What is covariance?

Covariance measures the directional relationship between the returns of two assets. A positive covariance means asset returns move together, while a negative covariance means they move in opposite directions.

Covariance is calculated by analysing return surprises (standard deviations from the expected return) or by multiplying the correlation between the two random variables by the standard deviation of each variable.


Covariance is a statistical tool used to determine the relationship between the movements of two random variables.

When two stocks tend to move together, they are considered to have a positive covariance; when they move in the opposite direction, the covariance is negative.

Covariance is different from the correlation coefficient, a measure of the strength of a correlative relationship.

Covariance is an important tool in modern portfolio theory used to determine which stocks to put in a portfolio.

Understanding Covariance

Covariance assesses how the mean values ​​of two random variables move together. If the return of security A increases each time the return of security B increases and the same relationship is found when the return of each security decreases, then these securities are said to have a positive covariance value. In finance, covariances are calculated to help diversify security holdings.

Risk and volatility can be reduced in a portfolio by matching assets that have a negative covariance.

Special Considerations

Covariance has big packages in finance and cutting-edge portfolio idea. For example, inside the capital asset pricing model (CAPM), that’s used to calculate the predicted go-back of an asset, the covariance between safety and the marketplace is used inside the components for one of the model’s key variables, beta. In the CAPM, beta measures the volatility, or systematic chance, of safety in evaluation to the marketplace as a whole; it is a sensible degree that attracts from the covariance to gauge an investor’s chance publicity particular to at least one safety.


Meanwhile, the portfolio idea makes use of covariances to statistically lessen the general chance of a portfolio via way of means of shielding in opposition to volatility via covariance-knowledgeable diversification.


 Possessing an economic property with returns that have comparable covariances does now no longer offer very a great deal of diversification; therefore, an assorted portfolio could probably incorporate a combination of economic properties which have various covariances.

Types of Covariance

The covariance equation is used to determine the direction of the relationship between two variables–in other words, whether they tend to move in the same or opposite directions. This relationship is determined by the sign (positive or negative) of the covariance value.

A positive covariance between two variables indicates that these variables tend to be higher or lower at the same time. In other words, a positive covariance between variables x and y indicates that x is higher than average at the same times that y is higher than average, and vice versa. When charted on a two-dimensional graph, the data points will tend to slope upwards.

When the calculated covariance is less than zero, this indicates that the two variables have an inverse relationship. In other words, an x value that is lower than average tends to be paired with a y that is greater than average, and vice versa.

Covariance vs. Variance

Covariance is associated with variance, a statistical degree for the unfolding of factors in a record set. Both variance and covariance degree how records factors are allotted around a calculated mean. However, variance measures the unfolding of records alongside an unmarried axis, even as covariance examines the directional dating among variables.

In a monetary context, covariance is used to study how special investments carry out about one another. A tremendous covariance suggests that belongings generally tend to carry out nicely on equal time, even as a bad covariance suggests that they generally tend to transport in contrary directions. Most buyers are seeking belongings with a bad covariance to diversify their holdings.

The Bottom Line

Covariance is a crucial statistical metric for evaluating the relationships among a couple of variables. In investing, covariance is used to pick out properties that can assist diversify a portfolio.

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