Bond Duration, explained.
Bond duration connects the timing of fixed cash payments with sensitivity to yield changes. Macaulay duration weights payment times by present value; modified duration gives a local price-change approximation.
Why it happens
Payments further away are discounted over more periods. Increasing yield therefore reduces their present values more strongly. Coupon payments return some value earlier, so duration is generally below maturity for a positive-coupon bond.
Macaulay duration is the present-value-weighted time of a bond's cash flows. Modified duration approximates its proportional price response to a small change in yield.
Read the result
Compare short and long maturities at the same coupon. Increase the yield shock and inspect the divergence between the exact price and the duration estimate. Expand the payment table to see which discounted flows receive the most weight.
A worked example
A five-year zero-coupon teaching bond
Set coupon to zero and maturity to five. All 100 face-value tokens arrive in year five.
At a 5% annual yield, price is 100/1.05⁵, about 78.35, and Macaulay duration is five years.
Raise yield to 6% and reprice exactly. Modified duration supplies an approximation, while the exact discount calculation captures the curve's nonlinearity.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
A 100-face-value annual-coupon bond is priced at a base yield of 5%. Reprice at 5% plus the selected shock. Duration uses discounted annual payments including principal; modified duration divides by 1.05. The estimate is base price × (1−modified duration × yield change).
Where this idea is useful
A practical use
Compare two- and ten-year bonds with the same coupon under a one-percentage-point yield increase.
A common misconception
“Duration is always identical to maturity.”
Only the fixed zero-coupon example places all payment value at maturity. Earlier coupons generally shorten the present-value-weighted average payment time.
What this explanation leaves out
- This fixed-cash-flow, annual-compounding model omits credit losses, embedded options, and nonparallel yield-curve changes. Duration is a local approximation, not an exact rule for large shocks.
Why does the estimate miss the exact price?
Modified duration uses a first-order change around the base yield. A bond price is nonlinear in yield, so approximation error generally grows as the shock grows.
Which promised payment looks stable in cash terms but changes value when the discount rate changes?
Associated thinkers
Associations marked provisional are awaiting source review.
Further reading
Explore the original research or the teaching reference behind this experiment.