Macaulay Duration Calculator
Calculate Macaulay Duration and Modified Duration for a fixed-coupon bond.
See DV01, interest rate sensitivity, and the average time to receive cash flows.
Macaulay Duration
Macaulay Duration is the weighted average time (in years) it takes to receive all of a bond’s cash flows. Each cash flow is weighted by its present value as a fraction of the total bond price. It measures how long, on average, you must wait to get your money back.
Formula:
D = Σ [t × PV(CF_t)] / Bond Price
Where:
- t = time period of each cash flow
- PV(CF_t) = present value of cash flow at time t
- Bond Price = sum of all discounted cash flows
Modified Duration converts Macaulay Duration into a direct price sensitivity measure:
Modified Duration = Macaulay Duration / (1 + y/m)
Where y = yield to maturity, m = coupon payments per year
DV01 (Dollar Value of 1 Basis Point):
DV01 = Modified Duration × Bond Price / 10000
DV01 tells you how many dollars the bond price changes for every 1 basis point (0.01%) move in yield.
Read the units carefully, because this is where people slip. The price in that formula is the price of one bond, so the answer is dollars per bond, not dollars per dollar of face value. A $1,000-face bond with a modified duration of 7.57, trading at $1,077.95, has a DV01 of about $0.82. That is 82 cents per bond. On a $1 million face position, which is a thousand such bonds, the same one-basis-point move is worth about $816.
Interpretation:
| Duration | Meaning |
|---|---|
| 2 years | Price changes ~2% for each 1% yield move |
| 5 years | Price changes ~5% for each 1% yield move |
| 10 years | Price changes ~10% for each 1% yield move |
A bond with Modified Duration of 7 will fall approximately 7% in price if yields rise 1%.
Where duration alone starts to lie: convexity
Duration is a straight line drawn against a curve, so it is only accurate for small moves, and it is wrong in a specific and useful direction. Take the 10-year 6% bond above at a 5% yield. Modified duration says a one-point move costs 7.57% either way. What actually happens is that the price falls 7.23% when yields rise a point and gains 7.94% when they fall a point. The loss is smaller than duration predicted and the gain is larger, both times.
That asymmetry is convexity, and for an ordinary bond it works in your favor. The second-order estimate is:
Price change % ≈ −ModDur × Δy + ½ × Convexity × (Δy)²
The calculator reports convexity and the corrected estimate alongside the plain duration figure, so you can see the size of the gap. At a quarter-point move it is negligible. At two or three points, on a long bond, duration alone is off by enough to matter.
Callable and mortgage-backed bonds can have negative convexity, where the relationship inverts and the asymmetry works against you. This calculator assumes a plain fixed-coupon bond with no call feature.
Duration rules:
- Zero-coupon bonds: Duration = maturity (all cash flow at end)
- Higher coupon rate → lower duration (more early cash flows)
- Higher yield → lower duration
- Longer maturity → higher duration
Why duration matters: Duration is the primary tool for managing interest rate risk in fixed income portfolios. Portfolio managers match asset and liability durations to immunize against rate changes.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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