Question

The covariance returns of stock 1 with stock 2nis 150. The covariance of stock 3 with stock 4 is 200. The covariance of stock 5 with stock 6 is -100. Which of following statements is(are) true?

I. The correlation coefficient between stock 1 and 2 is greater than that between stock 5 and 6.
II. Stock 1 and 2 have a lower correlation coefficient than stock 3 and 4.
III. Stock 5 and 6 have a lower correlation coefficient than stock 3 and 4.
IV. The correlation coefficient between stock 1 and 2 is positive.
A .All are definitely true
B. None are definitely true
C. I, II, and IV only
D. Only II
E. I and III only

Answer 1

The statement that the correlation coefficient between stock 1 and 2 is positive is definitely true; however, we cannot determine the truth of the other three statements without the standard deviations of each stock to calculate the actual correlation coefficients.

Step-by-step explanation:

The students' question asks which statements about the correlation coefficients of three pairs of stocks are true, based on the given covariance returns for each pair. To determine the truth of the statements, it's important to understand that the magnitude of the covariance can indicate the strength of the correlation, but without the standard deviations of each stock, we cannot determine the actual correlation coefficient. However, we do know that a positive covariance implies a positive correlation, and a negative covariance indicates a negative correlation.

The correlation coefficient is represented by the letter 'r' and ranges from -1 to +1, with 'r' closer to 1 or -1 indicating a stronger relationship. A positive 'r' indicates that the stocks move in the same direction, while a negative 'r' means they move in opposite directions. Given that the covariance of stocks 5 and 6 is -100, this pair has a negative correlation. Hence, statement IV is definitely true. Without more information, we cannot accurately compare the magnitudes of the correlation coefficients for statements I, II, and III.