1. Example 7.2* (Markowitz's bi-criteria model) An investor can invest in three securities. Based on the past 15 years of performance data, the means and standard deviations of the annual returns of the three securities have been computed as shown in Table 7.6. Note that security 1 has the highest average return of 14% per year, but its standard deviation of 20% makes it the most risky investment. The three securities are also positively correlated as shown in Table 7.6. TABLE 7.6 Data on Security Returns and Correlations between Security Returns (Example 7.2) Securities 1 2 3 Securities 1 and 2 Securities 1 and 3 Securities 2 and 3 Security Returns Mean Standard Deviation 0.14 0.20 0.11 0.15 0.10 0.08 Correlation Coefficient 0.6 0.4 0.7 You must assume that there are only 2 securities, Security 1 and Security 3. This is equivalent to assuming that X=0. Also assume that the total amount of money you have available for investment is 65000 dollars. Everything else is the same You can use any solver for solving linear and integer programs, use Google OR Tools. a) Find the maximum return ignoring the risk. b) Find the smallest risk ignoring the return. Here you must convert the quadratic objective into a linear objective using the technique we discussed in class. c) Find the smallest risk ignoring the return. This time you must use XL's nonlinear solver or any other nonlinear solver. Compare your answer to the one obtained in the previous step. It should be the same. d) What is the minimum risk for a return that is midway between the return in a) and b)? e) Use the results of parts a), b), and d) to draw the efficient frontier on a piece of paper.