Equity Swap Discounting discounted, comparing, practice, problems, question

soverby

Hey guys,
I was going over practice problems for the CFA lvl 2 and had a question about equity swap discounting. I noticed that when valuing an equity swap, you discount the fixed/floating leg to get the PV but the equity return portion is not discounted.
This seems counterintuitive as you should be comparing the PV of both legs in order to calculate the MV. Maybe I am looking at this the wrong way but it seems as if we are comparing PV and FV.
The way I see it is that since you don’t know the future payment amount, you only look at the current return, which is 100% accrued. Therefore, you don’t discount. Nevertheless, you still wont receive payment for those returns until a future date. Something seems off, I would appreciate it if you guys could share your thoughts.
Thanks!!

homie

Anytime, will always come to the rescue with derivatives. Just makes sure you say derivatives or SWAPS in the SUBJECT.

towardsutopia21

Gulfcfa,
Makes a lot more sense now. Thank you very much for the detailed reply!!

sharksfan

Most people will not get this. At least when I explain. But here it goes.
Take a pay fixed get floating SWAP (LIBOR not equity)
When we value the SWAP what are we doing. Basiclly we are seeing what it would cost us to replicate each side of the SWAP. If the cash flows you are getting are worth more, ie cost more to replicate, you win and you have a positive value.
Take this logic to equity SWAPS. The interest rate side you should easily understand correct?
Let me try to explain the equity side.
I agreed to pay you the return on S&P in one year, notional principle 1 million
at the start of our SWAP, S&P was 100.
Now 6 months later, and 6 months before I have to pay you.
S&P is at 110.
Assuming at first I entered as a gambler. And now I no longer want that risk and I wana hedge it cause I am worried S&P is gona spike even more.
In order for me to be able to meet my obligation on expiry, I dont have to buy 1 million worth of the S&P. Now I must buy 1.1 million of the S&P since the S&P moved up by 10%.
Note that regardless what happens to the S&P later. I am completely hedged. If it goes up to 120. I will end up with 1.2 million. And i will give you 0.2 of it
if it goes down back to 100, I end up with 1 million, and I give you nothing
if it goes down to 90, you will give me 0.1 million, and I end up with 1 million
(my analysis ignore the interest side, cause i assumed you get it already)
do you see why you do not need to discount? cause I HAVE to buy that much of the index TODAY….
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this note here might confuse more, or help, but i gota see it..
note that the way we “think” of swaps in the CFAI curriculum is by comparing them to bonds…
notice that in my analysis I kind of used a “face value” of 1 million. Dont let it confuse you. While in reality in SWAPS the face value is not exchanged. Thats is not a problem for analysis because the same face value assumption is made on the other side of the SWAP and they cancel each other….
i am not the best teacher, but i tried…