# Equity Swap. Recieve floating.

Hi,

Lets say we enter an Equity swap when index is 100 with quarterly settlements. Principle: \$ 1 000 000. We are recieving equity side and paying fixed. Lets ignore the fixed side for Now and focus on the floating payment on the equity side.

1Quarter: index: 110 --> payment floating: 110/100 x 1 000 000 = \$100 000.

Question 1: What is the value of the Swap right after settlement? Does it reset so the of the value swap is “0” at this stage? Or do you say that the value of the floating side is “0”?

Question 2:

2 Quarter the index is 120. Will the payment for the floating side be 120/110 x \$ 1 000 000 = 90.909 ?

Question 3:

1. If we are 30 days since last settlement (q1) (i.e. 60 days till next settlement) and the equity index is trading at 120. How do we value this side in this situation? Do we simply do 120/110 x \$ 1 000 000 = 90.909 and then multiply that with the 60 day discount factor?

Anyone?

1. At each reset date you completely sell the Eq position and reinvest funds to equal the original notional amount. If the Eq index increased the excess is paid to receiver of Eq. Notional is always the same at each reset date.

The rest I’m not too sure of because there isn’t anything in the material which explains what the subsequent payments would be but I believe that you are correct in the statement because since we are reinvesting to match the original notional we would be buying at the newer level 110 with the return being based off the increase to 120.

The FV of the Eq swap = PV of implied fixed rate bond - Eq return X NAeq

In a question they have it as currently trading index/index at contract initiation but that’s because the reset date hasn’t happened yet. There doesn’t appear to be any discounting on the side of the Eq leg.

Correct me if im wrong since its been a few days since i last looked at derivatives.

#1 - Remember at each payment date on a floating rate the value of the floating is the notional value. If before the payment you consider the next payment and notional value to be all paid on the next payment date. It makes valuing a floating side of the swap easier than the fixed side.

#2. I think the next payment would be \$100k as well. if the equity index went up 20% i would expect to receive 20% total.

#3. If we assume the equity swap will pay \$1,200,000 in 60 days. PV that and compare that to the PV of the fixed side payments.

I think he was referring to the FV of the Swap itself which is the formula I put above. It’s the Eq return x NA. So say index increased from 100 to 103 based on 20m NA, 103/100 X 20m = 20.6m vs PV of bond. The difference is the FV of the swap. The gain/loss from the position depends on which side you are long and which side you are short.

I would like if someone could chime in on the payment question in #2. From what I understand it’s the change in the equity index between each reset date. At the reset date we sell ALL of the Eq holding and use the full NA to repurchase the Eq index. Any excess is paid to receiver of Eq, any deficit is paid also by fixed payer. If they pay out the return at 103 how could they buy the same amount of shares if they pay the excess? Instead I think they invest the 20m notional back @ 103 and any change in that will be what they pay out next reset date. They wouldn’t base it on 100 again because say index level stayed at 103 from reset date, they wouldn’t be paying the same \$3 increase because the Eq index didn’t increase or decrease in that period.

I’d still like clarification on it because I’m making educated guesses here.