Difference Between Covariance and Correlation

Correlation and covariance are two statistical concepts used to determine the relationship between two random variables. Correlation defines how a change in one variable will impact the other, while covariance defines how two items vary together. Confusing? Let us dive in further to understand the difference between these closely related terms.

What is Covariance?

Covariance measures how the two variables move concerning each other and is an extension of the concept of variance (which tells about how a single variable varies). It can take any value from -∞ to +∞.

  • The higher this value, the more dependent the relationship is. A positive number signifies positive covariance and denotes a direct connection. Effectively this means that an increase in one variable would also lead to a corresponding increase in the other variable, provided other conditions remain constant.On the other hand, a negative number signifies negative covariance, which denotes an inverse relationship between the two variables. Though covariance is perfect for defining the type of relationship, it is not good for interpreting its magnitude.

You are free to use this image on you website, templates, etc., Please provide us with an attribution linkHow to Provide Attribution?Article Link to be HyperlinkedFor eg:Source: Covariance vs Correlation (wallstreetmojo.com)

What is the Correlation?

Correlation is a step ahead of covariance as it quantifies the relationship between two random variables. In simple terms, it is a unit measure of how these variables change concerning each other (normalized covariance value).

  • The correlation has an upper and lower cap on a range, unlike covariance. It can only take values between +1 and -1. A correlation of +1 indicates that random variables have a direct and strong relationship.On the other hand, the correlation of -1 indicates a strong inverse relationship, and an increase in one variable will lead to an equal and opposite decrease in the other variable. 0 means that the two numbers are independent.

The Formula for Covariance and Correlation

Let us express these concepts mathematically for two random variables, A and B, with mean values as Ua and Ub and standard deviation as Sa and Sb, respectively.

Effectively we can define the relationship between the two:

Both correlations and covariance find application in statistical and financial analysis fields. Since correlation standardizes the connection, it is helpful in comparison of any two variables. In addition, it helps analysts develop strategies like pair trade and hedgingHedgingHedging is a type of investment that works like insurance and protects you from any financial losses. Hedging is achieved by taking the opposing position in the market.read more for efficient returns on the portfolio and safeguarding these returns in terms of adverse movements in the stock market.

Correlation vs Covariance Infographics

Let us see the top differences between correlation and covariance.

Key Differences

  • Covariance is an indicator of how two random variables change concerning each other. Correlation, on the other hand, measures the strength of this relationship. The correlationCorrelationCorrelation is a statistical measure between two variables that is defined as a change in one variable corresponding to a change in the other. It is calculated as (x(i)-mean(x))*(y(i)-mean(y)) / ((x(i)-mean(x))2 * (y(i)-mean(y))2.read more value is bound to the upper by +1 and the lower by -1. Thus, it is a definite range. However, the range of covariance is indefinite. It can take any positive or negative value (theoretically, the range is -∞ to +∞). You can rest assured that a correlation of .5 is greater than .3, and the first set of numbers (with a correlation of .5) are more dependent on each other than the second set (with a correlation of .3). Interpreting such a result would be tough from covariance calculations.Change of scale affects covariance. For example, if the value of two variables is multiplied by similar or different constants, this affects these two numbers’ calculated covariance. However, applying the same mechanism for correlation, multiplication by constants does not change the previous result. That is because a change of scale does not affect correlation.Unlike covariance, correlation is a unit-free measure of the interdependence of two variables. That makes it easy for calculated correlation values to be compared across any two variables irrespective of their units and dimensions.We can calculate CovarianceCovarianceCovariance is a statistical measure used to find the relationship between two assets and is calculated as the standard deviation of the return of the two assets multiplied by its correlation. If it gives a positive number then the assets are said to have positive covariance i.e. when the returns of one asset goes up, the return of second assets also goes up and vice versa for negative covariance.read more for only two variables. On the other hand, correlation can be calculated for multiple sets of numbers. Another factor that makes the correlation desirable to analysts compared to covariance.

Covariance vs Correlation Comparative Table

Conclusion

Correlation and covariance are very closely related to each other, and yet they differ a lot. Covariance defines the type of interaction, but correlation represents the type and the strength of this relationship. Due to this reason, correlation is often termed the special case of covariance. However, if one must choose between the two, most analysts prefer correlation as it remains unaffected by the changes in dimensions, locations, and scale. Also, since it is limited to a range of -1 to +1, it is useful to draw comparisons between variables across domains. However, an important limitation is that these concepts measure only the linear relationshipLinear RelationshipA linear relationship describes the relation between two distinct variables - x and y - in the form of a straight line on a graph. When presenting a linear relationship through an equation, the value of y is derived through the value of x, reflecting their correlation.read more.

This article is a guide to Covariance vs. Correlation. Here, we discuss the top 5 differences between covariance and correlation and infographics, and a comparison table. You may also have a look at the following articles: –

  • Variance vs. Standard DeviationMean vs. Median DifferencesPortfolio Standard DeviationSharpe Ratio Guide with Excel Examples