Develop a Model That Minimizes Semivariance for the Data Given $d _ { s }$

question 54

Essay

Develop a model that minimizes semivariance for the data given below with a required return of 15 percent. Define a variable $d _ { s }$ for each scenario and let $d _ { s } \geq \bar { R } - R _ { s }$ with $d _ { s }$ = 0. Then make the objective function: Min $1 / 4 \sum _ { s = 1 } ^ { 4 } d _ { s } ^ { 2 }$ . $$\begin{array} { | l | c | c | c | c | } \hline && { \text { Scenario } } \\\hline \text { Mutual Fund } & \text { Year 1 } & \text { Year 2 } & \text { Year 3 } & \text { Year 4 } \\\hline \text { Large-Cap Growth } & 41.54 & 36.18 & 32.76 & - 20.63 \\\text { Large-Cap Value } & 32.45 & 44.78 & 28.61 & 38.49 \\\text { Small-Cap Growth } & 26.13 & 7.04 & - 23.97 & 45.67 \\\text { Small-Cap Value } & 37.56 & 18.53 & 27.53 & - 5.48 \\\hline\end{array}$$ Solve the model you developed with a required expected return of at least 15 percent.

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