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With the added constraint: High end return options should be at least twice as much as low return options. above 10% return is considered high return. answer in excel 4 5 STOCK 1 2 3 Expected return (%) 11.0 9.0 6.5 Beta 1.20 0.85 0.55 15.0 1.40 13.0 1.25 Daniel would like to minimize the beta of the stock portfolio (calculated using a weighted average of the amounts put into the different stocks) while maintaining an expected return of at least 11%. Since future conditions may change. Daniel has decided that no more than 35% of the portfolio should be invested in any one stock. (a) Formulate this as a linear progran. (Hint: Define each variables as the proportion of the total investment that would be put in that stock. Include a constraint that restricts the sum of these vari- ables to be 1.) (b) Solve this problem. What are the expected return and beta for this portfolio? (Portfolio selection problem) Daniel Grady is the financial advisor for a number of professional athletes. An analysis of the long-term goals for many of these athletes has resulted in a recommendation to purchase stocks with some of the income that they have set aside for investments. Five stocks have been identified as hav- ing very favorable expectations for future performance. Although the expected return is important in these investments, the risk, as measured by the beta of the