Q-154.1. The standard deviation of monthly changes in the spot price and futures price of silver is, respectively, $3.20 and $5.10. The correlation between them is 0.80. An industrial firm will need to purchase one million ounces of silver in six months but wants to hedge their price risk with silver futures (contract specifications are here http://www.cmegroup.com/trading/metals/precious/silver_contract_specifications.html). If the firm does not “tail its hedge,” how many long contracts are optimal?