Robust Portfolio Optimization Using Pseudodistances.

Area of Science:

• Quantitative Finance
• Statistical Modeling
• Financial Econometrics

Background:

• Financial asset returns frequently exhibit outliers, which can compromise the reliability of traditional mean-variance optimized portfolios.
• Outliers exert an unbounded influence on mean returns and covariance estimators, critical inputs for portfolio optimization.
• Existing portfolio optimization methods are sensitive to data anomalies, necessitating more robust approaches.

Purpose of the Study:

• To develop and present robust estimators for mean and covariance matrices in financial data.
• To address the unreliability of traditional portfolio optimization caused by outliers.
• To provide a practical alternative to classical estimators for constructing robust optimized portfolios.

Main Methods:

• Minimizing an empirical pseudodistance between the assumed statistical model and the true data-generating process.
• Developing robust estimators for mean and covariance matrix.
• Theoretical analysis of estimator properties: affine equivariance, B-robustness, asymptotic normality, and asymptotic relative efficiency.

Main Results:

• The proposed robust estimators demonstrate superior performance in the presence of outliers compared to classical methods.
• Theoretical properties such as affine equivariance and B-robustness ensure the stability and reliability of the estimators.
• Monte Carlo simulations and real-data applications confirm the advantages of the robust approach for portfolio optimization.

Conclusions:

• The presented robust estimators offer a reliable solution for constructing optimized portfolios resistant to outliers in financial asset returns.
• These estimators can be seamlessly integrated into existing portfolio optimization frameworks, replacing classical methods.
• The study highlights significant improvements in both in-sample and out-of-sample performance of robust portfolios over traditional ones.