The price of XYZ stock is currently $51.37 and it only pays an annual dividend. Investors expect next year's dividend to be $1.55 per share. Assume no transactions costs and you can both borrow and lend at the current market interest rate of 6.2% compounded annually. A futures contract in XYZ stock currently is being traded with a price of $51.05/share. This futures contract is for 100 shares and expires one year from today.
First, assume a goal of owning 100 shares of stock one year from now. You want to compare the cost of buying stock versus the cost of buying a futures contract.
1. What is the present value of the relevant (net) costs of buying 100 shares of stock? (Hint: Remember your goal is to hold stock one year from now. As a result all the cash flows between now and a year from now are relevant.) Answer with a positive number.
2. What is the present value of the relevant (net) costs of buying a futures contract in order to buy the 100 shares of stock you want to hold? Answer with a positive number.
3. Which is the least expensive way to acquire your stock? Answer 1 for buying stock now, and 2 for buying a futures contract now.
4. If you were to engage in a futures arbitrage to take into account the price disparity you found above, would you buy stock or sell stock short? (1=buy, -1=sell short)
5. If you were to engage in a futures arbitrage to take into account the price disparity you found above, would you buy or sell a futures contract? (1=buy, -1=sell)
Assume you do undertake this futures arbitrage concerning 100 shares of stock. For the next six questions, answer with a positive number if a cash inflow and a negative number if a cash outflow.
6. What would be your cash flow today with respect to stock?
7. What would be your cash flow today with respect to borrowing or lending money?
8. What would be your cash flow today with respect to the futures contract?
9. What would be your cash flow one year from now with respect to dividends?
10. What would be your cash flow one year from now with respect to the loan?
11. What would be your cash flow one year from now with respect to the futures contract?
12. What would your net profit one year from now be from this futures arbitrage?