Question 4 (10 marks) Suppose the spot price of gold is $1,500 per troy ounce today. The futures price of gold for delivery in 1 year is $1,530 per troy ounce. Assume that the one-year gold futures contract is correctly priced and there are no storage and insurance costs. Also assume that the risk-free rate is compounded annually and you can borrow and lend money at the risk-free rate. a). What is the theoretical parity price of a two-year gold futures contract, assuming a flat yield curve (same interest rates for all maturities)? (2 marks) b). Suppose you short 10 one-year gold futures contracts today and the contract size is 100 troy ounces. The initial margin requited by the clearing house is $10,000 for your 10 futures contracts. After three months, the futures price decreases to $1,525 per troy ounce. Assume that you did not replenish the margin and there was no margin calls over the three months. What is the balance in your margin account in three months? (3 marks) Part c) is not related to Parts a) b). c). The price of 1-year index futures contract for S&P 500 is 3,000, while the current S&P 500 index value is 2,952. It is also known that the dividend yield on S&P 500 is 1% per year compounded annually. Assume you can borrow and lend money at the riskless rate of 2% per year compound annually. Also, you can buy and short sell the S&P 500 index now. Design an arbitrage strategy and show that the strategy has a zero cost with a sure profit at the end of Year 1. (5 marks) Question 4 (10 marks) Suppose the spot price of gold is $1,500 per troy ounce today. The futures price of gold for delivery in 1 year is $1,530 per troy ounce. Assume that the one-year gold futures contract is correctly priced and there are no storage and insurance costs. Also assume that the risk-free rate is compounded annually and you can borrow and lend money at the risk-free rate. a). What is the theoretical parity price of a two-year gold futures contract, assuming a flat yield curve (same interest rates for all maturities)? (2 marks) b). Suppose you short 10 one-year gold futures contracts today and the contract size is 100 troy ounces. The initial margin requited by the clearing house is $10,000 for your 10 futures contracts. After three months, the futures price decreases to $1,525 per troy ounce. Assume that you did not replenish the margin and there was no margin calls over the three months. What is the balance in your margin account in three months? (3 marks) Part c) is not related to Parts a) b). c). The price of 1-year index futures contract for S&P 500 is 3,000, while the current S&P 500 index value is 2,952. It is also known that the dividend yield on S&P 500 is 1% per year compounded annually. Assume you can borrow and lend money at the riskless rate of 2% per year compound annually. Also, you can buy and short sell the S&P 500 index now. Design an arbitrage strategy and show that the strategy has a zero cost with a sure profit at the end of Year 1
