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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Definitions:

Analyzing Action Alternatives

The process of assessing different possible actions to determine which would be most effective in achieving desired objectives.

Implementing

The process of putting plans, strategies, or ideas into action to achieve desired outcomes.

Defining Objectives

The process of establishing clear, specific, measurable, and achievable targets that an organization or individual aims to reach.

Setting Objectives

The process of establishing specific, measurable, achievable, relevant, and time-bound goals for an individual, team, or organization.