The correlation coefficient is a measure of how closely two variables move in relation to one another.Â If one variable goes up by a certain amount, the correlation coefficient indicates which way the other variable moves and by how much.
The mathematical formula for the correlation coefficient looks like this:
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â whereÂ nÂ is the number of pairs of data.
Â By using the formula, you can generate a correlation coefficient that is in the range of 1 to zero to +1.Â
When two variables, X and Y, have a correlation coefficient approaching 1, if variable X goes up by one unit, variable Y will go down by one unit.Â If their correlation coefficient approaches +1, and X goes up by one unit, Y will also go up one unit.Â A correlation coefficient of zero means movement of the X and Y variables is unrelated. Â
Portfolio managers use the correlation coefficient to diversify a portfolio, removing unsystematic risk and reducing volatility. They do this by making sure the securities in the portfolio are as negatively correlated as possible.Â This allows some portions of the portfolio to grow despite a decline in others.
In This Series

Investing
Is the Stock Correlation Strategy Effective?
The synchronized movement among stocks and markets in recent years is challenging diversification. 
Investing
Understanding the Oil & Gas Price Correlation
Learn how the correlation between the commodity prices for natural gas and oil changed from 2004 to 2015 due to increased natural gas production. 
Investing
Calculating the Coefficient Of Variation (CV)
Coefficient of variation measures the dispersion of data points around the mean, a statistical average. 
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. 
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
Regression Basics For Business Analysis
This tool is easy to use and can provide valuable information on financial analysis and forecasting. Find out how. 
Insights
Understanding Regression
Regression is a statistical analysis that attempts to predict the effect of one or more variables on another variable. 
Investing
Diversification: Protecting Portfolios From Mass Destruction
This investing strategy retains its charm as a protection against random events in the market.