A portfolio is built systematically by calculating scores and rebalanced each month to invest only in the 80 best scores. Scores change frequently and therefore the portfolio changes each month, sometimes significantly. The benchmark is MSCI World.
At each month end I need to know what portion of the return is due to the market (Beta) and the idiosyncratic component not explained by the market (alpha).
I am thinking of running an OLS regression of daily portfolio returns vs daily market returns to calculate the Beta and deduce Alpha from the CAPM formula (if I have the actual portfolio return, the market return, the Beta, risk free rate, I can get alpha).
Is the fact that the Beta is calculated with OLS regression only 22 trading days (1 month between each rebalance) an issue? What is the market practice for this task?