Harry Markowitz received the 1990 Nobel Prize for his path-breaking work in portfolio optimization. One version of the Markowitz model is based on minimizing the variance of the portfolio subject to a constraint on return. We use the data and notation developed for the Hauck Index Fund in Section 12.4 to develop an example of the Markowitz mean-variance model. If each of the scenarios is equally likely and occurs with probability 1/5, then the mean return or expected return of the portfolio is

The variance of the portfolio return is

See Section 2 in Chapter 3 for a review of the mean and variance concept. Using the scenario return data given in Table 12.2, formulate the Markowitz mean-variance model. The objective function is the variance of the portfolio and should be minimized. Assume that the required return on the portfolio is 10%. There is also a unity constraint that all of the money must be invested in mutual funds. Solve this mean-variance model using either LINGO or Excelsolver.

R-R, S-1