Suppose the one-year futures price on a stock-index portfolio is 1220, the stock index currently is 1200, the one-year risk-free interest rate is 2%, and the year-end dividend that will be paid on a $1,200 investment in the index portfolio is $10.

a. Is there an arbitrage opportunity? If yes, then by how much is the futures contract mispriced?

b. Formulate a zero-net-investment arbitrage portfolio and show that you can lock in riskless profits equal to the futures mispricing. Assume there are no transaction costs in security and futures transactions.

c. Now assume that if you borrow at time 0, the interest rate is 4% per year (i.e., rather than the risk-free interest rate of 2%). Is there still an arbitrage opportunity? Briefly explain your reasoning.