So I know the floating rates will reset at a pre-determined interval (1mo, 6mo, etc…) so duration is shorter. But if duration is defined as the time it takes to recover your principal/money isn’t the maturity of the bond still whatever the original maturity is? 10yrs or whatever? So that doesn’t change?
slightly confused 
You’re confusing Macaulay duration (weighted average time to receipt of cash flows) with effective duration (percentage change in price for a 1% change in yield to maturity, allowing that cash flows may change when the yield changes). They can be very, very different from each other, as is the case with long-term, floating-rate bonds.
floating lowers your duration profile…payer swap is used to lower a bond portfolios duration, as you are receiving floating and paying fixed.
so basically this means because floating will “catch-up” to the current rate environment periodically so the movement from reset to reset will be smaller than a fixed?
so what if interest rates just oscillate from 1-2% forever? the effective duration of the floating and fixed would almost be the same right?
Correct.
No.
To get the percentage price change you multiply the change in yield by the duration; the change in yield and the duration are (essentially) independent of each other.
If interest rates oscillate between 1% and 2% forever, you’ll see only small price changes in both bonds, but the duration of the fixed-rate bond will still be bigger, so the price changes (though small) will also be bigger.
ok… thanks… by the way do you drive an s2000?
What do I drive?
An '01 with 240,000 miles on it; one owner.
Modified duration is the change in price.
In a floating rate note, every year the market interest rates would be observed and the coupon is set such that it equates the market interest rates. So now there is no reason for s hind to trade for s premium or a discount. Since the coupon is deliberately set equal to the market rate, there is no reason for a premium or a discount!
Thus, the price of a floating rate bond is at par on every reset date.
Not exactly.
Modified duration is the _ percentage _ change in price divided by the percentage change in yield (to maturity), assuming that cash flows don’t change when the yield changes.
There is if the bond is more or less risky than the risk implied in the reference rate. For example, if a corporate floater has its coupon reset to LIBOR, it will probably trade at a discount, because LIBOR is, essentially, a risk-free rate while the corporate bond is risky.