5. There are just three risky assets with rates of return 1, 2 and 3, respectively....

  

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5. There are just three risky assets with rates of return 1, 2 and 3, respectively. The covariance matrix and the expected rates of return are 1 0.5 = 1 2 and 0.5 2 = 0.4 0.8 0.8 1-8 respectively. Consider the following portfolio optimization problem max ' s.t. T1 T2 T3 = 1, where rf = 0.2 and = (T1, T2, T3)' is the portfolio of these three assets. (i) Find the optimal portfolio. (ii) Find the maximum value according to the optimal portfolio. [15 marks] [5 marks] 5. There are just three risky assets with rates of return 1, 2 and 3, respectively. The covariance matrix and the expected rates of return are 1 0.5 = 1 2 and 0.5 2 = 0.4 0.8 0.8 1-8 respectively. Consider the following portfolio optimization problem max ' s.t. T1 T2 T3 = 1, where rf = 0.2 and = (T1, T2, T3)' is the portfolio of these three assets. (i) Find the optimal portfolio. (ii) Find the maximum value according to the optimal portfolio. [15 marks] [5 marks]