Modified duration

Modified duration is a refined version of duration that estimates the percentage change in a bond's price for a one percentage point change in interest rates. It is derived directly from Macaulay duration by adjusting for the bond's yield and payment frequency.

The formula is:

A bond with a modified duration of six means its price is expected to fall by approximately six percent if yields rise by one percentage point, or rise by approximately six percent if yields fall by one percentage point.

This estimate holds reasonably well for small changes in rates, but becomes less accurate for larger rate moves, since it assumes a straight-line relationship between price and yield that does not perfectly hold in reality. The actual curvature in that relationship is captured separately by convexity.

Modified duration is widely used because it translates an abstract, years-based concept into a number an investor can apply directly to estimate a likely price impact from a given rate move. Bond funds routinely publish their portfolio's modified duration for exactly this reason, letting an investor gauge at a glance how much the fund's value might swing if interest rates shift.