Final answer:
The beta of the stock is calculated using its volatility, the market portfolio's volatility, and their correlation. In this case, the beta is 1.3334.
Step-by-step explanation:
The beta of a stock is a measure of the stock's volatility relative to the market. To calculate beta, you use the correlation between the stock and the market portfolio, and the ratio of their volatilities. Given that the stock has a volatility of 30%, a correlation with the market portfolio of 0.6667, and the market portfolio has a volatility of 15%, you can calculate the beta using the formula:
Beta = (Correlation between the stock and the market) × (Volatility of the stock / Volatility of the market)
So, the beta of the stock would be:
Beta = 0.6667 × (30% / 15%) = 0.6667 × 2 = 1.3334
Therefore, the beta of the stock in question is 1.3334.
The beta for a portfolio is determined by calculating the covariance of the portfolio's returns with the returns of a benchmark index, divided by the variance of the benchmark index.
It is a measure of the systematic risk or volatility of the portfolio in relation to the market as a whole.To calculate the beta of a portfolio, one needs to compare the portfolio's performance to that of a benchmark index, which represents the overall market.
The beta coefficient measures the sensitivity of the portfolio's returns to the movements of the market. First, the covariance between the portfolio's returns and the benchmark index returns is calculated. Covariance measures how the returns of the two assets move together.
A positive covariance indicates that the returns tend to move in the same direction, while a negative covariance suggests they move in opposite directions. Next, the variance of the benchmark index returns is calculated.