### Stock index futures

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1.A portfolio manager controls \$5 million in common stock. In anticipation of a stock market decline, the decision is made to hedge the portfolio using the S&P 500 futures contract. The portfolio's beta is 1.20, and the current value of the S&P 500 futures contract selected is 238.50.

a. Calculate the number of futures contracts that should be bought or sold.

b. Suppose that when the contracts are closed out, the portfolio has fallen in value to \$4.2 million and that the S&P 500 index has fallen to 215.00. Calculate the gain or loss on the combined positions (stock portfolio and futures contracts).

c. Why does the net gain or loss not exactly equal zero?

2.Suppose the S&P 500 index is at 315.34. According to the Outlook, the dividend yield on the index is 2.89 % . If T-bills yield 8.97%, what is the fair value of an S&P futures contract that calls for delivery in 106 days?

3.In problem 2, suppose that the futures contract in question sells for 322.50.  How would you take advantage of the price discrepancy?

4.If the S&P 500 index is about 400, how many futures contracts must be bought or sold to hedge 50% of the market risk of this portfolio?

5.You want to hedge half the market risk of a \$100 million stock portfolio with a beta of 0.90.  The December S&P500 stock index futures settled at 1065.25.  How many futures contracts are necessary to do so?  (The futures contract is \$250 times the value of the index.)

6.Interest rates in Japan are near zero at present.  Suppose the stocks in the shigotoba index (currently at 10,300) have an average dividend yield of 1.2%.  Would you expect a three-month shigotoba futures contract to settle at less than, about the same, or more than 10,300?  Explain your answer.

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