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Portfolio Optimization with a Mean-Entropy-Mutual Information Model.

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  • 1COPPEAD Graduate Business School, Federal University of Rio de Janeiro, Rio de Janeiro 21941-918, Brazil.

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Summary
This summary is machine-generated.

This study introduces a new portfolio optimization model using entropy and mutual information. While not always outperforming traditional methods, it offers better portfolio diversity and stability under return constraints.

Keywords:
entropymutual informationportfolio optimizationvariance and covariance

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Area of Science:

  • Quantitative Finance
  • Financial Modeling
  • Risk Management

Background:

  • Traditional portfolio optimization relies on variance and covariance for risk assessment.
  • The Markowitz model is a foundational mean-variance (MV) approach.
  • Alternative risk measures are explored to enhance portfolio construction.

Purpose of the Study:

  • To introduce and evaluate a novel portfolio optimization (PO) model based on entropy and mutual information.
  • To compare the performance of the proposed mean-entropy (ME) model against the Markowitz MV model and state-of-the-art shrinkage methods.
  • To analyze the impact of increasing return constraints on model stability and performance.

Main Methods:

  • Development of a new portfolio optimization model utilizing entropy and mutual information as risk measures.
  • In-sample and out-of-sample performance comparison of the ME model, MV model, and robust shrinkage methods.
  • Analysis of portfolio diversity metrics, including portfolio weight entropy.
  • Assessment of model stability and response to varying return constraints.

Main Results:

  • ME models demonstrated superior portfolio diversity, particularly in portfolio weight entropy, compared to MV and robust models.
  • ME models exhibited greater stability under increasing return constraints, with dampened responses in cumulative returns and Sharpe ratios.
  • Despite initial wider diversification, ME models concentrated portfolios more rapidly as constraints tightened.
  • The impact of increased return constraints on out-of-sample performance varied depending on market conditions.

Conclusions:

  • The proposed ME models offer advantages in portfolio diversity and stability, especially under stringent return requirements.
  • ME models do not universally outperform traditional MV or robust methods, indicating a nuanced trade-off.
  • Market-specific conditions and the degree of return constraints significantly influence the effectiveness of different portfolio optimization strategies.