Q4. An airline expects 10 purchase 2.5 million gallons of jet fuel in 1 month and decides to use heating oil

futures for hedging. Table gives 15 successive months of data on change of spot price and change of heating

oil futures contract

Table: Data to calculate minimum variance hedge ratio when heat mg oil is used to hedge purchase of jet fuel

Month	Change in Heating Oil Futures	Change in Jet Fuel Price
1	0.021	0.029
2	0.035	0.020
3	-0.046	-0.044
4	0.001	0.008
5	0.044	0.026
6	-0.029	-0.019
7	-0.026	-0.010
8	-0.029	-0.007
9	0.048	0.043
10	-0.006	0.011
11	-0.036	-0.036
12	-0.011	-0.018
13	0.019	0.009
14	-0.027	-0.032
15	0.029	0.023

Stdev of Heating Oil Futures = 0.0313

Stdev of Jet Fuel Prices = 0.0263

Correlation (Chg in Heating Oil Futures, Chg Jet Fuel Prices) = 0.928

Using minimum variance hedge ratio, calculate the optimal number of futures contracts that are needed to

hedge the risk. Each heating oil contract traded by CME group is on 45,000 gallons of heating oil. Also

calculate the effectiveness of hedging. Would you go long or short to hedge the risk? Show all calculations.