Financial Planner Minnie Margin Has a Substantial Number of Clients $\text { Annual Returns (Flanning Scenarios) }$

question 38

Essay

Financial planner Minnie Margin has a substantial number of clients who wish to own a mutual fund portfolio that matches, as a whole, the performance of the Russell 2000 index. Her task is to determine what proportion of the portfolio should be invested in each of the five mutual funds listed below so that the portfolio most closely mimics the performance of the Russell 2000 index. Formulate the appropriate nonlinear program. $\text { Annual Returns (Flanning Scenarios) }$
$\begin{array}{c|rrrr}\text { Mutual Fund } & \text { Year } 1 & \text { Year 2 } & \text { Year } 3 & \text { Year 4 }\\\hline \text { International Stock } & 22.37 & 26.73 & 4.86 & 2.17 \\\text { Large-Cap Value } & 15.48 & 19.64 & 11.50 & -5.25 \\\text { Mid-Cap Value } & 17.42 & 20.07 & -4.97 & -1.69 \\\text { Small-Cap Growth } & 23.18 & 12.36 & 3.25 & 3.81 \\\text { Short-Term Bond } & 9.26 & 8.81 & 6.15 & 4.04 \\\hline \text { Russell 2000 Index } & 20.00 & 22.00 & 8.00 & -2.00\end{array}$

Understand the concept of a sample space and identify it correctly in various contexts.

Define and distinguish between mutually exclusive and independent events.

Recognize the definition and examples of sample points and experimental outcomes.

Comprehend the principle behind the repetition of experiments and possible variations in outcomes.

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Definitions:

Facial Nerve

A cranial nerve that controls the muscles of facial expression, taste sensations from the anterior two-thirds of the tongue, and the production of saliva and tears.

Hyoid Bone

A unique U-shaped bone located in the anterior neck, which supports the tongue and provides attachment points for muscles associated with swallowing.

Platysma

A muscle in the neck region that plays a role in facial expression, such as lowering the lower jaw and lip.

Mandible

The lower jawbone in humans and some animals, which holds the lower teeth in place and plays a key role in biting and chewing.