Duration

What Is Duration?

Duration is a measure of how sensitive a bond's price is to changes in interest rates. It is expressed in years, but it is not the same as a bond's maturity. A bond with a longer duration generally experiences larger price swings when rates move, while a bond with a shorter duration is usually less affected.

Duration also has an older meaning: the weighted average time an investor waits to receive a bond's cash flows, including regular coupon payments and the final repayment of principal. This original version is called Macaulay duration, named after the economist Frederick Macaulay, who introduced the concept.

How Duration Is Calculated

Macaulay duration is found by multiplying the time until each cash flow by that cash flow's present value, adding those results together, and dividing by the bond's price:

Macaulay duration = (sum of t x present value of cash flow at time t) / bond price

Modified duration adjusts this figure so it shows price sensitivity directly:

Modified duration = Macaulay duration / (1 + yield / number of coupon periods per year)

Modified duration gives an approximate percentage change in a bond's price for each one-percentage-point change in its yield to maturity. For example, a bond with a modified duration of 5 would be expected to lose roughly 5% of its value if yields rose by one percentage point, and to gain roughly 5% if yields fell by the same amount. The estimate is least accurate for large rate moves, which is where convexity becomes relevant.

Why It Matters to Investors

Duration allows investors to compare how exposed different bonds are to rate changes, even when their maturities differ. Bond funds often report a single duration figure that summarizes their overall rate sensitivity.

Duration is a snapshot rather than a fixed property. It changes as yields move and as time passes. It also assumes relatively small, roughly parallel shifts in interest rates. For bonds with embedded options, such as callable bonds, analysts often use effective duration instead. Duration does not measure credit risk, meaning the chance that an issuer fails to make payments.