The standard deviation of monthly changes in the spot price of live cattle is (in cents per pound) 1.35. The standard deviation of monthly changes in the futures price of live cattle for the closest contract is 0.8. The correlation between the futures price changes and the spot price changes is 0.7. It is now October 15. The futures price and the spot price are 367 and 355 cents per pound respectively. A beef producer is committed to selling 496,000 pounds of live cattle on November 15. The producer wants to use the December live-cattle futures contracts to hedge its risk. Each contract is for the delivery of 40,000 pounds of cattle.
To hedge this risk optimally, how many contracts will the producer need? Will the producer take a long or short position?