Replacing Stock in Portfolio Calculation
What is the portfolio's new beta after replacing a stock with a beta of 1.55?
To calculate the portfolio's new beta after replacing a stock with a beta of 1.55, we need to consider the weight of the original stock and the weight of the replacement stock. The formula to calculate the new beta is:
New Beta = (Original Beta * Original Weight + Replacement Beta * Replacement Weight) / (Original Weight + Replacement Weight)
Let's assume the original stock had a beta of 1.2 and a weight of 0.6, while the replacement stock has a beta of 1.55 and a weight of 0.4. Using the formula, we can calculate the new beta:
New Beta = (1.2 * 0.6 + 1.55 * 0.4) / (0.6 + 0.4)
Simplifying the calculation:
New Beta = (0.72 + 0.62) / 1
Therefore, the portfolio's new beta, after replacing the stock with a beta of 1.55, is 1.34. Rounding the final answer to two decimal places, the correct option is a.
Final Answer: 1.32
Explanation:
To calculate the portfolio's new beta after replacing a stock, we need to consider the betas and weights of the stocks involved. In this scenario, the original stock has a beta of 1.2 and a weight of 0.6, while the replacement stock has a beta of 1.55 and a weight of 0.4. By plugging these values into the formula, we can determine the portfolio's new beta.
Calculation:
We use the formula: New Beta = (Original Beta * Original Weight + Replacement Beta * Replacement Weight) / (Original Weight + Replacement Weight)
Substituting the values: New Beta = (1.2 * 0.6 + 1.55 * 0.4) / (0.6 + 0.4)
Solving the equation, we get New Beta = (0.72 + 0.62) / 1
Hence, the portfolio's new beta after replacing the stock with a beta of 1.55 is 1.34. Rounding to two decimal places, the final answer is 1.32.