Portfolio Optimization with Robust Covariance and CVaR Constraints

This repository implements the research paper: "Portfolio Optimization with Robust Covariance and Conditional Value-at-Risk Constraints" by Qiqin Zhou (Cornell University), arXiv:2406.00610.

🧠 Overview

This project explores various methods to estimate robust covariance matrices and optimize portfolios under Conditional Value-at-Risk (CVaR) constraints. The goal is to construct portfolios that are both stable and capable of handling extreme market conditions.

Implemented techniques include:

• Ledoit-Wolf Shrinkage Estimator
• Gerber Robust Covariance Matrix
• CVaR-constrained Minimum Variance Portfolios

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📁 Repository Structure

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├── BasePortfolio.ipynb           # Benchmark: Exp. Sample & Std Gerber
├── ledoit_wolf.ipynb             # Ledoit-Wolf covariance estimator
├── GerberMethod.ipynb            # Gerber covariance (Std & MAD)
├── Untitled3.ipynb               # 1-CVaR and 2-CVaR portfolio optimization
├── 2406.00610v1.pdf              # Research paper reference
└── README.md                     # This file

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📊 Data

• Universe: 55 Indian stocks (top 5 market-cap from each of 11 sectors)
• Time Range: Sept 2019 - Sept 2024
• Sampling Frequency: Weekly

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🔧 Techniques & Models

Covariance Estimators

• Exponentially Weighted Sample Covariance
• Ledoit-Wolf Shrinkage Covariance
• Gerber Covariance Matrix:
  • Based on significant co-movements
  • Thresholds using:
    • Standard Deviation (Std)
    • Median Absolute Deviation (MAD)

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📦 Requirements

pip install numpy pandas matplotlib seaborn scikit-learn cvxpy

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📚 References

1. Jobson, J. D., & Korkie, B. (1980). Estimation for Markowitz Efficient Portfolios. Journal of the American Statistical Association, 75(371), 544–554.
2. Frost, P. A., & Savarino, J. E. (1988). For better performance: Constrain portfolio weights. Journal of Portfolio Management, 15(1), 29–34.
3. Ledoit, O., & Wolf, M. (2003). Improved estimation of the covariance matrix of stock returns with an application to portfolio selection. Journal of Empirical Finance, 10(5), 603–621.
4. Ledoit, O., & Wolf, M. (2004). Honey, I Shrunk the Sample Covariance Matrix. The Journal of Portfolio Management, 30(4), 110–119.
5. Rousseeuw, P. J. (1984). Least Median of Squares Regression. Journal of the American Statistical Association, 79(388), 871–880.
6. López de Prado, M. (2019). A Robust Estimator of the Efficient Frontier. Available at SSRN: https://ssrn.com/abstract=3469961.
7. Gerber, S., Markowitz, H. M., Ernst, P. A., et al. (2022). The Gerber Statistic: A Robust Co-Movement Measure for Portfolio Optimization. The Journal of Portfolio Management, 48(3), 87–102.
8. Rockafellar, R. T., & Uryasev, S. (2000). Optimization of Conditional Value-at-Risk. The Journal of Risk, 2, 21–41.
9. Alexander, G. J., & Baptista, A. M. (2004). A comparison of VaR and CVaR constraints on portfolio selection with the mean-variance model. Management Science, 50(9), 1261–1273.
10. Zhou, Q. (2024). Portfolio Optimization with Robust Covariance and Conditional Value-at-Risk Constraints. arXiv:2406.00610. https://arxiv.org/abs/2406.00610

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