Spread duration for FRNs

Just want to verify a thought here. Consider a normal fixed-rate bond. Its spread duration is equal to its duration. If the discount rate increases, the bond price falls the same whether the discount rate increased as a result of underlying risk-free rates increases or credit spreads widening.

A floating rate bond, however, is only protected from changes in the reference rate (LIBOR…). If credit spreads widen to a level wider than issue spread, your future coupons don’t fully account for that (assuming LIBOR and the credit spreads don’t have a perfect beta of one). In this case, the coupon rate will not equal the discount rate and the bond will have a spread duration different from its overall duration. Sound correct?

Yes, that’s correct.

Similarly if the credit spread narrows.