Variance vs. Covariance: Key Differences in Statistics and Investing

Variance vs. Covariance: An Overview

Variance and covariance are used in statistics and probability theory. Variance measures how much a set of data points differs from their average value, showing their spread or volatility. Covariance indicates how two variables move relative to each other, whether they rise and fall together or move in opposite directions. In investing, both concepts help assess risk and guide portfolio management by showing how assets behave alone and together.

Understanding Variance in Statistics and Finance

Variance is used in statistics to describe the spread of a data set from its mean value. It is calculated by finding the probability-weighted average of squared deviations from the expected value. Calculations can be made easier with the use of software like Excel.

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.

How Covariance Impacts Investments

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 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.

The Bottom Line

Variance shows how much investment returns fluctuate around the average, helping measure volatility. Covariance explains how two investments move in relation to each other, revealing whether they rise and fall together or move in opposite directions. By combining assets with negative covariance, you can balance your portfolio's performance swings and reduce overall portfolio risk.