Duration and convexity provide complementary measures of how a bond or a bond portfolio responds to changes in interest rates, shaping risk assessment and hedging choices. Duration captures the linear sensitivity of price to small parallel shifts in yields, while convexity quantifies the curvature and second-order effects that matter for larger yield moves. Frank J. Fabozzi Yale School of Management describes duration as the primary tool for gauging interest-rate exposure and for constructing duration-matched immunization strategies.
How duration measures sensitivity
Duration arises from the timing and size of cash flows: longer maturities and lower coupons increase a bond’s duration, making price more sensitive to rate changes. Modified duration gives an approximate percentage price change per one percentage-point change in yield; Macaulay duration is the weighted average time to receipt of cash flows. The practical consequence is that investors with liabilities, such as pension funds and insurers, use duration matching to reduce mismatch risk and stabilize funding ratios. In environments where central banks shift policy rates rapidly, duration misestimation can cause sudden valuation losses and force asset reallocations that affect markets and real-economy stakeholders.
Convexity: curvature and nonlinearity
Convexity measures how duration itself changes as yields move, capturing the nonlinearity of price-yield relationships. John C. Hull University of Toronto explains that positive convexity means a bond’s price rises more for a given fall in yields than it falls for the same rise, which benefits holders when large rate moves occur. Bonds with embedded options, notably many mortgage-backed securities, display negative convexity because prepayment behavior alters cash flows when rates decline; this has amplified feedback effects between housing markets and fixed-income investors. Higher convexity reduces approximation error when projecting price changes and informs the sizing of hedges with interest-rate derivatives.
Together, duration and convexity inform trade-offs: hedging to neutralize duration reduces first-order risk but leaves convexity exposure that can dominate during volatile episodes, while instruments that adjust convexity can be costly or introduce counterparty and liquidity risks. For portfolio managers and fiduciaries, continuous monitoring of both measures—aligned with liability profiles, market liquidity, and regional institutional constraints—remains essential to manage interest-rate risk and its economic and social consequences.