Calculator
What a yield move does to a bond
Most sensitive 10-year
-8.3%
Least sensitive 10-year
-7.5%
If yields fall instead
+9.1%
Bonds compared
6
A 30-year at 4%
-15.5%
A 2-year at 4%
-1.9%
Price sensitivity
Start from a real curve, or set your own bondStart from a real curve
Selecting a maturity sets the yield, the term and a coupon equal to the yield, which is roughly how a bond is priced when newly issued.
A zero-coupon bond moves most for a given change in yields.
Drag either way. Falling yields raise the price of a bond you already own.
If yields move +1.00
-7.5%
Your holding becomes
$92,464
Modified duration
7.90
Price change against the size of the move
The dashed line is what duration alone predicts. The solid line is the actual price, recomputed from the bond’s cash flows. They separate as the move grows: the real price falls less than predicted when yields rise and gains more than predicted when they fall. That curvature is called convexity, and it works in the holder’s favour in both directions.
This is the mechanism behind the most common surprise in investing: a government bond, widely described as the safe holding, losing a fifth of its value without the issuer missing a single payment. Nothing has gone wrong when that happens. A fixed stream of payments is simply worth less once new money can be lent at a higher rate. Hold to maturity and you still receive the face value; sell before then and you get the price. Figures assume a single yield applied to every cash flow and ignore accrued interest, tax and dealing costs.
A ten-year bond in each market
Issued today at that market's own yield| Market | 10-year yield | Duration | If yields rise 1 point | If yields fall 1 point |
|---|---|---|---|---|
| Japan | 2.80% | 8.67 | -8.25% | +9.11% |
| Euro area | 3.20% | 8.50 | -8.10% | +8.93% |
| Germany | 3.26% | 8.48 | -8.07% | +8.91% |
| Canada | 3.55% | 8.36 | -7.96% | +8.78% |
| United States | 4.72% | 7.90 | -7.54% | +8.29% |
| United Kingdom | 4.91% | 7.83 | -7.47% | +8.21% |
A lower-yielding bond is more sensitive to a given move, not less, because more of its value sits in payments far in the future. That is why Japan’s bonds move more than the United Kingdom’s for the same one-point shift, despite paying substantially less. Live curves for every market
Why the price moves at all
A bond is a fixed set of future payments. If you hold one paying 2% and new bonds start paying 4%, nobody will buy yours at the price you paid — they would buy the new one instead. Your bond has to fall in price until its return to a new buyer matches 4%.
That is the entire mechanism. No default, no downgrade, no missed payment. Just arithmetic about what a fixed stream is worth when the alternative changes.
What duration means
Duration is the weighted average time until you get your money back, and it doubles as the sensitivity measure: a duration of 8 means roughly an 8% price move for each percentage point that yields move.
Longer bonds have higher duration. So do lower-coupon bonds, because less of the money comes back early. A zero-coupon bond has a duration exactly equal to its term.
Where duration is wrong
Duration describes a straight line, but the real relationship is curved. The price falls less than duration predicts when yields rise, and gains more than it predicts when they fall.
That curvature is convexity, and it favours the holder in both directions. It is small for a modest move and material for a large one, which is precisely when it matters.
What this ignores
A single yield is applied to every payment, rather than a different rate at each date as the market actually does. Accrued interest, dealing spreads, tax and any credit risk are all excluded.
None of this is a forecast. It answers what the price becomes if yields move by an amount you choose, and says nothing about whether they will.