Why does a longer bond fall further when rates rise?

Because more of its value sits further in the future, where discounting bites hardest. That is exactly what duration measures.

Does a higher coupon raise or lower duration?

It lowers it. A larger coupon returns more of your money sooner, so the weighted average wait is shorter and the price is less sensitive.

Finance & Loansbonds

Bond Duration Calculator

How far a bond price moves when yields move. Duration is the number traders actually quote, because it converts a yield change into a price change in one multiplication.

Also called: macaulay duration calculator, modified duration.

Modified duration

6.8

A duration of 6.8 means the price falls about 6.8% if yields rise one percentage point, or $67.95 in money. Macaulay duration is 7.07 years.

Macaulay duration (years)

7.07

Price at this yield

$1,000.00

Price change per one point of yield

$67.95

Percentage move per point

6.8%

Price if yields rise a point

$934.96

How this is calculated

An estimate, not an offer or a guarantee. Projected returns assume the rate you entered holds for the whole term, which no market does.

Method and background

This is what the calculation gives for the numbers you entered. It is an estimate, not advice, and it knows nothing about your situation beyond those numbers. Rules for United States change on a published schedule; the effective date is shown on every rule-based tool.

How this is calculated

Macaulay duration is the average time you wait for the money, weighting each cashflow by its present value. Dividing by one plus the periodic yield turns that into modified duration, which is a price sensitivity: a bond with a modified duration of seven loses roughly seven percent of its value when yields rise one point. The approximation is good for small moves and understates the cushion on large ones, because the true price curve bends.

modified duration = Macaulay duration / (1 + periodic yield);  price change is roughly minus duration times the yield move

D_mac: Weighted average time to the cashflows (years)
y: Annual yield (decimal)
m: Coupons per year (periods)

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

a ten-year par bond has a duration near seven

Face value: $1,000.00
Coupon rate: 8%
Years to maturity: 10
Yield to maturity: 8%
Coupons paid: Twice a year

Modified duration6.8

Standard textbook case; Macaulay duration lands just under seven years

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a higher coupon shortens duration

Face value: $1,000.00
Coupon rate: 12%
Years to maturity: 10
Yield to maturity: 8%
Coupons paid: Twice a year

Modified duration6.29

More cash arrives sooner, so the weighted wait is shorter

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a one-period bond has almost no sensitivity

Face value: $1,000.00
Coupon rate: 8%
Years to maturity: 0.5
Yield to maturity: 8%
Coupons paid: Twice a year

Modified duration0.48

boundary: a single payment at six months has a duration of exactly half a year

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Method and limits

What it assumes

A parallel shift in yields, and no change in credit quality.

What it deliberately does not model

Duration is a first-order approximation. For large yield moves convexity matters and is not included here.
It does not apply to bonds whose cashflows change with rates, such as callable or floating-rate paper.

Formula version 1.0.0 · definition 1.0.0 · United States · Report a problem with this calculator

Frequently asked questions

Why does a longer bond fall further when rates rise?: Because more of its value sits further in the future, where discounting bites hardest. That is exactly what duration measures.
Does a higher coupon raise or lower duration?: It lowers it. A larger coupon returns more of your money sooner, so the weighted average wait is shorter and the price is less sensitive.