Macaulay and modified duration
Duration has two variants. Macaulay duration is the weighted average time to receive a bond’s cash flows (coupons and principal), where weights are the present values of each cash flow as a proportion of total bond price. A zero-coupon bond maturing in 5 years has Macaulay duration of exactly 5 — it pays all cash at maturity. A coupon bond has lower duration than its maturity — interim coupon payments reduce the weighted average time. Modified duration = Macaulay duration / (1 + yield/n) where n is the coupon frequency. Modified duration is the direct measure of price sensitivity: △P/P ≈ −Modified Duration × △y. For most practical applications (portfolio risk management, hedging), modified duration — often called simply "duration" — is the relevant measure.
Convexity and why it matters
Convexity measures the curvature of the price-yield relationship — how much the duration estimate changes as yields move. A more convex bond outperforms a less convex bond with the same duration in both directions: as yields fall, its price rises more than duration predicts; as yields rise, its price falls less than duration predicts. This asymmetric benefit means higher convexity is always desirable, and investors will accept lower yields for bonds with higher convexity. The full price approximation is: △P/P ≈ −Dᴹᴼᴷ × △y + ½ × Convexity × (△y)². For small yield changes, the convexity term is negligible; for large moves (100bps+), convexity contributes meaningfully to explaining actual price behaviour.
Duration in portfolio management
Portfolio duration — the weighted average duration of all bonds held — is the primary risk metric for fixed income portfolio managers. A government bond fund with duration of 8 years will lose approximately 8% if rates rise 1% across the yield curve. Duration management involves: adjusting duration to express a view on rates (shorten before expected rate rises; extend if rates expected to fall); immunising liabilities (matching asset duration to liability duration to eliminate interest rate risk — crucial for insurance companies and pension funds); and hedging residual duration risk using interest rate swaps or government bond futures. Duration is also the key input in the "DV01" metric — the dollar value of a 1 basis point move in yield — which standardises rate sensitivity for risk systems.
“Duration is the fixed income equivalent of beta — it tells you how much market risk you are taking. But unlike equity beta, you can control it precisely, which is why professional fixed income management is fundamentally about duration decisions.”
What this means for you
The 2022 interest rate shock was one of the most severe years for fixed income in modern history — long-duration government bond funds fell 15–30% as rates rose sharply. Understanding duration would have forewarned investors that long-duration bonds carry substantial rate risk in a rising rate environment. For bond fund investors, checking the fund’s disclosed duration is the single most important step before investing — a "bond fund" with duration of 15 years has very different risk characteristics to one with duration of 2 years. For corporate treasury and insurance ALM (asset-liability management), duration matching between assets and liabilities is the foundation of interest rate risk management — ensuring that liability changes are offset by equal and opposite asset changes when rates move.