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:

Expected Return of Portfolio=(wA×rA)+(wB×rB)\text{Expected Return of Portfolio} = (w_A \times r_A) + (w_B \times r_B)

Where:

  • wAw_A and wBw_B are the proportions of the portfolio invested in Stock A and Stock B, respectively.
  • rAr_A and rBr_B are the expected returns of Stock A and Stock B, respectively.

Given:

  • Expected return of Stock A, rA=10%r_A = 10\% or 0.10.
  • Expected return of Stock B, rB=5%r_B = 5\% or 0.05.
  • Proportion invested in Stock A, wA=40%w_A = 40\% or 0.40.
  • Proportion invested in Stock B, wB=60%w_B = 60\% or 0.60 (since 1wA=0.601 - w_A = 0.60).

Now, plug the values into the formula:

Expected Return of Portfolio=(0.40×0.10)+(0.60×0.05)\text{Expected Return of Portfolio} = (0.40 \times 0.10) + (0.60 \times 0.05)

=0.04+0.03=0.07= 0.04 + 0.03 = 0.07

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:

  1. How does diversification affect the risk and return of a portfolio?
  2. What is the difference between expected return and actual return in investments?
  3. How does changing the proportion of Stock A in the portfolio affect the expected return?
  4. Can expected return alone determine the best investment strategy?
  5. 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

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Suitable Grade Level

Undergraduate Finance or Economics