Question

You are managing a portfolio of common stocks with a current market value of $100 million. You have decided to hedge the price risk for approximately half of the portfolio using CME S&P 500 stock index futures contracts because you believe half of your portfolio's market value moves comparably with this index. Assume the CME S&P 500 stock index futures contract costs $250 per contract times the stated stock market index level. If you agree to sell futures contracts on this stock market index at a future index level of 1100.50 for a settlement date in 7 months, how many contracts do you need to sell (round up to the nearest whole number of contracts)? If the actual S&P 500 index is at 1125.00 today, what would be the net gain or net loss the hedged portion of your portfolio would experience if the actual S&P 500 stock index decreases to 1065.00 on the settlement date if you do the stock index futures contracts (and half your portfolio continues to track with that index)? Calculate percentage gains/losses to 6 decimal places, and round up the number of contracts to the next-highest whole contract. 182 contracts: net loss of about $1.450,000. 181 contracts: net loss of about $976,000. 182 contracts; net loss of about $1,055,280 XO181 contracts: net gain of about $397.500 182 contracts: net gain of about $1,055.280

Answer 1

number of contracts need to be sold = 50 million/250 *1100.50

= 181.78

Thus the total contract requires will be equal to 182

Since the index decrease there will gain in the hedged position thus the correct answer will be last option.