effective duration for FRN

CFA Level II
#1

why do floaters have an effective duration = time to next reset?

thanks

#2

Assuming that the coupon rate is the discount rate (e.g., the bond pays LIBOR, not, say, LIBOR + 10bps), then the price will reset to par at each coupon date, so you own a bond that is equivalent to a 1-period, zero coupon bond. A zero, as you know, has a Macaulay duration equal to its time to maturity, and a modified duration that is slightly less than the time to maturity, so the effective duration of the floater, which is equal to the modified duration of the zero, is slightly less than the time to maturity.