QUESTION

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# Suppose that Tesco will be in need of 70 tonnes of flour in 6 months, but currently has no storage space to buy at the spot price of $£ 1,243$ per tonne and store it until it is needed. However, Tesco expects the flour prices to rise which creates financial problems to the company. Assume that the continuously compounded interest rate is $r=5 \%$. (a) Explain how Tesco can hedge its position by entering a forward contract on flour. In particular, provide the following details: position (short/long), underlying asset and size of the contract, maturity $T$ and forward price. (b) Suppose that after 4 months the spot price for 1 tonne of flour is $£ 1,294$ and Tesco decides to close its position. Using the formula $V_{t}=70 S_{t}-70 S_{0} e^{r t}$ for the value of the long forward contract at time $t$, calculate the value of the forward contract for Tesco at $t=4$ months and specify if Tesco pays or receives such amount. (c) Suppose that at 4 months Tesco agrees to sell Waitrose the forward contract for $£ 1,400$, namely Tesco receives $£ 1,400$ at 4 months and has no obligation at 6 months, and Waitrose pays $£ 1,400$ at 4 months and will have to buy 70 tonnes of flour at 6 months at the forward price calculated in part (a). Construct an arbitrage strategy (for Waitrose) using ZCBs and forward contracts only (the arbitrage strategy should be set up at the current time of 4 months). Show that the strategy you identified leads to arbitrage.  