# Is dollar duration necessary positive?

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.