Final answer:
To find the expected return on Stock Q, the investment weights of all stocks in the portfolio were calculated and used to determine the weighted average of the expected returns. After computing the values, the expected return on Stock Q was found to be 13.83%, which is the correct answer.
Step-by-step explanation:
To calculate the expected return on Stock Q, we first need to understand the weight of each stock in the portfolio and then use that to find the weighted average of the expected returns. Given the total portfolio value of $53,500, investments in Stock O and Stock P are $16,500 and $24,300 respectively, we can find the value invested in Stock Q by subtracting these values from the total portfolio value.
The calculation for the investment in Stock Q is:
$53,500 - $16,500 - $24,300 = $12,700
Now we calculate the portfolio weights for each stock:
- Weight of Stock O = $16,500 / $53,500
- Weight of Stock P = $24,300 / $53,500
- Weight of Stock Q = $12,700 / $53,500
Using these weights, we can write the equation for the expected portfolio return as follows:
12.9% = (Weight of Stock O x Expected return on Stock O) + (Weight of Stock P x Expected return on Stock P) + (Weight of Stock Q x Expected return on Stock Q)
Substitute the known values and weights:
12.9% = ($16,500 / $53,500 x 17.7%) + ($24,300 / $53,500 x 10.9%) + ($12,700 / $53,500 x Expected return on Stock Q)
Solving the above equation for the expected return on Stock Q yields:
Expected return on Stock Q = 13.83%
After calculating, we find that the expected return on Stock Q is 13.83%, which is the correct option in the final answer.