Why is modified duration measured in years if it estimates a price percentage?
I understand the shortcut that bond price changes roughly by negative modified duration times the yield change. What I do not understand is why the duration number is still stated in years if the answer is a percent price move.
Modified duration is measured in years because it is a sensitivity ratio built from cash-flow timing. It tells you the approximate percentage price change for a 1.00 percentage point change in annual yield.
The useful way to see the unit is:
Modified duration = percent price change / annual yield change
If a bond has modified duration of 5.20, then a 0.25 percentage point yield increase gives:
-5.20 x 0.0025 = -0.0130 = -1.30%
The output is a price percentage. The input yield change is annual. The duration measure sits between them as the years-like sensitivity.
So the unit is not random. It reminds you that the price sensitivity came from the timing and present-value weighting of the bond's cash flows.
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