Which of the following statements is most accurate?
If the covariance of returns between to assets is 0.0023, then:
A) the assets’ risk is near zero
B) the asset returns are unrelated
C) the asset returns have a positive relationship
Why is answer C) correct?
Answer A) clearly is incorrect.
Answer B)
Correlation = Covariance / (SD(A) x SD(B))
so if the Covariance is close to zero
→ the correlation is close to zero
→ so there is no linear relationship
→ it could be a non-linear relationship
→ therefore, we can’t say it is uncorrelated?
If the covariance of Asset A’s returns and Asset B’s returns is 0.0023, and the standard deviation of Asset A’s returns is, say, 0.04, and the standard deviation of Asset B’s returns is, say, 0.06, then their correlation of returns is:
It could be. Or it could be a linear relationship. Or it could be random. The magnitude of the covariance doesn’t tell us much about the relationship.
“Uncorrelated” is a horrible word; banish it from your vocabulary.
If you want to say that the correlation is close to zero, then say so. “Uncorrelated” makes it sound as if there is no correlation (i.e., that a correlation coefficient cannot be calculated). Disgusting!
Calling it logic is being too generous.
Note that answer choice C) is pretty lame: what, exactly, is a positive relationship? Do they nurture each other? Does each help the other reach its full potential? Do they protect and support each other, while overlooking each other’s (obvious) flaws?
