Consider these futures market data for the June delivery S&P 500 contract, exactly one year from today. The S&P 500 index is at 1,950, and the June maturity contract is at F0 = 1,951.

a. If the current interest rate is 2.5%, and the average dividend rate of the stocks in the index is 1.9%, what fraction of the proceeds of stock short sales would need to be available to you to earn arbitrage profits?

b. Suppose now 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?

c. By how much does the actual futures price fall below the no-arbitrage bound?

d. Formulate the appropriate arbitrage strategy, and calculate the profits to that strategy.