Portfolio Optimization with Mean-Variance Analysis
By Daniel Chau
Founder, NeuroBacktest
Build efficient portfolios using modern portfolio theory, Sharpe-optimal weights, and risk parity approaches.
Modern Portfolio Theory, introduced by Harry Markowitz, shows that combining assets with low correlation can produce better risk-adjusted returns than any single asset alone. The key is finding the right weights.
Mean-Variance Optimization
Mean-variance optimization finds the portfolio weights that maximize expected return for a given level of risk. The result is the efficient frontier — a set of optimal portfolios.
Common Objective Functions
- Maximize Sharpe Ratio: Best risk-adjusted return.
- Minimize Volatility: Lowest risk for a target return.
- Risk Parity: Equal risk contribution from each asset.
- Maximum Diversification: Spread risk as evenly as possible.
Practical Caveats
Mean-variance optimization is sensitive to expected return estimates. Small errors in expected returns can lead to extreme weights. Many practitioners use shrinkage estimators or impose constraints like maximum position sizes.
Build a Portfolio in NeuroBacktest
Type: "Optimize a portfolio of AAPL, MSFT, GOOGL, and TSLA for maximum Sharpe ratio from 2019 to 2024."
Frequently Asked Questions
What is mean-variance optimization?▼
Mean-variance optimization, introduced by Harry Markowitz, finds portfolio weights that maximize expected return for a given level of risk. The result is the efficient frontier.
What is risk parity?▼
Risk parity allocates capital so that each asset contributes equally to total portfolio risk. It often leads to more diversified and stable portfolios than equal-dollar weights.
Can portfolio optimization fail out-of-sample?▼
Yes. Mean-variance optimization is sensitive to expected return estimates and can produce extreme weights. Adding constraints, shrinkage estimators, or out-of-sample testing helps.