Consider these futures market data for the June delivery S&P 500 contract, exactly 6 months hence. The S&P 500 index is at 1,350, and the June maturity contract is at F0= 1,351.
a. If the current interest rate is 2.2% semiannually, and the average dividend rate of the stocks in the index is 1.2% semiannually, what fraction of the proceeds of stock short sales would need to be available to you to earn arbitrage profits?
b. Suppose that you in fact have access to 90% of the proceeds from a short sale. What is the lower bound on the futures price that rules out arbitrage opportunities? By how much does the actual futures price fall below the no-arbitrage bound? Formulate the appropriate arbitrage strategy, and calculate the profits to that strategy.
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