On January 1, you sold one March maturity S&P; 500 Index futures contract at a f
ID: 2718556 • Letter: O
Question
On January 1, you sold one March maturity S&P; 500 Index futures contract at a futures price of 1,200. If the futures price is 1,250 on February 1, what is your profit or loss? The contract multiplier is $250. (Input the amount as positive value.) The one-year futures price on a particular stock-index portfolio is 1,218, the stock index currently is 1,200, the one-year risk-free interest rate is 3%, and the year-end dividend that will be paid on a $1,200 investment in the index portfolio is $15. By how much is the contract mispriced? (Input the amount as positive value.)Explanation / Answer
13. Loss in S& P 500 index = (1250-1200) * $250
= 50 * $250
= $12500
Note: as we have sold S &P 500 index, if on future date, index point increase, it will be loss due to fluctuation in our account.
14. Future price = spot price * e^ ( risk free interest rate -dividend rate)
Here dividend rate = D1/P*100
=15/1200*100
= 1.25%
interest rate (given) = 3%
Future price = $1200 * e^ ( 0.03-0.0125)
= $1200 * e^ (0.0175)
= $1200*1.0176540
= $1221
Contract should be prices at $ 1221 (proper value) rather than $ 1218.