Portfolio Theory

Mean Variance Optimization

A mathematical framework for finding the portfolio that maximizes return per unit of risk using historical means and covariances.

Mean Variance Optimization (MVO), pioneered by Harry Markowitz, is the mathematical engine behind the Efficient Frontier. Given a set of assets, their expected returns (means), variances, and pairwise correlations (covariances), MVO finds the set of portfolio weights that produces the best risk-return tradeoff.

The key inputs are: (1) expected return for each asset, typically estimated from historical returns; (2) the covariance matrix capturing how assets move together. MVO then solves a quadratic programming problem to identify the optimal weight vector for a target return or risk level.

MVO's main weakness is its extreme sensitivity to input assumptions. Small errors in expected return estimates can produce wildly different weight recommendations. A portfolio that is 'optimal' based on historical data is rarely optimal going forward — this is known as 'error maximization.' Robust alternatives like Hierarchical Risk Parity address this sensitivity.

On StressTest.pro, MVO is available under the Optimizations tab. Results should be treated as a starting point for portfolio construction, not a definitive prescription.

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Disclaimer

The information provided by StressTest.pro is for educational and informational purposes only and does not constitute financial advice. Investment involves risk, including possible loss of principal. Past performance is not indicative of future results. Calculations are based on historical data and statistical approximations.