Final answer:
The expected return of the portfolio is calculated as the weighted average of the expected returns of the two stocks. The direct answer is 17.65%, which can be rounded to 17.7%. Considering the short position in Stock A, its weight is negative in the portfolio.
Step-by-step explanation:
The expected return of the portfolio with Stock A and Stock B can be calculated by taking the weighted average of the expected returns, considering the amounts invested in each. The calculation is as follows:
- Proportion of Stock A = $7 million shorted = -7
- Proportion of Stock B = $17 million purchased = +17
- Total investment = -7 + 17 = $10 million
- Weight of Stock A in portfolio = -7 / 10 = -0.7
- Weight of Stock B in portfolio = 17 / 10 = +1.7
Using these weights, the expected return (ER) for the portfolio is:
Portfolio ER =
(-0.7 × 10%) + (1.7 × 14.5%) = -7% + 24.65% = 17.65%
However, because the fund manager has shorted Stock A, there is a gain when the stock decreases in value.
The expected return for this portfolio is 17.65%. Correct answer to the question is D. 17.7%.
In the portfolio, Stock A is shorted, which means that the manager is betting against it. As a result, the weight assigned to the expected return from Stock A is negative. When these weights are applied to the expected return figures for each stock, the combined expected return for the portfolio sums to a positive figure. Considering that the weights add up to the total investment, the overall expected portfolio return is calculated as a weighted sum, which gives us 17.65%, rounded to 17.7% as per the available options in the question.