Effective Duration = Modified Duration when Yield Curve is Flat? (for option-free bond)

Hey all! Why is it that if the yield curve is flat, the effective duration will be equal to the modified duration for an option-free bond?

The difference between modified duration and effective duration is that modified duration assumes that the cash flows don’t change while effective duration allows that the cash flows might change.

For an option-free, fixed-rate bond, they’re always equal to each other.

For an option-free, floating-rate bond, they’ll be equal if (and only if) the future coupon payments are expected not to change, which will typically happen when the yield curve is flat.

Thank you S2000magician!

My pleasure.