What this calculator does
Duration measures how sensitive a bond's price is to a change in yield. A modified duration of 7.67 years means a one percentage point rise in yield costs roughly 7.67 per cent of the price, which is the single most useful number for managing interest rate risk.
Convexity is the correction to that estimate. Duration assumes the price moves in a straight line with yield, but the true relationship curves, and convexity measures how much. It works in the bondholder's favour: prices rise slightly more than duration predicts and fall slightly less.
The formula
Macaulay duration is the weighted average time to receive the bond's cash flows, weighted by their present values. Modified duration divides that by one plus the periodic yield, and convexity is measured from prices at yields slightly either side of the current one.
| Term | Meaning |
|---|---|
| Macaulay duration | The weighted average time until the bond's cash flows arrive, in years. |
| Modified duration | The percentage price change for a one percentage point yield change. |
| Convexity | The curvature of the price-yield relationship, correcting the duration estimate. |
The inputs explained
| Field | What to enter |
|---|---|
| Face value ($) | Face value repaid at maturity. |
| Coupon rate (%) | The annual coupon rate as a percentage of face value. |
| Yield to maturity (%) | The current yield to maturity. |
| Years to maturity | Years remaining to maturity. |
| Payments per year | Coupon payments per year. |
When to use it
Managing interest rate risk
Duration tells you how much a portfolio would lose if rates rose, which is the first thing to know.
Matching assets to liabilities
Pension funds and insurers match the duration of their bonds to the duration of what they owe.
Comparing two bonds
A longer duration means more price sensitivity, regardless of what the coupon or maturity look like individually.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does maturity change interest rate sensitivity?
The same bond at four remaining maturities.
| Years to maturity | Modified duration | Convexity |
|---|---|---|
| 2 years | 1.87 years | 4.48 |
| 5 years | 4.34 years | 22.30 |
| 10 years | 7.67 years | 71.79 |
| 20 years | 12.01 years | 198.36 |
Questions
Why is duration measured in years?
Because Macaulay duration genuinely is a weighted average time until cash flows arrive. Modified duration inherits the unit even though it is used as a percentage sensitivity, which causes some confusion.
Why does convexity benefit the holder?
Because the price-yield curve bends upward. When yields fall the price rises by more than duration predicts, and when they rise it falls by less. Positive convexity is a free asymmetry in the bondholder's favour.
Why do longer bonds have more duration?
Because more of their value sits in distant cash flows, and distant cash flows are the most sensitive to discounting. A zero coupon bond, with everything at the end, has duration equal to its maturity.
Does a higher coupon reduce duration?
Yes. A larger coupon returns more of the value early, pulling the weighted average time forward, so a high coupon bond is less rate-sensitive than a low coupon bond of the same maturity.
For the yield being shocked, see the bond yield to maturity calculator. For a callable bond, see the yield to call calculator.