Kellogg will buy two million bushels of oats in two months. Kellogg finds that the ratio of the standard deviation of change in spot and futures prices over a two- month period for oats is 0.83 and the coefficient of correlation between the two- month change in price of oats and the two- month change in its futures price is 0.7.
a. Find the optimal hedge ratio for Kellogg.
b. How many contracts do they need to hedge their position? (The size of each oats contract is five thousand bushels; oats trades in the CME Group.)