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In the second pass, the independent variables are the first pass estimated betas. That is, you estimate $\hat{\beta_i}$ in time series for every stock i $$r_{i,t} - r_{f,t} = \alpha_i + \beta_i(r_{M,t}-r_{f,t}) + \epsilon_t$$ and then you estimate risk premia $\hat{\lambda}$ according to the following regression: $$\overline{r_{i,t} - r_{f,t}} = a_0 + ...


PerformanceAnalytics in R and PortfolioAnalytics in R Here is a tutorial from UW http://faculty.washington.edu/ezivot/econ424/portfolioFunctionsPowerPoint.pdf


Don't just run simple time-series regression to see if you get statistically significant betas. This procedure will not tell you if the factors are actually priced. You run a high risk of finding spurious correlations. There is a fairly well established standard program to test factor models, called the Fama-MacBeth method. It is based on two sets of ...

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