Billy is interested in shares in Dillon Ltd. Billy would like to enter a long forward position on 1 share in Dillon Ltd with counterparty Dutch, to be executed in 6 months time. The current price for a share in Dillon Ltd is $50. The risk-free rate of return is 5% p.a. compounding continuously, and anyone on the market is free to lend or borrow at this rate. For this question, ignore any transaction fees, taxes, and other expenses.

a) Once Billy and Dutch enter into the forward contract described above, has Billy agreed to buy a share, or sell a share, in 6 months time? [1 mark]

b) Calculate the arbitrage-free forward price that Billy and Dutch should use in their forward contract using the information provided above. [2 marks]

c) Suppose that Billy and Dutch have agreed to the forward price you calculated in part b), and 2 months have passed. The price for a share in Dillon Ltd. is now $53, and the risk-free rate of return is now 4% p.a. compounding continuously. What is the value of this contract from Billys perspective? [4 marks]

d) Given your results in part c), what is the value of the forward contract from Dutchs perspective? [1 mark]

e) Billy, thinking back to when he first entered the contract with Dutch, remembered a particular trader named Mac. Mac was willing to write forward contracts, long or short, to be executed in 6 months, for a forward price of $50.90. Using your result from part b), describe how Billy could have traded with Mac to make an arbitrage profit. Note: you do NOT need to perform any calculations for this part. [2 marks