Calculate the expected return of a portfolio with 30% of Stock A and 70% of Stock B, given their historical returns.

Here are the solutions to the questions:

Data from the table:

• Stock A Returns:
  • 2022: $12\%$
  • 2023: $18\%$
• Stock B Returns:
  • 2022: $14\%$
  • 2023: $12\%$

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1. Find the expected return of a portfolio made from 30% of A and 70% of B.

Step 1: Calculate the expected return for Stock A ($E(R_A)$).
The expected return is the average of the historical returns.

$$E(R_A) = \frac{12\% + 18\%}{2} = \frac{30\%}{2} = 15\% = 0.15$$

Step 2: Calculate the expected return for Stock B ($E(R_B)$).

$$E(R_B) = \frac{14\% + 12\%}{2} = \frac{26\%}{2} = 13\% = 0.13$$

Step 3: Calculate the expected return for the portfolio ($E(R_P)$).
The portfolio consists of $30\%$ Stock A and $70\%$ Stock B.

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