What is the beta of the given portfolio based on the stocks in the table provided?
The beta of the given portfolio is 1.44 (rounded off to two decimal places). The beta of a portfolio can be calculated using the formula:
\[ \beta_{Portfolio} = w_{1}\beta_{1} + w_{2}\beta_{2} + w_{3}\beta_{3} + w_{4}\beta_{4} \]
Where,
\[ \beta_{1}, \beta_{2}, \beta_{3}, \beta_{4} \] = Betas of the individual stocks
\[ w_{1}, w_{2}, w_{3}, w_{4} \] = Proportional weights of the respective stocks in the portfolio such that
\[ w_{1} + w_{2} + w_{3} + w_{4} = 1 \]
Now, let's substitute the values of invested amount and beta of each stock into the formula to find the beta of the portfolio:
\[ \beta_{Portfolio} = \frac{5058}{20439} \times 1.14 + \frac{7736}{20439} \times 1.81 + \frac{2187}{20439} \times 1.47 + \frac{3658}{20439} \times 1.79 \]
After calculating the above expression, we find that the beta of the given portfolio is 1.44 (rounded off to two decimal places).
Calculating the Beta of the Portfolio
Let's break down the calculation step by step:
Step 1: Calculate the proportional weight of each stock in the portfolio.
- For Stock A: \( \frac{5058}{20439} \)
- For Stock B: \( \frac{7736}{20439} \)
- For Stock C: \( \frac{2187}{20439} \)
- For Stock D: \( \frac{3658}{20439} \)
Step 2: Multiply the weight of each stock by its corresponding beta.
- Stock A: \( \frac{5058}{20439} \times 1.14 \)
- Stock B: \( \frac{7736}{20439} \times 1.81 \)
- Stock C: \( \frac{2187}{20439} \times 1.47 \)
- Stock D: \( \frac{3658}{20439} \times 1.79 \)
Step 3: Sum up the results from Step 2 to find the beta of the portfolio:
\[ \beta_{Portfolio} = \frac{5058}{20439} \times 1.14 + \frac{7736}{20439} \times 1.81 + \frac{2187}{20439} \times 1.47 + \frac{3658}{20439} \times 1.79 \]
By following these steps, we arrive at the beta of the given portfolio as 1.44 (rounded off to two decimal places). Beta is a measure of the volatility of a portfolio in relation to the overall market. A beta of 1 indicates that the portfolio moves in line with the market, while a beta greater than 1 indicates higher volatility.