04 An airline expects to 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 heating oil is used to hedge purchase of jet fuel Month Change in heating oil futures Change in jet fuel price Af AS 0.021 0.029 2 0.035 0.020 3 -0.046 -0.044 4 0.001 0.008 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 -0.027 -0.032 15 0.029 0.023 o Af=0.0313 O AS = 0.0263 Corr Af. AS = 0.928 Month 1 6 7 8 9 10 11 12 13 14 15 Change in heating oil futures 0.021 0.035 -0.046 0.001 0.044 -0.029 -0.026 -0.029 0.048 -0.006 -0.036 -0.011 0.019 -0.027 0.029 Change in jet fuel price AS 0.029 0.020 -0.044 0.008 0.026 -0.019 -0.010 -0.007 0.043 0.011 -0.036 -0.018 0.009 -0.032 0.023 G Af = 0.0313 O AS = 0.0263 Corr Af. AS 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