# Performance attribution and monthly rebalance: Is a month enough data to calculate Beta and Alpha?

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?

• Beta used to be calculated using monthly returns of the last >5 years. Daily data over the last 12 months is the most common approach nowadays, I think. One often requires >200 returns to be available. If you run your regression on less data, you'll get large standard errors. However, it is not unheard-of. Bali, Cakici, Tang (2009) refer to it as realised market beta and they were not the first ones to use it. In any case, I recommed to follow Lewellen and Nagel (2006) and to include lagged market returns to deal with nonsynchronous price movements, see also Scholes and Williams (1977)... – Kevin Apr 13 '20 at 17:56
• ... just to complete this, Lewellen and Nagel run the regression $R_{i,t}=\alpha_i+\beta_{i,0}R_{m,t}+\beta_{i,1}R_{m,t-1}+\beta_{i,2}(R_{m,t-2}+R_{m,t-3}+R_{m,t-4})/3+\varepsilon_{i,t}$ and set the firm's beta equal to $\beta_i=\beta_{i,0}+\beta_{i,1}+\beta_{i,2}$, – Kevin Apr 13 '20 at 18:01