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Bonds & fixed income

Duration (Bonds) Duration

Duration measures how sensitive a bond's price is to a change in interest rates — roughly the percent the price moves per 1% shift in yield.

Part of the Bonds, Rates & the Economy course · Lesson 4 of 12
Formula
Modified duration = Macaulay duration / (1 + yield per period); % price change ≈ −Modified duration × Δyield (in %)

What it is

Duration is a bond's sensitivity to interest rates, expressed as a number of years. Bond prices and yields move in opposite directions: when market yields rise, the price of an existing bond falls, and when yields fall, its price rises. Duration approximates how much. A bond with a duration of 5 would be expected to lose roughly 5% of its price if yields rose by 1 percentage point, and gain roughly 5% if yields fell by 1 point. There are two common versions. Macaulay duration is the weighted-average time until a bond's cash flows arrive. Modified duration, the one usually quoted, converts that into the percentage price change per 1% yield move.

Why it matters

Duration turns a vague worry — "what do interest rates do to a bond?" — into a single comparable number. Two bonds can share the same issuer and credit quality yet behave completely differently when yields move, and duration is what separates them. It also explains an outcome that surprises beginners: a bond fund can post a loss in a rising-rate period even though nothing defaulted and every coupon was paid on time. The price simply repriced to the new yield level. Longer maturities and lower coupons generally lengthen duration, which is why a long zero-coupon bond swings far more than a short coupon-paying one. Duration is only about interest-rate sensitivity; it says nothing about default risk, and it is an approximation that grows less accurate for large yield moves, where convexity matters.

How it's calculated

Start with Macaulay duration: take every future cash flow (each coupon plus the final principal), discount each to present value at the bond's yield, then compute the weighted-average time until they arrive, weighting each date by that cash flow's share of total present value. The result is in years. Modified duration divides that by (1 + yield per period), turning a time measure into a sensitivity measure. Data providers publish duration directly; bond funds publish an average effective duration across holdings. Callable and mortgage-backed bonds need effective duration, computed by repricing under small yield shifts, since their cash flows change when yields move.

FAQ

Does duration mean how many years until the bond matures?
No — that's maturity, a different thing. Macaulay duration is the weighted-average time to receive the bond's cash flows, not the final payment date. A bond paying coupons along the way returns money early, so its duration is shorter than its maturity. A zero-coupon bond pays nothing until the end, so its Macaulay duration equals its maturity. Modified duration, the version usually quoted, is not a waiting time — it is a sensitivity number.
If rates go up, does an existing bond lose money?
An existing bond's market price falls when yields rise — that's the inverse relationship, and duration estimates how far. An option-free bond held to maturity still pays its coupons and, absent default, its face value at the end; selling earlier converts the price change into a realised loss or gain. Two limits: a callable bond can be redeemed early by the issuer, and a bond fund has no maturity to hold to. Duration measures price sensitivity, never default risk.
Why is duration only an approximation?
Duration is a straight-line estimate of a curved relationship. The price-yield curve bends, so a linear rule drifts as the yield move grows. Convexity is the second-order term measuring that bend. For an option-free bond convexity is positive: the actual gain from a yield drop runs slightly bigger than duration predicts, and the loss from an equal yield rise slightly smaller. Callable and mortgage-backed bonds can show negative convexity, where the asymmetry reverses.
Related terms
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