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

Question

Suppose a farmer is expecting that her crop of grapefruit will be ready for harvest and sale as 150,000 pounds of grapefruit juice in 3 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 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 0.7. What is the approximate number of contracts she should purchase to minimize the variance of her payoff?

Explanation / Answer

Cross hedging and cross hedging

Total Quantity pf Grape Juice = 150,000 pound

Quantity of one contract = 15,000 Pound

Standard deviation of orange juice (SDO = 20%

Standard deviation of Grape Juice (SDG) = 25%

Correlation coefficient = 0.7

First of all calculate hedge ratio as calculated below using following formula:

Hedge ratio = Correlation coefficient × SDO / SDG

                    = 0.7 × 20% / 25%

                    = 0.56

Hedge ratio is 0.56.

Now number of contract is calculated below using following formula:

Number of contract = (Hedge ratio × Total Quantity of Grape Juice) / Quantity of one contract

                                 = (0.56 ×150,000) / 15,000

                                 = 5.6 contract

Hence, total number of contract is 5.6 contract.

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