I’m actually doing pretty good with valuing FRAs, swaps, etc but this one threw me off-
Consider a 1 yr semi-annual equity swap based on an index at 985 and a fixed rate of 4.4%. 90 days after initiation, the index is at 982 and LIBOR for 90 days is 4.6% and 4.8% for 270 days. The value of the swap to the equity payer based on a $2mil notional amount is what?
They show the answer as this: 982/985 - .022/1.0115 - .022/1.036 - 1/1.036 = -.0112821
then they do this: (-.0112821)*(2,000,000)=$22,564 is the negative value because the equity index fell
My questions: I completely understand the logic of comparing what the equity side ‘gets’ versus what the fixed side ‘gets’. But the way I went about solving this is I plotted each cash flow on the timeline. So the first payment was: (.022)*(2,000,000)=$44,000 cash flow at the 1st payment and then another $44,000 at the second payment as well as the notional $2mil.
Discounting these cash flows I got a PV 90 days after initiation of the swap to be = $2,016,472- so that’s the value of the fixed bond part of this.
Then I tried to get a PV of the equity side- that would just be (982/985)($2mil)=1,993,908 and then just discount this back to 30 days after initiation and we get 1,924,622.
Why can’t I now just do (1,924,622)-(2,016,472)=value of swap…it doesn’t come out to the right number…did I do something wrong? This is important to me because I’d much prefer to plot the cash flows whenever possible as opposed to doing it as they did above…