Consider a stock that will pay a dividend of D dollars in one year, which is when a futures contract matures. Consider the following strategy: Buy the stock, short a futures contract on the stock, and borrow S 0 dollars, where S 0 is the current price of the stock.
- What are the cash flows now and in one year? ( Hint: Remember the dividend the stock will pay.)
- Show that the equilibrium futures price must be F 0 5 S 0 (1 1 r ) 2 D to avoid arbitrage.
- Call the dividend yield d 5 D / S 0 , and conclude that F 0 5 S 0 (1 1 r 2 d ).