The conversion
Macaulay duration summarizes discounted cash-flow timing in years. Modified duration adjusts that timing measure for the yield convention and supplies the coefficient in the local price-change approximation.
Use annual nominal yield y with the same compounding frequency m used to price the bond.
| Symbol | Meaning |
|---|---|
| D_Mac | Macaulay duration in years |
| y | Nominal annual yield as a decimal |
| m | Coupon and yield-compounding periods per year |
A zero-coupon check
A five-year zero-coupon bond has Macaulay duration of five years because its only payment arrives at maturity. With annual compounding and a 5% yield, modified duration is 5/1.05, or approximately 4.7619. Do not substitute the quoted percentage 5 for the decimal 0.05.
Use it as a local sensitivity
For a small compatible yield change, the approximate fractional price change is −D_mod × Δy. The minus sign records the inverse relationship. This first-order result holds cash flows fixed; it does not include the curvature adjustment.