Modified Duration

What Is Modified Duration?

Modified duration is a standard way to estimate how sensitive a bond's price is to changes in interest rates. It is expressed as a number of years, and it is most useful as an approximation of the percentage price move that follows a small change in the bond's yield to maturity. Bond prices and yields generally move in opposite directions, so a bond with a higher modified duration will typically see a larger price change for the same move in yields.

How It Is Calculated

Modified duration is derived from Macaulay duration, which is the weighted average time until a bond's cash flows are received. Modified duration adjusts that figure for the bond's yield and payment frequency:

Modified Duration = Macaulay Duration / (1 + y / n)

Here y is the yield to maturity expressed as a decimal, and n is the number of coupon payments per year.

Using It to Estimate Price Changes

The main use is a rough estimate. The percentage change in price is approximately equal to negative modified duration multiplied by the change in yield. For example, a bond with a modified duration of 5 would be expected to fall by about 5 percent if its yield rose by one percentage point, and to rise by about 5 percent if its yield fell by one percentage point. This is only an approximation. For large yield moves, the estimate becomes less accurate because the relationship between price and yield is curved. That curvature is captured by convexity.

Limitations

Modified duration assumes a small, parallel shift in yields across the maturity range and does not account for changes in cash flows, such as those in callable bonds. Its value also changes over time and as yields move, so it must be recalculated periodically. Investors often consider it alongside other measures of interest rate risk when comparing bonds.