Covariance, Correlation, and Risk: Calculating the Correlation Coefficient between Stock and Market Returns

Calculating the Correlation Coefficient between Stock and Market Returns

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Question

The covariance of the market's returns with the stock's returns is .008. The standard deviation of the market's returns is .1 and the standard deviation of the stock's returns is .2. What is the correlation coefficient between the stock and market returns?

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A. B. C. D.

A

Covariance = (standard deviation 1)(standard deviation 2)(correlation coefficient 1,2) Correlation coefficient = cov/(st'd1)(st'd2) = .008/(.1)(.2) = .4

To calculate the correlation coefficient between the stock and market returns, we can use the formula:

Correlation coefficient (ρ) = Covariance of stock and market returns / (Standard deviation of stock returns * Standard deviation of market returns)

Given information: Covariance (Cov) = 0.008 Standard deviation of stock returns = 0.2 Standard deviation of market returns = 0.1

Let's substitute the values into the formula:

ρ = 0.008 / (0.2 * 0.1) ρ = 0.008 / 0.02 ρ = 0.4

Therefore, the correlation coefficient between the stock and market returns is 0.4.

The correct answer is A. 0.4.

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