Consider these data for the S&P 500 future’s contract maturing in, exactly one year. The S&P 500 index is at 4,290, and the contract price is F0 = 4,292.

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 1. Donna Doni, CFA, wants to explore potential inefficiencies in the futures market. The TOBEC stock index has a spot value of 185. TOBEC futures contracts are settled in cash and underlying contract values are determined by multiplying $100 times the index value. The current annual risk-free interest rate is 6.0%.

a. Calculate the theoretical price of the futures contract expiring six months from now, using the cost-of-carry model. The index pays no dividends.

b. The total (round-trip) transaction cost for trading a futures contract is $15. Calculate the lower bound for the price of the futures contract expiring six months from now. P-63