Looking for a logic behind the Par swap rate formula

Hello, In an attempt to save brain cells, I am trying to find a logic behind the Par-swap formula. So, for a 1 year swap, we got [1 - DF(1y)] / [0.5 X (DF(6m)+DF(1Y))] DF stands for Discount Factor So far, I understand that the numerator stand for the Float leg and that the denominator stand for the Fixed leg - and that’s about it. Does anyone have any logic that could be used in order to reconstruct the formula? Basically, how do you manage to memorize this one? Thank you, Olivier Wagner

Who knows? What is that formula and what does it do (for instance I don’t see an equal sign there)?

That’s the formula for the par swap rate (the rate which, if applied to the fixed leg would cause the value of the swap to be zero). Par swap rate = [1 - DF(1y)] / [0.5 X (DF(6m)+DF(1Y))] I got this formula from an NYU course. The curriculum uses the same formula to solve question 1.A. from reading 65 (ok, ok, they don’t have the 0.5 in the denominator, but then they double the rate to get an anualize the rate.) So I also understand that the 0.5 is there to bring a 180 days rate to an annualized rate (why would it be a 180 days rate without the 0.5? I have no idea)

That is for a plain vanilla interest rate swap indeed