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I am trying to find out Historical Alphas of a bunch of fund returns ${F_i}$ by Using Regression Model$(stepwise)$ with regressors as its underlying exposure-returns(risk-free rate subtracted) i.e. $$ \mathrm{E_i = X_i-R_f} $$ $$ \mathrm{F_i} = {a_i + \beta_{1i}E_{1}+\beta_{2i}E_{2}...} $$

Here, I assume that this regression model is representative of a Multi-factor CAPM model and the obtained ${\beta_i}$ are the CAPM-${\beta}$ i.e. systemic risk of ${F_i}$ w.r.t. ${E_i}$.

Then, I use these models to calculate average historical ${\alpha_i}$ which is excess return for fund ${F_i}$ using below formula.

$$ \mathrm{\alpha_i} = avg({F_i - F_i^{estimated})} $$

Is this simplistic approach correct, if not, what is the correct way?

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I think you should improve the notation. You have $n$ funds $(F_i)_{i=1}^n$ and $K$ predictors $(E_j)_{j=1}^K$ and you want to model $F_i = \alpha_i + \sum_{j=1}^K \beta_{i,j} E_j$ - right? So you should not have $E_{i,j}$ ... –  Richard Sep 18 '13 at 8:53

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