Modified Duration Calculator
Rate sensitivity adjusted for payment frequency
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Modified Duration Calculator turns the numbers behind rate sensitivity adjusted for payment frequency into a result, step by step. Type Macaulay Duration (years), Yield (%) and Compounding per Year (1, 2) into Modified Duration; each keystroke re-runs the math. Modified Duration ties each output to its formula. Use Modified Duration for a reliable number, fast. Modified Duration runs in your browser. Finance data stays in the tab. Modified Duration is part of the Finance collection on CalcProMaster, alongside modified duration calculator macaulay bond interest rate sensitivity, free calculators and more. Modified Duration has no learning curve. The fields are labeled. No sign-up or email — Modified Duration answers as you type.
What the defaults give
Macaulay duration 7.2 at a 6% yield with semi-annual payments gives a modified duration of 6.99.
A 1% rise in yield therefore costs roughly 6.99% of the bond price.
The formula
Modified duration = Macaulay duration ÷ (1 + yield ÷ payments per year)
Price change ≈ −modified duration × change in yield
Macaulay duration is the weighted average time until the cash flows arrive, in years. Modified duration converts that into a price sensitivity by dividing out one compounding period. The result is the percentage price move for a one percentage point move in yield, with the sign flipped: yields up, prices down.
Worked examples
7.2 at 6% semi-annual → 6.99
7.2 at 6% annual → 6.79
7.2 at 6% quarterly → 7.09
7.2 at 3% semi-annual → 7.09
7.2 at 12% semi-annual → 6.79
3.6 at 6% semi-annual → 3.50
14.4 at 6% semi-annual → 13.98
Duration scales linearly, so halving the Macaulay duration halves the risk. Yield and payment frequency move it only slightly: going from annual to quarterly payments changes the answer by 0.3, while doubling the duration changes it by 7.
What duration does and does not say
It is a first-order approximation. For a 1% yield move it is close; for a 3% move the price change is larger than duration predicts, because the price-yield curve is convex. Convexity is the second-order correction, and it always works in the bondholder's favour: gains on a yield fall exceed the duration estimate, losses on a yield rise fall short of it.
Duration also ignores credit risk. A bond can have a duration of 7 and still lose 40% of its value because the issuer deteriorates — that is a spread move, not a rate move, and duration says nothing about it. Callable and putable bonds complicate it further, because the cash-flow schedule itself depends on the rate path.
Using it in practice
Match duration to your horizon. If you need the money in five years, a bond fund with a duration of seven carries more rate risk than the horizon can absorb; a duration of five roughly immunises the value against a one-time rate shift. Two portfolios with the same duration have similar rate sensitivity even if the individual bonds differ.
The higher the coupon, the shorter the duration for the same maturity, because more of the cash arrives early. A zero-coupon bond has a duration equal to its maturity, which makes it the most rate-sensitive instrument of that term.
Frequently Asked Questions
What is modified duration?
The percentage price change for a one percentage point move in yield. A modified duration of 6.99 means about a 7% price fall for a 1% yield rise.
How is it different from Macaulay duration?
Macaulay is the weighted average time to cash flows in years. Modified divides it by 1 + yield ÷ payments to turn time into price sensitivity.
Why does payment frequency change it?
More frequent payments mean the compounding divisor is smaller. Quarterly payments give 7.09 against 6.79 for annual on the same 7.2 Macaulay duration.
Is the estimate exact?
No. It is a first-order approximation. For large yield moves, convexity adds a correction that works in the bondholder's favour.
Does duration cover credit risk?
No. It measures sensitivity to interest rates only. A widening credit spread can move a bond far more than duration predicts.
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