Please correct my conceptual understanding if needed, but I'm trying to calculate the mod duration of treasury curve pieces when the curves are DV01 hedged.
DV01 of 10 Year Note is 896.1705 and DV01 of ZB futures is 209.0188.
If I +3 10 Year Note and -13 ZB futures, I am very close to being DV01 hedged.
However, I'm sure the mod duration of this position is not close to 0, as I am taking on curve risk. In what way can I calculate mod duration for the example above?
I guess I'm not expressing myself clearly... I've also changed the title to reflect this. say that I have 2 curve pieces:
First curve: +1 5 Year Note -6 ZN futures
Second curve: +1 10 Year Note -4 ZB futures
ASSUME that they are perfectly DV01 hedged.
How do I find how many of the first curve to hedge the second curve? Obviously 10 Year ZB curve have greater ranges, so what's a fundamentally sound way to hedge this using 5 Year ZN curve?