Covariance calculates the directional relationship between two assets’ returns. A positive covariance means that the returns of assets move together while a negative covariance means that they move in the opposite direction.
Key Notes:
- Covariance is a statistical tool that is used to determine the relationship between the movements of two random variables.
- When two stocks tend to move together, they are seen as having a positive covariance; when they move inversely, the covariance is negative.
- Covariance is different from the correlation coefficient, a measure of the strength of a correlative relationship.
- Covariance is a significant tool in modern portfolio theory used to ascertain what securities to put in a portfolio.
- Risk and volatility can be reduced in a portfolio by pairing assets that have a negative covariance.
- This formulas can help predict the performance of one stock relative to the other.
Understanding Covariance
Covariance assesses how two variables’ mean values shift together. The returns of stock A grows higher whenever the returns of stock B grows higher.
On similar lines, the return of stock A may decrease depending on the dip in stock B. In this case, these stocks are said to have positive covariance. Covariances are measured in finance to assist in the diversification of defense assets.
While the covariance evaluates the directional relationship between two assets, it doesn’t display the strength of a relationship between the two assets. The correlation coefficient is an indicator of this strength that is more appropriate.
Possessing financial assets with returns having similar covariances does not provide much diversification. Therefore, a diversified portfolio will likely contain a mixture of financial assets with varying covariances.
Covariances have significant financial and conventional portfolio theory applications. For instance, the covariance between security and the market is used in the calculation for one of the main variables of the model, beta, in the capital asset pricing model (CAPM). This model is used to measure the expected return of an asset.
Calculation Covariance Formula
Uses of Covariance
Finding that two stocks have a high or low covariance might not be a useful metric on its own. Covariance can tell how the stocks move together, but to determine the strength of the relationship, we need to look at their correlation. The correlation should, therefore, be used in conjunction with the covariance, and is represented by this equation:
Covariance vs. Variance
Covariance is related to variance, a statistical measure for the spread of points in a data set. Both variance and covariance measure how data points are distributed around a calculated mean.
However, variance measures the spread of data along a single axis, while covariance examines the directional relationship between two variables.
In a financial context, covariance is used to examine how different investments perform in relation to one another.
A positive covariance indicates that two assets tend to perform well at the same time, while a negative covariance indicates that they tend to move in opposite directions.
Most investors seek assets with a negative covariance in order to diversify their holdings.
Covariance vs. Correlation
Covariance is also distinct from correlation, another statistical metric often used to measure the relationship between two variables. While covariance measures the direction of a relationship between two variables, correlation measures the strength of that relationship. This is usually expressed through a correlation coefficient, which can range from -1 to +1.
While the covariance does measure the directional relationship between two assets, it does not show the strength of the relationship between the two assets; the coefficient of correlation is a more appropriate indicator of this strength.
A correlation is considered to be strong if the correlation coefficient has a value that is close to +1 (positive correlation) or -1 (negative correlation).
A coefficient that is close to zero indicates that there is only a weak relationship between the two variables.
