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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.
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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