Suppose that the risk-free interest rate is 1% p.a. with continuous compounding and that the dividend yield (dividends are evenly distributed throughout the year) on a stock index is 2% p.a. The stock index is at 1000 and the futures price for a contract deliverable in 3 months is at 1050.
a. What is the fair value of the futures price?
b. Does an arbitrage opportunity exist? (you may borrow and lend freely at the risk free rate; you may also borrow the share portfolio at no cost).
c. If there is an arbitrage opportunity, how do you exploit it?