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]$-7.2 \%$[/tex] & [tex]$\$[/tex] 850[tex]$ & $[/tex]\[tex]$ 1,050$[/tex] & [tex]$\$[/tex] 1,175[tex]$ \\
\hline
$[/tex]5.8 \%[tex]$ & $[/tex]\[tex]$ 2,425$[/tex] & [tex]$\$[/tex] 1,950[tex]$ & $[/tex]\[tex]$ 550$[/tex] \\
\hline
[tex]$10.6 \%$[/tex] & [tex]$\$[/tex] 280[tex]$ & $[/tex]\[tex]$ 1,295$[/tex] & [tex]$\$[/tex] 860[tex]$ \\
\hline
$[/tex]3.6 \%[tex]$ & $[/tex]\[tex]$ 1,400$[/tex] & [tex]$\$[/tex] 745[tex]$ & $[/tex]\[tex]$ 550$[/tex] \\
\hline
[tex]$0.9 \%$[/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 2, Portfolio 1, Portfolio 3
D. Portfolio 3, Portfolio 1, Portfolio 2



Answer :

GinnyAnswer
To determine the weighted mean of the RORs (Rate of Returns) for each portfolio, we follow these steps:

1. Calculate the total investment in each portfolio.
2. Determine the weighted ROR for each portfolio.
3. Compare the weighted RORs and rank the portfolios from best to worst performance.

Step 1: Calculate the Total Investment for Each Portfolio

Portfolio 1:
[tex]\[ 850 + 2425 + 280 + 1400 + 2330 = 7285 \][/tex]

Portfolio 2:
[tex]\[ 1050 + 1950 + 1295 + 745 + 1050 = 7090 \][/tex]

Portfolio 3:
[tex]\[ 1175 + 550 + 860 + 550 + 2000 = 5135 \][/tex]

Step 2: Calculate the Weighted ROR for Each Portfolio

The weighted ROR is calculated using the formula:
[tex]\[ \text{Weighted ROR} = \sum \left(\frac{\text{Investment Amount} \times \text{ROR}}{\text{Total Investment}}\right) \][/tex]

Portfolio 1:
[tex]\[ \text{Weighted ROR}_1 = \left(\frac{850 \times -7.2}{7285}\right) + \left(\frac{2425 \times 5.8}{7285}\right) + \left(\frac{280 \times 10.6}{7285}\right) + \left(\frac{1400 \times 3.6}{7285}\right) + \left(\frac{2330 \times 0.9}{7285}\right) = 2.477693891557996 \][/tex]

Portfolio 2:
[tex]\[ \text{Weighted ROR}_2 = \left(\frac{1050 \times -7.2}{7090}\right) + \left(\frac{1950 \times 5.8}{7090}\right) + \left(\frac{1295 \times 10.6}{7090}\right) + \left(\frac{745 \times 3.6}{7090}\right) + \left(\frac{1050 \times 0.9}{7090}\right) = 3.465353037766831 \][/tex]

Portfolio 3:
[tex]\[ \text{Weighted ROR}_3 = \left(\frac{1175 \times -7.2}{5135}\right) + \left(\frac{550 \times 5.8}{5135}\right) + \left(\frac{860 \times 10.6}{5135}\right) + \left(\frac{550 \times 3.6}{5135}\right) + \left(\frac{2000 \times 0.9}{5135}\right) = 1.485102239532619 \][/tex]

Step 3: Rank the Portfolios from Best to Worst Performance

Comparing the weighted RORs:
[tex]\[ \text{Portfolio 2}: 3.465353037766831 \][/tex]
[tex]\[ \text{Portfolio 1}: 2.477693891557996 \][/tex]
[tex]\[ \text{Portfolio 3}: 1.485102239532619 \][/tex]

Order from best to worst performance:
[tex]\[ \text{Portfolio 2, Portfolio 1, Portfolio 3} \][/tex]

Thus, the list showing the comparison of the overall performance of the portfolios from best to worst is:
[tex]\[ \boxed{\text{Portfolio 2, Portfolio 1, Portfolio 3}} \][/tex]

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