A trader owns 55,000 units of a particular asset and wants to hedge the value of his position with futures contracts on another related asset. Each futures contract is on 5,000 units. The spot price of the owned asset is $28 and the standard deviation of its price change is $0.45. The futures price of the related asset is $27 and the standard deviation of price change is estimated to be $0.40. The correlation between the spot price of the owned asset and the futures price of the related asset is 0.94.

a) What is the optimal hedge ratio?

b) Should the trader long or short the futures? How many futures contracts?

c) If the spot price of the owned asset drops to $25 at the end of the hedge, is it possible for the trader to lose more than $165,000? Explain your answer.