Assume that you are considering selecting assets from among the following four candidates: Market Condition Good Average Poor Asset 1 Return 16 12 8 Prob. 1/4 1/2 1/4 Ass. 2 Ret. 4 6 8 Prob. 1/4 1/2 1/4 Ass.3 Ret. 20 14 8 Prob 1/4 1/2 1/4 Rainfall Ass. Ret. Plentiful 16 Average 12 Light 8 Prob. 1/3 1/3 1/3 Assume that there is no relationship between the amount of rainfall and the condition of the stock market. (i) Solve for the expected return and the standard deviation of return for each separate investment. (ii) Solve for the correlation coefficient and the covariance between each pair of investments. (iii) Solve for the expected return and variance of each of the portfolios shown in the following. Asset 3 Asset 4 Asset 2 1/2 1/2 1/2 Portfolio Asset 1 A 1/2 B 1/2 1/2 D E F 1/3 G H 1/3 1 1/4 1/2 1/2 1/3 1/3 1/2 1/2 1/3 1/3 1/3 1/4 1/3 1/3 1/4 1/4 (iv) Plot the original assets and each of the portfolios from (iii) in erpected return standard deviation space. Assume that you are considering selecting assets from among the following four candidates: Market Condition Good Average Poor Asset 1 Return 16 12 8 Prob. 1/4 1/2 1/4 Ass. 2 Ret. 4 6 8 Prob. 1/4 1/2 1/4 Ass.3 Ret. 20 14 8 Prob 1/4 1/2 1/4 Rainfall Ass. Ret. Plentiful 16 Average 12 Light 8 Prob. 1/3 1/3 1/3 Assume that there is no relationship between the amount of rainfall and the condition of the stock market. (i) Solve for the expected return and the standard deviation of return for each separate investment. (ii) Solve for the correlation coefficient and the covariance between each pair of investments. (iii) Solve for the expected return and variance of each of the portfolios shown in the following. Asset 3 Asset 4 Asset 2 1/2 1/2 1/2 Portfolio Asset 1 A 1/2 B 1/2 1/2 D E F 1/3 G H 1/3 1 1/4 1/2 1/2 1/3 1/3 1/2 1/2 1/3 1/3 1/3 1/4 1/3 1/3 1/4 1/4 (iv) Plot the original assets and each of the portfolios from (iii) in erpected return standard deviation space