Three investment portfolios are shown below.
| ROR | Portfolio 1 | Portfolio 2 | Portfolio 3 |
| :----------- | :---------- | :---------- | :---------- |
| -3.8 % | $700 | $1,250 | $1,025 |
| 2.1 % | $2,575 | $1,700 | $500 |
| 11.3 % | $220 | $1,515 | $790 |
| 5.8 % | $1,000 | $1,345 | $250 |
| 1.6 % | $1,430 | $1,675 | $2,500 |
Using technology, calculate the weighted average 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 1, Portfolio 3, Portfolio 2
B. Portfolio 2, Portfolio 3, Portfolio 1
C. Portfolio 1, Portfolio 2, Portfolio 3
D. Portfolio 3, Portfolio 2, Portfolio 1
Answer (1)
Calculate the total investment for each portfolio.
Calculate the weighted rate of return (ROR) for each portfolio.
Compare the weighted RORs for the three portfolios.
Rank the portfolios from highest weighted average ROR to lowest weighted average ROR: 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
Calculate Total Investments First, we need to calculate the total investment for each portfolio. For Portfolio 1, the total investment is: 700 + 2575 + 220 + 1000 + 1430 = 5925 For Portfolio 2, the total investment is: 1250 + 1700 + 1515 + 1345 + 1675 = 7485 For Portfolio 3, the total investment is: 1025 + 500 + 790 + 250 + 2500 = 5065
Calculate Weighted RORs Next, we calculate the weighted rate of return (ROR) for each portfolio. This is done by multiplying each ROR by its corresponding investment, summing these products, and then dividing by the total investment. For Portfolio 1, the weighted ROR is: 5925 ( − 0.038 × 700 ) + ( 0.021 × 2575 ) + ( 0.113 × 220 ) + ( 0.058 × 1000 ) + ( 0.016 × 1430 ) = 5925 − 26.6 + 54.075 + 24.86 + 58 + 22.88 = 5925 133.295 ≈ 0.02248 or 2.248% For Portfolio 2, the weighted ROR is: 7485 ( − 0.038 × 1250 ) + ( 0.021 × 1700 ) + ( 0.113 × 1515 ) + ( 0.058 × 1345 ) + ( 0.016 × 1675 ) = 7485 − 47.5 + 35.7 + 171.295 + 77.91 + 26.8 = 7485 264.255 ≈ 0.03529 or 3.529% For Portfolio 3, the weighted ROR is: 5065 ( − 0.038 × 1025 ) + ( 0.021 × 500 ) + ( 0.113 × 790 ) + ( 0.058 × 250 ) + ( 0.016 × 2500 ) = 5065 − 38.95 + 10.5 + 89.27 + 14.5 + 40 = 5065 115.37 ≈ 0.02277 or 2.277%
Rank Portfolios Comparing the weighted RORs, we have: Portfolio 1: approximately 2.248% Portfolio 2: approximately 3.529% Portfolio 3: approximately 2.277% Ranking the portfolios from best to worst performance based on their weighted RORs, we get: Portfolio 2, Portfolio 3, Portfolio 1
Final Answer Therefore, the list that shows a comparison of the overall performance of the portfolios, from best to worst, is Portfolio 2, Portfolio 3, Portfolio 1.
Examples
Understanding investment portfolios and their weighted returns is crucial in finance. For example, imagine you're managing a fund with different asset classes like stocks, bonds, and real estate. Each asset class has a different rate of return and a different amount invested. By calculating the weighted average return, you can assess the overall performance of your fund. This helps in making informed decisions about reallocating investments to optimize returns and manage risk effectively. This concept is also applicable in everyday life, such as calculating your grade in a course where different assignments have different weights.
