You are a portfolio manager and you would like to hedge a portfolio daily over a thirty-day horizon using futures. The table below provides data on the values of the spot portfolio and the futures that will be used as a hedging instrument:

a) Use the data to find the minimum variance hedge ratio you would use to achieve the hedge

b) Using the hedge ratio from a., calculate the daily change in value of the hedged portfolio.

c) What is the standard deviation of changes in value of the hedged portfolio? How does this compare to the standard deviation of changes in the unhedged spot position?

Day 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Spot 80 79.635 77.88 76.4 75.567 77.287 77.599 78.147 77.041 76.853 77.034 75.96 75.599 77.225 77.119 77.762 77.082 76.497 75.691 75.264 76.504 76.835 78.031 79.185 77.524 76.982 76.216 76.764 79.293 78.861 76.192 Futures 81 80.869 79.092 77.716 77.074 78.841 79.315 80.067 79.216 79.204 79.638 78.659 78.549 80.512 80.405 81.224 80.654 80.233 79.605 79.278 80.767 81.28 82.58 84.03 82.337 82.045 81.252 81.882 84.623 84.205 81.429 Day 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Spot 80 79.635 77.88 76.4 75.567 77.287 77.599 78.147 77.041 76.853 77.034 75.96 75.599 77.225 77.119 77.762 77.082 76.497 75.691 75.264 76.504 76.835 78.031 79.185 77.524 76.982 76.216 76.764 79.293 78.861 76.192 Futures 81 80.869 79.092 77.716 77.074 78.841 79.315 80.067 79.216 79.204 79.638 78.659 78.549 80.512 80.405 81.224 80.654 80.233 79.605 79.278 80.767 81.28 82.58 84.03 82.337 82.045 81.252 81.882 84.623 84.205 81.429