Math Problem Statement
Stock A has an expected return of 10% per year and Stock B has an expected return of 5%. If 40% of a portfolio's funds are invested in Stock A and the rest in Stock B, what is the expected return on the portfolio of Stock A and Stock B?
Group of answer choices
5%
1%
11%
7%
Solution
To find the expected return on a portfolio, we use the formula for the weighted average of the returns of the assets in the portfolio:
Where:
- and are the proportions of the portfolio invested in Stock A and Stock B, respectively.
- and are the expected returns of Stock A and Stock B, respectively.
Given:
- Expected return of Stock A, or 0.10.
- Expected return of Stock B, or 0.05.
- Proportion invested in Stock A, or 0.40.
- Proportion invested in Stock B, or 0.60 (since ).
Now, plug the values into the formula:
So, the expected return on the portfolio is 7%.
The correct answer is 7%.
Would you like more details or have any questions?
Here are 5 related questions to expand your understanding:
- How does diversification affect the risk and return of a portfolio?
- What is the difference between expected return and actual return in investments?
- How does changing the proportion of Stock A in the portfolio affect the expected return?
- Can expected return alone determine the best investment strategy?
- How would you calculate the risk or volatility of this portfolio?
Tip: When building portfolios, consider not just expected returns but also the correlation and volatility of the assets to manage risk effectively.
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Math Problem Analysis
Mathematical Concepts
Portfolio Management
Weighted Average
Expected Return
Formulas
Expected Return of Portfolio = (w_A * r_A) + (w_B * r_B)
Theorems
-
Suitable Grade Level
Undergraduate Finance or Economics
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