(the elements in column A and row 84) must be nonnegative; we would then obtain the restricted efficient frontier curve in Figure 8.13, which lies inside the frontier obtained allowing short sales. The superiority of the unrestricted efficient frontier reminds us that restrictions imposed on portfolio choice may be costly. The Solver allows you to add "no short sales" and other constraints easily. Once they are entered, you repeat the variance-minimization exercise until you generate the entire re- stricted frontier. By using macros in Excel or-even better-with specialized software, the entire routine can be accomplished with one push of a button. Table 8.4E presents a number of points on the two frontiers. The first column gives the required mean and the next two columns show the resultant variance of efficient portfolios with and without short sales. Note that the restricted frontier cannot obtain a mean return less than 10.5% (which is the mean in Canada, the country index with the lowest mean re- turn) or more than 21.7% (corresponding to Germany, the country with the highest mean return). The last seven columns show the portfolio weights of the seven country stock in- dexes in the optimal portfolios. You can see that the weights in restricted portfolios are never negative. For mean returns in the range from about 15% 17%, the two frontiers overlap since the optimal weights in the unrestricted frontier turn out to be positive (see also Figure 8.13).     12 If Solver does not show up under the Tools menu, you should select Add-Ins and then select Analysis. This should add Solver to the list of options in the Tools menu. 13 Inside Solver, highlight the constraint, click on Change, and enter the new value for the portfolios mean return. II. Portfolio Theory 8. Optimal Risky Portfolio The McGraw−Hill Companies, 2001           CHAPTER 8 Optimal Risky Portfolios 233     Figure 8.13 Efficient frontier with seven countries.     Expected return (%)     28     26 Restricted efficient frontier: 24 NO short sales