Question

"The 2-year S&P 500 index futures price is currently at $3425. If you are long 4 contracts of the S&P 500 index future contracts with 2-year maturity and with a delivery price of $3000, what's the value of your futures position. The continuously compounding interest rate on dollar is 1%. Each contract is 100 shares. Round to integer. "

Answer 1

Current S&P 500 Index Futures Price for 2 year contract = $3,425 | Number of contracts bought = 4

Delivery Price at 2-years = $3,000 | Rate of Interest = 1% | Each Contract = 100 shares

If someone bought a Futures Contract for 2-years now, It would cost $3,425 after 2 years as delivery price.

As both Current Futures Price and our Delivery price are at 2-years, we can calculate the Payoff at the time of delivery from the transaction.

Payoff = (Current Futures Price for 2-years contract - Delivery Price at 2-years) * Number of shares per contract

Payoff at the time of Delivery per contract = (3,425 - 3,000) * 100 = $42,500

Total Payoff at the time of Delivery = 4 Contract * Payoff on one contract = 4 * 42,500 = $170,000

Now using the Interest rate of 1%, we can discount the Total Payoff to Today which will be the Value of Futures position.

Value of Futures position = Total Payoff at Delivery * e^-RT

Value of Futures position = 170,000 * e^-1%*2

Value of Futures position = 170,000 * 0.98020

Value of Futures position = $166,633.77 or $ 166,634

Hence, Value of the Futures Position is $166,634