Modern Portfolio Theory

Modern Portfolio Theory, introduced by Harry Markowitz in 1952, provides the mathematical foundation for portfolio construction by treating investment selection as a mean-variance optimization problem in which expected return and variance characterize each asset and the covariance structure across assets determines the diversification benefit available from combining them. Markowitz showed that for given expected returns and covariances, the set of portfolios offering minimum variance for each level of return — the efficient frontier — can be derived by quadratic programming, and James Tobin's 1958 separation theorem extended the framework by showing that, with a riskless asset, all investors should hold the same risky-asset portfolio (the tangency portfolio) scaled by their risk preference. MPT directly motivated the Capital Asset Pricing Model and remains the foundational scaffolding for institutional asset allocation, even where its specific assumptions are relaxed.