Covariance - Explained
What is Covariance?
Covariance is a metric used in statistics and probability theory to measure
the directional relationship between the returns of two risky assets (two
variables). What the metric does is to evaluate to what extent and how
much the variables move together. However, it does not measure the
dependency between those variables.
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How does Covariance Work?
Generally, the covariance sign illustrates the propensity in the linear
relationship between two variables. It is tricky to interpret covariances
magnitude because there is normalization. So, the interpretation of this will
depend on the variables magnitude. Note that when the version of
covariance and the correlation coefficient are normalized, the magnitude of
the strength of the linear relation becomes evident. Covariance is
measured using units. You can compute the units by multiplying two-
variable units. The variance can take either a positive or a negative value.
Covariance assesses how and to what extent the mean value of two
variables move. A variance is positive when the returns on the asset are
moving in the same direction. On the other hand, the movement of the
returns in the opposite direction (inverse) means that the variance is
negative. For instance, in a stock market, if the returns of ABC stock
happens to move higher each time XYZ stock moves higher, and you
witness the same behavior when the returns of each stock decrease, it
means that the stock has a positive covariance. Individuals in finance use
the concept of portfolio theory. Through the method of diversification, those
individuals are able to assess covariance between security holdings in a
portfolio. By selecting security holdings that do not show a high positive
covariance with each other, it is possible to eliminate some of the risks that
prove impossible to diversify.
How Covariance Works
To calculate covariance, you will need to analyze standard deviations from
the expected return. You can also arrive at covariance by multiplying the
correlation between the two variables and then multiply it by the standard
deviation of each variable. When you have a set of data (x and y values),
