To determine the expected return on Stock Q, we use the formula for the expected return of a portfolio:

$E(R_p) = \frac{W_O \cdot E(R_O) + W_P \cdot E(R_P) + W_Q \cdot E(R_Q)}{1}$

Where:

• $E(R_p)$ is the portfolio's expected return (11.4% or 0.114).
• $W_O, W_P, W_Q$ are the weights of the investments in Stocks O, P, and Q, respectively.
• $E(R_O), E(R_P), E(R_Q)$ are the expected returns of Stocks O, P, and Q.

Step 1: Calculate weights of the stocks

1. The total portfolio value is $91,000.
2. Weight of Stock O: $W_O = \frac{18,000}{91,000} = 0.1978$
3. Weight of Stock P: $W_P = \frac{25,800}{91,000} = 0.2835$
4. Weight of Stock Q: $W_Q = 1 - W_O - W_P = 1 - 0.1978 - 0.2835 = 0.5187$

Step 2: Plug in known values into the formula

$0.114 = (0.1978 \cdot 0.157) + (0.2835 \cdot 0.12) + (0.5187 \cdot E(R_Q))$

Simplify: $0.114 = 0.03105 + 0.03402 + (0.5187 \cdot E(R_Q))$

$0.114 = 0.06507 + (0.5187 \cdot E(R_Q))$

$0.114 - 0.06507 = 0.5187 \cdot E(R_Q)$

$0.04893 = 0.5187 \cdot E(R_Q)$

Step 3: Solve for $E(R_Q)$

$E(R_Q) = \frac{0.04893}{0.5187} = 0.0943 \text{ or } 9.43\%$

Final Answer:

The expected return on Stock Q is 9.43%.

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Do you have any further questions or need details?

Here are 5 follow-up questions for exploration:

1. How would changing the weights of the portfolio affect the expected return?
2. What happens to the expected return of the portfolio if the return of Stock Q changes?
3. How is the weighted average used in other financial calculations?
4. What are the implications of having a stock with a much lower return in a portfolio?
5. How can diversification impact the overall risk and return of the portfolio?

Tip: Always double-check your weight calculations to ensure the sum equals 1 when dealing with proportions!