QUESTION 6 (14 marks] Donald wants to buy $100000 (face value) of a 3-year 6% p.a. Treasury bond in twelve months' time and wants to 'lock in the price today. Donald wants to arrange a forward contract to buy the bond after 12 months, and seeks to calculate the arbitrage-free forward rate of i per half-year. He is aware that the yield on an 4-year 6% p.a. Treasury bond in the spot market is currently 12 = 5.0% p.a. and he is able to borrow or invest for periods of up to one year at a rate of 112 = 6.0% p.a. a. [2 marks] Draw a cash flow diagram representing the forward contract into which Donald wishes to enter. b. [2 marks] Draw a cash flow diagram representing the cash flows associ- ated with the 4-year Treasury bond mentioned above with a face value of $100000). (Leave plenty of space above and below your diagram, as you will amend your diagram in a different colored ink in the question below.) What is its current price? c. [3 marks] By amending your cash flow diagram from b. in a different coloured ink, carefully explain how Donald could replicate the cash flows associated with the forward contract you drew in a. d. [3 marks] Calculate the arbitrage-free forward price for a $100 000 3- year 6% p.a. Treasury bond that Donald should pay in twelve months' time. QUESTION 6 (14 marks] Donald wants to buy $100000 (face value) of a 3-year 6% p.a. Treasury bond in twelve months' time and wants to 'lock in the price today. Donald wants to arrange a forward contract to buy the bond after 12 months, and seeks to calculate the arbitrage-free forward rate of i per half-year. He is aware that the yield on an 4-year 6% p.a. Treasury bond in the spot market is currently 12 = 5.0% p.a. and he is able to borrow or invest for periods of up to one year at a rate of 112 = 6.0% p.a. a. [2 marks] Draw a cash flow diagram representing the forward contract into which Donald wishes to enter. b. [2 marks] Draw a cash flow diagram representing the cash flows associ- ated with the 4-year Treasury bond mentioned above with a face value of $100000). (Leave plenty of space above and below your diagram, as you will amend your diagram in a different colored ink in the question below.) What is its current price? c. [3 marks] By amending your cash flow diagram from b. in a different coloured ink, carefully explain how Donald could replicate the cash flows associated with the forward contract you drew in a. d. [3 marks] Calculate the arbitrage-free forward price for a $100 000 3- year 6% p.a. Treasury bond that Donald should pay in twelve months' time
