What is Bond Duration? Definition, Formula, and Example
Bond duration measures a bond's price sensitivity to interest rate changes, expressed as the approximate percentage price move for a 1% change in yield.
What is bond duration?
Duration answers a specific question: if interest rates move by 1 percentage point, how much does this bond's price move? It's quoted in years, but functions as a risk multiplier, not a literal time-to-payback measure. A bond with a duration of 7 loses roughly 7% of its value if rates rise 1%, and gains roughly 7% if rates fall 1%. Longer maturities, lower coupons, and lower yields all increase duration because more of the bond's cash flow value sits far out in time, where present-value discounting is more sensitive to rate changes. Zero-coupon bonds have duration equal to their maturity, since 100% of the payment arrives at one distant date.
How duration is calculated
Macaulay duration is the weighted-average time to receive a bond's cash flows, weighted by each payment's present value:
D = Σ [t × PV(CFₜ)] / Price
where t is the time until each cash flow, PV(CFₜ) is that cash flow's present value, and Price is the bond's current market price (the sum of all PV(CFₜ)).
The more commonly quoted risk metric is Modified Duration:
Modified Duration = Macaulay Duration / (1 + y/n)
where y is the yield to maturity and n is the number of compounding periods per year. Modified duration plugs directly into the price-sensitivity approximation:
% Price Change ≈ −Modified Duration × Δy
For larger rate moves, traders add a convexity term to correct for the fact that the price/yield relationship curves rather than moves in a straight line: % Price Change ≈ −Modified Duration × Δy + 0.5 × Convexity × Δy².
Worked example
The 10-year U.S. Treasury note, coupon around 4.25%, trades with a modified duration of roughly 8.7. If the 10-year yield rises 100 basis points (1%), the approximate price impact is −8.7%. If you hold a Treasury ETF like TLT — which tracks 20+ year Treasuries and carries a much longer duration, around 16-17 — a 1% yield move implies roughly a 16-17% price swing, which is exactly why TLT is far more volatile than a short-term bond fund holding 2-year notes with a duration near 1.9.
When traders use duration
Bond and rates traders use duration to size positions so that a portfolio's aggregate rate exposure matches a target (duration-matching or immunization). Equity traders watch duration as a lens on rate-sensitive stocks: unprofitable growth companies with cash flows far in the future behave like long-duration assets, which is why they sell off harder than value stocks when yields spike — the same discounting mechanics apply to a discounted cash flow model as to a bond price. Options and futures desks use duration to hedge rate risk with Treasury futures or swaps, calculating the number of contracts needed via a "DV01" (dollar value of a 1bp move) matching exercise.
Limitations and misconceptions
Duration assumes a parallel shift in the yield curve — every maturity moving by the same amount — which rarely happens exactly; a curve steepening or flattening can produce a very different price outcome than duration alone predicts. It also assumes cash flows are fixed and known, so it doesn't directly apply to bonds with embedded options (callable bonds, mortgage-backed securities) without adjustment — those require "effective duration," which models price sensitivity accounting for the fact that expected cash flows themselves change as rates move. Finally, duration is a linear approximation; for large yield swings, ignoring convexity understates gains in a rally and overstates losses in a selloff.