Duration - The First-Order Measure of Interest-Rate Risk

By EC Assets Research Team, Fixed Income Research · Published 20 May 2026 · Updated 28 May 2026

Duration — Duration measures how much a bond's price moves when its yield changes: a duration of 8 means roughly an 8% price fall per one-point rise in yield. Modified duration gives the price sensitivity (%ΔP ≈ −duration × Δy), and DV01 expresses it in money per basis point - the bond market's equivalent of delta.

What Duration Measures

Duration is the headline measure of a bond's interest-rate risk. It answers a single, central question: if yields move, how much does the bond's price move? A bond with a duration of 8 will lose roughly 8% of its value if its yield rises by one percentage point, and gain roughly 8% if the yield falls by the same amount. It is the bond market's equivalent of delta - the first-order sensitivity that every fixed-income desk reviews before anything else.

The word carries two related meanings that are worth separating. Macaulay duration is the weighted-average time, in years, until a bond's cash flows are received, with each payment weighted by its present value. Modified duration rescales that into a price sensitivity - the percentage price change per unit change in yield - and is the number traders actually use.

Modified duration = Macaulay duration / (1 + y/k)

where y is the yield and k the number of compounding periods per year. The price relationship is then:

%ΔP ≈ −Modified duration × Δy

The minus sign captures the fundamental inverse relationship: when yields rise, bond prices fall.

What Drives a Bond's Duration

Three properties move duration in predictable ways:

• Maturity. Longer-maturity bonds have higher duration - their cash flows sit further in the future and are more sensitive to discounting. A 30-year bond is far more rate-sensitive than a 2-year note.
• Coupon. Higher coupons lower duration, because more of the bond's value is returned early. A zero-coupon bond has the highest duration for its maturity - its Macaulay duration equals its maturity, since the single cash flow arrives only at the end.
• Yield. Higher yields lower duration, because future cash flows are discounted more heavily and weigh less in the average.

Dollar Duration and DV01

For risk management, percentage sensitivity is converted into money. Dollar duration is the price change in currency terms; DV01 (the dollar value of one basis point), also called PV01 or BPV, is the workhorse:

DV01 = Modified duration × Price × 0.0001

DV01 lets a desk express and hedge rate risk in a single comparable unit across instruments of different coupons and maturities - the foundation of duration-neutral and curve-trading strategies.

Worked Example

Hold a 10m position in a bond with a modified duration of 8.0.

A 50 bps rise in yields: %ΔP ≈ −8.0 × 0.50% = −4.0%, a loss of about 400,000. DV01 = 8.0 × 10,000,000 × 0.0001 = 8,000 per basis point.

So each one-basis-point move in yield changes the position's value by roughly 8,000. To neutralise that risk against another bond, a desk matches DV01s - holding offsetting positions whose dollar durations cancel.

[!key] Duration is a linear, first-order estimate: price change ≈ −duration × yield change. It is highly accurate for small yield moves and progressively wrong for large ones, because the true price-yield relationship is curved. That curvature is convexity - duration's essential second-order companion.

When Duration Breaks Down

Duration assumes a small, parallel shift in yields. Two things undermine that:

• Large moves. Because the price-yield curve bends, duration overstates the loss when yields rise sharply and understates the gain when they fall. The correction is convexity.
• Non-parallel curve shifts. A single duration number assumes the whole curve moves together. When the curve steepens, flattens, or twists, key-rate (or partial) durations - sensitivities to specific points on the curve - are needed instead.
• Embedded options. Callable bonds and mortgage-backed securities have cash flows that change with rates, so their effective duration must be measured numerically, and can even shorten as rates fall (negative convexity).

Why It Matters for Institutional Investors

• The primary risk lever. For any bond portfolio, duration is the main dial controlling rate exposure. Lengthening duration is a bet that yields will fall; shortening it is a defensive move against rising rates.
• Liability matching. Pension funds and insurers match the duration of their assets to the duration of their liabilities so that a rate move hits both sides equally - the core of liability-driven investing.
• Hedging and relative value. DV01-matched trades let desks isolate views on the shape of the curve or on credit, while neutralising the direction of rates. Duration is the unit that makes those trades expressible.

[!warning] A portfolio's headline duration hides where on the curve the risk sits. Two books with identical duration can behave completely differently when the curve twists rather than shifts in parallel. For anything beyond a simple bullet portfolio, monitor key-rate durations, not just the single number.

References

1. Fabozzi, F. J. (2021). Bond Markets, Analysis, and Strategies (10th ed.). MIT Press.
2. Tuckman, B., & Serrat, A. (2011). Fixed Income Securities (3rd ed.). Wiley.
3. Hull, J. C. (2022). Options, Futures, and Other Derivatives (11th ed.). Pearson. Chapter 4.
4. CFA Institute. Fixed Income: Understanding the Risk and Return of Bonds. CFA Program Curriculum.