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a perfect negative relationship between the two variables.

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.

KEY TAKEAWAYS

  • Correlation coefficients are used to measure the strength of the relationship between two variables.
  • Pearson correlation is the one most commonly used in statistics. This measures the strength and direction of a linear relationship between two variables.
  • Values always range between -1 (strong negative relationship) and +1 (strong positive relationship). Values at or close to zero imply weak or no relationship.
  • Correlation coefficient values less than +0.8 or greater than -0.8 are not considered significant.

Calculation Details

To calculate the Pearson product-moment correlation, one must first determine the covariance of the two variables in question. Next, one must calculate each variable’s standard deviation. The correlation coefficient is determined by dividing the covariance 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.