# A Discussion On Index And Interest Rate Futures

1. A portfolio manager controls $5 million in common stocks. In anticipation of a stock market decline, the manager decides to hedge the portfolio using S&P 500 futures contract. The portfolio 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&P500 index has fallen to 215. Calculate the gain or loss on the combined position if stock portfolio and futures contracts

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

3. A speculator buys six T-bill futures contracts at 91.88 and closes them out three weeks later at 91.56. Calculate this person's gain or loss in dollars.

4. A T-bill matures in 60 days and sells for $9,950. What is the bond equivalent yield?

5. A $1,000 par, a 7.5 percent Treasury bond paid interest 57 days ago. It sells for 102 percent of par. Ignoring commissions, but including accrued interest, how much must you pay to buy one of the bonds?

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#### Solution Preview

1. A portfolio manager controls $5 million in common stocks. In anticipation of a stock market decline, the manager decides to hedge the portfolio using S&P 500 futures contract. The portfolio 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.

Since the manager is long in the stock market, he should short in the future market. As the portfolio's beta is 1.20 > 1, the stock is riskier than the market index. Then the number of futures contracts = 5,000,000 / 238.50 = 20,964.36

b) Suppose that when the contracts are closed out, the portfolio has fallen in value to $4.2 million and that the S&P500 index has fallen to 215. Calculate the gain or loss on the combined ...

#### Solution Summary

The solution provides a discussion on index and interest rate futures.