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High-dimensional covariance matrix estimators on simulated portfolios with complex structures.

Andrés García-Medina1

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This study introduces advanced two-step covariance estimators for high-dimensional portfolio allocation. These methods improve financial metrics, offering new risk management strategies for complex investment portfolios.

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Area of Science:

  • Quantitative Finance
  • Statistical Modeling
  • Complex Systems

Background:

  • High-dimensional covariance matrix structures are crucial for portfolio allocation.
  • Existing noise reduction methods have limitations in complex financial markets.
  • Understanding complex system interactions is key for robust investment strategies.

Purpose of the Study:

  • To develop and evaluate novel two-step covariance estimators for portfolio allocation.
  • To compare the performance of hierarchical nested, one-factor, and diagonal covariance models.
  • To assess the impact of noise reduction techniques on financial performance metrics.

Main Methods:

  • Utilizing random matrix theory, free probability, and deterministic equivalents for noise reduction.
  • Implementing a data science hierarchical method: two-step covariance estimators.
  • Analyzing portfolio allocation strategies: minimum variance and hierarchical risk parity.
  • Comparing simulation results with empirical S&P 500 data using moving window and walk-forward analysis.

Main Results:

  • The proposed hierarchical nested covariance model reveals complex system interactions.
  • Empirical data validate stylized portfolio facts observed in complex and one-factor models.
  • Two-step estimators significantly enhance financial metrics across analyzed investment strategies.
  • The methods show promise for scenarios with a high asset-to-day ratio.

Conclusions:

  • The developed two-step covariance estimators offer improved financial performance.
  • Hierarchical models capture intricate interactions within financial markets.
  • These findings support novel risk management and diversification approaches in high-dimensional settings.