An Investor Wants to Invest $50,000 in Two Mutual Funds

question 59

Essay

An investor wants to invest $50,000 in two mutual funds, A and B. The rates of return, risks and minimum investment requirements for each fund are:
$\begin{array}{cccc}\text { Fund } & \text { Rate of return } & \text { Risk } & \text { Minimum investment } \\\hline \mathrm{A} & 12 \% & 0.5 & \$ 20,000 \\\mathrm{~B} & 9 \% & 0.3 & \$ 10.000\end{array}$
Note that a low Risk rating means a less risky investment. The investor wants to maximize the expected rate of return while minimizing his risk. Any money beyond the minimum investment requirements can be invested in either fund. The investor has found that the maximum possible expected rate of return is 11.4% and the minimum possible risk is 0.32.
The following Excel spreadsheet has been created to solve a goal programming problem with a MINIMAX objective based on the following goal programming formulation with MINIMAX objective and corresponding solution.
with solution (X₁, X₂) = (15,370, 34,630).
What values should go in cells B2:D14 of the spreadsheet?
$$\begin{array} { | c | l | c | c | c | c | } \hline & { \text { A } } & \mathrm { B } & \mathrm { C } & \mathrm { D } & \mathrm { E } \\\hline 1 & \text { Problem deta } & \mathrm { A } & \mathrm { B } & & \\\hline 2 & \text { Expected return } & & & & \\\hline 3 & \text { Risk rating } & & & & \\\hline 4 & & & & & \\\hline 5 & \text { Variables } & \text { A } & \mathrm { B } & \text { Total } & \\\hline 6 & \text { Amount invested } & & & & \\\hline 7 & \text { Minimum required } & & & & \\\hline 8 & & & & & \\\hline 9 & & & & & \text { Weighted } \\\hline 10 & \text { Goals } & \text { Actual } & \text { Target } & \text { Weights } & \text { \% Devintion } \\\hline 11 & \text { Average retun } & & & 1 & \\\hline 12 & \text { Average risk } & & & 1 & \\\hline 13 & & & & & \\\hline 14 & \text { Objective: } & & & & \\\hline\end{array}$$

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Definitions:

Inertia

A physical principle stating that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force.

Momentum

The quantity of motion of a moving body, measured as a product of its mass and velocity.

Horsepower

A rating of the amount of work performed by an engine. Originally based on the amount of weight a horse could move in one minute. One HP is equal to about 746 watts.

Wet Sump System

An oil management system used in internal combustion engines where the oil is stored in a sump directly beneath the engine and pumped where needed.