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.
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%.
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.