A farmer has a crop of grapefruit juice that will be ready for harvest and sale as 150000 pounds of grapefruit juice in 3 months. He is worried about possible price changes, so he is considering hedging - a financial engineering technique that minimizes future uncertainties in the cash flow. Typically, hedging is carried out using futures contract. However, unfortunately, there is no futures contract for grapefruit juice, but there is a futures contract for orange juice. Still, the farmer might consider using the futures contract for orange juice as a replacement for futures contract for grapefruit juice, in the hope that these two contracts are highly correlated due to the similarity of the underlying products. Currently, the spot prices are $1.20 per pound for orange juice and $1.50 per pound for grapefruit juice. The standard deviation of the prices of orange juice and grapefruit juice is about 20% per year, and the correlation coefficient between their prices is about 0.7 (highly correlated). What is the minimum variance hedge for farmer, i.e. how many orange juice futures contracts does the farmer need to purchase in total?

A farmer has a crop of grapefruit juice that will be ready for harvest and sale as 150000 pounds of grapefruit juice in 3 months. He is worried about possible price changes, so he is considering hedging - a financial engineering technique that minimizes future uncertainties in the cash flow. Typically, hedging is carried out using futures contract. However, unfortunately, there is no futures contract for grapefruit juice, but there is a futures contract for orange juice. Still, the farmer might consider using the futures contract for orange juice as a replacement for futures contract for grapefruit juice, in the hope that these two contracts are highly correlated due to the similarity of the underlying products. Currently, the spot prices are $1.20 per pound for orange juice and $1.50 per pound for grapefruit juice. The standard deviation of the prices of orange juice and grapefruit juice is about 20% per year, and the correlation coefficient between their prices is about 0.7 (highly correlated). What is the minimum variance hedge for farmer, i.e. how many orange juice futures contracts does the farmer need to purchase in total?

Intermediate Financial Management (MindTap Course List)

13th Edition

ISBN:9781337395083

Author:Eugene F. Brigham, Phillip R. Daves

Publisher:Eugene F. Brigham, Phillip R. Daves

Chapter14: Real Options

Section: Chapter Questions

Problem 4MC

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Question: (Minimum-variance Hedging) A farmer has a crop of grapefruit juice that will be ready for harvest and sale as 150000 pounds of grapefruit juice in 3 months. He is worried about possible price changes, so he is considering hedging - a financial engineering technique that minimizes future uncertainties in the cash flow. Typically, hedging is carried out using a futures contract. However, unfortunately, there is no futures contract for grapefruit juice, but there is a futures contract for orange juice. Still, the farmer might consider using the futures contract for orange juice as a replacement for futures contract for grapefruit juice, in the hope that these two contracts are highly correlated due to the similarity of the underlying products. Currently, the spot prices are $1.20 per pound for orange juice and $1.50 per pound for grapefruit juice. The standard deviation of the prices of orange juice and grapefruit juice is about 20% per year, and the correlation coefficient…
uestion: (Minimum-variance Hedging) A farmer has a crop of grapefruit juice that will be ready for harvest and sale as 150000 pounds of grapefruit juice in 3 months. He is worried about possible price changes, so he is considering hedging - a financial engineering technique that minimizes future uncertainties in the cash flow. Typically, hedging is carried out using a futures contract. However, unfortunately, there is no futures contract for grapefruit juice, but there is a futures contract for orange juice. Still, the farmer might consider using the futures contract for orange juice as a replacement for futures contract for grapefruit juice, in the hope that these two contracts are highly correlated due to the similarity of the underlying products. Currently, the spot prices are $1.20 per pound for orange juice and $1.50 per pound for grapefruit juice. The standard deviation of the prices of orange juice and grapefruit juice is about 20% per year, and the correlation coefficient…
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