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Macaulay Duration

The weighted average time (in years) to receive the bond's cash flows.

Macaulay duration is the present-value-weighted average maturity of a bond's cash flows. It measures how long it takes, on average, for the bond's cash flows to 'pay back' the bond's price. Macaulay duration is always less than or equal to the bond's time to maturity (equal only for zero-coupon bonds). Modified duration is derived from Macaulay duration.

Formula
MacDur=1P∑t=1nt⋅CFt(1+y/m)t\text{MacDur} = \frac{1}{P} \sum_{t=1}^{n} t \cdot \frac{CF_t}{(1 + y/m)^t}
Where
PP=Bond price
CFtCF_t=Cash flow at period t
yy=Yield to maturity
mm=Coupon periods per year
tt=Period number
nn=Total number of periods