A global equity portfolio has for objective to outperform a benchmark (MSCI World). I hedge the sensitivity of the portfolio to MSCI World (the beta) so that only the alpha remains unhedged.
The ex-ante beta is calculated by looking at the covariance and volatility of the portfolio and MSCI World for the past 2 years. So if the Beta is say 0.98, I short 0.98*portfolio exposure (beta hedging).
Now I want to backtest how accurate the model has been in "predicting" the right beta by comparing the observed beta to the ex-ante (predicted by the model) beta.
How do I decompose the portfolio return in Beta and Alpha, so that I can check if the model was good when predicting beta?
(I must precise the portfolio is re balanced monthly, this means I don't have a lot of ex-post data to play with before another beta / hedge ratio is calculated and implemented)