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Example 3.5 Calculation of the minimimum variance hedge ratio An airline expects to purchase two million gallons of jet fuel in one month and decides
Example 3.5 Calculation of the minimimum variance hedge ratio An airline expects to purchase two million gallons of jet fuel in one month and decides to use heating oil futures for hedging. We suppose that Table 3.2 gives, for 15 successive months, data on the change, AS, in the jet fuel price per gallon and the corresponding change, AF, in the futures price for the contract on heating oil that would be used for hedging price changes during the month. To evaluate the minimum variance hedge ratio, we can use the STDEV and CORREL functions in Excel to obtain o p = 0.0313, os = 0.0263, and p= 0.928. Equation (3.1) then gives 0.0263 h* = 0.928 x = 0.7777 0.0313 Alternatively we can use the SLOPE function in Excel to get this answer directly. (See worksheet on author's website for the calculations.) This result means that the airline should hedge by taking a position in heating oil futures corresponding to 77.77% of its exposure. The hedge effectiveness is 0.9282 = 0.862. = Month Std Dev of heating oil futures Std Dev of Jet Fuel spot price Correlation 1 Minimum Variance Hedge Ratio (eqn 3.1) Change in heating Change in jet oil futures fuel price Change in F Change in S 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 1 -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 2 Minimum Variance Hedge Ratio (slope function) 3 Hedge effectiveness (correlation squared/R squared in regression function) 4 Number of Contracts (eqn 3.2)
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CHAPTER 3 Example 3.5 Calculation of the minimimum variance hedge ratio An airline expects to purchase two million gallons of jet fuel in one month and decides to use heating oil futures for hedging. We suppose that Table 3.2 gives, for 15 successive months, data on the change, AS, in the jet fuel price per gallon and the corresponding change, AF, in the futures price for the contract on heating oil that would be used for hedging price changes during the month. To evaluate the minimum variance hedge ratio, we can use the STDEV and CORREL functions in Excel to obtain o p = 0.0313, os = 0.0263, and p= 0.928. Equation (3.1) then gives 0.0263 h* = 0.928 x = 0.7777 0.0313 Alternatively we can use the SLOPE function in Excel to get this answer directly. (See worksheet on author's website for the calculations.) This result means that the airline should hedge by taking a position in heating oil futures corresponding to 77.77% of its exposure. The hedge effectiveness is 0.9282 = 0.862. = Month Std Dev of heating oil futures Std Dev of Jet Fuel spot price Correlation 1 Minimum Variance Hedge Ratio (eqn 3.1) Change in heating Change in jet oil futures fuel price Change in F Change in S 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 1 -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 2 Minimum Variance Hedge Ratio (slope function) 3 Hedge effectiveness (correlation squared/R squared in regression function) 4 Number of Contracts (eqn 3.2) CHAPTER 3 Example 3.5 Calculation of the minimimum variance hedge ratio An airline expects to purchase two million gallons of jet fuel in one month and decides to use heating oil futures for hedging. We suppose that Table 3.2 gives, for 15 successive months, data on the change, AS, in the jet fuel price per gallon and the corresponding change, AF, in the futures price for the contract on heating oil that would be used for hedging price changes during the month. To evaluate the minimum variance hedge ratio, we can use the STDEV and CORREL functions in Excel to obtain o p = 0.0313, os = 0.0263, and p= 0.928. Equation (3.1) then gives 0.0263 h* = 0.928 x = 0.7777 0.0313 Alternatively we can use the SLOPE function in Excel to get this answer directly. (See worksheet on author's website for the calculations.) This result means that the airline should hedge by taking a position in heating oil futures corresponding to 77.77% of its exposure. The hedge effectiveness is 0.9282 = 0.862. = Month Std Dev of heating oil futures Std Dev of Jet Fuel spot price Correlation 1 Minimum Variance Hedge Ratio (eqn 3.1) Change in heating Change in jet oil futures fuel price Change in F Change in S 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 1 -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 2 Minimum Variance Hedge Ratio (slope function) 3 Hedge effectiveness (correlation squared/R squared in regression function) 4 Number of Contracts (eqn 3.2)Step by Step Solution
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