Increase Duration via Swap

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cfaexam

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Long bond portfolio. This position moves inversely with the interest rate. To increase the bond portfolio duration by adding a swap, the swap should be pay floating and receive fixed, which creates a positive moves inversely with the interest rate.
Can anyone explain why pay floating and received fixed moves inversely with the interest rate?
 
Pay Fixed, Receive Floating has an Overall NEGATIVE Duration
Pay Floating, Recieve Fixed has an Overall POSITIVE Duration
 
If it moves inversely it is a typical Bond, IR increase –> Bond Prices Decrease. So your Duration is Positive. Now to Increase teh Duration you want to pick the Positive Duration SWAP which is Pay floating and Receive Fixed.
 
If you are rec floating and int rates increase then that is a positive for you as you rec more $$$ and payout the same fixed pmt
 
Thanks!
Can you further explain why pay floating, receive fixed has an overall positive duration?
 
If you PAY its Negative Duraiton, if you RECEIVE Its Postive
Also, Fixed Duration > Floating Duration
So Lets say we have a 4Y Swap settled SemiAnnually to Pay Floating and Receive Fixed
Now lets assume Floating Duration is .25 and Fixed is 75% of 4Y life so say 3.
Now Pay Floating = -0.25
Recieve Fixed = +3
Net = +2.75 Duration <—-Normal Duration, ie, inverse relationship with Int Rates
If we do the Opposite and do Pay Fixed and Receive Floating
Pay Fixed = -3
Receive Floating = +0.25
Net = -2.75 Duration <—-Negative Duration or Opposite Duration so this will move in same direction as Interest Rates…
 
When a bond portfolio manager uses a fixed for floating swap(receive fixed and pay floating) you are increasing duration i.e. increasing market value risk(higher duration implies greater sensitivity to interest rates) and increasing cash flow risk from an accounting perspective because with the floating payment leg there is uncertainty on cash outflows
 
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