Mr. Joseph brown has a capital of 1,000,000 which he wishes to invest in three sectors of the economy i.e. Agriculture, Service and Manufacturing. The funds will be allocated as follows. Sector Amount Invested Agriculture 400,000 Service 200,000 Manufacturing 400,000 Details on the possible future economic states, their probabilities of occurrence and the expected return for each of the sectors are as shown below; Possible future economic states Probability of occurrence Expected return of each sector Agriculture Service Manufacturing Recession 0.1 16 14 3 Average 0.4 14 19 5 Boom 0.5 20 22 6 Required i) Determine the return of each sector (6 marks) ii) Determine the risk associated with the investment in each of the sectors. (6 marks) ii) Determine the expected portfolio return. (2 Marks) iii) Determine the covariance and correlation co-efficient between: A and S (2 marks) A and M (2 marks) S and M