Mean Variance Optimization
The foundation of Modern Portfolio Theory introduced by Harry Markowitz.
What is it?
Mean Variance Optimization (MVO) is a quantitative tool that allows investors to construct a portfolio that maximizes expected return for a specific level of risk, or minimizes risk for a given expected return. It relies heavily on historical returns, volatilities, and correlations between assets.
The Core Concept
The "Mean" represents the expected return (calculated mathematically via historical averages), while "Variance" represents the risk or volatility of those returns. By combining assets with low correlations, MVO reduces the overall portfolio variance without necessarily sacrificing expected returns.
The Efficient Frontier
By simulating thousands of different portfolio weight combinations, MVO generates a curved line called the Efficient Frontier. Any portfolio sitting exactly on this line represents the maximum possible return for its specific level of risk. Portfolios below the line are sub-optimal.
Limitations
- Garbage in, Garbage out: MVO assumes that past returns and correlations will hold true in the future, which is rarely perfectly the case.
- Extreme Weights: Unconstrained MVO often allocates 100% of capital to just 1 or 2 assets that historically overperformed, disregarding diversification.
- Estimation Error Sensitivity: Small changes in inputs (like expected return) can cause dramatic shifts in the output asset weights.
Optimize your portfolio instantly
Our platform runs thousands of iterations in milliseconds to find your portfolio's optimal weights on the Efficient Frontier.
Run Optimization