Investment Manager Max Gaines Wishes to Develop a Mutual Fund $\text { Annual Returns (Flanning Scenarios) }$

Essay

Investment manager Max Gaines wishes to develop a mutual fund portfolio based on the Markowitz portfolio model. He needs to determine the proportion of the portfolio to invest in each of the five mutual funds listed below so that the variance of the portfolio is minimized subject to the constraint that the expected return of the portfolio be at least 4%. Formulate the appropriate nonlinear program. $\text { Annual Returns (Flanning Scenarios) }$
$\begin{array}{c|rrrr}\text { Mutual Fund } & \text { Year } 1 & \text { Year 2 } & \text { Year } 3 & \text { Year 4 }\\\hline \text { International Stock } & 26.73 & 22.37 & 6.46 & -3.19 \\\text { Large-Cap Blend } & 18.61 & 14.88 & 10.52 & 5.25 \\\text { Mid-Cap Blend } & 18.04 & 19.45 & 15.91 & -1.94 \\\text { Small-Cap Blend } & 11.33 & 13.79 & -2.07 & 6.85 \\\text { Intermediate Bond } & 8.05 & 7.29 & 9.18 & 3.92\end{array}$