Let's take 4 assets, whose values are known during a period of time of 2 years. Then I calculate the expected returns for each of these 4 assets thanks to these 2 years - historical data. I deduce the optimal weights that maximizes the expected return of the entire portfolio under a given risk (so I calculated the Makowitz's portfolio).
Now I want to test my algorithm dynamically. I want that the algorithm readjusts the optimal weights for each trading day (because until now I calculated my Markowitz's portfolio for a single period of time)
So my question is : if I am a trader who wants to calculate these optimal weights day after day, how to calculate the expected returns for each of these assets dynamically, day after day ?
Suppose I know their expected returns for the period [1:n], if I take into account the new datas at time n+1 to calculate the new expected return, is is the good procedure ?
Many thanks !