It is August 31, 2020, You are working for Southwest Airlines risk management division and are concerned about potentially rising jet fuel costs over the next 12 months. According to the 2020 Annual Report? You wish to hedge your exposure to some percentage of your future purchase - the predicted amount is 1.82 billion gallons of jet fuel. However, there are no liquid futures contracts on jet fuel available (some are now listed but with low volumes). You have narrowed down your search for a suitable hedging instrument to futures contracts* on the following underlying assets (there are 42 gallons in a barrel :-)): Type of product Where traded Brent Crude Oil NYMEX WTI Crude oil NYMEX RBOB Gasoline Heating oil Propane NYMEX NYMEX NYMEX Size of futures contract 1000 barrels (quoted in $) 1000 barrels (quoted in $) 42000 gallons (quoted in c) 42000 gallons (quoted in c) 42000 gallons (quoted in $) The spreadsheet PS3_Q3.xls gives historical prices (2011-2020) obtained from Bloomberg of jet fuel spot prices and prices of crude oil (WTI and Brent), gasoline, propane, and heating oil futures over the past 10 years: a) Estimate the correlations (or R values) between Jet Fuel price changes and the futures price changes. If you were to choose one contract to hedge with what would it be? b) In order to hedge your exposure to Jet Fuel prices what position in the futures contract selected in part a) would you enter into? (i.e what position and how many contracts?) c) Now using the data from September 2020 - August 2021 estimate how well your hedge from part b) has performed e.g was the change in the spot price offset by the change in the futures position if not did you end up paying less or more? Note: To simplify your answer assume that all of the Fuel was purchased on 31 August, 2020, at the quoted spot price ($1.1036) and that your futures contracts were entered into in 31 August, 2020 at the quoted futures price (e.g $1.1961 for heating oil) and mature in August 2021. d) If you could hedge using all five futures contracts, how would you construct your hedge? Would you expect this hedge to be better than your hedge in part b)? Explain your answer. e) Now using the data from September 2020 - August 2021 estimate how well your hedge from part d) has performed e.g was the change in the spot price offset by the change in the futures position - if not did you end up paying less or more? (Note: To simplify your answer assume that all of the Fuel was purchased on 31 August 2020, and that your futures contracts were entered into in August 2020 and mature in August 2021 )