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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.

Formula for calculating the correlation coefficient.

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 product-moment 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.

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