Consider a forward contract written on 25 tonnes of zinc, a metal that is currently trading at US$2,000 per tonne in the cash or spot market. Contract settlement is by making or taking delivery of 25 tonnes of zinc on contract settlement date. Zinc storage costs are US$0.40 per tonne per day, paid in arrears, and the risk free rate is 2% p.a. on a continuously compounded basis.

(a) Calculate the theoretical price of a zinc forward contract with 90 days to settlement.

(b) Consider an arbitrageur who does not hold any position in zinc. Show how this arbitrageur could make an arbitrage profit when the 90-day forward price is US$2,055. You should assume the arbitrageur takes an initial position (either short or long) of one forward contract. Your arbitrage strategy should be structured so that the net cash flow at initiation (time 0) is zero.