### Variance vs. Covariance: An Overview

Variance and covariance are mathematical terms frequently used in statistics and probability theory. Variance refers to the spread of a data set around its mean value, while a covariance refers to the measure of the directional relationship between two random variables.

In addition to their general use in statistics, both of these terms have specific meanings for investors as well, referring to measurements taken in the stock market and asset allocation, both of which are noted below.

- In statistics, a variance is the spread of a data set around its mean value, while a covariance is the measure of the directional relationship between two random variables.
- Variance is used by financial experts to measure an asset's volatility, while covariance describes two different investments' returns over a period of time when compared to different variables.
- Portfolio managers can minimize risk in an investor's portfolio by purchasing investments that have a negative covariance to one another.

### Variance

Variance is used in statistics to describe the spread between a data set from its mean value. It is calculated by finding the probability-weighted average of squared deviations from the expected value. So the larger the variance, the larger the distance between the numbers in the set and the mean. Conversely, a smaller variance means the numbers in the set are closer to the mean.

Along with its statistical definition, the term variance can also be used in a financial context. Many stock experts and financial advisors use a stock's variance to measure its volatility. Being able to express just how far a given stock's value can travel away from the mean in a single number is a very useful indicator of how much risk a particular stock comes with. A stock with a higher variance usually comes with more risk and the potential for higher or lower returns, while a stock with a smaller variance may be less risky, meaning it will come with average returns.

### Covariance

A covariance refers to the measure of how two random variables will change when they are compared to each other. In a financial or investment context, though, the term covariance describes the returns on two different investments over a period of time when compared to different variables. These assets are usually marketable securities in an investor's portfolio, such as stocks.

A positive covariance means both investments' returns tend to move upward or downward in value at the same time. An inverse or negative covariance, on the other hand, means the returns will move away from each other. So when one rises, the other one falls.

Covariance may measure the movements of two variables, but it does not indicate the degree to which those two variables are moving in relation to one another.

Covariance can also be used as a tool to diversify an investor's portfolio. In order to do so, a portfolio manager should look for investments that have a negative covariance to one another. That means when one asset's return drops, another (related) asset's return rises. So purchasing stocks with a negative covariance is a great way to minimize risk in a portfolio. The extreme peaks and valleys of the stocks' performance can be expected to cancel each other out, leaving a steadier rate of return over the years.