Stout Investments wishes to design a minimum variance portfolio of index funds. The funds selected for consideration and their variance€“covariance matrix and average returns are given below:

Stout Investments would like to achieve an average weekly return of 0.19%, or roughly a 10% annual return.
a. Formulate and solve a Markowitz portfolio optimization model for this situation.
b. Suppose the company wants to restrict the percentage of investments in each fund as follows:
Bond: between 10% and 50%
S&P 500: between 30% and 50%
Small cap: no more than 20%
Mid cap: no more than 20%
Large cap: no more than 20%
Emerging market: no more than 10%
Commodity: no more than 20%

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S&P Small Mid Large Emerging Bond 0.002% -0.0019 0.020% -0.0019 0.0279 0.047% -0.00190| 0.02400| 0.03990| 0.033% -0.001%| 0.019%| 0.027%| 0.023%| 0.027% 500 cap cap cap market Commodity Bond S&P 500 Small cap Mid cap Large cap Emerging market Commodity Average weekly return | 0.044%| 0.118%| 0.256%| 0.226%| 0.242%| 0.00090| 0.0329 0.05090| 0.04390| 0.04190| 0.08590 1 0.0009 0.00090| 0.00590| 0.005%| 0.009%| 0.015% 0.054% 0.477% 0.053%