Pearson Coefficient

The Pearson coefficient is a type of correlation coefficient that represents the relationship between two variables that are measured on the same interval or ratio scale. The Pearson coefficient is a measure of the strength of association between two continuous variables.

To find the Pearson coefficient the two variables are placed on a scatter plot. There must be some linearity for the coefficient to be calculated; a scatter plot not depicting any resemblance to a linear relationship will be useless. The closer the resemblance to a straight line of the scatter plot, the higher the strength of association. Numerically, the Pearson coefficient is represented the same way as a correlation coefficient that is used in linear regression; ranging from -1 to +1. A value of +1 is the result of a perfect positive relationship between two or more variables. Conversely, a value of -1 represents a perfect negative relationship. A zero indicates no correlation.

For an investor who wishes to diversify a portfolio, the Pearson coefficient can be useful. Calculations from scatter plots of historical returns between pairs of assets such as equities-bonds, equities-commodities, bonds-real estate, etc., or more specific assets such as large cap equities, small cap equities and debt-emerging market equities will produce Pearson coefficients to assist the investor in assembling a portfolio based on risk and return parameters. Note, however, that a Pearson coefficient measures correlation, not causation. If large cap and small cap equities have a coefficient of 0.8, it will not be known what caused the relatively high strength of association.

Karl Pearson (1857 - 1936) was an English academic and prolific contributor to the fields of mathematics and statistics. Aside from the eponymous coefficient, Pearson is known for the concepts of chi-squared test and p-value, among others, and development of linear regression and classification of distributions. Pearson was the founder of the Department of Applied Statistics at University College London in 1911.