Answered

Use the table to answer the question that follows.

\begin{tabular}{|l|l|l|l|}
\hline
ROR & Portfolio 1 & Portfolio 2 & Portfolio 3 \\
\hline
[tex]$4.6 \%$[/tex] & [tex]$\$[/tex] 850[tex]$ & $[/tex]\[tex]$ 1,050$[/tex] & [tex]$\$[/tex] 1,175[tex]$ \\
\hline
$[/tex]2.1 \%[tex]$ & $[/tex]\[tex]$ 2,425$[/tex] & [tex]$\$[/tex] 1,950[tex]$ & $[/tex]\[tex]$ 550$[/tex] \\
\hline
[tex]$13.8 \%$[/tex] & [tex]$\$[/tex] 280[tex]$ & $[/tex]\[tex]$ 1,295$[/tex] & [tex]$\$[/tex] 860[tex]$ \\
\hline
$[/tex]-6.5 \%[tex]$ & $[/tex]\[tex]$ 1,400$[/tex] & [tex]$\$[/tex] 745[tex]$ & $[/tex]\[tex]$ 550$[/tex] \\
\hline
[tex]$1.5 \%$[/tex] & [tex]$\$[/tex] 2,330[tex]$ & $[/tex]\[tex]$ 1,050$[/tex] & [tex]$\$[/tex] 2,000$ \\
\hline
\end{tabular}

Using technology, calculate the weighted mean of the RORs for each portfolio. Based on the results, which list shows a comparison of the overall performance of the portfolios, from best to worst?

A. Portfolio 1, Portfolio 2, Portfolio 3

B. Portfolio 3, Portfolio 2, Portfolio 1

C. Portfolio 1, Portfolio 3, Portfolio 2

D. Portfolio 2, Portfolio 3, Portfolio 1



Answer :

GinnyAnswer
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]

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