What are the typical limitations of creating an imaginary portoflio of shares and using models such as CAPM?

Answer 1

the most important critic is how the model takes in considerable historical data very bound to change. (namely, risk-return of securities comparing to the market and correlation between securities)

Answer 2

In an imaginary portfolio it is easy to assume that you can buy and sell when you make the decision to. In practise you need to take take care to select shares which trade in sufficient volumes to allow your trades to take place.