# 008 - 8 Stock Index Futures Refinements Answers to...

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50 Answers to Questions and Problems 1. Explain the market conditions that cause deviations from a computed fair value price and that give rise to no-arbitrage bounds. The villains are market imperfections, principally transaction costs. When trading is sufficiently costly, the futures price can deviate somewhat from fair value, and no market forces will arise to drive the futures price back to its fair value. The greater the costs of trading, the farther the futures price can stray from its theoret- ical fair value without arbitrage coming into play to restore the relationship. These trading costs include: the bid-asked spread and direct transaction costs such as brokerage commissions and taxes. Also, restrictions on the use of the proceeds from short sales can be important. 2. The No-Dividend Index consists only of stocks that pay no dividends. Assume that the two stocks in the index are priced at \$100 and \$48, and assume that the corresponding cash index value is 74.00. The cost of carrying stocks is 1 percent per month. What is the fair value of a futures contract on the index that expires in one year? Fair Value 5 74.00(1.01) 12 5 83.3851 3. Using the same facts as in Problem 2, assume that the round-trip transaction cost on a futures is \$30. The con- tract size, we now assume, is for 1,000 shares of each stock. Trading stocks costs \$.05 per share to buy and the same amount to sell. Based on this additional information, compute the no-arbitrage bounds for the futures price. From the cash-and-carry transactions we would buy the stocks, carry them to expiration, and sell the futures. This strategy would cost: Purchase and carry stock: 2 \$148,000(1.01) 12 52 \$166,770 Stock transaction cost: 1 1,000(2)(\$.05) 52 \$100 Futures transaction cost: 2 \$30 Total Outlay: 2 \$166,900 For this strategy to generate a profit, the futures must exceed 83.450 per contract. For the reverse cash-and- carry, we would sell the stocks, invest the proceeds, and buy the futures: Sell stock; invest proceeds: 2 \$148,000(1.01) 12 52 \$166,770 Stock transaction cost: 1 1,000(2)(\$.05) 52 \$100 Futures transaction cost: 2 \$30 Total Inflow: 2 \$166,640 8 Stock Index Futures: Refinements

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ANSWERS TO QUESTIONS AND PROBLEMS 51 For this strategy to generate a profit, the futures must be less than 83.320 per contract. The no-arbitrage bounds on the futures range from 83.320 to 83.450. 4. Using the facts in Problems 2 and 3, we now consider differential borrowing and lending costs. Assume that the 1 percent per month is the lending rate and assume that the borrowing rate is 1.5 percent per month. What are the no-arbitrage bounds on the futures price now? From the cash-and-carry transactions we would buy the stocks, carry them to expiration, and sell the futures. Now the financing cost is 1.5 percent per month. This strategy would cost: Purchase and carry stock: 2 \$148,000(1.015) 12 52 \$176,951 Stock transaction cost: 1 1,000(2)(\$.05) 52 \$100 Futures transaction cost: 2 \$30 Total Outlay:
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## This homework help was uploaded on 04/07/2008 for the course BA 4825 taught by Professor Danısoglu during the Spring '08 term at Middle East Technical University.

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008 - 8 Stock Index Futures Refinements Answers to...

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