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Two investment portfolios are shown with the amount of money placed in each investment and the ROR.

\begin{tabular}{|l|l|l|l|}
\hline \multicolumn{1}{|c|}{Investment} & Portfolio 1 & Portfolio 2 & \multicolumn{1}{c|}{ROR} \\
\hline Tech Company Stock & \[tex]$2,300 & \$[/tex]1,575 & 2.35\% \\
\hline Government Bond & \[tex]$3,100 & \$[/tex]2,100 & 1.96\% \\
\hline Junk Bond & \[tex]$650 & \$[/tex]795 & 10.45\% \\
\hline Common Stock & \[tex]$1,800 & \$[/tex]1,900 & -2.59\% \\
\hline
\end{tabular}

Which portfolio has a higher total weighted mean amount of money, and by how much?

A. Portfolio 1 has the higher total weighted mean amount of money by \[tex]$24.08.
B. Portfolio 2 has the higher total weighted mean amount of money by \$[/tex]24.08.
C. Portfolio 1 has the higher total weighted mean amount of money by \[tex]$18.90.
D. Portfolio 2 has the higher total weighted mean amount of money by \$[/tex]18.90.

Sagot :

GinnyAnswer
To determine which portfolio has a higher total weighted mean amount of money and by how much, we need to follow these steps:

1. Calculate the Weighted Mean Rate of Return (ROR) for each portfolio:
The weighted mean ROR takes into account the proportion of each investment within the total portfolio and applies the respective ROR.

For Portfolio 1:
[tex]\[ \text{Weighted Mean ROR}_1 = \left( \frac{2300 \times 2.35\% + 3100 \times 1.96\% + 650 \times 10.45\% + 1800 \times (-2.59\%)}{2300 + 3100 + 650 + 1800} \right) \][/tex]
After calculating, we find:
[tex]\[ \text{Weighted Mean ROR}_1 = 0.017339490445859872 \text{ or } 1.7339\% \][/tex]

For Portfolio 2:
[tex]\[ \text{Weighted Mean ROR}_2 = \left( \frac{1575 \times 2.35\% + 2100 \times 1.96\% + 795 \times 10.45\% + 1900 \times (-2.59\%)}{1575 + 2100 + 795 + 1900} \right) \][/tex]
After calculating, we find:
[tex]\[ \text{Weighted Mean ROR}_2 = 0.017588697017268444 \text{ or } 1.7589\% \][/tex]

2. Calculate the total weighted mean amount of money for each portfolio:
To get the total weighted mean amount of money, multiply the total value of each portfolio by its respective weighted mean ROR.

For Portfolio 1:
[tex]\[ \text{Total Value}_1 = 2300 + 3100 + 650 + 1800 = 7850 \][/tex]
[tex]\[ \text{Total Weighted Amount}_1 = 7850 \times 0.017339490445859872 = 136.115 \][/tex]

For Portfolio 2:
[tex]\[ \text{Total Value}_2 = 1575 + 2100 + 795 + 1900 = 6370 \][/tex]
[tex]\[ \text{Total Weighted Amount}_2 = 6370 \times 0.017588697017268444 = 112.040 \][/tex]

3. Determine which portfolio has the higher total weighted mean amount of money and by how much:
Comparing the total weighted amounts:
[tex]\[ \text{Portfolio 1: } 136.115 \][/tex]
[tex]\[ \text{Portfolio 2: } 112.040 \][/tex]
Since 136.115 is greater than 112.040, Portfolio 1 has the higher total weighted mean amount of money. The difference between the weighted amounts of the two portfolios is:
[tex]\[ 136.115 - 112.040 = 24.075 \][/tex]

Thus, Portfolio 1 has the higher total weighted mean amount of money by \$24.08.
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