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

Calculate the forward rates given the following zero rates.

Year	Zero rate	Forward rate
1	3.5
2	3.75
3	4.5
4	5.0

Answer 1

Optimal Hedge Ratio = Std. Dev. of Bief*correlation/Std. Dev. of Live Stock

= 68.25*0.93/56.35

= 1.1264

No of Contracts required = (Bief Required*Optimal Hedge Ratio)/No of Contracts

= (5000000*1.1264/400000)

= 14.08 Contracts

To Hedge the Future volitility of the prices we have to take the 14.08 Live Stock.

for the first year Zero rate and forward rate both are same that means the forward rate for the first year = 3.5%

Year 2 (forward rate) = (1+3.75%)^2/(1+3.5%)-1 = 4%

Year 3 (Forward Rate) = (1+4.5%)^3/(1+3.75%)^2-1= 6.02%

Year 4 (Forward Rate) = (1+5%)^4/(1+4.5%)^3 - 1 = 6.51%