Consider a 6-month futures contract on S&P/ASX200 index. The index itself trades at 5000 points (Multiplier...

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Consider a 6-month futures contract on S&P/ASX200 index. The index itself trades at 5000 points (Multiplier is $25 for this index) and pays no dividend. The 6-month LIBOR rate is 7% p.a. continuously compounded. Assume short selling is allowed and possible, no transaction costs and no daily settlement (i.e. futures and forwards are the same). a) Calculate the future price for the above contract. Use No-Arbitrage arguments to show that if the observed futures price is 5,300, there is arbitrage opportunity on the market. (6 marks) b) You have a position in Qantas of 100,000 shares, which currently trades at a price of $3 per share, which you want to hedge with the above futures. Qantas has a beta of ß= 0.8 with the above index. Calculate the optimal number of contracts and determine the position you need to take. Assume that you open the position when the futures price has value of 5178.10. (4 marks) c) You close your position 2 months before the futures contract expires and sell the shares. At that time Qantas trades at a price of $2.60, the index is at a level of 4,650 and the futures contract trades at 4,715. If you sold shares at this time, how much would you receive for each share taking the hedge into account? (6 marks) Consider a 6-month futures contract on S&P/ASX200 index. The index itself trades at 5000 points (Multiplier is $25 for this index) and pays no dividend. The 6-month LIBOR rate is 7% p.a. continuously compounded. Assume short selling is allowed and possible, no transaction costs and no daily settlement (i.e. futures and forwards are the same). a) Calculate the future price for the above contract. Use No-Arbitrage arguments to show that if the observed futures price is 5,300, there is arbitrage opportunity on the market. (6 marks) b) You have a position in Qantas of 100,000 shares, which currently trades at a price of $3 per share, which you want to hedge with the above futures. Qantas has a beta of ß= 0.8 with the above index. Calculate the optimal number of contracts and determine the position you need to take. Assume that you open the position when the futures price has value of 5178.10. (4 marks) c) You close your position 2 months before the futures contract expires and sell the shares. At that time Qantas trades at a price of $2.60, the index is at a level of 4,650 and the futures contract trades at 4,715. If you sold shares at this time, how much would you receive for each share taking the hedge into account? (6 marks)