What is the 'Correlation Coefficient'
The correlation coefficient is a statistical measure that calculates the strength of the relationship between the relative movements of the two variables. The range of values for the correlation coefficient bounded by 1.0 on an absolute value basis or between 1.0 to 1.0. If the correlation coefficient is greater than 1.0 or less than 1.0, the correlation measurement is incorrect. A correlation of 1.0 shows a perfect negative correlation, while a correlation of 1.0 shows a perfect positive correlation. A correlation of 0.0 shows zero or no relationship between the movement of the two variables.
BREAKING DOWN 'Correlation Coefficient'
While the correlation coefficient measures a degree of relation between two variables, it only measures the linear relationship between the variables. The correlation coefficient cannot capture nonlinear relationships between two variables.
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 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, 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 shows there is a positive relationship between the two variables, but it is weak and likely insignificant. Experts do not consider correlations significant until the value surpasses at least 0.8. However, a correlation coefficient with an absolute value of 0.9 or greater would represent a very strong relationship.
This statistic is useful in finance. For example, it can be helpful in determining how well a mutual fund performs relative to its benchmark index, or another fund or asset class. By adding a low or negatively correlated mutual fund to an existing portfolio, the investor gains diversification benefits.
Calculation Details
The most common calculation is the Pearson productmoment correlation. One may determine it by first calculating the covariance of the two variables in question. Next, one must calculate each variable's standard deviations. 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, one can calculate the normalized version of the statistic. This is the correlation coefficient.

Positive Correlation
Positive correlation is a relationship between two variables ... 
Negative Correlation
A perfect negative correlation is a relationship between two ... 
Pearson Coefficient
Pearson coefficient is a type of correlation coefficient that ... 
CrossCorrelation
Cross correlation is a measurement that tracks the movements ... 
Inverse Correlation
An inverse correlation, also known as negative correlation, is ... 
Line Of Best Fit
The line of best fit is an output of regression analysis that ...

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
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. 
Trading
Using Currency Correlations To Your Advantage
Knowing the relationships between pairs can help control risk exposure and maximize profits. 
Trading
Managing Currency Exposure In Your Portfolio
The value of your investments is impacted by changes in global currency exchange rates. Find out how. 
Investing
Behind United Airline's 91.6% Rise in 10 Years (UAL)
United Continental's stock has been impacted by oil prices and economic cycles, but its statistical correlation to the market has been very low. 
Investing
Do Oil and Natural Gas Prices Rise And Fall Together?
Do the prices of crude oil and natural gas affect each other? Investopedia explores price patterns and provides analysis. 
Investing
Portfolio Diversification Done Right
Diversifying your portfolio by means of different securities and asset classes is an essential approach to lower the overall risk of a portfolio. 
Financial Advisor
Life Insurance: Variable Vs. Variable Universal
Do you know why you might need one policy versus the other? Read on to find out the difference between Variable and Variable Universal life insurance. 
Investing
T Rowe Price Capital Appreciation Fund Risk Statistics Case Study (PRWCX)
Analyze PRWCX using popular risk metrics that are part of modern portfolio theory (MPT). Explore PRWCX's volatility, correlation and return statistics.

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 >> 
Does a negative correlation between two stocks mean anything?
Learn what the concept of negative correlation means, understand how it is generally calculated and see how it is used in ... Read Answer >> 
How do you calculate Rsquared in Excel?
Calculate Rsquared in Microsoft Excel by creating two data ranges to correlate. Use the correlation formula to correlate ... 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 >>