Converts Macaulay duration into a directly actionable price-sensitivity estimate for a given yield change.
How it works
Macaulay duration divided by one plus the yield to maturity gives modified duration. Multiplying that by the assumed yield change (with a negative sign, since bond prices move opposite to yields) estimates the percentage price change.
What this does not include
This is a linear approximation — for larger yield changes, actual bond price movement curves (convexity), meaning this estimate becomes less accurate the bigger the assumed yield change.
How to use this calculator
- Enter Macaulay duration (from this site’s bond duration calculator), yield to maturity, and an assumed yield change.
A worked example
A bond with Macaulay duration 2.8595, yield to maturity 5%: modified duration = Macaulay duration ÷ (1 + YTM) = 2.7233, estimating a −2.7233% price change for a 1% yield increase.
What the variables mean
| Variable | Meaning |
|---|---|
| Macaulay duration | The weighted-average time to receive the bond’s cash flows |
| Yield to maturity | The bond’s current yield |
| Yield change | Assumed change in yield, as a percentage |
Edge cases worth knowing
Modified duration is Macaulay duration adjusted for compounding — a small but important distinction, since modified duration is what actually predicts price sensitivity to yield changes, not Macaulay duration directly.
A Macaulay duration of zero makes the calculation meaningless, so the calculator declines to show a result for that input.
Frequently asked questions
Why does bond price move opposite to yield?
Rising yields make existing bonds with lower fixed coupons less attractive, so their price must fall to offer a competitive yield to new buyers — and vice versa when yields fall.
Why is the estimate less accurate for large yield changes?
Bond price-yield relationships are curved (convex), not linear — modified duration approximates that curve with a straight line, which diverges more from the actual curve as the yield change grows larger.
Does a higher modified duration always mean more risk?
In terms of interest rate sensitivity, yes — a bond with higher modified duration will see larger price swings for the same change in yield, all else equal.
