Modern portfolio theory

Modern portfolio theory selects portfolios by balancing expected return against risk, especially through diversification and analysis of how asset returns move together.

Mean–variance analysis: A method that evaluates investments by their expected returns and return variances. This is the framework’s core calculation for comparing portfolio choices.
Expected return: The probability-weighted average of an investment’s possible returns. Expected returns are the reward estimates that portfolio optimization seeks to balance.
Harry Markowitz: An American economist whose 1952 work formalized portfolio selection through expected return and variance. His portfolio-selection model founded modern portfolio theory.
Black–Litterman model: A portfolio-allocation model that combines market-implied returns with an investor’s views. It addresses the instability of portfolios built from uncertain expected-return estimates.
Efficient frontier: The set of portfolios offering the highest expected return for each level of risk. It traces the portfolios that survive the theory’s return-and-risk optimization.
Variance: A measure of how far values in a distribution spread from their mean. The framework uses return variance as its basic measure of investment risk.
Portfolio Selection: Harry Markowitz’s 1952 paper introducing mean–variance portfolio analysis. This paper set out the theory’s original mathematical formulation.
Risk parity: An allocation method that balances assets’ contributions to portfolio risk. It allocates by risk contribution rather than optimizing expected return against variance.
Covariance: A measure of how two variables vary together. Asset covariance determines how much diversification reduces portfolio variance.
Portfolio diversification: The practice of spreading investments across assets to reduce exposure to individual risks. Diversification is the portfolio-level effect that makes asset relationships matter.

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