A trader owns 55,000 troy oz of silver and decides to hedge with 6-month silver futures contracts. Each futures contract is on 5,000 troy oz. The spot price is $18.72 and the futures price $17.63 per troy oz. The standard deviation of the change in the spot price of silver is 0.43. The standard deviation of the change in silver futures prices is 0.40. The coefficient of correlation between the two is 0.95

a) What is the minimum variance hedge ratio?

b) What is the optimal number of futures contracts without tailing the hedge?

c) What is the optimal number of futures contracts with tailing the hedge? Assume the same hedge ratio.