Modified duration
By Jude Wallis
Modified duration is Macaulay duration divided by one plus the periodic yield. It estimates the percent change in a bond's price for a one percentage point change in yield.
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Macaulay duration is measured in years: the average time at which a bond's cash arrives, weighted by present value. Modified duration takes that number and turns it into a price sensitivity, so its units stop being time and start being percent per point of yield.
The division is small and easy to skip. Dividing by one plus the periodic yield, not the annual yield, is what keeps the adjustment right on a bond paying twice a year, and using the annual figure there overstates the correction.
The estimate is a straight line through a curved relationship, so it is accurate for small moves and understates the price gain on a large fall in yield. Convexity is the term that repairs it. The modified duration calculator is the conversion, how bond duration works is the explainer, and Macaulay against modified duration sets the two side by side.