Robust Portfolio Optimization

A robust mean-variance optimization framework for constructing long-only ETF portfolios.

This project investigates whether portfolio optimization can improve risk-adjusted performance while maintaining stable portfolio characteristics across different historical estimation windows.

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Overview

Traditional mean-variance optimization is highly sensitive to estimation error.

To mitigate this issue, this project incorporates shrinkage estimators for expected returns and covariance matrices and evaluates robustness through rolling lookback analyses.

The framework constructs and compares:

• Maximum Sharpe portfolio
• Minimum Variance portfolio
• Target Return (minimum-variance) portfolio

against several benchmark allocations, including:

• Equal Weight
• 80/20 Stock-Bond
• 60/40 Stock-Bond

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ETF Universe

Asset	ETF
Taiwan Equity	0050.TW
U.S. Equity	SPY
U.S. Nasdaq	QQQ
Global Equity	VT
Emerging Markets	VWO
Small Cap	IJR
Bonds	BND

Sample period:

2016-01-01 ~ 2026-05-31

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Methodology

1. Download historical ETF prices from Yahoo Finance.

2. Estimate expected returns and covariance matrices using shrinkage estimators.

3. Generate candidate portfolios under long-only allocation constraints.

4. Construct:

   • Maximum Sharpe portfolio
   • Minimum Variance portfolio
   • Target Return portfolio

5. Compare optimized portfolios with benchmark allocations.

6. Evaluate robustness using different lookback windows:

   • 3 years
   • 5 years
   • 10 years

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Efficient Frontier

The optimized portfolios lie closer to the efficient frontier than benchmark allocations, indicating improved risk-return efficiency under the current model assumptions.

Observation

The target-return portfolio was constructed using a minimum-volatility objective with a return floor of 12%.

In this dataset, the minimum-variance portfolio already achieved an expected return above 12%, making the return constraint non-binding.

As a result, the Target Return portfolio became nearly identical to the Minimum Variance portfolio and appears very close to it on the efficient frontier.

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Portfolio NAV Comparison

The Maximum Sharpe portfolio achieves the highest ending NAV, while more conservative allocations provide smoother wealth trajectories.

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Drawdown Comparison

Lower drawdowns imply better downside protection.

The 60/40 Stock-Bond portfolio exhibits the shallowest drawdowns, whereas return-oriented portfolios experience larger peak-to-trough losses.

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Maximum Sharpe Portfolio Weights

The optimized portfolio allocates capital unevenly across assets according to their estimated returns and covariance structure.

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Performance Metrics

Portfolio	Annualized Return	Volatility	Sharpe Ratio
Max Sharpe	18.42%	12.76%	1.32
Min Variance	16.03%	12.39%	1.16
Target Return	16.03%	12.39%	1.16

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Robustness Analysis

Mean-variance optimization is sensitive to the historical estimation window.

To evaluate robustness, the optimization is repeated independently using:

• 3-year lookback
• 5-year lookback
• 10-year lookback

Although optimized weights vary across windows, several portfolio characteristics remain relatively stable.

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Key Findings

• Mean-variance optimization improves risk-adjusted performance relative to benchmark portfolios.

• Shrinkage estimators help reduce estimation error and stabilize portfolio characteristics.

• Portfolio weights remain sensitive to lookback windows and allocation constraints.

• Portfolio performance appears to be considerably more robust than the corresponding asset allocations.

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Future Work

Potential extensions include:

• Black-Litterman model
• Resampled efficiency
• Risk parity portfolio
• Regularized portfolio optimization
• Dynamic asset allocation

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References

1. James, W., & Stein, C. (1961). Estimation with Quadratic Loss.

2. Ledoit, O., & Wolf, M. (2004). A Well-Conditioned Estimator for Large-Dimensional Covariance Matrices.

3. Michaud, R. O. (1989). The Markowitz Optimization Enigma: Is "Optimized" Optimal?

4. DeMiguel, V., Garlappi, L., & Uppal, R. (2009). Optimal Versus Naive Diversification.

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Project Structure

config/
data/
notebooks/
reports/readme/
src/
README.md
requirements.txt

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Author

Kevin Lin

M.S. Statistics

Cost Analyst @ China Steel Corporation

Interested in:

• Data Science
• Quantitative Finance
• Portfolio Optimization
• Machine Learning

Disclaimer

This repository is intended for educational, research, and portfolio demonstration purposes only.

The analyses, models, results, and conclusions presented in this project are based on the available data, assumptions, and methodologies at the time of development. They may not reflect real-world outcomes and should not be interpreted as professional advice.

This project does not constitute financial, investment, or trading advice.

Users are responsible for independently evaluating any information provided in this repository before applying it to real-world decisions.