Answer:
To calculate the portfolio's beta, we need to determine the weighted average beta of the two stocks, considering the amount invested in each stock.
Let's denote the beta of stock x as βx, the beta of stock y as βy, the amount invested in stock x as Ax, and the amount invested in stock y as Ay.
Given:
- Total investment: $100,000
- Amount invested in stock x: $30,000
- Amount invested in stock y: $100,000 - $30,000 = $70,000
We are given the betas:
- βx = 1.50 (beta of stock x)
- βy = 0.85 (beta of stock y)
To calculate the portfolio's beta, we can use the following formula:
βportfolio = (Ax * βx + Ay * βy) / (Ax + Ay)
Substituting the given values:
βportfolio = ($30,000 * 1.50 + $70,000 * 0.85) / ($30,000 + $70,000)
βportfolio = ($45,000 + $59,500) / $100,000
βportfolio = $104,500 / $100,000
βportfolio ≈ 1.045
Therefore, the portfolio's beta is approximately 1.045.
Now, let's discuss what beta measures and what it tells us about the risk of the asset:
Beta is a measure of a stock's sensitivity to changes in the market. It quantifies the relationship between the stock's returns and the overall market returns. A beta greater than 1 indicates that the stock tends to be more volatile or risky than the market. A beta less than 1 suggests that the stock is less risky than the market. A beta of 1 means the stock is expected to move with the market.
In the context of a portfolio, the portfolio's beta helps us understand the overall risk of the portfolio compared to the market. If the portfolio's beta is greater than 1, it means the portfolio is expected to be more volatile than the market. Conversely, if the portfolio's beta is less than 1, it indicates the portfolio is expected to be less risky than the market. Having a balanced portfolio with a beta close to 1 can help mitigate risk by spreading investments across different assets with varying betas.
Step-by-step explanation:
To calculate the portfolio's beta, we need to determine the weighted average beta of the two stocks, considering the amount invested in each stock.
Let's denote the beta of stock x as βx, the beta of stock y as βy, the amount invested in stock x as Ax, and the amount invested in stock y as Ay.
Given:
- Total investment: $100,000
- Amount invested in stock x: $30,000
- Amount invested in stock y: $100,000 - $30,000 = $70,000
We are given the betas:
- βx = 1.50 (beta of stock x)
- βy = 0.85 (beta of stock y)
To calculate the portfolio's beta, we can use the following formula:
βportfolio = (Ax * βx + Ay * βy) / (Ax + Ay)
Substituting the given values:
βportfolio = ($30,000 * 1.50 + $70,000 * 0.85) / ($30,000 + $70,000)
βportfolio = ($45,000 + $59,500) / $100,000
βportfolio = $104,500 / $100,000
βportfolio ≈ 1.045
Therefore, the portfolio's beta is approximately 1.045.
Now, let's discuss what beta measures and what it tells us about the risk of the asset:
Beta is a measure of a stock's sensitivity to changes in the market. It quantifies the relationship between the stock's returns and the overall market returns. A beta greater than 1 indicates that the stock tends to be more volatile or risky than the market. A beta less than 1 suggests that the stock is less risky than the market. A beta of 1 means the stock is expected to move with the market.
In the context of a portfolio, the portfolio's beta helps us understand the overall risk of the portfolio compared to the market. If the portfolio's beta is greater than 1, it means the portfolio is expected to be more volatile than the market. Conversely, if the portfolio's beta is less than 1, it indicates the portfolio is expected to be less risky than the market. Having a balanced portfolio with a beta close to 1 can help mitigate risk by spreading investments across different assets with varying betas.