a. The current price of a stock is $52 and the stock is expected to pay a dividend of $4 in three months time. The risk-free rate of return is 5.00% p.a. (continuously compounded). If the price on a eight month forward contract is F_0,8/12 = $50, is there an arbitrage opportunity? If arbitrage is possible, design a strategy to take advantage of it. What is the arbitrage profit earned from this strategy? (6 marks) b. A fund manager has a bond portfolio worth $100 million. The (Macaulay) duration of the portfolio in October will be 8.2 years. The December 10-year Treasury bond futures price is currently 94.37 (implying a yield of 5.63% p.a.) with duration 7.7 years. How should the portfolio manager immunise the portfolio against changes in interest rates (i.e. target zero duration) over the next two months? Remember that the assumed coupon rate for the Treasury bond futures is 6% p.a. (semi-annual) with a face value of $100,000. (5 marks)