Modified Duration

Modified duration is calculated by dividing Macaulay duration by one plus the bond's yield per period. It turns duration from a measure of time into a measure of price sensitivity.

For example, a two-year bond with a Macaulay duration of about 1.95 years and a yield of 5% has a modified duration of about 1.86. If its yield rises by one percentage point, its price would be expected to fall by about 1.86%; if the yield falls by one point, its price would rise by about 1.86%.

Longer-term bonds and bonds with lower coupons have higher modified durations, so their prices are more sensitive to interest rate changes. Investors use modified duration to measure and manage interest rate risk across bond portfolios.

Modified duration is an approximation that works well for small yield changes. For larger changes, the relationship between price and yield is curved rather than straight, an effect called convexity, which analysts add to improve the estimate. For bonds whose cash flows can change, such as callable bonds, effective duration is used instead.