Hull.03.16
Category:Hull -> Chapter 03
Questions:
The standard deviation of monthly changes in the spot price of live cattle is (in cents per pound) 1.2. The standard deviation of monthly changes in the futures price of live cattle for the closest contract is 1.4. The correlation between the futures price changes and the spot price changes is 0.7. It is now October 15. A beef producer is committed to purchasing 200,000 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. What strategy should the beef producer follow?
Answers:
03.16 .The optimal hedge ratio is
0.7 x 1.2/1.4 = 0.6
The beef producer requires a long position in 200000 x 0.6 = 120,000 lbs of cattle. The beef producer should therefore take a long position in 3 December contracts closing out the position on November 15.
03.16b. To tail the hedge, replace size with values:
Instead of: Optimal number of contracts = hedge ratio * Size of Position / Size of 1 futures contract
Use: Optimal number of contracts = hedge ratio * Value of Position / Value of 1 futures contract
In this case, value of position = 0.70 * 200,000 = $140,000 and value of 1 futures contract = $1 & 40,000 = $40,000
Such that “tailing the hedge” implies = 0,6 * $140,000/$40,000 = 2.1 or about 2 contracts