To determine which portfolio has a higher total weighted mean amount of money and by how much, we take the following steps:
1. Identify the investment amounts and their corresponding Rates of Return (ROR) for each portfolio:
- Tech Company Stock: Portfolio 1 has \[tex]$2,300, Portfolio 2 has \$[/tex]1,575, with an ROR of 2.35%.
- Government Bond: Portfolio 1 has \[tex]$3,100, Portfolio 2 has \$[/tex]2,100, with an ROR of 1.96%.
- Junk Bond: Portfolio 1 has \[tex]$650, Portfolio 2 has \$[/tex]795, with an ROR of 10.45%.
- Common Stock: Portfolio 1 has \[tex]$1,800, Portfolio 2 has \$[/tex]1,900, with an ROR of -2.59%.
2. Convert the ROR percentages into decimal form for accurate calculations:
- Tech Company Stock: [tex]\( 2.35\% \rightarrow 0.0235 \)[/tex]
- Government Bond: [tex]\( 1.96\% \rightarrow 0.0196 \)[/tex]
- Junk Bond: [tex]\( 10.45\% \rightarrow 0.1045 \)[/tex]
- Common Stock: [tex]\( -2.59\% \rightarrow -0.0259 \)[/tex]
3. Calculate the weighted mean amount of money for each portfolio by summing the product of the amount invested in each category and its ROR:
For Portfolio 1:
[tex]\[
\text{Weighted Mean}_1 = (2300 \times 0.0235) + (3100 \times 0.0196) + (650 \times 0.1045) + (1800 \times -0.0259)
\][/tex]
[tex]\[
\text{Weighted Mean}_1 = 54.05 + 60.76 + 67.93 - 46.62 = 136.115
\][/tex]
For Portfolio 2:
[tex]\[
\text{Weighted Mean}_2 = (1575 \times 0.0235) + (2100 \times 0.0196) + (795 \times 0.1045) + (1900 \times -0.0259)
\][/tex]
[tex]\[
\text{Weighted Mean}_2 = 37.0125 + 41.16 + 83.0475 - 49.18 = 112.039
\][/tex]
4. Calculate the absolute difference between the weighted mean amounts of the two portfolios:
[tex]\[
\text{Difference} = |136.115 - 112.039| = 24.075
\][/tex]
5. Determine which portfolio has the higher total weighted mean amount of money:
[tex]\[
\text{Portfolio 1} (\$136.115) > \text{Portfolio 2} (\$112.039)
\][/tex]
Therefore, Portfolio 1 has the higher total weighted mean amount of money by \$24.08.
