Which of the following statements regarding covariance is correct?
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A. B. C. D.D
Covariance is a statistical measure that helps in understanding the relationship between two variables. In finance, it is used to measure the degree to which the returns of two securities move together. The covariance can be used to determine the level of risk and diversification in a portfolio of investments.
Now let's analyze each of the given statements to identify the correct one:
A. Covariance always lies in the range -1 to +1: This statement is incorrect. The range of covariance is not limited to -1 to +1, and it can take on any value, positive, negative or zero.
B. Covariance, because it involves a squared value, must always be a positive number (or zero): This statement is incorrect. Covariance can take on negative or zero values as well, depending on the relationship between the two variables being compared. The squared term arises only when calculating the variance.
C. Low co-variances among returns for different securities leads to high portfolio risk: This statement is also incorrect. Low covariance between the returns of different securities implies that the returns of the securities are not highly correlated, which can reduce portfolio risk through diversification.
D. Co-variances can take on positive, negative, or zero values: This statement is correct. Covariance can take on positive values when the returns of two securities move in the same direction, negative values when they move in opposite directions, and zero when there is no relationship between the two variables.
Therefore, the correct answer is D. Covariances can take on positive, negative, or zero values.