Equity Swaps
What you'll learn
- LOS 28.gDescribe how equity swaps are priced, and calculate and interpret their no arbitrage value.
Equity Swaps
To price an N period pay fixed equity swap, we can use the same formula as for a plain vanilla swap:
To value this swap, consider two scenarios:
1. Valuation on settlement date (immediately after settlement): We can continue to use the valuation formula discussed for valuation of interest rate swaps.
2. Valuation between settlement dates (for equity swaps, this is covered in the curriculum): We calculate the values of the two sides of the swap separately as shown in the following example.
A $10 million principal, one year, quarterly settlement equity swap has a fixed rate of 6.05%. The index at inception is 985. After 30 days have passed, the index stands at 996 and the term structure of MRR is 6%, 6.5%, 7%, and 7.5% for terms of 60, 150, 240, and 330 days, respectively.
The respective discount factors are 0.99010, 0.97363, 0.95541, and 0.93567. Calculate the value of the swap to the fixed rate payer on Day 30.
Solution
The value of $10,000,000 invested in the index after 30 days is:
From the standpoint of the fixed rate payer, the value of the swap after 30 days is:
A swap of returns on two different stocks can be viewed as buying one stock (receiving the returns) and shorting an equal value of a different stock (paying the returns). There is no “pricing” at swap initiation, and we can value the swap at any point in time by taking the difference in returns (since the last payment date) times the notional principal.
An investor is the Stock A returns payer (and Stock B returns receiver) in a $1 million quarterly pay swap. After one month, Stock A is up 1.3% and Stock B is down 0.8%. Calculate the value of the swap to the investor.
Solution
The investor pays the Stock A returns and receives Stock B returns. However, the Stock B returns are negative, so he pays those as well: