Find solutions to your problems with the expert advice available on IDNLearn.com. Find the answers you need quickly and accurately with help from our knowledgeable and experienced experts.
Sagot :
Alright, let's tackle this problem step by step.
First, we'll define the problem clearly:
- We are given the average rates of return (AOR) for different portfolios over a certain period.
- Our task is to determine the weighted mean of the rates of return (ROR) for each portfolio.
Here is the table presented:
[tex]\[ \begin{tabular}{|c|c|c|c|} \hline AOR & Portfolio 1 & Portfolio 2 & Portfolio 3 \\ \hline 7.3 & 81,150 & 8,500 & 1,100 \\ \hline 100 & 51,800 & 52,500 & 8,525 \\ \hline -6.7 & 81,405 & 250 & 825 \\ \hline 20.4 & 81,065 & 81,200 & 5,400 \\ \hline 270 & 81,450 & 511,800 & 12,225 \\ \hline \end{tabular} \][/tex]
### Step-by-Step Solution:
1. Calculate the total value for each portfolio:
- Sum of the values in Portfolio 1:
[tex]\[ 81,150 + 51,800 + 81,405 + 81,065 + 81,450 = 376,870 \][/tex]
- Sum of the values in Portfolio 2:
[tex]\[ 8,500 + 52,500 + 250 + 81,200 + 511,800 = 654,250 \][/tex]
- Sum of the values in Portfolio 3:
[tex]\[ 1,100 + 8,525 + 825 + 5,400 + 12,225 = 28,075 \][/tex]
2. Calculate the weighted mean for each portfolio:
- For Portfolio 1:
[tex]\[ \text{Weighted Mean Portfolio 1} = \frac{(7.3 \times 81,150) + (100 \times 51,800) + (-6.7 \times 81,405) + (20.4 \times 81,065) + (270 \times 81,450)}{376,870} \][/tex]
This results in:
[tex]\[ 76.6105221959827 \][/tex]
- For Portfolio 2:
[tex]\[ \text{Weighted Mean Portfolio 2} = \frac{(7.3 \times 8,500) + (100 \times 52,500) + (-6.7 \times 250) + (20.4 \times 81,200) + (270 \times 511,800)}{654,250} \][/tex]
This results in:
[tex]\[ 221.86145204432557 \][/tex]
- For Portfolio 3:
[tex]\[ \text{Weighted Mean Portfolio 3} = \frac{(7.3 \times 1,100) + (100 \times 8,525) + (-6.7 \times 825) + (20.4 \times 5,400) + (270 \times 12,225)}{28,075} \][/tex]
This results in:
[tex]\[ 151.94701691896705 \][/tex]
3. Determine and compare the overall performance of the portfolios:
- The weighted means we have computed are as follows:
- Portfolio 1: 76.6105221959827
- Portfolio 2: 221.86145204432557
- Portfolio 3: 151.94701691896705
4. Sort the portfolios from worst to best based on their weighted means:
- Lower weighted mean indicates poorer performance, while a higher weighted mean indicates better performance.
- Sorting the portfolios in ascending order of their weighted means:
[tex]\[ \text{Portfolio 1 (76.61)}, \text{Portfolio 3 (151.95)}, \text{Portfolio 2 (221.86)} \][/tex]
Thus, the correct order from worst to best is:
[tex]\[ \text{Portfolio 1, Portfolio 3, Portfolio 2} \][/tex]
So, the correct list that shows a comparison of the overall performance of the portfolios, from worst to best, is:
[tex]\[ \text{Portfolio 1, Portfolio 3, Portfolio 2} \][/tex]
First, we'll define the problem clearly:
- We are given the average rates of return (AOR) for different portfolios over a certain period.
- Our task is to determine the weighted mean of the rates of return (ROR) for each portfolio.
Here is the table presented:
[tex]\[ \begin{tabular}{|c|c|c|c|} \hline AOR & Portfolio 1 & Portfolio 2 & Portfolio 3 \\ \hline 7.3 & 81,150 & 8,500 & 1,100 \\ \hline 100 & 51,800 & 52,500 & 8,525 \\ \hline -6.7 & 81,405 & 250 & 825 \\ \hline 20.4 & 81,065 & 81,200 & 5,400 \\ \hline 270 & 81,450 & 511,800 & 12,225 \\ \hline \end{tabular} \][/tex]
### Step-by-Step Solution:
1. Calculate the total value for each portfolio:
- Sum of the values in Portfolio 1:
[tex]\[ 81,150 + 51,800 + 81,405 + 81,065 + 81,450 = 376,870 \][/tex]
- Sum of the values in Portfolio 2:
[tex]\[ 8,500 + 52,500 + 250 + 81,200 + 511,800 = 654,250 \][/tex]
- Sum of the values in Portfolio 3:
[tex]\[ 1,100 + 8,525 + 825 + 5,400 + 12,225 = 28,075 \][/tex]
2. Calculate the weighted mean for each portfolio:
- For Portfolio 1:
[tex]\[ \text{Weighted Mean Portfolio 1} = \frac{(7.3 \times 81,150) + (100 \times 51,800) + (-6.7 \times 81,405) + (20.4 \times 81,065) + (270 \times 81,450)}{376,870} \][/tex]
This results in:
[tex]\[ 76.6105221959827 \][/tex]
- For Portfolio 2:
[tex]\[ \text{Weighted Mean Portfolio 2} = \frac{(7.3 \times 8,500) + (100 \times 52,500) + (-6.7 \times 250) + (20.4 \times 81,200) + (270 \times 511,800)}{654,250} \][/tex]
This results in:
[tex]\[ 221.86145204432557 \][/tex]
- For Portfolio 3:
[tex]\[ \text{Weighted Mean Portfolio 3} = \frac{(7.3 \times 1,100) + (100 \times 8,525) + (-6.7 \times 825) + (20.4 \times 5,400) + (270 \times 12,225)}{28,075} \][/tex]
This results in:
[tex]\[ 151.94701691896705 \][/tex]
3. Determine and compare the overall performance of the portfolios:
- The weighted means we have computed are as follows:
- Portfolio 1: 76.6105221959827
- Portfolio 2: 221.86145204432557
- Portfolio 3: 151.94701691896705
4. Sort the portfolios from worst to best based on their weighted means:
- Lower weighted mean indicates poorer performance, while a higher weighted mean indicates better performance.
- Sorting the portfolios in ascending order of their weighted means:
[tex]\[ \text{Portfolio 1 (76.61)}, \text{Portfolio 3 (151.95)}, \text{Portfolio 2 (221.86)} \][/tex]
Thus, the correct order from worst to best is:
[tex]\[ \text{Portfolio 1, Portfolio 3, Portfolio 2} \][/tex]
So, the correct list that shows a comparison of the overall performance of the portfolios, from worst to best, is:
[tex]\[ \text{Portfolio 1, Portfolio 3, Portfolio 2} \][/tex]
We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. IDNLearn.com is committed to your satisfaction. Thank you for visiting, and see you next time for more helpful answers.
