What is the 'Correlation Coefficient'
The correlation coefficient is a measure that determines the degree to which two variables' movements are associated. The range of values for the correlation coefficient is 1.0 to 1.0. If a calculated correlation is greater than 1.0 or less than 1.0, a mistake has been made. A correlation of 1.0 indicates a perfect negative correlation, while a correlation of 1.0 indicates a perfect positive correlation.
BREAKING DOWN 'Correlation Coefficient'
While the correlation coefficient measures a degree to which two variables are related, it only measures the linear relationship between the variables. Nonlinear relationships between two variables cannot be captured or expressed by the correlation coefficient.
A value of exactly 1.0 means there is a perfect positive relationship between the two variables. For a positive increase in one variable, there is also a positive increase in the second variable. A value of exactly 1.0 means there is a perfect negative relationship between the two variables. This shows the variables move in opposite directions; for a positive increase in one variable, there is a decrease in the second variable. If the correlation is 0, this simply means there is no relationship between the two variables. The strength of the relationship varies in degree based on the value of the correlation coefficient. For example, a value of 0.2 indicates there is a positive relationship between the two variables, but it is weak.
This type of statistic is useful in many ways in finance. For example, it can be helpful in determining how well a mutual fund is behaving compared to its benchmark index, or it can be used to determine how a mutual behaves in relation to another fund or asset class. By adding a low or negatively correlated mutual fund to an existing portfolio, diversification benefits are gained.
Calculation Details
The most common calculation is known as the Pearson productmoment correlation. It is determined by first calculating the covariance of the two variables in question. Next, the standard deviations of each variable must be calculated. To find the correlation coefficient, take the covariance and divide it by the product of the two variables' standard deviations.
Standard deviation is a measure of the dispersion of data from its average. Covariance is a measure of how two variables change together, but its magnitude is unbounded so it is difficult to interpret. By dividing covariance by the product of the two standard deviations, a normalized version of the statistic is calculated. This is the correlation coefficient.

Positive Correlation
A relationship between two variables in which both variables ... 
Pearson Coefficient
Pearson coefficient is a type of correlation coefficient that ... 
Variable Cost Ratio
Variable costs expressed as a percentage of sales. The variable ... 
Multiple Linear Regression  MLR
Multiple linear regression (MLR) is a statistical technique that ... 
Serial Correlation
The relationship between a given variable and itself over various ... 
Correlation
In the world of finance, a statistical measure of how two securities ...

Investing
Is the Stock Correlation Strategy Effective?
The synchronized movement among stocks and markets in recent years is challenging diversification. 
Financial Advisor
4 Reasons Why Market Correlation Matters
Learn about how correlation can be used to measure how broader markets move in relation to each other. See how correlation is used to manage risk. 
Investing
Calculating Covariance for Stocks
Learn how to figure out how two stocks might move together in the future by calculating covariance. 
Insights
Prices of Stocks and Bonds Move More in Tandem
Correlation between stock and bond prices in the U.S. have reached a 10year high, reversing a broader trend of negative correlation. 
Investing
How To Trade Currency And Commodity Correlations
Relationships between currencies and commodities exist throughout the financial markets. Find out how to trade these trends. 
Investing
Stock and Flow Variables Explained: A Closer Look at Apple
The difference between stock and flow variables is an essential concept in finance and economics. We illustrate with financial statements from Apple Inc. 
Investing
Tales From The Trenches: Perfectly Negative Profitability
Use correlations to profit when two specific instruments move in opposite directions. 
Investing
The Market Is Assessing Trump Implications
Stocks are no longer moving in unison, and active fund managers are cheering.

Can the correlation coefficient be used to measure dependence?
Understand the coefficient of correlation and its use in determining the relationship between two variables through the concepts ... Read Answer >> 
What is the correlation between American stock prices and the value of the U.S. dollar?
The correlation between any two variables (or sets of variables) summarizes a relationship, whether or not there is any realworld ... Read Answer >> 
What does a negative correlation coefficient mean?
Discover the meaning of a negative correlation coefficient, how this compares to other correlation coefficients and examples ... Read Answer >> 
How does correlation affect the stock market?
Learn about the role correlation plays in prudent stock market investing, and how the correlation coefficient is used to ... Read Answer >> 
How do I find positive correlation in the stock market?
Learn how positive correlation is found in the stock market, how correlation is calculated and how positive correlation is ... Read Answer >> 
How should I interpret a negative correlation?
Learn more about correlation and how businesses analyze variables. Find out how negative correlations are interpreted by ... Read Answer >>