Question

Briefly discuss what’s typically included in 2nd stage regressions in empirical tests of the CAPM and why.

Answer 1

Empirical testing of the CAPM model is based on the rolling regression methodology which is a two staged regression testing.

Explanation of the methodology and what is included in the testing: We first need to know what is the two staged regression testing, it the regression analysis using two different stages of testing.

First Stage: In the first stage of testing we use time series regression analysis where we calculate Beta of the security by taking dependent variable as stock return and independent variable as market return and we run regression model to test the methods.

Equation of regression testing: Rit = i + i Rmt + it

the above written equation explains the first stagen of two staged regression, where, Rit and Rmt are return of stock 'i' and market return respectively at point "t". Alpha and Beta are the intercept and slope coefficient of the regression equation and is the error.

Second Stage: This stage is a cross-sectional regression where we use Beta of each security and we regress excess return of each security on beta of the security. Here slope coefficient market risk premium of the stock or portfolio.

Equation of second stage regression: [E(Rit) - Rft] = it [E(Rmt) - Rft]

We test the CAPM by using rolling regreesion technique which is used to test the robustness of the model used in the analysis.

What's included in the CAPM regression technique: Two staged model, Analysis of the stock return or portfolio return using regression technique, slope and intercept of the data used for the analysis.