Final answer:
The beta of stock T in a portfolio, when given the portfolio beta and the betas of other stocks with their respective weights, is calculated using the weighted average formula. In this case, the beta of stock T is approximately 1.276.
Step-by-step explanation:
The question asks for the beta of stock T in a portfolio that's invested 20% in stock R, 38% in stock S, and the remainder in stock T. The betas for stocks R and S are provided as 0.75 and 1.30, respectively, and the overall portfolio beta is 1.18.
To find the beta of stock T, we use the concept of the weighted average of the betas of the individual investments, which should be equal to the portfolio beta. The beta of the portfolio is calculated using the formula:
Beta(portfolio) = (Weight of R * Beta of R) + (Weight of S * Beta of S) + (Weight of T * Beta of T)
Given that the weights of R and S are 20% and 38% and the weights must sum to 100%, stock T's weight is 100% - 20% - 38% = 42%. With this information, the equation becomes:
1.18 = (0.20 * 0.75) + (0.38 * 1.30) + (0.42 * Beta of T)
Solving this equation:
Beta of T = (1.18 - 0.15 - 0.494) / 0.42 = 0.536/0.42 ≈ 1.276
Therefore, the beta of stock T is approximately 1.276.