Question

use the table to answer the question that follows.

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 3, portfolio 1, portfolio 2
• portfolio 2, portfolio 3, portfolio 1
• portfolio 1, portfolio 2, portfolio 3
• portfolio 3, portfolio 2, portfolio 1

Explanation:

Calculate total value of each portfolio

We sum the asset values for each portfolio to find the total investment.

For Portfolio 1:

$$ \text{Total}_1 = 1150 + 1825 + 1405 + 1045 + 1450 = 6875 $$

For Portfolio 2:

$$ \text{Total}_2 = 800 + 2500 + 250 + 1200 + 1880 = 6630 $$

For Portfolio 3:

$$ \text{Total}_3 = 1100 + 525 + 825 + 400 + 2225 = 5075 $$

Calculate weighted return for Portfolio 1

We multiply each Rate of Return (ROR) by its corresponding asset value, sum them, and divide by the total value.

$$
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$$

$$ \text{Weighted Mean}_1 = \frac{170.495}{6875} \approx 2.48\% $$

Calculate weighted return for Portfolio 2

We repeat the weighted sum calculation for Portfolio 2.

$$
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$$

$$ \text{Weighted Mean}_2 = \frac{262.21}{6630} \approx 3.96\% $$

Calculate weighted return for Portfolio 3

We repeat the weighted sum calculation for Portfolio 3.

$$
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$$

$$ \text{Weighted Mean}_3 = \frac{136.15}{5075} \approx 2.68\% $$

Compare performance from best to worst

We rank the portfolios based on their weighted mean rates of return.

Comparing the calculated values:

• Portfolio 2: \(3.96\%\) (Best)
• Portfolio 3: \(2.68\%\) (Middle)
• Portfolio 1: \(2.48\%\) (Worst)

Thus, the ranking from best to worst is: Portfolio 2, Portfolio 3, Portfolio 1.

Answer:

• Portfolio 3, Portfolio 1, Portfolio 2
• Portfolio 2, Portfolio 3, Portfolio 1 (Correct answer)
• Portfolio 1, Portfolio 2, Portfolio 3
• Portfolio 3, Portfolio 2, Portfolio 1