Beginner Level
What Is It?
Duration is the sensitivity of a bond's price to changes in interest rates, measured in years. A bond with a duration of 7 will fall about 7 percent in price when yields rise by 1 percent and rise by about 7 percent when yields fall by 1 percent. It is the single most important number for understanding bond risk.
Origin
The concept was developed by Frederick Macaulay in 1938. Modified duration, which is what most practitioners use, refines Macaulay's measure to relate price changes directly to yield changes. Convexity, which captures the second-order effect, was added to the toolkit in the 1970s.
Why It Matters
Duration translates abstract yield moves into concrete price changes. It governs how much a bond portfolio will gain or lose as central banks raise or cut rates. For pension funds, insurers, and banks, duration is also a liability-matching tool — assets and liabilities must move together to stay solvent.
Intermediate Level
Market Mechanics
Modified duration approximates the percentage price change for a 1 percent change in yield. Effective duration handles bonds with embedded options (callables, MBS) where cash flows shift with rates. Key-rate duration decomposes sensitivity along the yield curve, distinguishing parallel shifts from steepening or flattening.
How It Behaves
Long-dated zero-coupon bonds have the highest duration; short-dated coupon bonds the lowest. Mortgage-backed securities have negative convexity — their duration extends when rates rise and contracts when rates fall, magnifying losses in selloffs. Duration estimates degrade for large rate moves; convexity adjustments restore accuracy.
Key Data to Watch
- Bloomberg or ICE bond-index durations
- Treasury futures DV01 (dollar value of one basis point)
- MBS effective duration and convexity
- Pension and insurer duration gaps
- Swap-curve key-rate duration
Advanced Level
Institutional Behavior
Insurers and defined-benefit pensions match asset duration to liability duration to immunize against rate moves. Banks measure net interest income and equity sensitivity to rate changes through duration of equity. MBS desks hedge convexity continuously through swap and Treasury overlays. Macro funds trade duration as a top-down view on policy and growth.
Professional Use Cases
- Liability-driven investing for pensions and insurers
- Duration-targeted bond fund construction
- Convexity hedging in MBS portfolios
- Curve trades expressed as key-rate duration neutrality
AI Interpretation in Systems Like Arkhe
- Macro Agent: Forecasts duration P&L from rate-path scenarios.
- Risk Agent: Decomposes portfolio duration by key rate.
- Portfolio Agent: Targets duration to match risk and liability profile.
- Crisis Agent: Watches for convexity-hedging cascades that amplify rate moves.
Key Takeaways
Duration is the language of fixed income. Understanding modified duration, key-rate duration, and convexity is non-negotiable for any investor running rate exposure. Duration mismatches between assets and liabilities are the root cause of most bank and insurer failures.