Convexity is the curvature in the relationship between an asset's price and an underlying variable such as yield — the second-order term beyond linear (delta or duration) sensitivity. Positive convexity means gains accelerate and losses decelerate as the variable moves, an asymmetry that rewards holders when volatility rises.
How it works
For a bond, duration is the first derivative of price to yield and convexity the second: it corrects the linear duration estimate, making the price-yield curve bow upward so prices rise more from a yield fall than they drop from an equal yield rise. In options and rate-cut bets, convexity captures payoff asymmetry — small inputs producing outsized, non-linear payoffs when a regime shift or threshold is crossed.
Why it matters now
A Fed that disavows forward guidance offers traders less convexity on rate-cut bets: without a pre-committed easing path, the asymmetric upside of positioning early for cuts shrinks, since the policy reaction function stays data-dependent and two-sided rather than primed to deliver an accelerating sequence of cuts.
Example
A 10-year Treasury with duration 8 and convexity 0.7 falls roughly 8% in price for a +100bp yield move under the linear estimate, but convexity adds back about +0.35%, so the actual decline is nearer 7.65%; for a -100bp move the gain is nearer 8.35%. The asymmetry is the convexity.
Frequently asked
- What is convexity in bonds?
- Convexity is the curvature of a bond's price-yield relationship — the second-order correction beyond duration
Glossary · duration
Duration is the sensitivity of a bond's price to a change in interest rates, expressed in years. A duration of 7 means a 100bp yield rise cuts price roughly 7%. It is the primary measure of interest-rate risk in fixed-income portfolios.
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- Why does positive convexity matter when volatility rises?
- Positive convexity rewards holders when volatility rises because gains accelerate and losses decelerate as the underlying variable swings. The bigger the move in either direction, the more the convexity term adds to return relative to a linear duration estimate. This makes long-convexity positions effectively long volatility, valuable precisely when rate uncertainty is highest.
- How does convexity differ from duration?
- Duration is the first derivative of price to yield — a linear, symmetric sensitivity — while convexity is the second derivative capturing the curvature duration misses. Duration alone overstates losses and understates gains for large moves. Convexity corrects this: for a 100bp shock on an 8-duration bond, the convexity term adds back roughly 0.35 percentage points of price.
- What is negative convexity in mortgages?
- Negative convexity describes assets, chiefly mortgage-backed securities and callable bonds, whose duration extends as yields rise and shortens as yields fall — the opposite of a vanilla bond. Holders face accelerating losses and decelerating gains. MBS hedgers selling Treasuries as yields rise can amplify rate moves, a dynamic prominent in the 2003 and 2013 convexity-driven sell-offs.
- How does convexity affect rate-cut bets?
- Convexity captures the payoff asymmetry in positioning for rate cuts: a credible pre-committed easing path delivers accelerating, non-linear upside as cuts compound. A data-dependent Fed that disavows forward guidance
Glossary · forward guidance
Forward guidance is a central bank's communication about the likely future path of policy rates, used to shape market expectations and steer financial conditions today. It comes in calendar-based (date-contingent), state-based (outcome-contingent on inflation or unemployment thresholds), or qualitative open-ended forms.
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