swap fixed rates

CFA Level II Fixed Income
#1

SFR3 (P1 + P2 + P3) + P3 = 1

This is the swap fixed rate formula. I came across a question where we are given a table of various zero-coupon bonds and their prices. Then also given was a tabe of government bond spot rates for various maturities (bonds with similar default risk). The question asked for the swap fixed rate for 3 years.

I’ll be honest I can’t wrap my head around the logic of the formula above. Why would adding P3 to that factor above need to be equal to 1? Is there a common sense way to think about this formula?

Maybe I don’t even understand what the swap fixed rate truly represents and its relationship to prices of bonds…

#2

I wrote an article on calculating the swap fixed rate that may be of some help here: http://financialexamhelp123.com/pricing-plain-vanilla-interest-rate-swaps/

#3

That is seriously an awesome article- thanks!

Present value factor was throwing me but I do think I understand it now…also starting with the logic that the variable rate bond would have a PV of 1 makes the formula I wrote above much clearer…