Convexity
The curvature in the price-yield relationship of a bond — measuring how duration itself changes as yields move, improving accuracy of price change estimates.
Formula
%ΔPrice ≈ −(Modified Duration × ΔYield) + ½ × Convexity × (ΔYield)²
Convexity is the second-order correction to duration. Duration assumes a linear price-yield relationship, but the true relationship is curved (convex). For large yield moves, convexity accounts for the fact that duration underestimates price gains when yields fall and overestimates price losses when yields rise.
All else equal, higher convexity is better for bond holders — a more convex bond gains more when yields fall and loses less when yields rise than a less convex bond with the same duration. Mortgage-backed securities (MBS) have negative convexity because prepayments accelerate when rates fall, capping price appreciation.
Related Terms
Bond Yield
The return an investor earns by holding a bond — driven by its price, coupon, and time to maturity. Moves inversely with price.
BeginnerCallable Bond
A bond the issuer can redeem early at a set call price, usually after rates fall — capping the holder's upside and adding reinvestment risk.
IntermediateCheapest to Deliver (CTD)
The specific deliverable bond a short Treasury-futures holder will choose to deliver because it is the least costly to source net of the invoice received.
AdvancedDuration
A measure of a bond's sensitivity to interest rate changes — the approximate percentage price change for a 1% move in yield.
AdvancedPrice-Yield Inverse Relationship
The fundamental bond market law: when yields rise, bond prices fall; when yields fall, bond prices rise — always and mechanically.
BeginnerYield to Maturity
The total annualized return an investor earns if they hold a bond to maturity — accounting for coupon payments, price paid, and time remaining.
Intermediate