negative convexity is a fixed income property where a bond's duration decreases as yields fall and increases as yields rise — the exact opposite of the beneficial convexity exhibited by standard government bonds. This counterintuitive behavior arises from embedded options that allow the issuer or underlying borrower to alter cash flow timing in response to the interest rate environment.

In a standard bond, the price-yield relationship curves upward (positive convexity): prices rise faster than duration implies when yields fall, and fall slower than duration implies when yields rise. A negatively convex instrument has an inflected price-yield curve — above a critical yield threshold, it behaves normally, but below that threshold, the curve flattens or inverts as the embedded option moves in-the-money. The primary sources of negative convexity in practice are mortgage-backed securities (MBS) via prepayment optionality, callable corporate bonds, and certain structured credit instruments.

Why It Matters for Traders

Negative convexity creates a fundamentally asymmetric risk profile that many investors underestimate. For agency MBS — the largest fixed income sector by outstanding notional in the U.S. — when rates fall sharply, homeowners refinance en masse, returning principal to investors at par precisely when reinvestment rates are lowest. When rates rise, prepayments slow, extending duration at the worst possible time (known as extension risk). This dynamic is often described as "the investor loses in both directions."

For macro traders and rate strategists, aggregate MBS convexity hedging by large holders (primarily banks, the Fed, and GSEs) creates systematic, predictable convexity hedging flows that amplify Treasury yield moves. When rates rise sharply, MBS holders must sell Treasuries or pay fixed in interest rate swaps to extend their hedges — this selling begets more selling, a feedback loop that contributed to the volatility of the 2022 rate sell-off.

How to Read and Interpret It

Convexity is typically reported as a number alongside duration. Negative values signal negatively convex instruments:

• Positive convexity (e.g., +5 to +10): Standard Treasuries and investment-grade bonds. Price-yield curve works in the investor's favor.
• Near-zero convexity (0 to -2): Lightly in-the-money callables or seasoned MBS with limited refinancing optionality remaining.
• Materially negative (< -3 to -5): Current-coupon or premium MBS, freshly callable bonds near call date. High sensitivity to rate volatility.

The OAS (option-adjusted spread) is the companion metric — it isolates credit spread from the embedded option cost. A wide OAS on a negatively convex bond may appear attractive but can be entirely explained by the option value being sold to the issuer, not genuine credit premium.

Historical Context

The 2022 Federal Reserve tightening cycle produced the most dramatic convexity event in decades. As the 10-year Treasury yield rose from approximately 1.5% in January 2022 to 4.25% by October 2022, the average duration of agency MBS indices extended from roughly 4.5 years to nearly 7 years — a near 60% duration extension. This forced mortgage holders to execute massive hedging programs, selling Treasuries and paying fixed in swap markets, contributing to the yield overshoot. The ICE BofA MOVE Index (rates volatility) reached its highest level since the GFC. Banks holding large MBS portfolios — as Silicon Valley Bank infamously did — had accepted enormous extension risk without adequate hedging, a factor central to SVB's collapse in March 2023.

Limitations and Caveats

Modeling negative convexity accurately requires robust prepayment models that are sensitive to regional housing market dynamics, borrower credit quality, and loan age — all of which shift over time. During extreme stress events, model-implied prepayment speeds can diverge sharply from actual behavior. Additionally, negative convexity calculations are highly sensitive to the assumed interest rate volatility input: in low-vol regimes, the option is cheap and convexity appears less negative; in high-vol regimes, the option is expensive and the convexity cost rises. This vol-dependency creates a procyclical trap — convexity risk is worst exactly when volatility is highest.

What to Watch

• Weekly MBA mortgage refinancing application index — surges indicate prepayments are rising and MBS convexity profiles are improving (less negative).
• Federal Reserve MBS reinvestment policy under quantitative tightening — the pace of runoff affects market-wide convexity supply.
• 10-year Treasury yield relative to prevailing mortgage coupon rates — when current coupons are near outstanding pool coupons, refinancing optionality is maximum.
• MOVE Index levels, which proxy the cost of convexity hedging across the rates complex.