What is the difference between regression analysis and CAPM?
Regression analysis is a statistical tool that describes the linear relationship between a dependent variable and one or more independent variables. CAPM is a theory. It states that the excess return of an asset is linearly related to the excess return of the market. As Stated by Bill Sharpe, the market that you should use is the market for all assets — including human capital and non-traded assets. These data are impossible to get — so CAPM in its purest form is impossible to compute. However, people use the excess returns for the stock market as a proxy for the market. If you do a linear regression of the excess returns of a stock against the excess returns of the stock market (e.g., S&P 500), then the regression coefficient is the beta of the stock. Excess returns are the returns minus the return of the risk-free security. Many people just regress gross returns of the stock against gross returns of the market. This is a little sloppy — but gives a beta close to the actual one.
