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."
