MPT (Harry Markowitz)

Definition

Modern Portfolio Theory (MPT), from Harry Markowitz, models portfolio choice as a trade-off between expected return and variance (risk). The efficient frontier is the set of portfolios that maximize return for each level of variance. The “optimal” portfolio depends on the investor’s risk tolerance (often represented by a utility function).

Key idea: diversification reduces variance when assets are not perfectly correlated; the portfolio variance depends on covariances, not only individual variances.

Why it matters

• Diversification: Formalizes the benefit of holding uncorrelated or negatively correlated assets.
• Efficient frontier: Guides allocation toward portfolios that are mean–variance efficient.
• Input sensitivity: Optimal weights are sensitive to expected returns and the covariance matrix; small changes in inputs can cause large shifts in weights.

Limitations

• Assumes returns are normally distributed (or quadratic utility); underestimates tail risk.
• Expected returns are hard to estimate; in practice, many use equal expected returns or risk parity instead.
• Covariance estimation is noisy; shrinkage and robust methods are often used.

Linked concepts

Equal vs market-cap weighted, position sizing, hierarchical risk parity, shrinkage.