Question

A barley farmer fearing of falling barley prices can use wheat futures to hedge. The two grains have a 0.8 correlation. Barley price changes have a standard deviation of 0.2 and wheat price changes have a standard deviation of 0.4.

Barely harvest is expected in October. The farmer should use the ______________ (March/June/September/December) wheat contract.

The sensitivity (beta) of barely price changes to wheat price movements is ______________ (round to two decimals).

Rounded to the nearest integer, the farmer will need to go____________ (<--write long or short) of  number of _______________ wheat contracts if he is expecting his barley harvest to yield about $300,000 worth of grain and the value of one contract of wheat futures is currently 10,000.

Answer 1

Barely harvest is expected in October. The farmer should use the September (We have to take the futures contracts that is nearer to the transaction date) wheat contract.

The sensitivity (beta) of barely price changes to wheat price movements is 0.40 (Correlation * SD of Barley * SD of Wheat / Variance of Wheat) = 0.8 * 0.2 * 0.4 / 0.4^2 (round to two decimals).

Rounded to the nearest integer, the farmer will need to go Short (Because the farmer is going to sell on a future date)of  number of 12 (300000 * 0.40 / 10000) wheat contracts if he is expecting his barley harvest to yield about $300,000 worth of grain and the value of one contract of wheat futures is currently 10,000.