Answered

Use the table to answer the question that follows.

\begin{tabular}{|l|l|l|l|}
\hline
OR & Portfolio 1 & Portfolio 2 & Portfolio 3 \\
\hline
[tex]$3 \%$[/tex] & [tex]$\$[/tex] 1,150[tex]$ & $[/tex]\[tex]$ 800$[/tex] & [tex]$\$[/tex] 1,100[tex]$ \\
\hline
$[/tex]8 \%[tex]$ & $[/tex]\[tex]$ 1,825$[/tex] & [tex]$\$[/tex] 2,500[tex]$ & $[/tex]\[tex]$ 525$[/tex] \\
\hline
[tex]$-6.7 \%$[/tex] & [tex]$\$[/tex] 1,405[tex]$ & $[/tex]\[tex]$ 250$[/tex] & [tex]$\$[/tex] 825[tex]$ \\
\hline
$[/tex]10.4 \%[tex]$ & $[/tex]\[tex]$ 1,045$[/tex] & [tex]$\$[/tex] 1,200[tex]$ & $[/tex]\[tex]$ 400$[/tex] \\
\hline
[tex]$2.7 \%$[/tex] & [tex]$\$[/tex] 1,450[tex]$ & $[/tex]\[tex]$ 1,880$[/tex] & [tex]$\$[/tex] 2,225$ \\
\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 3, Portfolio 1, 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 determine the overall performance of the portfolios based on their rates of return (ROR), we need to calculate the weighted mean of the RORs for each portfolio. Here's a step-by-step explanation of how you would arrive at that calculation:

1. Identify the RORs and investment amounts:

The RORs are:
- [tex]\(3\% = 0.03\)[/tex]
- [tex]\(8\% = 0.08\)[/tex]
- [tex]\(-6.7\% = -0.067\)[/tex]
- [tex]\(10.4\% = 0.104\)[/tex]
- [tex]\(2.7\% = 0.027\)[/tex]

The investment amounts for each portfolio are given in the table.

2. Calculate the total investment for each portfolio:

For Portfolio 1:
[tex]\[ 1150 + 1825 + 1405 + 1045 + 1450 = 7875 \][/tex]

For Portfolio 2:
[tex]\[ 800 + 2500 + 250 + 1200 + 1880 = 6630 \][/tex]

For Portfolio 3:
[tex]\[ 1100 + 525 + 825 + 400 + 2225 = 5075 \][/tex]

3. Calculate the weighted mean ROR for each portfolio:

- For Portfolio 1:
[tex]\[ (1150 \times 0.03 + 1825 \times 0.08 + 1405 \times -0.067 + 1045 \times 0.104 + 1450 \times 0.027) / 7875 = 0.034064727273 \][/tex]

- For Portfolio 2:
[tex]\[ (800 \times 0.03 + 2500 \times 0.08 + 250 \times -0.067 + 1200 \times 0.104 + 1880 \times 0.027) / 6630 = 0.057739064857 \][/tex]

- For Portfolio 3:
[tex]\[ (1100 \times 0.03 + 525 \times 0.08 + 825 \times -0.067 + 400 \times 0.104 + 2225 \times 0.027) / 5075 = 0.023921182266 \][/tex]

4. Compare the weighted means to rank the portfolios:

Based on the calculations:
- Portfolio 1 Weighted Mean: [tex]\(0.034064727273\)[/tex]
- Portfolio 2 Weighted Mean: [tex]\(0.057739064857\)[/tex]
- Portfolio 3 Weighted Mean: [tex]\(0.023921182266\)[/tex]

Ranking them from highest to lowest weighted mean:
- Portfolio 2 ([tex]\(0.057739064857\)[/tex])
- Portfolio 1 ([tex]\(0.034064727273\)[/tex])
- Portfolio 3 ([tex]\(0.023921182266\)[/tex])

Therefore, the list that correctly shows the overall performance of the portfolios from best to worst is:
Portfolio 2, Portfolio 1, Portfolio 3.