1. Complete each of the following:

(a) Using a mean-variance framework, compute the optimal hedge ratio of a producer using oil futures contracts if in the oil market, the current spot price is $50, the current futures price is $45, the expected futures price is $35, the variance of the futures price is 300, the variance of the spot price is 400, the correlation between the spot and futures prices is 0.84 and the level of risk aversion has a value of 0.5 (NB: all prices are per barrel of oil). [6 marks]

(b) Using the information from Part 1(a) above, determine the producers profit under risk minimization if at maturity; the futures price is $50 per barrel of oil, the spot price is $53 per barrel of oil, the company produces 100 barrels of oil and the producers cost function is given by: () = 50 Where is the number of barrels of oil produced. [5 marks]