1) The estimate of expected fuel consumption for year 2008 is 1511000000 gallons. We assume that the fuel consumption is uniform across months. Then the estimated fuel consumption for 2008Q1 will be 1511000000/4=377750000 gallons. Since we need to hedge 75% of the expected fuel consumption over 2008Q1, the amount of fuel we need to hedge over 2008Q1 will be 75%×377750000=283312500 gallons, 283312500/3=94437500 gallons each month. Because the crude oil futures contracts trade in units of 1000 U.S. barrels (42000 gallons), the total number of contract we need to enter will be 283312500 gallons/42000 gallons= 6745.5 We have three contracts (Feb.08, Mar.08, Apr.08) available. Our strategy is: On Dec 31st 2007, we long 6745.5/3=2248.5 contracts for each one, i.e., we long 2248.5 Feb.08 contracts, 2248.5 Mar.08 contracts, and 2248.5 Apr.08 contracts. On January 22nd, the last day of Feb.08 contract trading date, we short 2248.5 Feb.08 contracts to close the position and buy 377750000/3=125920000 gallons for January consumption. On February 20th, the last day of Mar.08 contract trading date, we short 2248.5 Mar.08 contracts to close the position and buy 377750000/3=125920000 gallons for February consumption. On March 19th, the last day of Apr.08 contract trading date, we short 2248.5 Mar.08 contracts to close the position and buy 377750000/3=125920000 gallons for March consumption
2) On March 22nd, 2008, we calculate the P&L of the hedging strategy. Feb.08 contract P&L：
The P&L of the future is (89.85-95.98)/42= -0.146$/gallon So the P&L of the total future is 94437500×(-0.146)=-13787875$. The Jet fuel price that Southwest would implicitly pay is: 125920000×2.54+13787875=319836800+13787875=333624675$ The actual price is 125920000×2.54=319836800$
The hedge is not beneficial.
Mar.08 contract P&L:
The P&L of the future is (100.74-95.98)/42= 0.1133$/gallon So the P&L of the...