Chapter 3. Correlation
Often financial analysts are interested in investigating the nature of the relationship between different variables, such as the amount of debt that companies hold and their market capitalization or their risk and return. Correlation is an important way of numerically quantifying the relationship between two variables. A related concept, introduced in future chapters, is regression, which is essentially an extension of correlation to cases of three or more variables. As you will quickly find as you read through this chapter and those that follow, it is no exaggeration to say that correlation and regression are the most important unifying concepts of this book.
In this chapter, we will first describe the theory behind correlation, and then work through a few examples designed to think intuitively about the concept in different ways.
Let X and Y be two variables (e.g. market capitalization and debt, respectively) and let us also suppose that we have data on i = 1, ..., N different units (e.g. companies). The correlation between X and Y is denoted by the small letter, r, and its precise mathematical formula is given in Appendix 3.1. Of course, in practice, you will never actually have to use this formula directly. Any spreadsheet or statistics software package will do it for you. In Excel, you can use the Tools/Data Analysis or Function Wizard© to calculate them. It is usually clear from the context to which variables r refers. However, ...