Question 6 a. Consider the following information about a futures contract written on a stock market index expiring in six months Contract size (i.e., multiplier) $1.00 Current level of the underlying index 1700 Dividend rate 6% per annum Risk-free interest rate 3% per annum Note: Both the interest rate and dividend rate in the above table are annually compounded (i.e., payable annually in arrears). What is the theoretical futures price that meets the spot-future parity condition? (Rounded to two decimal places) (3 mark) b. Suppose you took a short position in 5 index future contracts in part a), and held the position till the maturity of the future contracts. At the maturity date, the level of the underlying index became 1785. Based on the given information, evaluate whether your total gain in the 5 futures contracts is above $500? Briefly explain (3 marks) C. (not related to parts a and b) The one-year silver futures and the three-year silver futures contracts are priced at $26.50 and $28.11 per troy ounce, respectively. The current risk-free interest rate for both lending and borrowing is 3% p.a. (annually compounded) for all maturities. The contract size is 1 troy ounce. Furthermore, silver can be bought and short-sold today at the same spot price and there are no storage cost or convenience yields. There are no margin requirements, transaction costs, or taxes. Design an arbitrage strategy to realize an arbitrage profit today, and show the cash flow today. (4 marks) Question 6 a. Consider the following information about a futures contract written on a stock market index expiring in six months Contract size (i.e., multiplier) $1.00 Current level of the underlying index 1700 Dividend rate 6% per annum Risk-free interest rate 3% per annum Note: Both the interest rate and dividend rate in the above table are annually compounded (i.e., payable annually in arrears). What is the theoretical futures price that meets the spot-future parity condition? (Rounded to two decimal places) (3 mark) b. Suppose you took a short position in 5 index future contracts in part a), and held the position till the maturity of the future contracts. At the maturity date, the level of the underlying index became 1785. Based on the given information, evaluate whether your total gain in the 5 futures contracts is above $500? Briefly explain (3 marks) C. (not related to parts a and b) The one-year silver futures and the three-year silver futures contracts are priced at $26.50 and $28.11 per troy ounce, respectively. The current risk-free interest rate for both lending and borrowing is 3% p.a. (annually compounded) for all maturities. The contract size is 1 troy ounce. Furthermore, silver can be bought and short-sold today at the same spot price and there are no storage cost or convenience yields. There are no margin requirements, transaction costs, or taxes. Design an arbitrage strategy to realize an arbitrage profit today, and show the cash flow today. (4 marks)
