Suppose the one-year futures price on a stock-index portfolio is 1990, the stock index currently is 2000, the one-year risk-free interest rate is 1%, and the year-end dividend that will be paid on a $2000 investment in the index portfolio is $50.

By how much is the contract mispriced?

Formulate a zero-net-investment arbitrage portfolio and show that you can lock in riskless profits equal to the futures mispricing. Assume that you can borrow and lend at the risk-free rate.

Now assume that the rate of interest on the amount of money you borrow is 3% (i.e., higher than the risk-free rate of 1%). Is there still an arbitrage opportunity?