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.
