1 A grapefruit producer/processor will be selling in three months 50,000 gal- lons of grapefruit juice but she is worried about the possibility that in that time the price of grapefruit might tank so she wants to hedge using futures contracts. As there are no futures contracts on grapefruit juice she will use futures contracts on orange juice which are available in the futures markets. Currently, the prices per gallon of orange juice and grapefruit juice are $1.20 and $1.50, respectively. From historical data, she determines that the standard deviation of the prices of orange juice and grapefruit juice are 20% and 22% per year, respectively; and that the correlation coefficient between them is 0.75. She wants to implement a minimum variance hedge. Find a The optimal value of the hedging ratio h; b The variance of her final cash flow (her cash flow at the end of the three months) if she does not hedge at all; c The variance of her final cash flow if she does implement the minimum variance hedge