Southern Plains is a farming cooperative that is located near Wichita, Kansas. Southern Plains would like to hedge its 450,000 bushel inventory of sorghum. Sorghum is a type of cereal grain that is used to feed livestock and to create biofuels. Since there are no futures contracts on sorghum, Southern Plains would like to cross hedge using either corn futures or wheat futures. The size of 1 corn futures is 5,000 bushels, which is also the size of 1 wheat futures. The historical data for this question can be found in a spreadsheet which below the question

a) Which futures contract, wheat or corn, offers the better hedge? If Southern Plains chooses the better hedge, how much of the variance can be eliminated by cross hedging? If the target beta is zero, how many contracts should be traded? Should Southern Plains go long or short to hedge?

b) Can the hedge be improved by using a portfolio that contains both types of futures contracts? Please explain your answer.

The table shows 57 historical days of prices for wheat futures, corn futures, and sorghu Note: after calculating day-to-day price changes, you will have 56 observations for estir Wheat futures Corn futures Sorghum spot Historical price price price Day $/bushel $/bushel $/bushel 1 $5.00 $3.95 $3.60 2 $5.05 $3.92 $3.57 3 $5.18 $3.97 $3.62 4 $5.07 $3.93 $3.58 5 $4.85 $3.88 $3.53 6 $4.72 $3.82 $3.47 7 $4.70 $3.85 $3.50 8 $4.59 $3.83 $3.48 9 $4.74 $3.84 $3.49 10 $4.96 $3.91 $3.56 11 $4.89 $3.92 $3.57 12 $5.01 $3.96 $3.61 13 $4.95 $3.93 $3.58 14 $5.05 $3.99 $3.64 15 $5.08 $3.98 $3.63 16 $4.91 $3.90 $3.55 17 $4.83 $3.89 $3.54 18 $4.86 $3.85 $3.50 19 $4.69 $3.79 $3.44 20 $4.67 $3.85 $3.50 21 $4.66 $3.90 $3.55 22 $4.58 $3.88 $3.58 23 $4.63 $3.84 $3.54 24 $4.72 $3.89 $3.59 25 $4.90 $3.96 $3.66 26 $4.85 $3.96 $3.66 27 $4.95 $4.07 $3.77 28 $5.19 $4.17 $3.87 29 $5.32 $4.17 $3.87 30 31 32 33 34 35 36 37 38 39 40 41 42 43 $5.67 $5.50 $5.49 $5.50 $5.43 $5.82 $5.80 $5.74 $5.70 $5.64 $5.62 $5.56 $5.50 $5.30 $5.22 $5.18 $5.22 $5.13 $5.05 $5.11 $5.02 $4.99 $4.99 $4.96 $4.92 $4.97 $4.97 $5.02 $4.47 $4.47 $4.52 $4.50 $4.48 $4.49 $4.54 $4.60 $4.67 $4.54 $4.55 $4.56 $4.46 $4.31 $4.33 $4.29 $4.29 $4.18 $3.99 $4.01 $3.93 $3.99 $3.96 $3.92 $3.94 $3.98 $3.96 $3.99 $4.17 $4.17 $4.22 $4.20 $4.18 $4.19 $4.24 $4.30 $4.37 $4.24 $4.25 $4.26 $4.16 $4.01 $3.98 $3.94 $3.94 $3.83 $3.64 $3.66 $3.58 $3.64 $3.61 $3.57 $3.59 $3.63 $3.56 $3.59 44 45 46 47 48 49 50 51 52 53 54 55 56 57 The table shows 57 historical days of prices for wheat futures, corn futures, and sorghu Note: after calculating day-to-day price changes, you will have 56 observations for estir Wheat futures Corn futures Sorghum spot Historical price price price Day $/bushel $/bushel $/bushel 1 $5.00 $3.95 $3.60 2 $5.05 $3.92 $3.57 3 $5.18 $3.97 $3.62 4 $5.07 $3.93 $3.58 5 $4.85 $3.88 $3.53 6 $4.72 $3.82 $3.47 7 $4.70 $3.85 $3.50 8 $4.59 $3.83 $3.48 9 $4.74 $3.84 $3.49 10 $4.96 $3.91 $3.56 11 $4.89 $3.92 $3.57 12 $5.01 $3.96 $3.61 13 $4.95 $3.93 $3.58 14 $5.05 $3.99 $3.64 15 $5.08 $3.98 $3.63 16 $4.91 $3.90 $3.55 17 $4.83 $3.89 $3.54 18 $4.86 $3.85 $3.50 19 $4.69 $3.79 $3.44 20 $4.67 $3.85 $3.50 21 $4.66 $3.90 $3.55 22 $4.58 $3.88 $3.58 23 $4.63 $3.84 $3.54 24 $4.72 $3.89 $3.59 25 $4.90 $3.96 $3.66 26 $4.85 $3.96 $3.66 27 $4.95 $4.07 $3.77 28 $5.19 $4.17 $3.87 29 $5.32 $4.17 $3.87 30 31 32 33 34 35 36 37 38 39 40 41 42 43 $5.67 $5.50 $5.49 $5.50 $5.43 $5.82 $5.80 $5.74 $5.70 $5.64 $5.62 $5.56 $5.50 $5.30 $5.22 $5.18 $5.22 $5.13 $5.05 $5.11 $5.02 $4.99 $4.99 $4.96 $4.92 $4.97 $4.97 $5.02 $4.47 $4.47 $4.52 $4.50 $4.48 $4.49 $4.54 $4.60 $4.67 $4.54 $4.55 $4.56 $4.46 $4.31 $4.33 $4.29 $4.29 $4.18 $3.99 $4.01 $3.93 $3.99 $3.96 $3.92 $3.94 $3.98 $3.96 $3.99 $4.17 $4.17 $4.22 $4.20 $4.18 $4.19 $4.24 $4.30 $4.37 $4.24 $4.25 $4.26 $4.16 $4.01 $3.98 $3.94 $3.94 $3.83 $3.64 $3.66 $3.58 $3.64 $3.61 $3.57 $3.59 $3.63 $3.56 $3.59 44 45 46 47 48 49 50 51 52 53 54 55 56 57