Bond duration vs maturity
Maturity is the date face value is repaid. Macaulay duration is the present-value-weighted wait for every remaining cash flow, coupons included. A 5-year 5 percent par bond matures in 5 years and has a Macaulay duration of 4.55 years, because some of the value arrives as coupons first.
| Maturity | Macaulay duration | |
|---|---|---|
| What it measures | When face is repaid. | When, on average, the value arrives. |
| 5-year par bond, 5 percent annual | 5 years. | 4.55 years. Modified duration 4.33 years. DV01 $0.43. |
| 10-year premium, 6 percent coupon | 10 years. | 7.76 years. More of the value sits in the coupons, so duration sits further inside maturity. |
| Zero-coupon bond | Equal to duration. | Equal to maturity. Nothing arrives before face. |
| What a rate move does | Nothing to this date. The contract does not move. | Modified duration is the percent price move for a 1 point yield move, for a small move. |
| Unit | Years, a date. | Years, a wait. Saying a bond 'has duration 4.55' without the unit mixes it with modified duration. |
On this page
Coupons pull the average date forward
A coupon bond pays along the way and face at the end. Maturity is the end. Macaulay duration is the average of those dates, each weighted by the present value of that cash flow. On a 5-year annual 5 percent bond at a 5 percent yield the price is par, $1,000, and duration is 4.55 years, not 5, because some of the value arrives as $50 coupons before the $1,000 face.
A 10-year 6 percent semiannual bond at a 5 percent yield prices at $1,077.95. Maturity is 10 years. Macaulay duration is 7.76 years. Premium bonds have shorter duration than par bonds of the same maturity, because more of the value sits in the coupons.
How bond duration works is the long form. Macaulay against modified duration is the next split: a wait, then that wait divided by so it can move the price.
Maturity does not measure interest-rate risk
Two bonds can share a maturity and not share a duration, so they do not share a price sensitivity. Immunisation matches Macaulay duration to a liability date, not maturity to that date. Mixing the two is how a hedge comes out the factor too large or too small.
The bond duration calculator returns both waits, modified duration and DV01. This is educational material, not financial advice.
Worked examples
A 5-year par bond, annual coupons
Face $1,000, 5 percent annual coupon, 5 percent yield, 5 years, annual payments. Price, Macaulay duration, modified duration, DV01?
- Each coupon is , so $50. At a 5 percent yield the bond is at par: price $1,000.
- Macaulay duration, the present-value-weighted wait, is 4.55 years.
- Modified duration: years.
- DV01: , so $0.43 per basis point.
The bond prices at $1,000. Macaulay duration is 4.55 years, modified duration 4.33 years, and DV01 is $0.43. Coupon each year is $50.
A 10-year premium bond, semiannual coupons
Face $1,000, 6 percent coupon, 5 percent yield, 10 years, two payments a year. Price and duration?
- Coupon each half-year: , so $30.
- Price, discounting 20 coupons and the face at 2.50 percent a half-year: $1,077.95.
- Macaulay duration 7.76 years, modified duration 7.57 years, DV01 $0.82.
The bond prices at $1,077.95, a premium because the coupon sits above the yield. Macaulay duration is 7.76 years, modified duration 7.57 years, DV01 $0.82. Each half-year coupon is $30.
A zero-coupon 5-year bond at 5 percent
Face $1,000, coupon 0, yield 5 percent, 5 years, annual. Confirm Macaulay duration equals maturity.
- Price is .
- The only cash flow is at year 5, so Macaulay duration is 5.00 years.
- Modified duration: years. DV01: .
Price $783.53. Macaulay duration is 5.00 years, equal to maturity, because nothing arrives before then. Modified duration is 4.76 years and DV01 is $0.37. The coupon each period is $0.
Common questions
Can duration be longer than maturity?
Not for an option-free coupon bond paying a positive coupon. Coupons arrive before face, so they pull the weighted wait inside maturity. A zero-coupon bond is the case where duration equals maturity.
Is modified duration the same as Macaulay duration?
No. Modified duration is Macaulay duration divided by . It is the percent the price moves when the yield moves by 1 percentage point, for a small move. Macaulay against modified duration is that pair.
Does a longer maturity always mean more interest-rate risk?
Usually, not always. Duration is the risk measure. On a deeply discounted bond so much of the value already sits in the final repayment that adding years can move duration less than the extra wait suggests.
Keep reading
This page is educational material, not financial advice. The figures come from the formula shown and assume the inputs you enter hold for the whole term. Your own rate, fees, taxes and timing will differ, so treat the output as arithmetic to check a decision against, not as a recommendation.