Mean–variance analysis

Mean–variance analysis evaluates investments by comparing expected returns with the variance of returns, often to construct portfolios that balance reward and risk.

Expected return: The probability-weighted average of the possible returns on an investment. It supplies the reward measure that mean–variance analysis seeks to maximize.
Portfolio theory: The study of how investors can combine assets to manage risk and return. Mean–variance analysis is a foundational framework within portfolio theory.
Harry Markowitz: An American economist who developed modern portfolio theory and received the 1990 Nobel Memorial Prize in Economic Sciences. His 1952 portfolio model established the central mean–variance framework.
Value at risk: A quantile-based measure of potential portfolio loss over a specified horizon and confidence level. Unlike variance, it focuses on a loss threshold rather than overall return dispersion.
Portfolio optimization: The selection of asset weights to meet investment objectives under specified constraints. Mean–variance analysis provides a standard mathematical formulation for choosing those weights.
Variance: The average squared deviation of values from their mean. It measures return dispersion and serves as the basic risk measure in the analysis.
Probability distribution: A mathematical description of the possible values of a random variable and their probabilities. Investment returns are uncertain outcomes summarized by their moments.
Portfolio Selection: Harry Markowitz’s 1952 paper introducing portfolio choice through expected return and variance. This paper gave the method its influential formal statement.
Conditional value at risk: The expected loss in the tail beyond a specified value-at-risk threshold. It captures the severity of extreme losses that variance can treat symmetrically.
Diversification (finance): The reduction of portfolio risk by combining assets whose returns do not move identically. Covariances show how combining investments can lower portfolio variance.

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