Final answer:
Portfolio Beta, a measure of volatility, is calculated based on the market value and individual betas of the stocks in the portfolio. For a portfolio with Stock A having a beta of 0.8 and Stock B with a beta of 1.9, and corresponding market values of $3000 and $7000, the portfolio Beta is 1.57.
Step-by-step explanation:
The portfolio Beta is a measure used to determine the volatility of a portfolio compared to that of the market as a whole. In this scenario, the student has investments in two stocks, Stock A with a beta of 0.8 and Stock B with a beta of 1.9, and we want to calculate the combined portfolio Beta. The formula to find the portfolio Beta is calculated by summing the product of the market value of each stock, its beta, and the total market value of the portfolio.
First, we calculate the market value of each stock as a proportion of the total portfolio:
- Proportion of Stock A = $3000 / ($3000 + $7000) = 0.3
- Proportion of Stock B = $7000 / ($3000 + $7000) = 0.7
Next, we calculate the portfolio beta (βp) as follows:
βp = (Proportion of Stock A × βA) + (Proportion of Stock B × βB)
βp = (0.3 × 0.8) + (0.7 × 1.9) = 0.24 + 1.33 = 1.57
Therefore, the portfolio Beta is 1.57, indicating that the portfolio is 57% more volatile than the market.