13.7 Mean variance portfolio selection An investor wishes to invest a certain amount of money. He is evaluating four different securities (as- sets) for his investment. The securities are US Treasury Bills (T-bills), a computer hardware company, a computer software company, and a high-risk investment in a theater production. He estimates the mean yield on each dollar he invests in each of the securities, and also adopts the Markowitz idea of getting es- timates of the variance/covariance matrix of estimated returns on the securities. (For example, hardware Economics and finance 206 Applications of optimization with Xpress-MP and software company worths tend to move together, but are oppositely correlated with the success of theatrical production, as people go to the theater more when they have become bored with playing with their new computers and computer games.) The return on theatrical productions are highly variable, whereas the T-bill yield is certain. The estimated returns and the variance/covariance matrix are given in Table 13.12 Table 13.12: Estimated returns and variance covariance matrix Hardware Software Show-biz T-bills Estimated return 8 9 12 7 Hardware 4 3 -1 0 Software 3 6 1 0 Show-biz -1 1 10 T-bills 0 Question 1: Which investment strategy should the investor adopt to minimize the variance subject to getting some specified minimum target yield? Question 2: Which is the least variance investment strategy if the investor wants to choose at most two different securities (again subject to getting some specified minimum target yield)? 13.7 Mean variance portfolio selection An investor wishes to invest a certain amount of money. He is evaluating four different securities (as- sets) for his investment. The securities are US Treasury Bills (T-bills), a computer hardware company, a computer software company, and a high-risk investment in a theater production. He estimates the mean yield on each dollar he invests in each of the securities, and also adopts the Markowitz idea of getting es- timates of the variance/covariance matrix of estimated returns on the securities. (For example, hardware Economics and finance 206 Applications of optimization with Xpress-MP and software company worths tend to move together, but are oppositely correlated with the success of theatrical production, as people go to the theater more when they have become bored with playing with their new computers and computer games.) The return on theatrical productions are highly variable, whereas the T-bill yield is certain. The estimated returns and the variance/covariance matrix are given in Table 13.12 Table 13.12: Estimated returns and variance covariance matrix Hardware Software Show-biz T-bills Estimated return 8 9 12 7 Hardware 4 3 -1 0 Software 3 6 1 0 Show-biz -1 1 10 T-bills 0 Question 1: Which investment strategy should the investor adopt to minimize the variance subject to getting some specified minimum target yield? Question 2: Which is the least variance investment strategy if the investor wants to choose at most two different securities (again subject to getting some specified minimum target yield)