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 evaluates 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.
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.

Correlation Coefficient
The correlation coefficient is a statistical measure that calculates ... 
CrossCorrelation
Cross correlation is a measurement that tracks the movements ... 
Inverse Correlation
An inverse correlation, also known as negative correlation, is ... 
Y
Y is a letter that appears on a stock symbol specifying that ... 
Regulation X
Regulation X is a rule that limits the amount of credit foreign ... 
Regression
A statistical measure that attempts to determine the strength ...

Investing
Regression Basics For Business Analysis
Regression analysis is a quantitative tool that is easy to use and can provide valuable information on financial analysis and forecasting. Find out how. 
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
Example of Applying Modern Portfolio Theory (MPS)
See how an investor can maximize expected return for a given level of risk by altering the proportions of the assets held. 
Investing
The 10 Largest Holdings in the S&P 500 (AAPL,AMZN)
What is the investing potential of each of the 10 largest companies in the S&P 500 Index? 
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
10 Dividend Stocks Warren Buffet Loves (KO,KHC)
Want to invest like Warren Buffet? Consider these 10 dividendpaying stocks. 
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. 
Financial Advisor
A Guide on the RiskAdjusted Discount Rate
When a project or investment faces higher amounts of risk or uncertainty, it may be appropriate to utilize the riskadjusted discount rate. 
Managing Wealth
Modern Portfolio Theory: Why It's Still Hip
Investors still follow an old set of principles, known as modern portfolio theory (MPT), that reduce risk and increase returns through diversification. 
Investing
How Investment Risk Is Quantified
FInancial advisors and wealth management firms use a variety of tools based in modern portfolio theory to quantify investment risk.

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 >> 
What's the difference between alpha and beta?
Alpha is a measurement of a portfolio manager's performance in relation to the overall market. Beta gauges the volatility ... Read Answer >> 
What is the formula for calculating net present value (NPV)?
Net present value (NPV) is a method of determining the current value of all future cash flows generated by a project after ... Read Answer >> 
How can I calculate the expected return of my portfolio?
To calculate the expected return of a portfolio, an investor needs to add up the weighted averages of each security's expected ... Read Answer >>