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:

Crisis Management

The process of dealing with sudden and significant negative events or emergencies that impact an organization or community.

Unexpected High-impact Events

Rare, unpredictable occurrences that have significant and often adverse effects on businesses, economies, or societies.

Nonprogrammed Decision

Decisions made in response to situations that are unique, poorly defined, and largely unstructured, requiring specific solutions.

Unique Situation

A set of circumstances that is distinct and does not closely resemble any other situation.