The investment universe is composed of a set of following 4 assets: With a correlation structure R=10.20.50.30.210.70.40.50.710.90.30.40.91 Denote the column vector of asset weights by w, the column vector of asset returns , and the covariance matrix by . 1. Compute the covariance matrix . 2. Consider the following optimization: wmin21wTw Subject to constraints wT1=1wT=0.1 - Explain in plain English what this optimization does. - Solve this optimization using the Lagrangian method. - Compute the standard deviation of this optimal portfolio. - On a graph of expected returns plotted against standard deviation, identify this optimal portfolio. 3. Now, consider a less constrained optimization: minw21wTw Subject to a constraint wT1=1 - Explain in plain English what this optimization does. - Solve this optimization using the Lagrangian method. - Compute the return and standard deviation of this optimal portfolio. - On a graph of expected returns plotted against standard deviation, identify and name this optimal portfolio. The investment universe is composed of a set of following 4 assets: With a correlation structure R=10.20.50.30.210.70.40.50.710.90.30.40.91 Denote the column vector of asset weights by w, the column vector of asset returns , and the covariance matrix by . 1. Compute the covariance matrix . 2. Consider the following optimization: wmin21wTw Subject to constraints wT1=1wT=0.1 - Explain in plain English what this optimization does. - Solve this optimization using the Lagrangian method. - Compute the standard deviation of this optimal portfolio. - On a graph of expected returns plotted against standard deviation, identify this optimal portfolio. 3. Now, consider a less constrained optimization: minw21wTw Subject to a constraint wT1=1 - Explain in plain English what this optimization does. - Solve this optimization using the Lagrangian method. - Compute the return and standard deviation of this optimal portfolio. - On a graph of expected returns plotted against standard deviation, identify and name this optimal portfolio