Compute the efficient frontier when short sales are not allowed. Use the Solver tool in Excel (on the Datatab in the analysis section. To set the Solver parameters Set the objective to be the cell that computes the annual) portfolio standard deviation Minimize this value b. Set the "By Changing Variable cells to the cells containing the portfolio welchts. Hold the Control key and click in each of the 12 cells containing the weights of each stock) c. Add constraints by clicking the Add button next to the subject to the Constraints box. The first constraints that the cell containing the sum of all the portfolio weights must equal one. The next set of constraints is that each portfolio weight is non negative. You can enter these constraints individually, or check the box "Make Linconstrained Variables Non-Negative a compute the portfolio with the lowest standard deviation. If the parameters are set correctly, you should get a solution when you click "Solve" if there is an error, you will need to double check the parameters, especially the constraints. 4. Next, compute portfolios that have the lowest standard deviation for a targer level of the expected retur, a. Start by finding the portfolio with an expected return of 2% higher than the annual return for the minimum variance portfolio you computed in Step 3. rounded to the nearest whole percentage. To do this, add a constraint that the (annual) portfolio return equals this target level. Click Solve and record the standard deviation and mean return of the solution and be sure the mean retum equals target--if not, check your constraint) d. Repeat Step (a) raising the target return in 26 increments, recording the result for each step. Continue to increase the target return and record the result until Solver can no longer find a solution Next, repeat Step lal by lowering the target return in 29 increments from the return of the minimum vanance portfolio, again recording each result At what level does Solver fail to find a solution? Why? Plot the efficient frontier with the constraint of no short sales to do this create an XY Scatter Plot with portfolio standard deviation on the x-axis and the return on the yaxs, using the data for the minimum variance portfolio and the portfolios you computed in step 4 How do these portfolios compare to the mean and standard deviation for the equally weighted portfolio analyzed before 6. Redo your analysis to allow for short sales by removing the constraint that each portfolio weight is greater than or equal to zero. Use Solver to calculate the annual) portfolio standard deviation for annual returns in 54 increments from os to 40. Plot the unconstrained efficient frontieron an XY Scatter Plot. How does allowing short sales affect the frontier 7. Redo your analysis adding a new risk free security that has a 3 annual return, or 0.25 0.0025) each month, Include weight for this security when calculating the monthly portfolio returns. That is there will now be 13 weights, one for each of the 12 stocks and one for the risk-free security Again, these weights must sum to 1 Allow for short sales and use Solver to calculate the annual) portfolio Standard deviation when the annual portfolio returns are set to 3 10 20 40. Plot the results on the same XY Scatter Plot and in addition keep track of the portfolio weights of the optimal portfolio. What do you notice about the relative weights of the different stocks in the portfolio as you change the target return? Can you identity the tangent portfolio? Compute the efficient frontier when short sales are not allowed. Use the Solver tool in Excel (on the Datatab in the analysis section. To set the Solver parameters Set the objective to be the cell that computes the annual) portfolio standard deviation Minimize this value b. Set the "By Changing Variable cells to the cells containing the portfolio welchts. Hold the Control key and click in each of the 12 cells containing the weights of each stock) c. Add constraints by clicking the Add button next to the subject to the Constraints box. The first constraints that the cell containing the sum of all the portfolio weights must equal one. The next set of constraints is that each portfolio weight is non negative. You can enter these constraints individually, or check the box "Make Linconstrained Variables Non-Negative a compute the portfolio with the lowest standard deviation. If the parameters are set correctly, you should get a solution when you click "Solve" if there is an error, you will need to double check the parameters, especially the constraints. 4. Next, compute portfolios that have the lowest standard deviation for a targer level of the expected retur, a. Start by finding the portfolio with an expected return of 2% higher than the annual return for the minimum variance portfolio you computed in Step 3. rounded to the nearest whole percentage. To do this, add a constraint that the (annual) portfolio return equals this target level. Click Solve and record the standard deviation and mean return of the solution and be sure the mean retum equals target--if not, check your constraint) d. Repeat Step (a) raising the target return in 26 increments, recording the result for each step. Continue to increase the target return and record the result until Solver can no longer find a solution Next, repeat Step lal by lowering the target return in 29 increments from the return of the minimum vanance portfolio, again recording each result At what level does Solver fail to find a solution? Why? Plot the efficient frontier with the constraint of no short sales to do this create an XY Scatter Plot with portfolio standard deviation on the x-axis and the return on the yaxs, using the data for the minimum variance portfolio and the portfolios you computed in step 4 How do these portfolios compare to the mean and standard deviation for the equally weighted portfolio analyzed before 6. Redo your analysis to allow for short sales by removing the constraint that each portfolio weight is greater than or equal to zero. Use Solver to calculate the annual) portfolio standard deviation for annual returns in 54 increments from os to 40. Plot the unconstrained efficient frontieron an XY Scatter Plot. How does allowing short sales affect the frontier 7. Redo your analysis adding a new risk free security that has a 3 annual return, or 0.25 0.0025) each month, Include weight for this security when calculating the monthly portfolio returns. That is there will now be 13 weights, one for each of the 12 stocks and one for the risk-free security Again, these weights must sum to 1 Allow for short sales and use Solver to calculate the annual) portfolio Standard deviation when the annual portfolio returns are set to 3 10 20 40. Plot the results on the same XY Scatter Plot and in addition keep track of the portfolio weights of the optimal portfolio. What do you notice about the relative weights of the different stocks in the portfolio as you change the target return? Can you identity the tangent portfolio