Tejeda Investment Management, LLC manages 401K retirement plans. A client has asked them to recommend a portfolio. In discussing options with the client, 15 mutual funds were selected. The variance–covariance matrix and other relevant information are provided in the Problem 19 tab of the Chapter 14 Problem Data Excel file (using the quotation symbols for these funds). The client would like to achieve a minimum return of at least 10%. The company also recommends the following:

• At least five funds be selected.

• No more than three funds in the portfolio should have a Morningstar rating of three or less.

• At most two funds should have an above average risk rating.

• If a fund is selected, then at least 5% but no more than 25% should be invested in that fund.

a. Formulate and solve an integer nonlinear optimization model to minimize the portfolio variance and meet the recommended restrictions. Use Evolutionary Solver.

b. Suppose the client wants to maximize the expected return with the restriction that the portfolio variance be no higher than 15%. How does the solution change?