Which of the following statements about covariance and correlation is least likely correct? A. A zero covariance implies there is no linear relationship between the returns on two assets. B. If two assets have perfect negative correlation, the variance of returns for a portfolio that consists of these two assets will equal zero. C. The covariance of a two-stock portfolio is equal to the correlation coefficient times the standard deviation of one stock’s returns times the standard deviation of the other stock’s returns. ANyone know whats the right asnwer?
B. The variance of the portfolio will equal var(asset a) + var(asset b) - 2*cov(a,b) which does not have to equal zero.
Yeah B for sure. A and C are correct.
I was thinking A because I thought that a zero correlation coefficient, not covariance, implied a non linear relationship between the two assets. Just by definition?
That is not the definition of correlation. Zero correlation simply means there is an absense of linear relationship, and does NOT imply a non-linear relationship. Covariance is a measure of linear association by definition. Correlation is a standardized bounded measure. The answer is B.
yea option A is incorrect because the zero covariance graph is a circle…which implies no linear relationship
This video may help understand the difference a little. I highly recommend you use YouTube and Google when a little unsure on a topic. The Bionic Turtle vids are great, I used them throughout the L1 study and the guy will even answer questions in the comments section… http://www.youtube.com/watch?v=35NWFr53cgA