To determine the overall performance of the portfolios, we need to calculate the weighted mean of the Return on Rates (RORs) for each portfolio. Here is the step-by-step process:
### Step 1: Extract Data
First, take note of the given RORs and the corresponding capital investments for each portfolio.
#### Return on Rates (RORs):
- [tex]\(4.6\%\)[/tex]
- [tex]\(2.1\%\)[/tex]
- [tex]\(13.8\%\)[/tex]
- [tex]\(-6.5\%\)[/tex]
- [tex]\(1.5\%\)[/tex]
#### Capital Investments for Each Portfolio:
- Portfolio 1: \[tex]$850, \$[/tex]2425, \[tex]$280, \$[/tex]1400, \[tex]$2330
- Portfolio 2: \$[/tex]1050, \[tex]$1950, \$[/tex]1295, \[tex]$745, \$[/tex]1050
- Portfolio 3: \[tex]$1175, \$[/tex]550, \[tex]$860, \$[/tex]550, \$2000
### Step 2: Calculate the Weighted Mean for Each Portfolio
The weighted mean for a portfolio is calculated using the formula:
[tex]\[
\text{Weighted Mean} = \frac{\sum (ROR_i \times \text{capital}_i)}{\sum \text{capital}_i}
\][/tex]
#### Portfolio 1:
- Weighted Mean: 0.9967741935483871
#### Portfolio 2:
- Weighted Mean: 3.863464696223317
#### Portfolio 3:
- Weighted Mean: 3.4767283349561833
### Step 3: Compare the Weighted Means
Based on the calculated weighted means, we can rank the portfolios from best to worst:
1. Portfolio 2: Weighted Mean = 3.863464696223317
2. Portfolio 3: Weighted Mean = 3.4767283349561833
3. Portfolio 1: Weighted Mean = 0.9967741935483871
### Conclusion
The correct order of overall performance from best to worst is:
Portfolio 2, Portfolio 3, Portfolio 1
Hence, the correct answer is:
[tex]\[
\text{Portfolio 2, Portfolio 3, Portfolio 1}
\][/tex]
