Patek Philippe needs to buy 400 pounds of 18 karat gold for its ongoing business of making luxury wristwatches. The company plans to buy the gold on the spot market six months from today and it wants to hedge its risk using 6-month gold futures. Todays gold futures price is $1,810 per ounce and the size of one futures contract is 100 ounces, which is 6.25 pounds. The underlying asset for the gold futures contract is 24 karat gold. A financial analyst at Patek Philippe has calculated a beta equal to 14.25. To calculate the beta, the analyst used a linear regression of 18 karat gold spot price changes per pound against gold futures price changes per ounce. The regression R-squared is 0.956. The company's target beta is zero.

Should Patek Philippe go long or short to hedge? How many futures contracts should be used for cross-hedging? How much of the variance is eliminated by hedging?

Note: question 2 involves cross-hedging since 24 karat gold and 18 karat gold are not perfectly correlated. 24 karat gold is 100% pure gold. 18 karat gold is 75% gold (18 out of 24 parts) and 25% (6 out of 24 parts) other metals such as copper, zinc, and nickel.