A tool that measures the average length of time the holder of a bond has to wait before receiving cash interest payments. The duration of a zero-coupon bond is equal to the life of the bond. However, the duration of an interest-bearing bond that lasts “n” years is less than “n” years, because the holder receives coupon payments on a periodical basis before maturity date, not just the principal at the end of the bond life. The duration of a bond can be calculated using the following formula:
where y is the bond yield (continuously compounded), ci is the cash flows at time ti, and B is the bond price (i.e., the present value of all coupon payments and the principal):
As such, the duration is a weighted average of the times of payment (e.g., the weight assigned to time ti is equal to the proportion of the bond’s present value provided by the cash flow at time ti). The sum of the weight is one.
For an example, see: tutorial- bond duration: an example.
