Question

Closing prices of two stocks are recorded for 50 trading days. The sample standard deviation of stock X is 4.638 and the sample standard deviation of stock Y is 9.084. The sample covariance is −36.111. (a) Calculate the sample correlation coefficient.

Answer 1

Answer:

a) The correlation coeffcient is given by:

$r = \frac{Cov(X,Y)}{S_x S_y}$

And replacing we got:

$r = \frac{-36.111}{4.638 *9.084}= -0.857$

b) For this case we can conclude that we have a strong, negative linear association between the two stock prices.

Explanation:

Part a

For this case we have the following info:

$s_x = 4.638$ represent the sample deviation for the variable X

$s_y = 9.084$ represent the sample deviation for the variable Y

$Cov(X,Y)= -36.111$ represent the covariance between the variables X and Y

The correlation coeffcient is given by:

$r = \frac{Cov(X,Y)}{S_x S_y}$

And replacing we got:

$r = \frac{-36.111}{4.638 *9.084}= -0.857$

Part b

Describe the relationship between prices of these two stocks.

For this case we can conclude that we have a strong, negative linear association between the two stock prices.