Today American Airlines (AAL) wishes to hedge its exposure to changes in the jet fuel price by using heating oil futures. It expects to purchase 800,000 gallons of jet fuel in 3 months (on November 15, 2022) in the spot market and decides to use December 2022 heating oil futures for hedging. Historical market price data shows that (over a period of 3 months) changes in the jet fuel spot price have a 0.8 correlation with heating oil futures price changes, and the changes in the heating oil futures price have a standard deviation that is 15% lower than the standard deviation of spot price changes in jet fuel. The contract size of heating oil futures is 42,000 gallons, and December 2022 heating oil futures currently trade at $3.48 per gallon. (a) If December 2022 heating oil futures are used to hedge AALs exposure to changes in jet fuel price, what is the minimum variance hedge ratio? (b) What position should AAL take in the heating oil futures? What is the optimal number of futures contracts? Suppose that on November 15, 2022, the jet fuel spot price is $3.50 per gallon, and AAL closes out its position in the futures contracts at the then prevailing December 2022 heating oil futures price of $4.00 per gallon. (c) What would be AALs total P&L from its trade in the futures contracts on November 15, 2022, in this scenario? Roger 13:38:42 (d) How much money would AAL effectively pay (including its profit or loss from the hedge) to purchase the 800,000 gallons of jet fuel on November 15, 2022, in the spot market in this scenario? Is AAL better off with the hedge?

(10 points) Today American Airlines (AAL) wishes to hedge its exposure to changes in the jet fuel price by using heating oil futures. It expects to purchase 800,000 gallons of jet fuel in 3 months (on November 15, 2022) in the spot market and decides to use December 2022 heating oil futures for hedging. Historical market price data shows that (over a period of 3 months) changes in the jet fuel spot price have a 0.8 correlation with heating oil futures price changes, and the changes in the heating oil futures price have a standard deviation that is 15% lower than the standard deviation of spot price changes in jet fuel. The contract size of heating oil futures is 42,000 gallons, and December 2022 heating oil futures currently trade at $3.48 per gallon. (a) If December 2022 heating oil futures are used to hedge AAL's exposure to changes in jet fuel price, what is the minimum variance hedge ratio? (b) What position should AAL take in the heating oil futures? What is the optimal number of futures contracts? Suppose that on November 15, 2022, the jet fuel spot price is $3.50 per gallon, and AAL closes out its position in the futures contracts at the then prevailing December 2022 heating oil futures price of $4.00 per gallon. (c) What would be AAL's total P\&L from its trade in the futures contracts on November 15 , 2022 , in this scenario? (d) How much money would AAL effectively pay (including its profit or loss from the hedge) to purchase the 800,000 gallons of jet fuel on November 15, 2022, in the spot market in this scenario? Is AAL better off with the hedge? (10 points) Today American Airlines (AAL) wishes to hedge its exposure to changes in the jet fuel price by using heating oil futures. It expects to purchase 800,000 gallons of jet fuel in 3 months (on November 15, 2022) in the spot market and decides to use December 2022 heating oil futures for hedging. Historical market price data shows that (over a period of 3 months) changes in the jet fuel spot price have a 0.8 correlation with heating oil futures price changes, and the changes in the heating oil futures price have a standard deviation that is 15% lower than the standard deviation of spot price changes in jet fuel. The contract size of heating oil futures is 42,000 gallons, and December 2022 heating oil futures currently trade at $3.48 per gallon. (a) If December 2022 heating oil futures are used to hedge AAL's exposure to changes in jet fuel price, what is the minimum variance hedge ratio? (b) What position should AAL take in the heating oil futures? What is the optimal number of futures contracts? Suppose that on November 15, 2022, the jet fuel spot price is $3.50 per gallon, and AAL closes out its position in the futures contracts at the then prevailing December 2022 heating oil futures price of $4.00 per gallon. (c) What would be AAL's total P\&L from its trade in the futures contracts on November 15 , 2022 , in this scenario? (d) How much money would AAL effectively pay (including its profit or loss from the hedge) to purchase the 800,000 gallons of jet fuel on November 15, 2022, in the spot market in this scenario? Is AAL better off with the hedge