Is dollar duration necessary positive? Why?
I wouldn’t think so. What if you’re short a futures contract?
Dollar duration is positive if duration is positive.
IO has a negative duration.
negative duration is important to understand for managing bond portfolios using swaps…
Suppose you have a bond portfolio with typical +duration. Further suppose we want to decrease the duration of the portfolio by combining the bond portfolio with a swap. Which swap should we use and why?
Pay fixed / receive floating swap = short fixed rate bond + long floating rate bond
Duration(Swap)=Duration(short fixed bond)+Duration(long floating bond)
Since the duration of a fixed bond is greater than the duration of a floating bond and given that we are SHORT the fixed bond, the Duration(short fixed bond) is more negative than the Duration (long floating bond) is positive.Hence the Duration(Swap)=negative.
Combining the +DUR bond portfolio with a -DUR swap yields a lower overall DUR for the combined position,achieving the objective of lowering the Duration.