What is Macaulay Duration?
Macaulay Duration is the weighted average time (in years) to receive a bond's cash flows, where the weights are the present values of each cash flow as a proportion of the bond's total price. A bond with a Macaulay Duration of 7 years means the investor, on average, receives cash flows equivalent to a lump sum in 7 years. Duration is the primary measure of interest rate risk: longer duration = greater price sensitivity to yield changes. A zero-coupon bond's duration equals its maturity; coupon bonds always have duration shorter than maturity because interim coupon payments arrive before maturity. Duration is also used as an immunisation tool to match asset and liability sensitivities.
Formula
D_mac = Σ [t × PV(CF_t)] / Bond Price
PV(CF_t) = CF_t / (1 + y)^t
t = time period (years)
CF_t = cash flow at time t
y = yield per period
Bond Price = sum of all PV(CF_t)
Calculator
How to Use
- 1List all cash flows: Each coupon payment and the final par value repayment at maturity.
- 2Discount each cash flow: PV(CF_t) = CF_t / (1+y)^t, where y is the yield per period.
- 3Weight by time: Multiply each PV(CF_t) by t (the time in years to that cash flow).
- 4Divide by bond price: Sum the time-weighted PVs and divide by the total bond price.
Worked Example
Example: 5% coupon, 5-year bond at par
Coupon
5%
Years
5
YTM
5%
A 5% coupon bond priced at par with 5 years to maturity has Macaulay Duration ≈ 4.33 years (shorter than the 5-year maturity because coupons arrive early). A zero-coupon 5-year bond would have duration exactly 5.0 years. Modified Duration ≈ 4.33 / (1.05) ≈ 4.12; for every 1% yield rise, price falls ~4.12%.