Modern Portfolio Theory (MPT) is an investment theory introduced by economist Harry Markowitz in the 1950s. It provides a framework for constructing a portfolio of assets that aims to maximize expected return for a given level of risk, or conversely, to minimize risk for a given level of expected return.
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Mean-variance optimization balances expected linear return against a positive-definite quadratic variance penalty.
Modern portfolio theory constructs portfolios by comparing expected return with variance risk and the effects of diversification.