Final answer:
Tje correct answer is not listed. After calculating the portfolio's beta by considering the betas of Stock A and Stock B, and the fact that the portfolio beta equals the market beta, it was deduced that the value of the investment in Stock A is $22,680, which doesn't match any of the options provided.
Step-by-step explanation:
To find the value of the investment in Stock A when the portfolio has the same beta as the market, we must first understand the concept of a portfolio's beta, which is a weighted average of the betas of the individual stocks that make up the portfolio. Since the portfolio beta matches the market beta, we assume the market beta is 1. Hence, the portfolio beta is a blend of Stock A's beta (1.48) and Stock B's beta (0.72).
Let's denote the value of the investment in Stock A as X and in Stock B as Y. Since the total value of the portfolio is $36,800, we have X + Y = $36,800. Given that the portfolio beta equals the market beta, we can set up the following equation:
(X/36,800) * 1.48 + (Y/36,800) * 0.72 = 1
We know that X + Y = $36,800, so we can substitute Y with (36,800 - X) in the equation and solve for X.
(X/36,800) * 1.48 + ((36,800 - X)/36,800) * 0.72 = 1
Solving this equation leads to X (the value of the investment in Stock A) being $22,680. Therefore, the correct answer is not listed among the options provided in the question.