At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
Here are the solution steps for determining which portfolio has a higher total weighted mean amount of money and by how much:
1. Understanding the Data:
- Portfolio 1 investments: [tex]$2300, $[/tex]3100, [tex]$650, $[/tex]1800
- Portfolio 2 investments: [tex]$1575, $[/tex]2100, [tex]$795, $[/tex]1900
- Rates of Return (ROR): 2.35%, 1.96%, 10.45%, -2.59%
2. Calculate the Weighted Mean ROR for Portfolio 1:
- The weighted mean ROR is calculated by taking the sum of each investment amount multiplied by its rate of return, then dividing by the total amount invested.
- Let's denote [tex]\( A_i \)[/tex] as the amount invested in each asset and [tex]\( R_i \)[/tex] as the corresponding rate of return.
- For Portfolio 1:
[tex]\[ \text{Weighted Mean ROR (Portfolio 1)} = \frac{\sum (A_i \times \frac{R_i}{100})}{\sum (A_i)} \][/tex]
- Performing calculations yields:
[tex]\[ \text{Weighted Mean ROR (Portfolio 1)} ≈ 0.017339490445859872 \][/tex]
3. Calculate the Weighted Mean ROR for Portfolio 2:
- Similarly, we calculate the weighted mean ROR for Portfolio 2:
- For Portfolio 2:
[tex]\[ \text{Weighted Mean ROR (Portfolio 2)} = \frac{\sum (A_i \times \frac{R_i}{100})}{\sum (A_i)} \][/tex]
- Performing calculations yields:
[tex]\[ \text{Weighted Mean ROR (Portfolio 2)} ≈ 0.017588697017268444 \][/tex]
4. Determine Which Portfolio Has a Higher Weighted Mean ROR:
- Comparing the two weighted mean ROR values:
[tex]\[ 0.017339490445859872 \text{ (Portfolio 1)} < 0.017588697017268444 \text{ (Portfolio 2)} \][/tex]
- Therefore, Portfolio 2 has a higher weighted mean ROR.
5. Calculate the Difference:
- The difference between the two weighted mean ROR values:
[tex]\[ \text{Difference} = 0.017588697017268444 - 0.017339490445859872 ≈ 0.0002492065714085716 \][/tex]
6. Translate to Monetary Terms:
- Convert the difference back to a monetary equivalent understanding (as a better gain per dollar invested).
- Here, monetary values for weighted ROR differences are often translated as consistent returns per unit invested. However, our comparison is directly in these fractional returns indicating portfolio benefit margins.
Therefore, Portfolio 2 has the higher total weighted mean amount of money by approximately [tex]$0.0002492065714085716, and it's safe to contextualize it as "Portfolio 2 has the higher total weighted mean amount of money by \$[/tex]0.000249 or approximately 24 cents per 1000 USD."
1. Understanding the Data:
- Portfolio 1 investments: [tex]$2300, $[/tex]3100, [tex]$650, $[/tex]1800
- Portfolio 2 investments: [tex]$1575, $[/tex]2100, [tex]$795, $[/tex]1900
- Rates of Return (ROR): 2.35%, 1.96%, 10.45%, -2.59%
2. Calculate the Weighted Mean ROR for Portfolio 1:
- The weighted mean ROR is calculated by taking the sum of each investment amount multiplied by its rate of return, then dividing by the total amount invested.
- Let's denote [tex]\( A_i \)[/tex] as the amount invested in each asset and [tex]\( R_i \)[/tex] as the corresponding rate of return.
- For Portfolio 1:
[tex]\[ \text{Weighted Mean ROR (Portfolio 1)} = \frac{\sum (A_i \times \frac{R_i}{100})}{\sum (A_i)} \][/tex]
- Performing calculations yields:
[tex]\[ \text{Weighted Mean ROR (Portfolio 1)} ≈ 0.017339490445859872 \][/tex]
3. Calculate the Weighted Mean ROR for Portfolio 2:
- Similarly, we calculate the weighted mean ROR for Portfolio 2:
- For Portfolio 2:
[tex]\[ \text{Weighted Mean ROR (Portfolio 2)} = \frac{\sum (A_i \times \frac{R_i}{100})}{\sum (A_i)} \][/tex]
- Performing calculations yields:
[tex]\[ \text{Weighted Mean ROR (Portfolio 2)} ≈ 0.017588697017268444 \][/tex]
4. Determine Which Portfolio Has a Higher Weighted Mean ROR:
- Comparing the two weighted mean ROR values:
[tex]\[ 0.017339490445859872 \text{ (Portfolio 1)} < 0.017588697017268444 \text{ (Portfolio 2)} \][/tex]
- Therefore, Portfolio 2 has a higher weighted mean ROR.
5. Calculate the Difference:
- The difference between the two weighted mean ROR values:
[tex]\[ \text{Difference} = 0.017588697017268444 - 0.017339490445859872 ≈ 0.0002492065714085716 \][/tex]
6. Translate to Monetary Terms:
- Convert the difference back to a monetary equivalent understanding (as a better gain per dollar invested).
- Here, monetary values for weighted ROR differences are often translated as consistent returns per unit invested. However, our comparison is directly in these fractional returns indicating portfolio benefit margins.
Therefore, Portfolio 2 has the higher total weighted mean amount of money by approximately [tex]$0.0002492065714085716, and it's safe to contextualize it as "Portfolio 2 has the higher total weighted mean amount of money by \$[/tex]0.000249 or approximately 24 cents per 1000 USD."
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.
