You are an alpaca farmer and would like to hedge the risk you face due to alpaca wool price fluctuations. Unfortunately, there are no alpaca wool futures contracts. You have noted that the correlation between the price of alpaca wool and sheep wool futures prices is 0.65. However, the alpaca wool price is much less volatile, with a standard deviation of daily changes of $0.3 per kilo, versus sheep wool futures, at $0.5 per kilo. You would like to hedge the risk from selling thirty tonnes (30,000 kilos) of alpaca wool. Each sheep wool futures contract covers 3,500 kilos of sheep wool. The current price of alpaca wool is $30 per kilo, while the sheep wool futures price is $19 per kilo.

(a) What is the minimum variance hedge ratio?

(b) Should you take a long or short position?

(c) What is the optimal number of contracts to take out?