Question

A food company is planning to purchase 5,000,000 pounds of beef in six months. The company is concerned about changes in the price of beef. Your assignment is to construct a futures contract hedge to protect the company’s cost. The current wholesale price of beef is 106 Cents per pound.

The livestock futures contracts are for 40,000 pounds. The futures contract quoted price is Cents per pound. The coefficient of correlation between livestock and beef is 0.93. The standard deviation of livestock and beef are 56.35 and 68.25 respectively.

The available futures contracts are This information was downloaded from CME Group website:

Month	Last (cents)	Change	Prior Settle	Open	High	Low
Aug-18	106.075	-0.3	106.375	106.85	107.325	105.775
Oct-18	108.65	-0.975	109.625	109.9	110.275	108.3
Dec-18	112.825	-0.875	113.7	113.775	114.05	112.4
Feb-19	116.325	-0.2	116.525	116.5	116.775	115.35
Apr-19	117.825	-0.425	118.25	118.45	118.45	117.125
Jun-19	110.65	-0.5	111.15	111.175	111.175	110
Aug-19	109.675	-0.325	110	109.7	110	108.95
Oct-19	111	-0.6	111.6	111	111	111

(Your assignment is to construct a futures contract hedge to protect the company’s cost.)

Answer 1

Answer:

Planning purchase in six months, which is Jan 2019. The closest future contract is Feb 2019.

The hedge ratio = Correlation * Standard Deviation of beef / Standard deviation of livestock

= 0.93 * 68.25 / 56.35 = 1.1264

The number of future contract = The hedge ratio * Quantity demanded / futures contract

= 1.1264 * 5,000,000 / 40,000 = 140.799 = 141

Therefore, we should long 141 contracts of Feb 2019 livestock futures at a future price of $116.325 per pound. The initial cost of this position is zero. The effective cost of the beef relies on hedge effectiveness and the interest of the margin account.