Which of the following statements is most accurate? If the covariance of returns between two assets is 0.0023, then:
the assets’ risk is near zero.
the asset returns are unrelated.
the asset returns have a positive relationship.
Solution
C is correct. The covariance of returns is positive when the returns on both assets tend to be on the same side (above or below) their expected values at the same time.
If the covariance between two assets is not 0, then the assets are not unrelated (2 is wrong).
If the covariance of returns is positive, even slightly, there is a positive relationship between both assets (3 is definetly right).
Where is the error in statement 1? I believe that “assets’ risk” may refer to:
Individual assets’ variance: in this case, we don’t have any information about each asset idiosyncratic risk, so we can’t affirm that the risk for both is near zero;
However, idiosyncratic risk is diversifiable, i.e the assets’ individual risk can be reduced if the pairwise covariance (and consequently the correlation) is negative, which is not the case.
Therefore, either interpretation makes statement (1) inaccurate.
Hope it helps! If not, please let me know. Best regards and good luck