A farmer is currently growing wheat and plans to sell it in September next year. He needs to plan his budget now, because of upcoming expenses. Suppose that the futures price of wheat for September delivery is 100 per ton. There is 50% probability that the spot price of wheat in September will be 90 per ton or 110 per ton.

a) Suppose that the farmer is certain that he will need to sell 2 tons of wheat in September. Explain how the farmer could lock in today his

future revenue.

b) Suppose now that the farmer is not certain about the quantity of wheat he will produce and therefore will need to sell in September. For each possible price of wheat, there are two equally likely quantities, i.e., there are four equally likely price-quantity pairs, which are shown in the Table below.

i.

Suppose the farmer takes a futures position on his expected production of wheat in September. Will this strategy help him reduce his risk? Explain why.

ii.

Design a hedging strategy that minimizes the variance of the farmers revenue in September.

Price () 90 90 110 110 Production (tons) 2.5 1.8 2 1.5 Price () 90 90 110 110 Production (tons) 2.5 1.8 2 1.5