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

a) The correlation coeffcient is given by:

`r = (Cov(X,Y))/(S_x S_y)`

And replacing we got:

`r = (-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.

Step-by-step 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 = (Cov(X,Y))/(S_x S_y)`

And replacing we got:

`r = (-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.