You have been working as a futures trader at Deutsche Bank, New York

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Question

You have been working as a futures trader at Deutsche Bank, New York. You have collected the
following information on Lean Hog. The standard deviation of monthly changes in the spot price of Lean
Hog Futures is (in cents per pound) 6. The standard deviation of monthly changes in the futures price of
Lean Hog Futures the closest contract is 8. The correlation between the futures price changes and the
spot price changes is 0.8. It is now December 17, 2019. Your client, a pork producer, is committed to
purchasing 400,000 pounds of lean hog on January 15. The producer wants to use February Lean Hog
futures contracts to hedge its risk. Each contract is for the delivery of 80,000 pounds of cattle.




a. What is the optimal hedge ratio?Blank 1 (sample answer: 0.75)




b. Should the pork producer take a long or short hedge?Blank 2(sample answer:Long; or Short)




c. How many contracts of lean hog futures does your client need to take to hedge the risk? Blank 3
(sample answer: 7 Contracts)

Answer

a. Optimal Hedge Ratio (h)

The optimal hedge ratio is calculated as:

h=ρ×σS/σFh

Where:

 ρ\rhoρ = Correlation between spot and futures price changes = 0.8

 σS\sigma_SσS = Standard deviation of spot price changes = 6

 σF\sigma_FσF = Standard deviation of futures price changes = 8

=0.6


Answer (a): Optimal Hedge Ratio = 0.6