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]$3.9 \%$[/tex] & [tex]$\$[/tex] 1,250[tex]$ & $[/tex]\[tex]$ 950$[/tex] & [tex]$\$[/tex] 900[tex]$ \\
\hline $[/tex]1.7 \%[tex]$ & $[/tex]\[tex]$ 575$[/tex] & [tex]$\$[/tex] 2,025[tex]$ & $[/tex]\[tex]$ 2,350$[/tex] \\
\hline [tex]$10.6 \%$[/tex] & [tex]$\$[/tex] 895[tex]$ & $[/tex]\[tex]$ 1,185$[/tex] & [tex]$\$[/tex] 310[tex]$ \\
\hline$[/tex]-3.2 \%[tex]$ & $[/tex]\[tex]$ 800$[/tex] & [tex]$\$[/tex] 445[tex]$ & $[/tex]\[tex]$ 1,600$[/tex] \\
\hline [tex]$8.1 \%$[/tex] & [tex]$\$[/tex] 1,775[tex]$ & $[/tex]\[tex]$ 625$[/tex] & [tex]$\$[/tex] 2,780$ \\
\hline
\end{tabular}

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 3, Portfolio 2
B. Portfolio 2, Portfolio 3, Portfolio 1
C. Portfolio 1, Portfolio 2, Portfolio 3
D. Portfolio 3, Portfolio 2, Portfolio 1



Answer :

GinnyAnswer
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]

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