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I'm trying to create a static hedge for a forward swap using two spot starting zero coupon swaps (to prove that there is no convexity adjustment needed). Here are the instruments -

  1. Paying fixed in 1y1y forward swap
  2. Paying fixed in spot starting 1y zero coupon swap
  3. Receiving fixed in spot starting 2y zero coupon swap

Problem is #3 does not have cash flows at t=1y, so there is no way to cancel out that exposure from #2. Could someone please point out my mistake.

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There needs to be a 4th transaction: the cashflow at t=1y needs to be invested at Libor until t=2y. You will then find that all the cashflows cancel. This means that the hedge is not quite static, but the convexity adjustment is still zero, because we assume money can be invested (or borrowed) at Libor for free at any time. (Note: this is not quite correct in the current era of Fed funds discounting, but it's pretty close).

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