# Definition of Correlation

Two random variables are positively correlated if high values of one are likely to be associated with high values of the other. They are negatively correlated if high values of one are likely to be associated with low values of the other.

Formally, a correlation coefficient is defined between the two random variables (x and y, here). Let sx and xy denote the standard deviation of x and y. Let sxy denote the covariance of x and y. The correlation coefficent between x and y, denoted sometimes rxy, is defined by:

rxy = sxy / sxsy

Correlation coefficients are between -1 and 1, inclusive, by definition. They are greater than zero for positive correlation and less than zero for negative correlations.

### Terms related to Correlation:

• Standard deviations
• Durbin-Watson Statistic
• Is the Value of the Canadian Dollar related to Oil Prices?
• Does the Superbowl Predict Economic Growth?
• Will the Canadian Dollar Hit Par?

### Books on Correlation:

• Volatility and Correlation: The Perfect Hedger and the Fox
• Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences
• Volatility and Correlation: In the Pricing of Equity, FX and Interest-Rate Options