There are many assumptions on mean-variance portfolio theory and they seem to be very unrealistic, for example
1) investors have the same information at the same time:
calculating expected returns for assets and their covariance requires many statistical knowledge and the calculation may differ greatly from one forecasting method to the others.
2) investors make their decision solely on the means and covariances of asset returns:
Even if all investors have the same expected returns and covariances, some investors may make their decision based on their asset preferences for example: if you like apple, you may invest in apple without considering any of those statistical information. It seems to be very irrational but I saw some people doing in this way.
Apart from this, there are many counter-examples for underlying assumptions. So, can we actually make our decisions using mean-variance portfolio?