An analyst is interested in the relationship between the stock prices of two companies. After downloading a time series of stock prices for each company, the analyst concludes that Company A has a variance equal to 0.25 and Company B has a variance equal to 0.20, and the covariance between the two stocks is -
0.10. Calculate the correlation coefficient between the two stocks.
Click on the arrows to vote for the correct answer
A. B. C.A
To calculate the correlation coefficient between two stocks, you need to use the formula:
Correlation Coefficient (ρ) = Covariance / (Standard Deviation of Company A * Standard Deviation of Company B)
Given the information in the question, the analyst concludes that the variance of Company A (σA^2) is 0.25 and the variance of Company B (σB^2) is 0.20. The covariance between the two stocks (Cov(A, B)) is -0.10.
To calculate the standard deviation (σ), we take the square root of the variance (σ^2):
Standard Deviation of Company A (σA) = √(0.25) = 0.5 Standard Deviation of Company B (σB) = √(0.20) = 0.447
Now we can substitute the values into the correlation coefficient formula:
ρ = Cov(A, B) / (σA * σB) = -0.10 / (0.5 * 0.447) ≈ -0.10 / 0.2235 ≈ -0.447
Therefore, the correlation coefficient between the two stocks is approximately -0.447.
Looking at the provided answer choices: A. -0.45 (approximately -0.447): This is close to the calculated correlation coefficient. B. -0.50: This is not the same as the calculated correlation coefficient. C. -1.00: This is not the same as the calculated correlation coefficient.
The closest answer choice is A. -0.45, which matches the calculated correlation coefficient of approximately -0.447.