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Robust Portfolio Optimization Using Pseudodistances.

Aida Toma1, Samuela Leoni-Aubin2

  • 1Department of Applied Mathematics, Bucharest Academy of Economic Studies, Bucharest, Romania; "Gh. Mihoc-C. Iacob" Institute of Mathematical Statistics and Applied Mathematics, Romanian Academy, Bucharest, Romania.

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Summary
This summary is machine-generated.

Outliers in financial data can create unreliable investment portfolios. This study introduces robust statistical estimators to improve portfolio optimization, ensuring more dependable financial strategies.

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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.