This is a soft question about terminology.
Let B be a bond with coupon payments. There seem to be two uses of the word duration in finance:
- Sensitivity of B's log price to B's continuously compounded yield
- Sensitivity of B's log price to B's discretely (with the same frequency as the coupons) compounded yield
We also have three terms for duration: "duration", modified duration and Macaulay duration.
If I read Wikipedia correctly, then
- Modified duration: Sensitivity of B's log price to B's yield
- Macaulay duration: Weighted average time
The article specifically says that Macaulay duration equals the modified duration if you're working with continuously compounded yield.
Based on this: Macaulay duration is a special case of modified duration, and thus, adding the word "modified" to "duration" adds no extra meaning.
So, rather disappointingly, the 3 terms aren't able to disambiguate the 2 meanings.
How does one work around this issue? Is there better terminology?