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Difference Between Variance and Covariance

18 Sep 2023

Introduction

Covariance and variance are both mathematical terms that are used by investors to measure the stock market’s volatility and investment returns. Variance is a measure of magnitude and consists of a mean value data set used to measure stock market volatility and asset allocation. 

While Covariance compares the two different investment returns with different variables over a specific period and gives direction to a relationship between them. Now, let’s have a quick overview of the difference between covariance and variance.

What is covariance? 

In a financial context, it compares and measures the returns of two different investments with different variables over a time period. These are used to diversify the portfolio of investors. Positive covariance shows that both investment returns are simultaneously moving upward in value. Whilst negative covariance refers to the returns that are moving downward in value together, so when one return rises, the other one falls. 

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What is variance?

Many financial advisors and stock experts use variance to measure the volatility of stocks. This indicates the risk associated with particular stocks. Many experts utilize the variance to compare the relative performance of assets in a particular portfolio. Higher variance refers to stocks with more risk, with potentially higher or lower returns. Meanwhile, the stocks with lower variances indicate that it is less risky with average return potentials.  

What is the difference between variance and covariance? 

  • ​Definition and Usage

Variance is a measure of magnitude that is often expressed in numbers. Whereas, Covariance explains the direction of the relationship between two variables. The Variance value is used to analyze the risk of investment. It estimates the volatility of stock prices. So, the higher variance of any stock implies that the stock is dangerous and too risky. 

On the other hand, covariance compares the relationship between the returns of one asset to another, financial experts use this to diversify their portfolios. Majorly negative covariance is included in the portfolio to give a high return in the future. In statistical applications, variance is used to calculate the standard deviation while Covariance is used to measure the correlation.

  • Formula

The formula of covariance for X and Y variables: σ​xy= [Σ{(x−μx)(y−μy)}]/N

Whereas, the formula of variance for X and Y variables: σ​2=Σ(x−μ)​2/N

Key takeaways

Both the variance and covariance are essential parts of investment. Each one displays significant outcomes to give a clear picture to the investor and help them make wise investing decisions. Variance and covariance can both be used together in the regression analysis, where investors calculate the slope and intercept of the regression line using these tools. Though they are used together for various purposes, they have major differences in terms of calculation, financial context, dimensions, etc.

 

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