a. Assume that the FTSE100 stock index level is 5000, and there is a futures contract on the index maturing one year from today. Index stocks will pay dividends over the life of the contract, and these dividends can be reinvested whenever they are received to provide a total cash flow equivalent to 200 index points at futures maturity. Assume also that you can costlessly short sell the index basket of stocks and you can borrow and lend any amount of money at an annual rate of 5%. Assume also that you can ignore marking to market cash flows. What is the price of this futures contract maturing in an year?
b. Assume that you can borrow any amount at an annual rate of 5.5% and lend any amount of money at an annual rate of 4.5%. What are the lowest and highest futures prices that will not allow arbitrage?
c. In addition to the borrowing and lending rates indicated above, assume that the bid level of the index is 4950 and that the ask level of the index is 5050. Compute the range of futures prices that can exist without permitting the opportunity to arbitrage.
d. In addition, assume you face an additional 25 index points cost in short selling. What are the lowest and highest futures prices that will not allow arbitrage?