using technology, calculate the weighted mean of the rors for each portfolio. based on the results, which list shows a comparison of the overall performance of the portfolios, from best to worst? portfolio 1, portfolio 2, portfolio 3 portfolio 3, portfolio 2, portfolio 1 portfolio 1, portfolio 3, portfolio 2 portfolio 2, portfolio 3, portfolio 1

Question

Accepted Answer

# Explanation:
## Step1: Calculate the total investment for each portfolio
- **Portfolio 1**: $850 + 2425+280 + 1400+2330=\$7285$
- **Portfolio 2**: $1050+1950 + 1295+745+1050=\$6090$
- **Portfolio 3**: $1175+550+860+550+2000=\$5135$

## Step2: Calculate the weighted - mean ROR for each portfolio
The formula for the weighted mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}w_{i}}{\sum_{i = 1}^{n}w_{i}}$, where $x_{i}$ is the ROR and $w_{i}$ is the investment amount.
- **Portfolio 1**:
$$
\begin{align*}
\bar{x}_{1}&=\frac{0.046\times850+0.021\times2425 + 0.138\times280+(- 0.065)\times1400+0.015\times2330}{7285}\
&=\frac{39.1+50.925+38.64-91+34.95}{7285}\
&=\frac{72.615}{7285}\approx0.01 = 1.0\%
\end{align*}
$$
- **Portfolio 2**:
$$
\begin{align*}
\bar{x}_{2}&=\frac{0.046\times1050+0.021\times1950+0.138\times1295+(-0.065)\times745 + 0.015\times1050}{6090}\
&=\frac{48.3+40.95+178.71-48.425 + 15.75}{6090}\
&=\frac{235.285}{6090}\approx0.0386=3.86\%
\end{align*}
$$
- **Portfolio 3**:
$$
\begin{align*}
\bar{x}_{3}&=\frac{0.046\times1175+0.021\times550+0.138\times860+(-0.065)\times550+0.015\times2000}{5135}\
&=\frac{54.05+11.55+118.68-35.75 + 30}{5135}\
&=\frac{178.53}{5135}\approx0.0348 = 3.48\%
\end{align*}
$$

## Step3: Compare the weighted - mean RORs
Since $3.86\%>3.48\%>1.0\%$, the order from best to worst is Portfolio 2, Portfolio 3, Portfolio 1.

# Answer:
Portfolio 2, Portfolio 3, Portfolio 1

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the total investment for each portfolio

Step2: Calculate the weighted - mean ROR for each portfolio

Step3: Compare the weighted - mean RORs

Answer: