Mean-variance portfolio theory in brief

Explain the main ideas of Modern Portfolio Theory.

Markowitz theory chooses portfolios by expected return and variance alone, showing diversification lowers risk for a given return. Portfolio variance depends on covariances, so combining imperfectly correlated assets reduces it. The portfolios with the highest return for each level of risk form the efficient frontier; adding a risk-free asset makes the best risky choice the tangency portfolio, and investors mix it with cash along the capital market line. Its weaknesses are sensitivity to estimated inputs and the focus on variance.