The variance of monthly changes in the spot price of live cattle is (in cents per pound)is 1.7.The variance of monthly changes in the futures price of live cattle for the April contract is 1.5.The correlation between these two price changes is 0.75.Today is March 11.The beef producer is committed to purchasing 400,000 pounds of live cattle on April 15.The producer wants to use the April cattle futures contract to hedge its risk.How many contracts should the producer buy,if the contract size is 40,000 pounds?

Question

Quizplus · Accepted Answer

The first step in calculating the number of futures contracts to purchase is to determine the variance of the change in the spot price of live cattle that is not accounted for by changes in the futures price. This is given by:

σ_spot^2 = σ_total^2 - σ_futures^2 - 2ρσ_totalσ_futures
where
σ_total = 1.7^(0.5) = 1.305
σ_futures = 1.5^(0.5) = 1.225
ρ = 0.75

Plugging in the values, we get:

σ_spot^2 = (1.7 - 1.5 - 2*0.75*1.305*1.225) = 0.522

The second step is to calculate the number of futures contracts needed to hedge the 400,000-pound purchase of live cattle. This is given by:

Number of contracts = (Weight of cattle to be purchased) / (Contract size) * (σ_total/σ_futures)

Plugging in the values, we get:

Number of contracts = 400,000/40,000 * (1.305/1.225) = 8.44

We need to round up to the nearest integer, so the answer is 8.

The Variance of Monthly Changes in the Spot Price of Live