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

question 57

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:
$\begin{array}{lll}\text { Fund }&\text { Rate of return }&\text { Risk }&\text { Minimum investment }\\\hline \text { A } & 12 \% & 0.5&\$20,000 \\\text { B } & 9 \% & 0.3&\$10,000\end{array}$
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.
MINIMIZE Q
Subject to: ^X₁ ^{+ X}₂ ^{= 50000}
X₁ ≥ 20000
X₂ ≥ 10000
$w _ { 2 } \left( \frac { \left( \frac { 0.5 X _ { 1 } + 0.3 X _ { 2 } } { 50000 } \right) - 0.32 } { 0.32 } \right) \leq Q$
$w _ { \mathrm { i } } \left( \frac { \left( 0.114 - \frac { 0.12 X _ { 1 } + 0.09 X _ { 2 } } { 50000 } \right) } { 0.114 } \right) \leq Q$
$w_{\mathrm{i}}\left(\frac{\left(0.114-\frac{0.12 X_{1}+0.09 X_{2}}{50000}\right)}{0.114}\right) \leq Q$
$w_{2}\left(\frac{\left(\frac{0.5 x_{i}+0.3 X_{2}}{50000}\right)-0.32}{0.32}\right) \leq Q$
X_i ≥ 0 for all i,Q ≥ 0
with solution X₁,X₂)= 15,370,34,630).
What values should go in cells B2:D14 of the spreadsheet?
$\begin{array}{|c|l|c|c|c|c|}\hline &{\text { A }} & \text { B } & \text { C } & \text { D } & \text { E } \\\hline 1 & \text { Problem data } & \text { A } & \text { B } & & \\\hline 2 & \text { Expected retum } & & & & \\\hline 3 & \text { Risk rating } & & & & \\\hline 4 & & & & \\\hline 5 & \text { Variables } & \text { A } & \text { B } & \text { Total } \\\hline 6 & \text { Amount invested } & & & \\\hline 7 & \text { Minimum required } & & & \\\hline 8 & & & & \\\hline 9 & & & & & \text { Weighted } \\\hline 10 & \text { Goals } & \text { Actual } & \text { Target } & \text { Weights } & \% \text { Deviation } \\\hline 11 & \text { Average return } & & & 1 & \\\hline 12 & \text { Average risk } & & & 1 & \\\hline 13 & & & & & \\\hline 14 & \text { Objective: } & & & &\\\hline\end{array}$

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Definitions:

Parameter

A measurable attribute that defines or sets the boundaries for a system, or statistical population, often used in mathematical or statistical modeling.

Curvilinear Relationship

A relationship between two variables where the change in one variable is related to a non-linear change in another variable, often depicted as a curved graph.

Construct Validity

The degree to which a test or instrument measures the theoretical construct it is intended to measure.

Extraverted

Describes a person who is outgoing, sociable, and derives energy from interacting with other people.