modified duration

Modified duration means the percentage price change if market yield changes 1%. If it’s the percentage change, why is the unit of modified duration year?

like modified duration = 5 years. why use year?

The definition of modified duration is the percentage change in the bond’s price for a 100bp change in the bond’s YTM. The percentage change in the bond’s price is just a number: no units. The YTM is an interest rate _ per year _: its units are 1/years. When you divide a number (no units) by 1/years, the resulting quantity has units of years.

I wrote an article on duration that covers this:

Great artical… I have been wondering about a specific interpretation of duration. I may have gotten confused somewhere in my studies, but along the way I got the impression that duration is the years until the unique time where it would be equally beneficial to 1) hold the bond and continue to collect coupons … or 2) sell the bond for a capital gain. before and after that date either 1 or 2 would be advantageous. (given a steady state environment)

I am not sure if I have competely mislead myself or if this is a valid interpretion of one of the duration functions.

You’re correct: that’s one interpretation of Macaulay duration.