Question Accounting Q A stock sells at $55 and is expected to pay a dividend of $1 per share at the end of each quarter from today. The risk free interest rate is 4% per annum continuously compounded for all maturities. An investor takes a long position on the eleven-month forward contract today. (a) What is the theoretical eleven-month forward price? (2 marks) (b) The current eleven-month forward price in the market is $53. Is there an arbitrage opportunity? Please show all the details. (3 marks) (c) Based on part b) above, what will be the value of the forward contract seven months from now if the forward price in seven months is $51? (1 mark) Question 2 (9 marks) You are presented with the following market quotes: Currency market Spot exchange rate: CAD 1.6688 / GBP Three-month forward: 1.6647 Six-month forward: 1.6612 AP/ADMS4503 M&N Assignment #1 Winter 2016 Page 2 Nine-month forward: 1.6585 Canadian Treasury bill yields Three-month: 3.95% Six-month: 4.15% Nine-month: 4.30% (a) Compute the three-month, six-month and nine-month interest rates that you should expect to observe in the U.K. market. (3 marks) (b) Suppose that the six-month U.K. interest rate is 5.15% instead. Is there any arbitrage profit to be made? Please show all the details. Use 1,000 units of either CAD or GBP in your answer. (3 marks) (c) Now suppose that the nine-month U.K. interest rate is in fact 4.20%. Is there an arbitrage opportunity? Please show all the details. Use 1,000 units of either CAD or GBP in your answer. (3 marks) Question 3 (6 marks) The following table shows some hypothetical data on the monthly changes in the spot price and futures price of a commodity. Also assume that you want to purchase 10,000 units of the commodity in one month from now. S (in $)  4.00 2.45 1.96 1.87 2.36 -1.40 1.00 0.00 0.50 -2.00 F (in $)  -1.84 1.80 -2.00 1.50 3.00 2.46 0.12 1.30 -2.00 3.00 (a) If each futures contract is for a delivery of 100 units of the commodity, what position should you take, i.e., long vs. short and number of contracts? (3 marks) (b) The futures price today is $47 per unit. Suppose in one month from today when you close out your hedging position, the futures price and the spot price at that time are both $53 per unit. What is the effective cost per unit for the commodity? Did the hedge work in your favour? (3 marks) Question 4 (6 marks) A portfolio manager wants to use the CME futures contracts on the S&P 500 index to hedge her portfolio worth $50 million over the next six months. The beta of the portfolio is 1.5. The index level is now 1,120 and each contract is on $250 times the index. The S&P 500 dividend yield is 2% and the risk free interest rate is 4%. Both rates are annual and continuously compounded. (a) What is the six-month futures price? (1 mark) (b) How many long or short futures contracts should the manager take?