2. An investment advisor must invest $200,000 for a client (all of this must be invested). The annual rate of return for the portfolio must be at least 10%, and no stock can account for more than 40% of the total investment. The four stocks being considered and the relevant financial data are as follows: Stock Acme Bravo Centaur Delta Price per share $100 $50 $80 $40 Annual rate of return 0.12 0.09 0.08 0.11 beta 1.5 1.3 0.9 1.4 Beta is a measure of risk. A high beta indicates that the return on a stock is volatile. Thus, a low beta is usually desirable. The beta (or average beta) for a portfolio of stocks is a weighted average of the betas and the weights are determined by the amount of money that is put into each stock. For example, if $40,000 were put into each of the first two stocks, and $60,000 were put into each of the other two, the beta for the portfolio would be: Total beta for portfolio =1.5(40,000) + 1.3(40,000) + 0.9(60,000) + 1.4(60,000) = 250,000 Average beta (or simply beta) = (total beta)/(total dollars invested) = 250,000/200,000 = 1.25 Linear programming is used to develop an investment portfolio that minimizes risk. The variables are defined as: A = $ invested in Acme B = $ invested in Bravo C = $ invested in Centaur D = $ invested in Delta Minimize total beta = 1.5A + 1.3B + 0.9C + 1.4D Subject to: A + B + C + D = 200,000 Total invested 0.12A + 0.09B + 0.08C + 0.11D > 20,000 Return is at least 10% of investment A < 80,000 Maximum $ in Acme B < 80,000 Maximum $ in Bravo C < 80,000 Maximum $ in Centaur D < 80,000 Maximum $ in Delta A, B, C, D > 0 Find the optimal solution using computer software and fill in the table on the answer sheet. Note: The objective is expressed as the total beta and the return in constraint 2 is expressed in dollars. This is to avoid round-off errors. You will calculate the average beta (or simply beta) and the percent return after finding the optimal solution.