# Understand variance versus covariance

By Mark Holland / last week ## Variance vs. Covariance: Overview

Variance and covariance are mathematical terms that are frequently used in statistics and probability theory. Variance refers to the dispersion 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 terms have specific meanings to investors, referring to measurements taken in the stock market and asset allocation, which are described below.

## Difference

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 the squared deviations from the expected value. So the larger the variance, the greater the distance between the numbers in the set and the mean. In contrast, a smaller variance means that 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 advisers use the change in a stock to measure its volatility. Being able to express how far the value of a given stock can travel from the average in a single number is a very useful indicator of how much risk a particular stock carries. A stock with a higher variance generally carries more risk and the potential for higher or lower returns, while a stock with a smaller variance may be less risky, meaning it will have average returns.

## Covariance

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

A positive covariance means that the returns on both investments tend to go up or down in value at the same time. An inverse or negative covariance, on the other hand, means that the returns will move away from each other. So when one goes up, the other falls.

### Covariance can measure the movements of two variables, but it does not indicate the degree to which those two variables move relative to each other.

Covariance can also be used as a tool to diversify an investor’s portfolio. To do this, a portfolio manager must look for investments that have a negative covariance with each other. That means that when the performance of one asset falls, the performance of another (related) asset increases. Therefore, buying stocks with a negative covariance is a great way to minimize risk in a portfolio. Extreme peaks and troughs in stock performance can be expected to cancel each other out, leaving a more stable rate of return over the years.

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