By reading the explanation and example of Modern Portfolio Theory (Markowitz, 1952) from this link, I saw a picture as below
From this website, I also see
The portion of the minimum-variance curve that lies above and to the right of the global minimum variance portfolio is known as the Markowitz efficient frontier as it contains all portfolios that rational, risk-averse investors would choose. (...). As we move to higher levels of risk, the resulting increase in return begins to diminish. The slope begins to flatten.
I understand the idea of the document. I understand the rational investors will follow this portfolio construction. However, why the risk-averse also would choose this one. I am wondering which type of investors would not choose the Markowitz efficient frontier ( in the meaning of opposite to risk-averse (e.g. high risk-takers))? In another word, why risk-takers will not choose this efficient frontier ?