Receiver Swap 10yrs
Payer Swap 20yrs
Looking at this fictitious example, I want to understand why this position will generate negative mark-to-market whenever the yield curve is shifted (parallel) up or down? The DV01s of both swaps are of equal magnitude (i.e. notionals have been adjusted in such a way to render both swaps having same DV01 magnitude, correct?), so therfore a parallel move in any direction of the yields will mean that the MtM of the swaps offset each other? Surely, convexity does not play a role because the DV01s are of equal magnitude?
I am confused, and any help is greatly appreciated.