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Problem - Chicago Board of Trade has just introduced a new single stock futures contract on the stock of Mango, company currently paying no dividends. Each contract calls for delivery of 1000 shares of stock in one year. The T-bill rate is 6% per year.
i. If Mango stock now sells at $120 per share, what should the futures price be?
ii. If the Mango stock price drops by 3%, what will be the change in the futures price and the change in the investor's margin account?
iii. If the margin on the contract is $12,000, what is the percentage return on the investor's position?
Suppose a Russell index portfolio pays a dividend yield of 3% annually. The index value currently is 900. The T-bill rate is 5% and the Russell futures price for delivery in one year is $912. Construct an arbitrage strategy to exploit the mispricing and show that your profits one year hence will equal the mispricing in the futures market.
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