0.2010 0.1380 0.4178 0.1090 119 21.0 22.523 0.0000 0.8014 0.1739 0.0247 0.0000 0.0000 0.0000 120 22.0 20.028 not feasible 0.6052 0.4880 0.2341 0.1994 0.1442 0.5343 0.1365 121 26.0 25.390 not feasible 0.7931 0.7262 0.3665 0.1929 0.1687 1.0006 0.2467 II. Portfolio Theory 8. Optimal Risky Portfolio The McGraw−Hill Companies, 2001           232 PART II Portfolio Theory     compute the standard deviation and expected return of the equally weighted portfolio (for- mulas in cells B62, B63) and find that they yield an expected return of 16.5% with a stan- dard deviation of 17.7% (results in cells B78 and B79). To compute points along the efficient frontier we use the Excel Solver in Table 8.4D (which you can find in the Tools menu).12 Once you bring up Solver, you are asked to en- ter the cell of the target (objective) function. In our application, the target is the variance of the portfolio, given in cell B93. Solver will minimize this target. You next must input the cell range of the decision variables (in this case, the portfolio weights, contained in cells A85-A91). Finally, you enter all necessary constraints into the Solver. For an unrestricted efficient frontier that allows short sales, there are two constraints: first, that the sum of the weights equals 1.0 (cell A92 1), and second, that the portfolio expected return equals a target mean return. We will choose a target return equal to that of the equally weighted portfolio, 16.5%, so our second constraint is that cell B95 16.5. Once you have entered the two constraints you ask the Solver to find the optimal portfolio weights. The Solver beeps when it has found a solution and automatically alters the portfolio weight cells in row 84 and column A to show the makeup of the efficient portfolio. It ad- justs the entries in the border-multiplied covariance matrix to reflect the multiplication by these new weights, and it shows the mean and variance of this optimal portfolio-the min- imum variance portfolio with mean return of 16.5%. These results are shown in Table 8.4D, cells B93-B95. The table shows that the standard deviation of the efficient portfolio with same mean as the equally weighted portfolio is 17.2%, a reduction of risk of about one-half percentage point. Observe that the weights of the efficient portfolio differ radically from equal weights. To generate the entire efficient frontier, keep changing the required mean in the con- straint (cell B95),13 letting the Solver work for you. If you record a sufficient number of points, you will be able to generate a graph of the quality of Figure 8.13. The outer frontier in Figure 8.13 is drawn assuming that the investor may