Suppose a farmer is expecting that her crop of oranges will be ready for harvest and sale as 150,000 pounds of orange juice in 3 months time. Suppose each orange juice futures contract is  for 15,000 pounds of orange juice, and the current futures price is F0 = 118.65 cents-per-pound. The volatility, i.e. the standard deviation, of the prices of orange juice and grape fruit juice is 20% and 25%, respectively, and the correlation coefficient is 0.70.  What is the approximate number of contracts she should purchase to minimize the variance of her payoff?

Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
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Suppose a farmer is expecting that her crop of oranges will be ready for harvest and sale as 150,000 pounds of orange juice in 3 months time. Suppose each orange juice futures contract is  for 15,000 pounds of orange juice, and the current futures price is F0 = 118.65 cents-per-pound.

The volatility, i.e. the standard deviation, of the prices of orange juice and grape fruit juice is 20% and 25%, respectively, and the correlation coefficient is 0.70.  What is the approximate number of contracts she should purchase to minimize the variance of her payoff?

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