What it means
Duration began as a weighted average of the time it takes to receive a bond's cash flows, with each payment weighted by its present value. That version, called Macaulay duration, is quoted in years and tells you the average waiting time for your money.
Modified duration converts that figure into the more useful form: the approximate percentage change in price for a one percentage point move in yield. It matters because treasurers, pension trustees and finance teams hold bonds or lend at fixed rates, and interest rates move constantly.
Duration turns a vague worry about rates into a single number that can be compared across holdings and added up across a portfolio. Two bonds paying the same yield can behave very differently when rates shift, and duration is what tells them apart.
In practice duration rises with the time left to maturity and falls when the bond pays a bigger coupon, meaning the regular interest payment, because larger early payments pull the average waiting time forward. A thirty-year bond with a small coupon can carry a duration above twenty, while a two-year bond might sit near 1.9.
A portfolio's duration is simply the value-weighted average of the durations of the bonds inside it. Finance teams use the number in two directions.
They estimate the loss under a rate shock, and they deliberately match the duration of their assets to the duration of their liabilities so that both move together, a practice known as immunisation. A pension scheme with liabilities of duration eighteen will therefore hold long bonds rather than short ones, so that a fall in rates lifts both sides of its balance sheet.
The important nuance is that duration is a straight-line approximation and only holds well for small moves in rates. For larger moves the real price curve bends, and analysts add convexity, a second measure that captures that curvature.
Duration also assumes the cash flows are fixed, so bonds that can be repaid early need effective duration, which allows for the borrower changing the timetable.
In practice
Real-world examples.
Example
A corporate treasurer holding $40,000,000 of government bonds with an average duration of 6.0 works out that a 0.5 percentage point rise in yields would cost about $1,200,000 of market value. Ahead of an expected rate rise she sells long bonds and buys short ones, cutting portfolio duration to 3.0 and halving the exposure.
Example
A pension scheme has liabilities of $250,000,000 with a duration of 18, but bond assets with a duration of only 8. When long-term rates fall by 0.25 percentage points, the liabilities rise by roughly 4.5% while the bonds rise by only 2%, and the funding deficit widens by several million dollars.
Example
An insurer pricing a five-year fixed annuity buys a bond portfolio with a matching duration so that the promise and the assets backing it move together. When rates jump the following quarter, the fall in bond values is largely offset by the fall in the present value of the payments the insurer owes.
Think of it
“Duration shows how much a bond's price will move when interest rates change-longer means more sensitive.
Formula
Calculation
Modified duration = Macaulay duration / (1 + yield per period)
Estimated price change % = -Modified duration x change in yield
Worked example: a corporate bond has a Macaulay duration of 5.25 years and yields 5% a year, paid annually.
Modified duration = 5.25 / 1.05 = 5.0.
If market yields rise by one percentage point, that is a change of 0.01, the estimated price change is -5.0 x 0.01 = -0.05, a fall of 5%.
On a $1,000,000 holding that is a loss of 1,000,000 x 0.05 = $50,000, leaving the position worth $950,000. If instead yields fell by half a percentage point, the estimated gain would be 5.0 x 0.005 = 2.5%, or $25,000.Case study
Seen in the real world.
Brackenfield Utilities is a fictional water company used here as an illustrative example. Its treasury team held $180,000,000 in a bond portfolio built to cover a debt repayment due in three years, and had drifted into long-dated bonds because they paid a better yield. The average duration of the portfolio had reached 9.0, against a liability the team was effectively trying to fund in three years.
When yields rose by 1.2 percentage points over two quarters, the portfolio lost roughly 10.8% of its value, about $19,400,000, while the size of the debt repayment did not change at all. The board asked why a fund built to meet a fixed obligation had been exposed to that risk in the first place.
The treasury policy was rewritten so that portfolio duration had to stay within one year of the duration of the obligation it funded, with any breach reported to the audit committee within a month. In this illustrative case nothing about the credit quality of the bonds was wrong; the mismatch was entirely a duration problem.
Watch out
Common mistakes.
- Confusing duration with maturity, and assuming a ten-year bond must have a duration of ten, when a high coupon can pull it closer to eight.
- Applying the straight-line estimate to very large rate moves, which overstates the loss when rates rise and understates the gain when they fall.
- Setting a portfolio's duration once and forgetting it, when duration falls naturally as time passes and drifts every time bonds are bought or sold.
Questions
People also ask.
Is a high duration always bad?
No, it is only bad if rates rise; a long duration portfolio gains more than a short one when rates fall, which is why investors expecting cuts deliberately extend it.
What is convexity?
It is the measure of how much the price and yield relationship curves, and it explains why a bond gains slightly more from a rate fall than it loses from an identical rate rise.
Do floating rate bonds have duration?
Very little, because the coupon resets to the market rate every few months, so their price barely moves when rates change.
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