Suppose a farmer is expecting that her crop of grapefruit will be ready for

harvest and sale as150,000

pounds of grapefruit juice in3

months time. She would like to use futures to hedge her risk but unfortunately there

are no futures contracts on grapefruit juice. Instead she will use orange juice futures.

Suppose each orange juice futures contract is for15,000

pounds of orange juice and the current futures price isF

0

=118.65

cents-per-pound.

The volatility, i.e. the standard deviation, of the prices of

orange juice and grape fruit juice is20%

and25%

, respectively,

and the correlation coefficient is0.7

. What is the approximate number

of contracts she should purchase to minimize the variance of her payoff?

Please submit your answer rounded to the nearest integer. So for example, if your calculations result in 10.78 contracts you should submit an answer of 11.