Variance vs Covariance: What’s the Difference

Variance and co-variance are two of the most important statistical terms used to measure the spread and relationship between variables in a dataset. Understanding the difference between variance and covariance is essential for anyone working with data. In this article, we will explore the definitions and the relationship between the two.

What is variance?

Variance measures the width of the spread of the data points from their mean value. The deviations of each data point from the mean are squared and their probability-weighted average is calculated. When the variance is high, it means that the data point is further away from the mean of all data points, and vice versa.

With that background in mind, one must note that the term ‘variance’ also has significance in finance. The variance of a particular stock price helps traders determine the volatility of that stock over a defined period of time. The extent of price movement thus comes to light and it indicates how risky that investment can be. Simply put, a stock with high variance is riskier than a stock with low variance.

Variance helps in budgeting activities as the actual expenses usually vary from the estimated expenses. It helps one establish and maintain a buffer in the financial planning process. It is also helpful in making informed decisions as it is indicative of performance in comparison with historic data.

What is covariance?

As the name suggests, this statistical measure calculates how two variables will move relative to each other. Covariance in finance is nothing but two different investment returns evaluated over a period of time with respect to different variables. These investments are tradable securities such as stocks and bonds.

When the covariance is positive, it means that both securities will move in the same direction when the underlying variable changes. This movement could be up or down. Similarly, a negative covariance shows an inverse movement of these securities when their underlying variable changes. So, if one falls, the other will rise.

Inverse covariance is very important in the world of finance as investors are constantly looking to build a diversified portfolio, which means the loss from one security should be offset by another. And this is nothing but negative covariance. This arrangement stabilizes the returns generated over time.

Covariance allows investors to even compare the volatility between stocks as they can now see how one investment moves along with the other. This helps them analyze which stocks must be grouped together to create a balanced portfolio.

Variance vs Covariance - Comparison

Here’s a simple comparison between the two that will help you eliminate any confusion between the two immediately. There are four key points of comparison under variance vs covariance:

1. Definition

The distance of a data point from the mean value of the entire data set is called variance, whereas covariance establishes the relationship between two variables.

2. Direction/Dimension

Variance is a unidirectional measure, which means it identifies the reaction of one variable to a change in another. On the other hand, covariance is a two-dimensional measure that signals how two variables will move with respect to each other.

3. Number of variables

As suggested above, variance observes how single variable changes, whereas covariance observes how two variables change simultaneously.

4. Financial context

Variance indicates the extent of the volatility of a stock and thus is a measure of risk. Covariance shows the relative movement of two stocks and helps in diversification.

Conclusion – Variance vs Covariance

In conclusion, variance and covariance are two essential statistical concepts that are widely used in data analysis. While both are used to measure the relationship between variables in a dataset, they have distinct meanings and applications.