What is the difference between regression analysis and CAPM?

Question

Is it possible to calculate beta using regression analysis and CAPM? If so what is the difference in Layman's terms?

Answer 1

single regressions are often expressed as y = (m)x + b.

so CAPM should look familiar.  it's  Er = Rf + b(ERP).

multilinear regressions (which would be more akin to teh Arbitrage Pricing Method) look at multiple independent variables to determine relationships w/expected returns.

CAPM and regression analysis is different in that regressions allow you to select whichever independent variable you want to use to run the regression.  CAPM uses beta as the variable, so it's focused on the variance in one stock's returns relative to the overall market's returns.

w/a linear regression, you also typically get additional statistical information that will tell you teh 'goodness' of your results.  such as the R-squared and p-test results.

Answer 2

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.