A trader wants to buy 122,000 units of a particular asset and decides to hedge the value of her position with futures contracts on another related asset. Each futures contract is on 4,000 units. The spot price of the asset that is owned is $32 and the standard deviation of the change in this price over the life of the hedge is estimated to be $0.56. The futures price of the related asset is $33 and the standard deviation of the change in this over the life of the hedge is $0.48. The coefficient of correlation between the spot price change and futures price change is 0.97. a) What is the minimum variance hedge ratio? (2 pts) b) Should the hedger take a long or short futures position? ( 1pt) c) What is the optimal number of futures contracts needed to hedge the trader position when issues associated with daily settlement are taken into account? ( 2 pts) d) What should be the correlation between the spot price change and the futures price change if the trader discovers that 30 futures contract are optimal to hedger her positions (issues associated with daily settlement are taken into account)? (4 pts)