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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.

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