# Equity Swap Doubt

OTS has an investment portfolio with similar weighting as the S&P500. Smith believes that the U.S. equity market could suffer further declines and OTS could hedge the equity risk using an equity swap. Smith obtained the outlook of the U.S. equity market in Exhibit 4.
Exhibit 4: Performance of S&P500 for the Next Three Quarters
Swap initiation: 1,190
1st quarter: 1,000
2nd quarter: 980
3rd quarter: 1,050
4th quarter: 1,130

Smith is proposing for OTS to be the party paying the equity return on a USD500 million one-year equity swap. OTS will be receiving fixed rate of 1% on a semi-annual basis.

Using the information what is the market value of the equity swap to OTS three months after swap initiation?

+USD80.35 million.

+USD85.33 million.

+USD88.76 million.

Explanation

OTS is paying the equity return and the value is:

(1000 / 1190) × USD500m = USD420.17 million

The value of fixed payments is equivalent to the value of a one-year fixed coupon bond with 0.5% semi-annual coupon. The value of bond is the present value of the two coupon payments and the par value:

[(0.005 × 0.9979) + (1.005 × 0.9911)] × 500m = USD 500.52 million.

Value to OTS: USD500.52m – USD420.17m = USD80.35 million

Just one doubt, when the equity value declines, shouldn’t the equity payer actually receive the amount?

Come the end of the swap that is in effect what will happen.

Here we are valuing 3 months.

The PV of of what they are due = 500.52
The value fo what they need to payout = 420.17

If we were to stop now they would receive 80.35

But why should the pay, the equity index has fallen in value right? The pmt should be made for an increase in value of the index right?

Yes, actually the equity payer receives the part that the value decreases, which is 500-420.17. And the another part he receives is from bonds, which is 0.52. But the swap are not closed.

In this answer, they calculate the swap value by the different PV between two parties.

okay…thanks