An investor has just taken a short position in a six-month forward contract on a dividend-paying stock. The stock price is 132.00, and the risk-free rate of interest is 3 | Page 6% per annum with continuous compounding for all maturities. The stock is expected to pay a dividend of 2 per share in two months and in five months.

Required

(a) What are the forward price and the initial value of the forward contract? (2 marks)

(b) Three months later, the price of the stock is 48 and the risk-free rate of interest is still 6% per annum. What are the forward price and the value of the short position in the forward contract? (3 marks)

The risk-free rate of interest is 5% per annum with continuous compounding, and the dividend yield on a stock index is 3.5% per annum. The current value of the index is 1,000.

Required

(c) What is the six-month futures price? (2 marks)

(d) Assume that the futures price for a contract deliverable in six months is 1,015. What arbitrage opportunities does this create? (3 marks)

(e) The futures price of gold can be calculated from its spot price and other observable variables whereas the futures price of copper cannot. Discuss why this is the case.