# Correlation Coefficient

## 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.

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## 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 product-moment 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.

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