Answer:
C) Portfolio 1, Portfolio 2, Portfolio 3
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5 cm}\underline{Weighted Mean Formula}\\\\$ \overline{x}=\dfrac{\displaystyle\sum^{n}_{i=1}x_iw_i}{\displaystyle\sum^{n}_{i=1}w_i}$\\\\\\where:\\\phantom{ww} $\bullet$ $x_i$ is the data value\\\phantom{ww} $\bullet$ $w_i$ is the weight\\\end{minipage}}[/tex]
To calculate the weighted mean of the RoR for each portfolio:
- Multiply the RoR (xi) in decimal form by the corresponding amount invested (wi).
- Sum the values calculated in step 1.
- Divide the sum from step 2 by the sum of the amounts invested (in that portfolio).
Portfolio 1
[tex]\implies \overline{x}=\dfrac{1250 \cdot 0.039+575 \cdot 0.017 + 895 \cdot .0106 + 800 \cdot -0.032 + 1775 \cdot 0.081}{1250+575+895+800+1775}[/tex]
[tex]\implies \overline{x}=\dfrac{271.57}{5295}[/tex]
[tex]\implies \overline{x}=0.051288075...[/tex]
[tex]\implies \overline{x}=5.13\%\;\; \sf (2 \;d.p.)[/tex]
Portfolio 2
[tex]\implies \overline{x}=\dfrac{950\cdot 0.039+2025\cdot 0.017 + 1185\cdot .0106 + 445\cdot -0.032 + 625\cdot 0.081}{950+2025+1185+445+625}[/tex]
[tex]\implies \overline{x}=\dfrac{233.47}{5230}[/tex]
[tex]\implies \overline{x}=0.0446405353...[/tex]
[tex]\implies \overline{x}=4.46\%\;\; \sf (2 \;d.p.)[/tex]
Portfolio 3
[tex]\implies \overline{x}=\dfrac{900\cdot 0.039+2350\cdot 0.017 + 310\cdot .0106 + 1600\cdot -0.032 + 2780\cdot 0.081}{900+2350+310+1600+2780}[/tex]
[tex]\implies \overline{x}=\dfrac{281.89}{7940}[/tex]
[tex]\implies \overline{x}=0.0355025188...[/tex]
[tex]\implies \overline{x}=3.55\%\;\; \sf (2 \;d.p.)[/tex]
The RoR (rate of return) is the net gain (or loss) of an investment over a specified time period, expressed as a percentage of the investment's initial cost.
Therefore, based on the weighted means of the RoRs for each portfolio, the best to worst portfolios are:
- Portfolio 1, Portfolio 2, Portfolio 3
(as Portfolio 1 has the highest RoR and Portfolio 3 has the lowest RoR).
