What is 'Covariance'
Covariance is a measure of the directional relationship between the returns on two risky assets. A positive covariance means that asset returns move together while a negative covariance means returns move inversely. Covariance is calculated by analyzing atreturn surprises (standard deviations from expected return) or by multiplying the correlation between the two variables by the standard deviation of each variable.
BREAKING DOWN 'Covariance'
Covariance measures how the mean values of two variables move together. If stock A's return moves higher whenever stock B's return moves higher and the same relationship is found when each stock's return decreases, then these stocks are said to have a positive covariance. In finance, covariances are calculated to help diversify security holdings.
When an analyst has a set of data, a pair of x and y values, covariance can be calculated using five variables from that data. They are:
 x_{i} = a given x value in the data set
 x_{m} = the mean, or average, of the x values
 y_{i} = the y value in the data set that corresponds with x_{i}
 y_{m} = the mean, or average, of the y values
 n = the number of data points
Given this information, the formula for covariance is: Cov(x,y) = SUM [(x_{i}  x_{m}) * (y_{i}  y_{m})] / (n  1)
It's important to note that while the covariance does measure the directional relationship between two assets, it does not show the strength of the relationship between the two assets. The coefficient of correlation is a more appropriate indicator of this strength.
Covariance Applications
Covariances have significant applications in finance and modern portfolio theory. For example, in the capital asset pricing model (CAPM), which is used to calculate the expected return of an asset, the covariance between a security and the market is used in the formula for one of the model's key variables, beta. In the CAPM, beta measures the volatility, or systematic risk, of a security in comparison to the market as a whole; it's a practical measure that draws from the covariance to gauge an investor's risk exposure specific to one security.
Meanwhile, portfolio theory uses covariances to statistically reduce the overall risk of a portfolio by protecting against volatility through covarianceinformed diversification. Possessing financial assets with returns that have similar covariances does not provide very much diversification; therefore, a diversified portfolio would likely contain a mix of financial assets that have varying covariances. For more on this, see How is covariance used in portfolio theory?
Example of Covariance Calculation
Assume an analyst in a company has a fivequarter data set that shows quarterly gross domestic product (GDP) growth in percentages (x) and a company's new product line growth in percentages (y). The data set may look like:
 Q1: x = 2, y = 10
 Q2: x = 3, y = 14
 Q3: x = 2.7, y = 12
 Q4: x = 3.2, y = 15
 Q5: x = 4.1, y = 20
The average x value equals 3, and the average y value equals 14.2. To calculate the covariance, the sum of the products of the x_{i} values minus the average x value, multiplied by the y_{i} values minus the average y values would be divided by (n1), as follows:
Cov(x,y) = ((2  3) x (10  14.2) + (3  3) x (14  14.2) + ... (4.1  3) x (20  14.2)) / 4 = (4.2 + 0 + 0.66 + 0.16 + 6.38) / 4 = 2.85
Having calculated a positive covariance here, the analyst can say that growth of the company's new product line has a positive relationship with quarterly GDP growth. To learn more about how covariance is calculated, see Calculating Covariance for Stocks.

Portfolio Variance
Portfolio variance is the measurement of how the actual returns ... 
CrossCorrelation
Cross correlation is a measurement that tracks the movements ... 
Correlation
Correlation is a statistical measure of how two securities move ... 
Inverse Correlation
An inverse correlation, also known as negative correlation, is ... 
Forward Price
The predetermined delivery price of a forward contract, as agreed ... 
Gas (Ethereum)
Gas is the pricing value required to conduct a transaction or ...

Investing
Calculating covariance for stocks
Covariance can help you calculate how two stocks might move together and help you in building a diversified investment portfolio. 
Investing
How to Pick the Best Stocks? Listen to Customers (AMZN, PZZA)
Rated top in customer service, these companies have delivered impressive stock performance over the past year. 
Financial Advisor
10 Companies With No Debt (DOX,NHTC,PAYX)
These 10 companies have no debt, a big positive in today's economic environment. Three stand out above the rest. 
Investing
What's the Correlation Coefficient?
The correlation coefficient is a measure of how closely two variables move in relation to one another. If one variable goes up by a certain amount, the correlation coefficient indicates which ... 
Investing
Is Apple's Stock Over Valued Or Undervalued?
Despite several drawbacks, the CAPM gives an overview of the level of return that investors should expect for bearing only systematic risk. Applying Apple, we get annual expected return of about ... 
Investing
How to Find Quality Stocks Amid the Wreckage
Finding companies with good earnings and hitting on all cylinders in this environment, although possible, is not easy. 
Investing
Optimize your portfolio using normal distribution
Normal or bell curve distribution can be used in portfolio theory to help portfolio managers maximize return and minimize risk. 
Investing
Investing $100 a Month in Stocks for 20 Years
Learn how a monthly investment of just $100 can help build a future nest egg using properly diversified stocks or stock mutual funds. 
Investing
How to calculate required rate of return
The required rate of return is used by investors and corporatefinance professionals to evaluate investments. In this article, we explore the various ways it can be calculated and put to use. 
Trading
Apple Earnings: A Lot Depends on iPhone X Outlook
With reports of sluggish iPhone 8 sales, the outlook for Apple's iPhone X will be key.

How do you interpret the magnitude of the covariance between two variables?
Learn more about covariance and how financial planners and economists use the concept. Explore an example of covariance in ... Read Answer >> 
How does covariance impact portfolio risk and return?
Understand how covariance is related to the risk and return of a portfolio of stocks, and learn how covariance is used to ... Read Answer >> 
According to the CAPM, the expected return on a stock, that is part of a portfolio, ...
A. the covariance between the stock and the market. B. the variance of the market. C. the market risk premium. D. ... Read Answer >> 
How can I measure portfolio variance?
Find out more about portfolio variance, the formula to calculate portfolio variance and how to calculate the variance of ... Read Answer >> 
How do you calculate beta in Excel?
Learn how to calculate the beta of an investment using Microsoft Excel. Read Answer >>