Suppose the 1-year futures price on a stock-index portfolio is 1,624, the stock index currently is 1,600, the 1-year risk-free interest rate is 3%, and the year-end dividend that will be paid on a $1,600 investment in the market index portfolio is $20.
a. By how much is the contract mispriced?
b. Formulate a zero-net-investment arbitrage portfolio and show that you can lock in riskless profits equal to the futures mispricing.
c. Now assume (as is true for small investors) that if you short sell the stocks in the market index, the proceeds of the short sale are kept with the broker, and you do not receive any interest income on the funds. Is there still an arbitrage opportunity (assuming that you don’t already own the shares in the index)? Explain.
d. Given the short-sale rules, what is the no-arbitrage band for the stock-futures price relationship? That is, given a stock index of 1,600, how high and how low can the futures price be without giving rise to arbitrage opportunities?