Donald wants to buy $100 000 (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 j2 = 5.0% p.a. and he is able to borrow or invest for periods of up to one year at a rate of j12 = 6.0% p.a.

a. Draw a cash flow diagram representing the forward contract into which Donald wishes to enter.

b. Draw a cash flow diagram representing the cash flows associated with the 4-year Treasury bond mentioned above (with a face value of $100 000). (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. 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. 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. Vladimir offers Donald a $100000 3-year 6% p.a. Treasury bond at the end of 12 months at a forward rate of j2 = 5.0% p.a.

e. Donald has an arbitrage opportunity here. Explain how it arises and how Donald can exploit it (no calculations are required).

f. How much arbitrage profit can Donald earn in these circumstances?