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# Derivatives-index and interest rate futures

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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 1438.50.
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 \$4.8 million and that the S&P 500 index has fallen to 1315. Calculate the gain or loss on the combined position if stock portfolio and futures contracts.

2. Suppose the S&P 500 index is at 1517. The dividend yield on the index is 2 percent. If T-bills yield 3 percent, what is the fair value of an S&P futures contract that calls for delivery in 106 days?

3. A speculator buys 3 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?

#### 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 1438.50.

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

Value of portfolio= \$5,000,000
Portfolio beta= 1.2
Current value of S&P 500 futures contract= 1438.50
size of S&P 500 futures contract (multiplier)= \$250
Therefore the underlying asset value of 1 S&P contract= \$359,625 =1438.5x250

Since the portfolio manager is long on the assets (common stocks), he will go short (sell) on the futures contract

Number of futures contract sold= Beta x Value of the portfolio / Underlying asset value of one future contract
= 16.68 =1.2 x \$5,000,000. / \$359,625.
Or rounding off, number of contracts sold= 17

Answer: Number of futures contracts sold= 17

b)     ...

#### Solution Summary

The solution provides detailed answers to 5 questions on derivatives dealing with hedging of portfolio, fair value of an S&P futures contract, gain/loss on futures contracts, bond equivalent yield for a T-bill and the price of bond including accrued interest.

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