I am studying the Markowitz portfolio optimization theory, and I just wanted to ask if I understood this correctly. For a stock portfolio we distinguish two kinds of risks: an unsystematic risk, which is due to the correlations between the stocks and which can be minimized by diversification, and a systematic risk, which is due to general trends in the market and which cannot be reduced by diversification.
So, Markowitz portfolio optimization is a procedure to minimize this unsystematic risk by choosing appropriate weights. Right? It only deals with the unsystematic risk and not with the systematic one. Is there a way to reduce the systematic risk?
To answer your first question: Under the necessary assumptions, the Markowitz portfolio optimization framework can be used to obtain the minimum variance portfolio for a given level of return. Together all the portfolio with a minimum variance for a specified level of return are (or span) the efficient frontier. By definition it is not possible to get another portfolio with a lower variance than the lowest variance portfolio on this frontier. This risk can't be diversified away and is called systematic risk.
For your second question, if a risk free asset exists it is of course possible to have no risk at all: create a portfolio fully invested in the risk free asset. If you want to create a portfolio with a higher return than the risk free rate you can combine the risk free asset with some asset. However, this will always lead to exposure to systematic, undiversifiable risk.