Floating Rate Notes

Hi Guys, I am struggling with the following concept. Why are floating rate notes more stable than fixed rate bonds? My understanding of a fixed rate bond is that the coupon rate does not change and therefore the coupon payment will be the same every time (therefore highly stable.) Surely when the rate is floating then the coupon rate will constantly be unstable. i think I have completely the wrong end of the stick. Any help would be much appreciated.

They’ve lesser interest rate risk (duration risk) than fixed bonds I.e price changes are way lesser than fixed bonds’ price changes. It’s price fluctuations are less and thus stable. For a higher maturity fixed bond, if yields go higher the price risk is high. A floater’s price risk is only till the next coupon reset period.