Answer :
To address this question, we need to find the weighted mean Rates of Return (RORs) for each portfolio and then compare them. Let's break it down step-by-step.
### Step 1: Gather the Data
We have the following data:
[tex]\[ \begin{array}{|l|l|l|l|} \hline \text{ROR (\%)} & \text{Portfolio 1 (\$)} & \text{Portfolio 2 (\$)} & \text{Portfolio 3 (\$)} \\ \hline 3.9 & 1250 & 950 & 900 \\ 1.7 & 575 & 2025 & 2350 \\ 10.6 & 895 & 1185 & 310 \\ -3.2 & 800 & 445 & 1600 \\ 8.1 & 1775 & 625 & 2780 \\ \hline \end{array} \][/tex]
### Step 2: Calculate the Total Investment for Each Portfolio
- Total investment for Portfolio 1:
[tex]\[ 1250 + 575 + 895 + 800 + 1775 = 5,295 \][/tex]
- Total investment for Portfolio 2:
[tex]\[ 950 + 2025 + 1185 + 445 + 625 = 5,230 \][/tex]
- Total investment for Portfolio 3:
[tex]\[ 900 + 2350 + 310 + 1600 + 2780 = 7,940 \][/tex]
### Step 3: Calculate the Weighted Mean ROR for Each Portfolio
- For Portfolio 1:
[tex]\[ \text{Weighted Mean ROR}_1 = \frac{(3.9 \times 1250) + (1.7 \times 575) + (10.6 \times 895) + (-3.2 \times 800) + (8.1 \times 1775)}{5295} = 5.1288\% \][/tex]
- For Portfolio 2:
[tex]\[ \text{Weighted Mean ROR}_2 = \frac{(3.9 \times 950) + (1.7 \times 2025) + (10.6 \times 1185) + (-3.2 \times 445) + (8.1 \times 625)}{5230} = 4.4641\% \][/tex]
- For Portfolio 3:
[tex]\[ \text{Weighted Mean ROR}_3 = \frac{(3.9 \times 900) + (1.7 \times 2350) + (10.6 \times 310) + (-3.2 \times 1600) + (8.1 \times 2780)}{7940} = 3.5503\% \][/tex]
### Step 4: Compare the Weighted Means
The weighted mean RORs for each portfolio are:
1. Portfolio 1: 5.1288\%
2. Portfolio 2: 4.4641\%
3. Portfolio 3: 3.5503\%
### Step 5: Order the Portfolios from Best to Worst
Comparing the RORs:
- Portfolio 1: 5.1288\%
- Portfolio 2: 4.4641\%
- Portfolio 3: 3.5503\%
Thus, the list from best to worst is:
1. Portfolio 1
2. Portfolio 2
3. Portfolio 3
So, the correct comparison of the overall performance is:
Portfolio 1, Portfolio 2, Portfolio 3
Hence, the correct answer is:
[tex]\[ \text{Portfolio 1, Portfolio 2, Portfolio 3} \][/tex]
### Step 1: Gather the Data
We have the following data:
[tex]\[ \begin{array}{|l|l|l|l|} \hline \text{ROR (\%)} & \text{Portfolio 1 (\$)} & \text{Portfolio 2 (\$)} & \text{Portfolio 3 (\$)} \\ \hline 3.9 & 1250 & 950 & 900 \\ 1.7 & 575 & 2025 & 2350 \\ 10.6 & 895 & 1185 & 310 \\ -3.2 & 800 & 445 & 1600 \\ 8.1 & 1775 & 625 & 2780 \\ \hline \end{array} \][/tex]
### Step 2: Calculate the Total Investment for Each Portfolio
- Total investment for Portfolio 1:
[tex]\[ 1250 + 575 + 895 + 800 + 1775 = 5,295 \][/tex]
- Total investment for Portfolio 2:
[tex]\[ 950 + 2025 + 1185 + 445 + 625 = 5,230 \][/tex]
- Total investment for Portfolio 3:
[tex]\[ 900 + 2350 + 310 + 1600 + 2780 = 7,940 \][/tex]
### Step 3: Calculate the Weighted Mean ROR for Each Portfolio
- For Portfolio 1:
[tex]\[ \text{Weighted Mean ROR}_1 = \frac{(3.9 \times 1250) + (1.7 \times 575) + (10.6 \times 895) + (-3.2 \times 800) + (8.1 \times 1775)}{5295} = 5.1288\% \][/tex]
- For Portfolio 2:
[tex]\[ \text{Weighted Mean ROR}_2 = \frac{(3.9 \times 950) + (1.7 \times 2025) + (10.6 \times 1185) + (-3.2 \times 445) + (8.1 \times 625)}{5230} = 4.4641\% \][/tex]
- For Portfolio 3:
[tex]\[ \text{Weighted Mean ROR}_3 = \frac{(3.9 \times 900) + (1.7 \times 2350) + (10.6 \times 310) + (-3.2 \times 1600) + (8.1 \times 2780)}{7940} = 3.5503\% \][/tex]
### Step 4: Compare the Weighted Means
The weighted mean RORs for each portfolio are:
1. Portfolio 1: 5.1288\%
2. Portfolio 2: 4.4641\%
3. Portfolio 3: 3.5503\%
### Step 5: Order the Portfolios from Best to Worst
Comparing the RORs:
- Portfolio 1: 5.1288\%
- Portfolio 2: 4.4641\%
- Portfolio 3: 3.5503\%
Thus, the list from best to worst is:
1. Portfolio 1
2. Portfolio 2
3. Portfolio 3
So, the correct comparison of the overall performance is:
Portfolio 1, Portfolio 2, Portfolio 3
Hence, the correct answer is:
[tex]\[ \text{Portfolio 1, Portfolio 2, Portfolio 3} \][/tex]