Use the table to answer the question that follows.
| ROR | Portfolio 1 | Portfolio 2 | Portfolio 3 |
| -------- | ----------- | ----------- | ----------- |
| 7.3 % | $1,150 | $800 | $1,100 |
| 1.8 % | $1,825 | $2,500 | $525 |
| -6.7 % | $1,405 | $250 | $825 |
| 10.4 % | $1,045 | $1,200 | $400 |
| 2.7 % | $1,450 | $1,880 | $2,225 |
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?
A. Portfolio 3, Portfolio 1, Portfolio 2
B. Portfolio 2, Portfolio 3, Portfolio 1
C. Portfolio 1, Portfolio 2, Portfolio 3
D. Portfolio 3, Portfolio 2, Portfolio 1
Answer (2)
Calculate the total investment for each portfolio.
Calculate the weighted sum of the RORs for each portfolio.
Calculate the weighted mean ROR for each portfolio.
Rank the portfolios based on their weighted mean ROR from best to worst: Portfolio 2, Portfolio 3, Portfolio 1. The answer is P or t f o l i o 2 , P or t f o l i o 3 , P or t f o l i o 1 .
Explanation
Understanding the Problem We are asked to calculate the weighted mean of the Rates of Return (RORs) for three different portfolios and then rank these portfolios based on their performance, from best to worst. The weighted mean is calculated by multiplying each ROR by its corresponding investment amount, summing these products, and then dividing by the total investment amount for each portfolio.
Calculating Total Investments First, let's calculate the total investment for each portfolio:
Portfolio 1: 1150 + 1825 + 1405 + 1045 + 1450 = 6875 Portfolio 2: 800 + 2500 + 250 + 1200 + 1880 = 6630 Portfolio 3: 1100 + 525 + 825 + 400 + 2225 = 5075
Calculating Weighted Sum of RORs Next, we calculate the weighted sum of the RORs for each portfolio:
Portfolio 1: ( 0.073 × 1150 ) + ( 0.018 × 1825 ) + ( − 0.067 × 1405 ) + ( 0.104 × 1045 ) + ( 0.027 × 1450 ) = 83.95 + 32.85 − 94.135 + 108.68 + 39.15 = 170.575 Portfolio 2: ( 0.073 × 800 ) + ( 0.018 × 2500 ) + ( − 0.067 × 250 ) + ( 0.104 × 1200 ) + ( 0.027 × 1880 ) = 58.4 + 45 − 16.75 + 124.8 + 50.76 = 262.21 Portfolio 3: ( 0.073 × 1100 ) + ( 0.018 × 525 ) + ( − 0.067 × 825 ) + ( 0.104 × 400 ) + ( 0.027 × 2225 ) = 80.3 + 9.45 − 55.275 + 41.6 + 60.075 = 135.15
Calculating Weighted Mean RORs Now, we calculate the weighted mean ROR for each portfolio by dividing the weighted sum by the total investment:
Portfolio 1: 6875 170.575 ≈ 0.0248 = 2.48% Portfolio 2: 6630 262.21 ≈ 0.0395 = 3.95% Portfolio 3: 5075 135.15 ≈ 0.0266 = 2.66%
Ranking the Portfolios Finally, we rank the portfolios based on their weighted mean ROR from best to worst:
Portfolio 2: 3.95% Portfolio 3: 2.66% Portfolio 1: 2.48%
Therefore, the ranking from best to worst is Portfolio 2, Portfolio 3, Portfolio 1.
Final Answer Based on the calculations, the comparison of the overall performance of the portfolios, from best to worst, is Portfolio 2, Portfolio 3, Portfolio 1.
Examples
Weighted mean is a useful concept in finance. For example, if you are investing in multiple stocks, the weighted mean return helps you understand the overall performance of your portfolio, taking into account the amount you've invested in each stock. This gives a more accurate picture of your investment's success than simply averaging the returns of each stock, as it considers the relative importance of each investment based on its size.
After calculating the weighted means, Portfolio 2 shows the best performance at 3.95%, followed by Portfolio 3 at 2.66%, and lastly Portfolio 1 at 2.48%. Therefore, the correct ranking from best to worst is Portfolio 2, Portfolio 3, and Portfolio 1.
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