Logic Test: Two Bond Hedge

Test my logic here… The reason we make the average change in the MBS for both the parallel shifts and the twists NEGATIVE in the system of equations in the final step of the two-bond hedge is… To hedge. Because if we didn’t, the position we would take would effectively double our exposure to the yield curve shifts/twists. We make them negative to do the actual hedge. (i.e., give us the opposite exposure to what we already have) Does that make sense? and is it right?