Equity swaps - Why do we not calculate PV of equity return?

CFA Level II
#1

Let’s say an equity swap where we receive the equity return and pay the floating rate, and the next payment is in 80 days:

PV of the next floating payment plus the $1 market value of the remaining floating payments is 0.9906(1.0108) = 1.0013. The value of the equity payment is 1595/1561 = 1.0221.

Based on a notional principal of $50 million, the market value of the swap to the party that pays floating and receives the equity return is (1.0221 − 1.0013)50,000,000 = $1,040,000.

My question is why do we not have to discount the equity return as we do with the floating payment? The floating payment will be in 80 days, will we not also receive the equity return in 80 days?

#2

We will receive the equity return in 80 days, but what value will it be in 80 days? We know what value it is today – 2.21% – but we do not know what its value will be in 80 more days. Therefore, we assume that it will grow in 80 days by the 80-day risk-free rate; when we discount that back to today (at the 80-day risk-free rate), we get the value of the return today: 2.21%.

#3

Good question. Good answer.

It’s goood.

#4

Thanks. Good explanation. I agree we do not know the equity return in 80 days, but I thought the value should be calculated provided that 2,21% would be the return in 80 days.

#5

My pleasure.