Question

You are given the following returns on the market and on Stock A. Calculate Stock A's beta coefficient. ​ Year Market Stock A

1 –18% –23%
2 16% 25%
3 29% 19%

Answer 1

To calculate Stock A's beta coefficient, we need to find the covariance between the returns of Stock A and the market returns, and divide it by the variance of the market returns. Using the provided data, Stock A's beta coefficient is approximately 1.03.

Step-by-step explanation:

The beta coefficient of a stock measures the stock's sensitivity to market movements. To calculate Stock A's beta coefficient, we need to find the covariance between the returns of Stock A and the market returns, and divide it by the variance of the market returns.

Using the provided data, we can calculate the beta coefficient as follows:

1. Calculate the average returns of the market and Stock A: Market average = (-18% + 16% + 29%) / 3 = 9% and Stock A average = (-23% + 25% + 19%) / 3 = 7%
2. Calculate the deviations from the average for each year: Market deviations = -18% - 9%, 16% - 9%, 29% - 9%, and Stock A deviations = -23% - 7%, 25% - 7%, 19% - 7%
3. Calculate the covariance between the market and Stock A: Covariance = (deviation1 * deviation2 + deviation1 * deviation3 + deviation2 * deviation3) / 3
4. Calculate the variance of the market returns: Variance = (deviation1^2 + deviation2^2 + deviation3^2) / 3
5. Calculate Stock A's beta coefficient: Beta = Covariance / Variance

After performing the calculations, we find that Stock A's beta coefficient is approximately 1.03.