If the distribution of returns for an asset has a variance of zero, then covariance of returns between that asset and the returns any other asset must equal zero.
True or False
false
True.
To understand why, first let's define some terms. Variance measures the spread or dispersion of a distribution of returns, while covariance measures the linear relationship between the returns of two assets.
If the distribution of returns for an asset has a variance of zero, it means that the returns of that asset always have the same value and do not change. In other words, there is no variability or risk associated with the asset's returns.
Now, suppose we want to calculate the covariance between the returns of this asset and the returns of any other asset. Since the variance of the first asset is zero, it implies that the returns of this asset do not change. Therefore, regardless of whether the returns of the second asset are highly variable or not, there is no linear relationship between the two sets of returns.
In simpler terms, if the returns of one asset are always the same, they have no influence on the returns of any other asset. This lack of change or variability eliminates any potential association between the returns of the two assets, resulting in a covariance of zero.
Hence, if the distribution of returns for an asset has a variance of zero, then the covariance of returns between that asset and the returns of any other asset must equal zero.