Cash flow to party paying stock and receiving fixed
IVM enters into a swap with FNS to pay S&P 500 Total Return and receive a fixed rate of 3.45%. The index starts at 2710.55. Payments every 90 days for one year. Net payment will be $25,000,000 [0.0345 x (90/360) - Return on stock index over settlement period].
After-the-Fact Payments in Equity Swap to Pay S&P 500 Total Return Index and Receive a Fixed Rate of 3.45% (Notional Principal: $25,000,000)
Note: This combination of outcomes on the above dates represents only one of an infinite number of possible outcomes to the swap. They are used to illustrate how the payments are determined and not the likely results.
If IVM had received floating, the payoff formula would be (Notional principal) x [LIBOR x (days/360) - Return on stock over settlement period].
If the swap were structured so that IVM pays the return on one stock index and receives the return on another, the payoff formula would be (Notional principal) x [Return on one stock index - Return on the other stock index].
Pricing and Valuation of Equity Swaps
For a swap to pay fixed and receive equity, we replicate as follows:
Assume payments on days 180 and 360.
The value of the position is the value of the swap. In general for n payments, the value at the start is
Setting the value to zero and solving for R gives
This is precisely the formula for the fixed rate on an interest rate swap or a currency swap.
Continue with IVM's swap:
With q = 90/360, the 1/q = 4, and the fixed rate would, therefore, be R = 4 [(1 - 0.9662) / (0.9926 + 0.9843 + 0.9758 + 0.9662)] = 0.0345. Thus, the rate would be 3.45%.
To value the swap at time t during its life, consider the party paying fixed and receiving equity.
The cost to do this strategy at time t is
This is the value of the swap.
Suppose we are now 60 days into the life of the IVM swap. The new term structure is as follows:
The stock index is at 2739.60. Thus, the value of the swap per $1 notional principal is (2739.60/2710.55) - 0.9677 - 0.0345 (90/360) (0.9971 + 0.9877 + 0.9778 + 0.9677) = 0.00911854.
The formulation, however, is from the perspective of the party paying the fixed rate and receiving the equity return. So to IVM, the value is actually -0.00911854 per $1 notional principal. Thus, for a notional principal of $25 million, the value of the swap is $25,000,000 x (-0.00911854) = -$227,964.
To value the equity swap receiving floating and paying equity, note the equivalence to
So we can use what we already know.
For swaps to pay one equity and receive another, replicate by selling short one stock and buy the other. Each period withdraw the cash return, reinvesting $1. Cover short position by buying it back, and then sell short $1. So each period start with $1 long one stock and $1 short the other.
For the IVM swap, suppose we pay the S&P and receive NASDAQ, which starts at 1835.24 and goes to 1915.71. The value of the swap is (1915.71/1835.24) - (2739.60/2710.55) = 0.03312974. For $25 million notional principal, the value is $25,000,000 (0.03312974) = $828,244.
A. Brokerage firm makes a net payment of $400,000.
A proper swap would involve the brokerage firm making payments equal to S&P 500 returns in exchange for LIBOR.
Brokerage pays 12% of 10 million = $1,200,000. Pension Pays 8% of 10 million = 800,000. Net payable (broker's perspective): $400,000