6 Optimal Cross-Hedging (20 points) In this question, you will work with data to calculate an optimal number of contracts to cross-hedge a position. You will need to download the relevant data from the course's Blackboard page. If you want to use Excel, I have provided a file Assignment1.xlsx which contains the data as an Excel spreadsheet. If you want to use software that prefers a csv file, I have also provided Assignment1. csv which contains exactly the same data. Pick your favorite. You are working for an airline company and you know that you will need 1,000,000 gallons of jet fuel in one month. You are looking to hedge against one-month price changes. You decide to hedge against these price changes using light sweet crude oil futures. 1 In particular, you will want to open a position in crude oil futures with a delivery date in two months, and then close out of them next month. However, as jet fuel and crude oil are not the same asset, the optimal hedge ratio may not be 1 . In this problem, you will compute the minimum-variance hedge ratio using historical data, and then you will come up with a hedging strategy. Futures prices are quoted in US dollars per barrel, while spot prices for jet fuel are quoted in US dollars per gallon. Each futures contract is for 1,000 barrels of crude oil. In case you are curious, a barrel of oil is defined to be 42 US gallons, which is just below 159 liters. The data I have given you is already given as differences. The change in the spot price (of jet fuel) is given as the listed month's spot price minus the previous month's spot price, and the change in the futures price (of crude oil) is given as the listed month's 1-month futures contract minus the previous month's 2-month futures contract. (a) (10 points) Make a scatter plot with F, the change in the futures prices, on the x-axis, and S, the change in the spot prices, on the y-axis. Add a regression line, and make sure to show the slope with your plot. Submit your plot (with the scatter, line of best fit, and slope). In newer versions of Excel, after you create a scatter plot, go to Chart Tools > Design > Add Chart Element > Trendline > Linear. Make sure to adjust your trendline (double click on it) to "Display Equation on chart" so that it tells you the slope. If you are using other software where adding the line to the plot is slightly inconvenient (such as R ), please submit the scatter plot together with your software's regression analysis output. (b) (6 points) What is the optimal hedge ratio (h) ? Briefly describe what this value means. (c) (4 points) Suppose the current spot price for jet fuel is $2.8962 per gallon, and the current 2-month futures contract for crude oil has forward price $84.51 per barrel. How many contracts would you buy to hedge your position? (In case you have learned about "tailing a hedge," do not do that.) 6 Optimal Cross-Hedging (20 points) In this question, you will work with data to calculate an optimal number of contracts to cross-hedge a position. You will need to download the relevant data from the course's Blackboard page. If you want to use Excel, I have provided a file Assignment1.xlsx which contains the data as an Excel spreadsheet. If you want to use software that prefers a csv file, I have also provided Assignment1. csv which contains exactly the same data. Pick your favorite. You are working for an airline company and you know that you will need 1,000,000 gallons of jet fuel in one month. You are looking to hedge against one-month price changes. You decide to hedge against these price changes using light sweet crude oil futures. 1 In particular, you will want to open a position in crude oil futures with a delivery date in two months, and then close out of them next month. However, as jet fuel and crude oil are not the same asset, the optimal hedge ratio may not be 1 . In this problem, you will compute the minimum-variance hedge ratio using historical data, and then you will come up with a hedging strategy. Futures prices are quoted in US dollars per barrel, while spot prices for jet fuel are quoted in US dollars per gallon. Each futures contract is for 1,000 barrels of crude oil. In case you are curious, a barrel of oil is defined to be 42 US gallons, which is just below 159 liters. The data I have given you is already given as differences. The change in the spot price (of jet fuel) is given as the listed month's spot price minus the previous month's spot price, and the change in the futures price (of crude oil) is given as the listed month's 1-month futures contract minus the previous month's 2-month futures contract. (a) (10 points) Make a scatter plot with F, the change in the futures prices, on the x-axis, and S, the change in the spot prices, on the y-axis. Add a regression line, and make sure to show the slope with your plot. Submit your plot (with the scatter, line of best fit, and slope). In newer versions of Excel, after you create a scatter plot, go to Chart Tools > Design > Add Chart Element > Trendline > Linear. Make sure to adjust your trendline (double click on it) to "Display Equation on chart" so that it tells you the slope. If you are using other software where adding the line to the plot is slightly inconvenient (such as R ), please submit the scatter plot together with your software's regression analysis output. (b) (6 points) What is the optimal hedge ratio (h) ? Briefly describe what this value means. (c) (4 points) Suppose the current spot price for jet fuel is $2.8962 per gallon, and the current 2-month futures contract for crude oil has forward price $84.51 per barrel. How many contracts would you buy to hedge your position? (In case you have learned about "tailing a hedge," do not do that.)