The number of contracts to change the DD of a portfolio is the (D_Target – D_current)/DD of instrument used

Since we use only one contract with swaps, we set the number of contracts equal to 1.0:

1 = (DD_Target – DD_current)/DD_swap

Then convert dollar duration, DD, into value times duration, D:

1 = [D_Target(VP) – D_current(VP)] / D_S(NP) → (VP) (D_Target – D_current) / D_S(NP)

If we then rearrange the equation by moving NP to the other side we get…

NP = (VP)(D_Target – D_current) / D_S

With the target duration = 2 X current portfolio duration with the swap having the same duration as the current portfolio we then have

NP = (VP)(2D_Target – D_current) / D_S

NP = (VP)(D) / D

NP = VP